needs "../formal_lp/formal_interval/m_taylor_arith2.hl";; needs "../formal_lp/formal_interval/m_verifier.hl";; needs "../formal_lp/arith/informal/informal_m_verifier.hl";; let reset_all () = Arith_cache.reset_stat(); Arith_cache.reset_cache(); Arith_float.reset_stat(); Arith_float.reset_cache();; let dest_int int = let f1, f2 = Informal_interval.dest_interval int in Informal_float.dest_float f1, Informal_float.dest_float f2;; let dest_f = Informal_float.dest_float;; let dest_dom dom = map dest_f dom.Informal_taylor.lo, map dest_f dom.Informal_taylor.hi, map dest_f dom.Informal_taylor.y, map dest_f dom.Informal_taylor.w;; let dest_ti ti = dest_int ti.Informal_taylor.f, map dest_int ti.Informal_taylor.df, map (map dest_int) ti.Informal_taylor.ddf;; (******************************) (* dummy functions *) let eval_d0 i pp t1 t2 = failwith "eval_d0";; let eval_dd0 i j pp t1 t2 = failwith "eval_dd0";; let eval_0 pp t1 t2 = failwith "eval_0";; let eval_diff2 t1 t2 = failwith "eval_diff2";; (******************************) (* real tests *) let n = 6;; let pp = 15;; let pp = 8;; (* delta_y *) let delta_y_poly = let tm = (rand o concl o SPEC_ALL o REWRITE_RULE[Sphere.delta_x]) Sphere.delta_y in expr_to_vector_fun tm;; (* delta_y4 *) let delta_y4_poly = let tm = (rand o concl o SPECL[`y1*y1`; `y2*y2`; `y3*y3`; `y4*y4`; `y5*y5`; `y6*y6`]) Sphere.delta_x4 in expr_to_vector_fun tm;; (* 4 * y1 * delta_y *) let four_y1_delta_y_poly = let x_var, tm = dest_abs delta_y_poly in mk_abs (x_var, mk_binop mul_op_real `&4` (mk_binop mul_op_real `(x:real^6)$1 * x$1` tm));; (* - delta_y4 *) let neg_delta_y4_poly = let x_var, tm = dest_abs delta_y4_poly in mk_abs (x_var, mk_comb (neg_op_real, tm));; let eval_neg_delta_y4, tf_neg_delta_y4, ti_neg_delta_y4 = mk_verification_functions pp neg_delta_y4_poly false `&0`;; let eval_4y1_delta_y, tf_4y1_delta_y, ti_4y1_delta_y = mk_verification_functions pp four_y1_delta_y_poly false `&0`;; let eval_pi2, tf_pi2, ti_pi2 = mk_verification_functions pp `\x:real^6. pi / &2` false `&0`;; let eval_pi2_plus, tf_pi2_plus, ti_pi2_plus = mk_verification_functions pp `\x:real^6. pi / &2 - #1.893` false `&0`;; (* dih_y *) open Univariate;; let tf_dih_y_hi = let denom = Uni_compose (uinv, Uni_compose (usqrt, tf_4y1_delta_y)) in Plus (tf_pi2_plus, Uni_compose (uatan, Product (tf_neg_delta_y4, denom)));; let eval_dih_y_hi p_lin p_second th = let inv, atn, sqrt, ( * ), ( + ) = eval_m_taylor_inv2 n p_lin p_second, eval_m_taylor_atn2 n p_lin p_second, eval_m_taylor_sqrt2 n p_lin p_second, eval_m_taylor_mul2 n p_lin p_second, eval_m_taylor_add2 n p_lin p_second in let poly1 = eval_4y1_delta_y.taylor p_lin p_second th and poly2 = eval_neg_delta_y4.taylor p_lin p_second th and pi2 = eval_pi2_plus.taylor p_lin p_second th in pi2 + atn (poly2 * inv (sqrt (poly1)));; let ti_dih_y_hi p_lin p_second th = let inv, atn, sqrt, ( * ), ( + ) = Informal_taylor.eval_m_taylor_inv p_lin p_second, Informal_taylor.eval_m_taylor_atn