Details

Time bar (total: 1.2min)

analyze10.0s (13.9%)

Algorithm
search
egg-herbie
Rules
395×associate-/l/_binary64_2412
281×neg-mul-1_binary64_2461
225×distribute-neg-frac_binary64_2429
202×distribute-rgt-in_binary64_2415 distribute-lft-in_binary64_2414
193×associate-*r/_binary64_2407
179×distribute-rgt-neg-in_binary64_2423
170×*-commutative_binary64_2396
161×associate-*l*_binary64_2406
160×associate-*l/_binary64_2408
157×distribute-lft-neg-in_binary64_2422
148×associate-/l*_binary64_2410
118×associate-*r*_binary64_2405
106×cancel-sign-sub-inv_binary64_2431
92×swap-sqr_binary64_2432
87×sqr-pow_binary64_2437
84×neg-sub0_binary64_2460
62×unswap-sqr_binary64_2433
53×sub-neg_binary64_2458
38×distribute-lft-neg-out_binary64_2424
37×+-commutative_binary64_2395
33×times-frac_binary64_2471 div-sub_binary64_2470
29×unpow2_binary64_2530 unpow1/2_binary64_2529 unpow1_binary64_2523 rem-sqrt-square_binary64_2478
16×difference-of-squares_binary64_2434
11×associate-/r/_binary64_2411
10×associate-/r*_binary64_2409
distribute-rgt-neg-out_binary64_2425
1-exp_binary64_2509
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_2728 erf-erfc_binary64_2727 erf-odd_binary64_2726 if-if-and-not_binary64_2725 if-if-and_binary64_2724 if-if-or-not_binary64_2723 if-if-or_binary64_2722 if-not_binary64_2721 if-same_binary64_2720 if-false_binary64_2719 if-true_binary64_2718 not-gte_binary64_2717 not-lte_binary64_2716 not-gt_binary64_2715 not-lt_binary64_2714 gte-same_binary64_2713 lte-same_binary64_2712 gt-same_binary64_2711 lt-same_binary64_2710 sinh---cosh_binary64_2657 sinh-+-cosh_binary64_2656 sinh-cosh_binary64_2655 tanh-def-c_binary64_2654 tanh-def-b_binary64_2653 tanh-def-a_binary64_2652 cosh-def_binary64_2651 sinh-def_binary64_2650 tan-neg_binary64_2597 cos-neg_binary64_2596 sin-neg_binary64_2595 tan-0_binary64_2594 cos-0_binary64_2593 sin-0_binary64_2592 hang-m-tan_binary64_2591 hang-p-tan_binary64_2590 hang-m0-tan_binary64_2589 hang-p0-tan_binary64_2588 hang-0m-tan_binary64_2587 hang-0p-tan_binary64_2586 tan-+PI/2_binary64_2585 tan-+PI_binary64_2584 tan-PI_binary64_2583 tan-PI/3_binary64_2582 tan-PI/4_binary64_2581 tan-PI/6_binary64_2580 cos-+PI/2_binary64_2579 cos-+PI_binary64_2578 cos-PI_binary64_2577 cos-PI/2_binary64_2576 cos-PI/3_binary64_2575 cos-PI/4_binary64_2574 cos-PI/6_binary64_2573 sin-+PI/2_binary64_2572 sin-+PI_binary64_2571 sin-PI_binary64_2570 sin-PI/2_binary64_2569 sin-PI/3_binary64_2568 sin-PI/4_binary64_2567 sin-PI/6_binary64_2566 sub-1-sin_binary64_2565 