p_lin p_second, Informal_taylor.eval_m_taylor_sqrt p_lin p_second, Informal_taylor.eval_m_taylor_mul p_lin p_second, Informal_taylor.eval_m_taylor_add p_lin p_second in let poly1 = ti_4y1_delta_y.Informal_verifier.taylor p_lin p_second th and poly2 = ti_neg_delta_y4.Informal_verifier.taylor p_lin p_second th and pi2 = ti_pi2_plus.Informal_verifier.taylor p_lin p_second th in pi2 + atn (poly2 * inv (sqrt (poly1)));; let eval_taylor = {taylor = eval_dih_y_hi; f = eval_0; df = eval_d0; ddf = eval_dd0; diff2_f = eval_diff2};; let ti = {Informal_verifier.taylor = ti_dih_y_hi; Informal_verifier.f = eval_0; Informal_verifier.df = eval_d0; Informal_verifier.ddf = eval_dd0};; (************) (* Small domain *) let xx_s = `[&2; &2; &2; &2; &2; &2]` and zz_s = `[#2.1; #2.1; #2.1; #2.1; #2.1; #2.1]`;; (* domain *) let domain_th = let xx1_s = convert_to_float_list pp true xx_s and zz1_s = convert_to_float_list pp false zz_s in mk_m_center_domain n pp xx1_s zz1_s;; let dom = let xx2_s = Informal_taylor.convert_to_float_list pp true xx_s and zz2_s = Informal_taylor.convert_to_float_list pp false zz_s in Informal_taylor.mk_m_center_domain pp xx2_s zz2_s;; (* 10: 9.121 (pp = 15) *) (* 300: 5.5 (pp = 8) *) (* 100 (cached, float_cached, pp = 8): 2.68 *) (* 100 (optimization): 1.732 *) (* 200 (m_taylor_arith2): 1.428 *) reset_all();; test 1 (eval_dih_y_hi pp pp) domain_th;; (* 100: 1.668 *) (* 200 (optimization): 0.580 *) (* 200 (m_taylor_arith2): 0.328 *) test 1 (eval_dih_y_hi pp pp) domain_th;; (* 100: 0.088 *) test 1 (ti_dih_y_hi pp pp) dom;; Arith_cache.print_stat();; Arith_float.print_stat();; (***) let th1 = eval_4y1_delta_y.taylor pp pp domain_th;; let th2 = eval_neg_delta_y4.taylor pp pp domain_th;; let pi2_th = eval_pi2_plus.taylor pp pp domain_th;; let r1 = eval_m_taylor_sqrt2 n pp pp th1;; let r2 = eval_m_taylor_inv2 n pp pp r1;; let r3 = eval_m_taylor_mul2 n pp pp th2 r2;; let r4 = eval_m_taylor_atn2 n pp pp r3;; let r5 = eval_m_taylor_add2 n pp pp pi2_th r4;; reset_all();; (* 100: 0.264 (second: 0.084) *) test 1 (eval_4y1_delta_y.taylor pp pp) domain_th;; (* 100: 0.032 (second: 0.020) *) test 1 (eval_neg_delta_y4.taylor pp pp) domain_th;; (* 100: 0.000 (second: 0.000) *) test 1 (eval_pi2_plus.taylor pp pp) domain_th;; (* 100: 0.356 (second: 0.168); 0.300 (0.116) *) test 1 (eval_m_taylor_sqrt n pp pp) th1;; (* 200: 0.220 (second: 0.048) *) test 1 (eval_m_taylor_sqrt2 n pp pp) th1;; (* 100: 0.412 (second: 0.188); 0.316 (0.104) *) test 1 (eval_m_taylor_inv n pp pp) r1;; (* 200: 0.264 (second: 0.056) *) test 1 (eval_m_taylor_inv2 n pp pp) r1;; (* 100: 0.384 (second: 0.212); 0.316 (0.140) *) test 1 (eval_m_taylor_mul n pp pp th2) r2;; (* 200: 0.244 (second: 0.092) *) test 1 (eval_m_taylor_mul2 n pp pp th2) r2;; (* 100: 0.616 (second: 0.272); build2: 0.504 (0.132) *) test 1 (eval_m_taylor_atn n pp pp) r3;; (* 200: 0.436 (second: 0.060) *) test 1 (eval_m_taylor_atn2 n pp pp) r3;; (* 100: 