sub-1-cos_binary64_2564 -1-add-sin_binary64_2563 -1-add-cos_binary64_2562 1-sub-sin_binary64_2561 1-sub-cos_binary64_2560 cos-sin-sum_binary64_2559 log-E_binary64_2555 log-pow_binary64_2554 log-rec_binary64_2553 log-div_binary64_2552 log-prod_binary64_2551 pow-base-0_binary64_2549 unpow1/3_binary64_2532 unpow3_binary64_2531 pow-plus_binary64_2528 exp-to-pow_binary64_2527 pow-base-1_binary64_2525 unpow0_binary64_2524 unpow-1_binary64_2522 exp-lft-cube_binary64_2521 exp-lft-sqr_binary64_2520 exp-cbrt_binary64_2519 exp-sqrt_binary64_2518 exp-prod_binary64_2517 div-exp_binary64_2516 rec-exp_binary64_2515 prod-exp_binary64_2514 exp-diff_binary64_2513 exp-neg_binary64_2512 exp-sum_binary64_2511 e-exp-1_binary64_2510 exp-1-e_binary64_2508 exp-0_binary64_2507 rem-log-exp_binary64_2506 rem-exp-log_binary64_2505 cube-unmult_binary64_2502 cube-mult_binary64_2495 cube-div_binary64_2494 cube-prod_binary64_2493 cube-neg_binary64_2492 rem-3cbrt-rft_binary64_2491 rem-3cbrt-lft_binary64_2490 rem-cbrt-cube_binary64_2489 rem-cube-cbrt_binary64_2488 sqr-abs_binary64_2480 sqr-neg_binary64_2479 rem-square-sqrt_binary64_2477 unsub-neg_binary64_2459 mul-1-neg_binary64_2457 /-rgt-identity_binary64_2456 *-rgt-identity_binary64_2455 *-lft-identity_binary64_2454 remove-double-neg_binary64_2453 sub0-neg_binary64_2452 --rgt-identity_binary64_2451 +-rgt-identity_binary64_2450 +-lft-identity_binary64_2449 mul0-rgt_binary64_2448 mul0-lft_binary64_2447 div0_binary64_2446 *-inverses_binary64_2445 +-inverses_binary64_2444 lft-mult-inverse_binary64_2443 rgt-mult-inverse_binary64_2442 remove-double-div_binary64_2441 pow-sqr_binary64_2438 difference-of-sqr--1_binary64_2436 difference-of-sqr-1_binary64_2435 cancel-sign-sub_binary64_2430 distribute-frac-neg_binary64_2428 distribute-neg-out_binary64_2427 distribute-neg-in_binary64_2426 distribute-rgt1-in_binary64_2421 distribute-lft1-in_binary64_2420 distribute-rgt-out--_binary64_2419 distribute-rgt-out_binary64_2418 distribute-lft-out--_binary64_2417 distribute-lft-out_binary64_2416 count-2_binary64_2413 associate--r-_binary64_2404 associate--l-_binary64_2403 associate--l+_binary64_2402 associate--r+_binary64_2401 associate-+l-_binary64_2400 associate-+r-_binary64_2399 associate-+l+_binary64_2398 associate-+r+_binary64_2397
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02491925
17101925
224411925
348741925
451411925
055
155
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
6.2%93.5%0.2%11
6.2%93.5%0.2%12
7.8%92%0.2%13
8.6%91.2%0.2%14
Compiler