0.096 (second: 0.072); 0.072 (0.052) *) test 1 (eval_m_taylor_add n pp pp pi2_th) r4;; (* 200: 0.032 (second: 0.024) *) test 1 (eval_m_taylor_add2 n pp pp pi2_th) r4;; (***) let xx = `[&2; &2; &2; &2; &2; &2]` and zz = `[#2.52; #2.52; #2.52; #2.52; #2.52; #2.52]`;; let xx_s = `[&2; &2; &2; &2; &2; &2]` and zz_s = `[#2.52; #2.1; #2.1; #2.1; #2.1; #2.1]`;; let xx_s2 = `[&2; &2; &2; &2; &2; &2]` and zz_s2 = `[#2.52; #2.2; #2.2; #2.2; #2.2; #2.2]`;; let pp0 = 3;; let pp0 = 5;; let xx1 = convert_to_float_list pp0 true xx and zz1 = convert_to_float_list pp0 false zz and xx1_s = convert_to_float_list pp0 true xx_s and zz1_s = convert_to_float_list pp0 false zz_s and xx1_s2 = convert_to_float_list pp0 true xx_s2 and zz1_s2 = convert_to_float_list pp0 false zz_s2;; let xx2 = Informal_taylor.convert_to_float_list pp0 true xx and zz2 = Informal_taylor.convert_to_float_list pp0 false zz and xx2_s = Informal_taylor.convert_to_float_list pp0 true xx_s and zz2_s = Informal_taylor.convert_to_float_list pp0 false zz_s and xx2_s2 = Informal_taylor.convert_to_float_list pp0 true xx_s2 and zz2_s2 = Informal_taylor.convert_to_float_list pp0 false zz_s2;; let xx_float, zz_float, xx_s_float, zz_s_float, xx_s2_float, zz_s2_float = let pad = replicate 0.0 (8 - length (dest_list xx1)) in map float_of_float_tm (dest_list xx1) @ pad, map float_of_float_tm (dest_list zz1) @ pad, map float_of_float_tm (dest_list xx1_s) @ pad, map float_of_float_tm (dest_list zz1_s) @ pad, map float_of_float_tm (dest_list xx1_s2) @ pad, map float_of_float_tm (dest_list zz1_s2) @ pad;; (***) let c_dih_y_s = run_test tf_dih_y_hi xx_s_float zz_s_float false 0.0 true false true false 0.0;; let c_dih_y_s2 = run_test tf_dih_y_hi xx_s2_float zz_s2_float false 0.0 true false true false 0.0;; let c_dih_y0 = run_test tf_dih_y_hi xx_float zz_float false 0.0 true false false false 0.0;; (* pass = 4 *) result_stat c_dih_y_s;; (* pass = 63 *) result_stat c_dih_y_s2;; (* pass = 4294, mono = 10 *) result_stat c_dih_y0;; let p_split = pp and p_min = 1 and p_max = pp;; let cp_s = Informal_verifier.m_verify_raw0 p_split p_min p_max ti c_dih_y_s xx2_s zz2_s;; let cp_s2 = Informal_verifier.m_verify_raw0 p_split p_min p_max ti c_dih_y_s2 xx2_s2 zz2_s2;; (*********************) reset_all();; (* 10 (pp = 15): 38.418 *) (* 300 (pp = 8): 22.289 *) (* 100 (cached, float_cached, pp = 8): 12.229; 9.372 (MY_BETA_RULE); 8.028 (build2) *) (* 200 (m_taylor_arith2) : 6.548 *) let _ = let start = Sys.time() in let result = m_verify_raw0 n pp eval_taylor c_dih_y_s xx1_s zz1_s in let finish = Sys.time() in let _ = report (sprintf "Verification time: %f" (finish -. start)) in result;; Arith_cache.print_stat();; Arith_float.print_stat();; (* 100 (cached, float_cached, pp = 8): 8.025; 5.116 (MY_BETA_RULE); 3.700 (build2) *) (* 200 (m_taylor_arith2): 2.496 *) reset_all();; let _ = let start = Sys.time() in let result = m_p_verify_raw0 n p_split eval_taylor cp_s xx1_s zz1_s in let finish = Sys.time() in let _ = report (sprintf "Verification time: %f" (finish -. start)) in result;; (* stats *) result_p_stat false cp_s2;; (* 100 (cached, float_cached, pp = adaptive): 129.788; 87.729 (MY_BETA_RULE); 64.884 (build2) *) (* (pp = 8: 233.80) *) (* 200: 63.984 (build2) *) (* 200 (m_taylor_arith2): 43.927 *) reset_all();; let _ = let start = Sys.time() in let result = m_p_verify_raw0 n p_split eval_taylor cp_s2 xx1_s2 zz1_s2 in let finish = Sys.time() in let _ = report (sprintf "Verification time: %f" (finish -. start)) in result;; (*****************) let cp = Informal_verifier.m_verify_raw0 p_split p_min p_max ti c_dih_y0 xx2 zz2;; result_p_stat false cp;; (* 100: 9105 (was 15202)*) (* 200 (build2): 4242 *) (* 200 (m_taylor_arith2): 3121 *) (* 200 (mixed_partials): 2880 *) reset_all();; let _ = let start = Sys.time() in let result = m_p_verify_raw0 n p_split eval_taylor cp xx1 zz1 in let finish = Sys.time() in let _ = report (sprintf "Verification time: %f" (finish -. start)) in result;; (**************************************) (* 3318775219 *) let tf_dih_y = let denom = Uni_compose (uinv, Uni_compose (usqrt, tf_4y1_delta_y)) in Plus (tf_pi2, Uni_compose (uatan, Product (tf_neg_delta_y4, denom)));; let eval_dih_y p_lin p_second th = let inv, atn, sqrt, ( * ), ( + ) = eval_m_taylor_inv2 n p_lin p_second, eval_m_taylor_atn2 n p_lin p_second, eval_m_taylor_sqrt2 n p_lin p_second, eval_m_taylor_mul2 n p_lin p_second, eval_m_taylor_add2 n p_lin p_second in let poly1 = eval_4y1_delta_y.taylor p_lin p_second th and poly2 = eval_neg_delta_y4.taylor p_lin p_second th and pi2 = eval_pi2.taylor p_lin p_second th in pi2 + atn (poly2 * inv (sqrt (poly1)));; let ti_dih_y p_lin p_second th = let inv, atn, sqrt, ( * ), ( + ) = Informal_taylor.eval_m_taylor_inv p_lin p_second, Informal_taylor.eval_m_taylor_atn p_lin p_second, Informal_taylor.eval_m_taylor_sqrt p_lin p_second, Informal_taylor.eval_m_taylor_mul p_lin p_second, Informal_taylor.eval_m_taylor_add p_lin p_second in let poly1 = ti_4y1_delta_y.Informal_verifier.taylor p_lin p_second th and poly2 = ti_neg_delta_y4.Informal_verifier.taylor p_lin p_second th and pi2 = ti_pi2.Informal_verifier.taylor p_lin p_second th in pi2 + atn (poly2 * inv (sqrt (poly1)));; (* - #1.629 + (#0.414 * (y2 + y3 + y5 + y6 - #8.0)) - (#0.763 * (y4 - #2.52)) - (#0.315 * (y1 - #2.0)) *) let neg_poly3318 = expr_to_vector_fun `-- (-- #1.629 + (#0.414 * (y2 + y3 + y5 + y6 - #8.0)) - (#0.763 * (y4 - #2.52)) - (#0.315 * (y1 - #2.0)))`;; let eval_poly3318, tf_poly3318, ti_poly3318 = mk_verification_functions pp neg_poly3318 false `&0`;; let tf_3318 = let dih = tf_dih_y in let poly = tf_poly3318 in Plus (poly, Scale (dih, mk_interval (-1.0, -1.0)));; let eval_3318 p_lin p_second th = let ( - ) = eval_m_taylor_sub2 n p_lin p_second in let dih = eval_dih_y p_lin p_second th and poly = eval_poly3318.taylor p_lin p_second th in poly - dih;; let ti_3318 p_lin p_second th = let ( - ) = Informal_taylor.eval_m_taylor_sub p_lin p_second in let dih = ti_dih_y p_lin p_second th and poly = ti_poly3318.Informal_verifier.taylor p_lin p_second th in poly - dih;; let eval_taylor = {taylor = eval_3318; f = eval_0; df = eval_d0; ddf = eval_dd0; diff2_f = eval_diff2};; let ti = {Informal_verifier.taylor = ti_3318; Informal_verifier.f = eval_0; Informal_verifier.df = eval_d0; Informal_verifier.ddf = eval_dd0};; (* domain *) let xx = `[&2; &2; &2; #2.52; &2; &2]` and zz = `[#2.52; #2.52; #2.52; sqrt(&8); #2.52; #2.52]`;; let xx_s = `[&2; &2; &2; #2.52; &2; &2]` and zz_s = `[#2.52; #2.1; #2.1; sqrt(&8); #2.1; #2.1]`;; let pp0 = 3;; let xx1 = convert_to_float_list pp0 true xx and zz1 = convert_to_float_list pp0 false zz and xx1_s = convert_to_float_list pp0 true xx_s and zz1_s = convert_to_float_list pp0 false zz_s;; let xx2 = Informal_taylor.convert_to_float_list pp0 true xx and zz2 = Informal_taylor.convert_to_float_list pp0 false zz and xx2_s = Informal_taylor.convert_to_float_list pp0 true xx_s and zz2_s = Informal_taylor.convert_to_float_list pp0 false zz_s;; let xx_float, zz_float, xx_s_float, zz_s_float = let pad = replicate 0.0 (8 - length (dest_list xx1)) in map float_of_float_tm (dest_list xx1) @ pad, map float_of_float_tm (dest_list zz1) @ pad, map float_of_float_tm (dest_list xx1_s) @ pad, map float_of_float_tm (dest_list zz1_s) @ pad;; (* certificates *) let c_s = run_test tf_3318 xx_s_float zz_s_float false 0.0 true false false false 0.0;; let c0 = run_test tf_3318 xx_float zz_float false 0.0 true false false false 0.0;; let c_test = run_test tf_3318 xx_float zz_float false 0.0 true true true true 0.0;; (* pass = 355, mono = 21 *) result_stat c_s;; (* pass = 16165, mono = 1036 *) result_stat c0;; (* pass = 15924 (raw = 1), mono = 796, pass_mono = 240 *) result_stat c_test;; let p_split = pp and p_min = 1 and p_max = pp;; let cp_s = Informal_verifier.m_verify_raw0 p_split p_min p_max ti c_s xx2_s zz2_s;; let cp0 = Informal_verifier.m_verify_raw0 p_split p_min p_max ti c0 xx2 zz2;; (*********************) reset_all();; (* 200 (m_taylor_arith2): 282.7 *) let _ = let start = Sys.time() in let result = m_p_verify_raw0 n p_split eval_taylor cp_s xx1_s zz1_s in let finish = Sys.time() in let _ = report (sprintf "Verification time: %f" (finish -. start)) in result;; reset_all();; (* 200 (m_taylor_arith2): 14175.2 *) let _ = let start = Sys.time() in let result = m_p_verify_raw0 n p_split eval_taylor cp0 xx1 zz1 in let finish = Sys.time() in let _ = report (sprintf "Verification time: %f" (finish -. start)) in result;; (**************************************) (* 9922699028 *) (* #1.6294 - (#0.2213 * (y2 + y3 + y5 + y6 - #8.0)) + (#0.913 * (y4 - #2.52)) + (#0.728 * (y1 - #2.0)) *) let neg_poly9922 = expr_to_vector_fun `-- (#1.6294 - (#0.2213 * (y2 + y3 + y5 + y6 - #8.0)) + (#0.913 * (y4 - #2.52)) + (#0.728 * (y1 - #2.0)))`;; let eval_poly9922, tf_poly9922, ti_poly9922 = mk_verification_functions pp neg_poly9922 false `&0`;; let tf_9922 = let dih = tf_dih_y in let poly = tf_poly9922 in Plus (dih, poly);; let eval_9922 p_lin p_second th = let ( + ) = eval_m_taylor_add2 n p_lin p_second in let dih = eval_dih_y p_lin p_second th and poly = eval_poly9922.taylor p_lin p_second th in dih + poly;; let ti_9922 p_lin p_second th = let ( + ) = Informal_taylor.eval_m_taylor_add p_lin p_second in let dih = ti_dih_y p_lin p_second th and poly = ti_poly9922.Informal_verifier.taylor p_lin p_second th in dih + poly;; let eval_taylor = {taylor = eval_9922; f = eval_0; df = eval_d0; ddf = eval_dd0; diff2_f = eval_diff2};; let ti = {Informal_verifier.taylor = ti_9922; Informal_verifier.f = eval_0; Informal_verifier.df = eval_d0; Informal_verifier.ddf = eval_dd0};; (* domain *) let xx = `[&2; &2; &2; #2.52; &2; &2]` and zz = `[#2.52; #2.52; #2.52; sqrt(&8); #2.52; #2.52]`;; let xx_s = `[&2; &2; &2; #2.52; &2; &2]` and zz_s = `[#2.52; #2.1; #2.1; sqrt(&8); #2.1; #2.1]`;; let pp0 = 3;; let xx1 = convert_to_float_list pp0 true xx and zz1 = convert_to_float_list pp0 false zz and xx1_s = convert_to_float_list pp0 true xx_s and zz1_s = convert_to_float_list pp0 false zz_s;; let xx2 = Informal_taylor.convert_to_float_list pp0 true xx and zz2 = Informal_taylor.convert_to_float_list pp0 false zz and xx2_s = Informal_taylor.convert_to_float_list pp0 true xx_s and zz2_s = Informal_taylor.convert_to_float_list pp0 false zz_s;; let xx_float, zz_float, xx_s_float, zz_s_float = let pad = replicate 0.0 (8 - length (dest_list xx1)) in map float_of_float_tm (dest_list xx1) @ pad, map float_of_float_tm (dest_list zz1) @ pad, map float_of_float_tm (dest_list xx1_s) @ pad, map float_of_float_tm (dest_list zz1_s) @ pad;; (* certificates *) let c_s = run_test tf_9922 xx_s_float zz_s_float false 0.0 true false false false 0.0;; let c0 = run_test tf_9922 xx_float zz_float false 0.0 true false false false 0.0;; let c_test = run_test tf_9922 xx_float zz_float false 0.0 true true true true 0.0;; (* pass = 179, mono = 26 *) result_stat c_s;; (* pass = 6322, mono = 235 *) result_stat c0;; (* pass = 6307 (raw = 5), mono = 220, pass_mono = 15 *) result_stat c_test;; let p_split = pp and p_min = 1 and p_max = pp;; let cp_s = Informal_verifier.m_verify_raw0 p_split p_min p_max ti c_s xx2_s zz2_s;; let cp0 = Informal_verifier.m_verify_raw0 p_split p_min p_max ti c0 xx2 zz2;; (*********************) reset_all();; (* 200 (m_taylor_arith2): 157.2 *) let _ = let start = Sys.time() in let result = m_p_verify_raw0 n p_split eval_taylor cp_s xx1_s zz1_s in let finish = Sys.time() in let _ = report (sprintf "Verification time: %f" (finish -. start)) in result;; reset_all();; (* 200 (m_taylor_arith2): 5039.6 *) let _ = let start = Sys.time() in let result = m_p_verify_raw0 n p_split eval_taylor cp0 xx1 zz1 in let finish = Sys.time() in let _ = report (sprintf "Verification time: %f" (finish -. start)) in result;;