Compiled 110 to 84 computations (23.6% saved)

sample1.2s (1.7%)

Algorithm
intervals
Results
278.0ms46×body4096valid
222.0ms34×body4096invalid
213.0ms55×body2048valid
147.0ms40×body2048invalid
68.0ms28×body1024valid
59.0ms108×body128valid
52.0ms20×body1024invalid
40.0msbody8192invalid
30.0ms16×body512valid
14.0ms32×body128invalid
14.0msbody8192valid
12.0msbody512invalid
7.0msbody256invalid
2.0msbody256valid
Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify35.0ms (0%)

Algorithm
egg-herbie
Rules
600×associate-/l/_binary64_2412
540×associate-/r*_binary64_2409
529×associate-/r/_binary64_2411
263×distribute-rgt-in_binary64_2415
260×distribute-lft-in_binary64_2414
145×associate-*l*_binary64_2406
138×associate-*r*_binary64_2405
112×associate-/l*_binary64_2410
103×associate-*r/_binary64_2407
99×associate-*l/_binary64_2408
83×distribute-neg-frac_binary64_2429
65×swap-sqr_binary64_2432
55×times-frac_binary64_2471 distribute-rgt-neg-in_binary64_2423
52×unswap-sqr_binary64_2433
50×*-commutative_binary64_2396
46×distribute-lft-neg-in_binary64_2422
44×div-sub_binary64_2470
43×cancel-sign-sub-inv_binary64_2431
26×neg-sub0_binary64_2460
25×distribute-lft-neg-out_binary64_2424
24×neg-mul-1_binary64_2461 sqr-pow_binary64_2437
19×sub-neg_binary64_2458
18×distribute-rgt-neg-out_binary64_2425
16×distribute-neg-in_binary64_2426
unpow2_binary64_2530 unpow1/2_binary64_2529 pow-plus_binary64_2528 unpow1_binary64_2523 cube-unmult_binary64_2502 rem-sqrt-square_binary64_2478
+-commutative_binary64_2395
difference-of-squares_binary64_2434
unsub-neg_binary64_2459 sub0-neg_binary64_2452 +-rgt-identity_binary64_2450 associate-+l-_binary64_2400 associate-+r-_binary64_2399
1-exp_binary64_2509 distribute-frac-neg_binary64_2428
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_2728 erf-erfc_binary64_2727 erf-odd_binary64_2726 if-if-and-not_binary64_2725 if-if-and_binary64_2724 if-if-or-not_binary64_2723 if-if-or_binary64_2722 if-not_binary64_2721 if-same_binary64_2720 if-false_binary64_2719 if-true_binary64_2718 not-gte_binary64_2717 not-lte_binary64_2716 not-gt_binary64_2715 not-lt_binary64_2714 gte-same_binary64_2713 lte-same_binary64_2712 gt-same_binary64_2711 lt-same_binary64_2710 sinh---cosh_binary64_2657 sinh-+-cosh_binary64_2656 sinh-cosh_binary64_2655 tanh-def-c_binary64_2654 tanh-def-b_binary64_2653 tanh-def-a_binary64_2652 cosh-def_binary64_2651 sinh-def_binary64_2650 tan-neg_binary64_2597 cos-neg_binary64_2596 sin-neg_binary64_2595 tan-0_binary64_2594 cos-0_binary64_2593 sin-0_binary64_2592 hang-m-tan_binary64_2591 hang-p-tan_binary64_2590 hang-m0-tan_binary64_2589 hang-p0-tan_binary64_2588 hang-0m-tan_binary64_2587 hang-0p-tan_binary64_2586 tan-+PI/2_binary64_2585 tan-+PI_binary64_2584 tan-PI_binary64_2583 tan-PI/3_binary64_2582 tan-PI/4_binary64_2581 tan-PI/6_binary64_2580 cos-+PI/2_binary64_2579 cos-+PI_binary64_2578 cos-PI_binary64_2577 cos-PI/2_binary64_2576 cos-PI/3_binary64_2575 cos-PI/4_binary64_2574 cos-PI/6_binary64_2573 sin-+PI/2_binary64_2572 sin-+PI_binary64_2571 sin-PI_binary64_2570 sin-PI/2_binary64_2569 sin-PI/3_binary64_2568 sin-PI/4_binary64_2567 sin-PI/6_binary64_2566 sub-1-sin_binary64_2565 sub-1-cos_binary64_2564 -1-add-sin_binary64_2563 -1-add-cos_binary64_2562 1-sub-sin_binary64_2561 1-sub-cos_binary64_2560 cos-sin-sum_binary64_2559 log-E_binary64_2555 log-pow_binary64_2554 log-rec_binary64_2553 log-div_binary64_2552 log-prod_binary64_2551 pow-base-0_binary64_2549 unpow1/3_binary64_2532 unpow3_binary64_2531 exp-to-pow_binary64_2527 pow-base-1_binary64_2525 unpow0_binary64_2524 unpow-1_binary64_2522 exp-lft-cube_binary64_2521 exp-lft-sqr_binary64_2520 exp-cbrt_binary64_2519 exp-sqrt_binary64_2518 exp-prod_binary64_2517 div-exp_binary64_2516 rec-exp_binary64_2515 prod-exp_binary64_2514 exp-diff_binary64_2513 exp-neg_binary64_2512 exp-sum_binary64_2511 e-exp-1_binary64_2510 exp-1-e_binary64_2508 exp-0_binary64_2507 rem-log-exp_binary64_2506 rem-exp-log_binary64_2505 cube-mult_binary64_2495 cube-div_binary64_2494 cube-prod_binary64_2493 cube-neg_binary64_2492 rem-3cbrt-rft_binary64_2491 rem-3cbrt-lft_binary64_2490 rem-cbrt-cube_binary64_2489 rem-cube-cbrt_binary64_2488 sqr-abs_binary64_2480 sqr-neg_binary64_2479 rem-square-sqrt_binary64_2477 mul-1-neg_binary64_2457 /-rgt-identity_binary64_2456 *-rgt-identity_binary64_2455 *-lft-identity_binary64_2454 remove-double-neg_binary64_2453 --rgt-identity_binary64_2451 +-lft-identity_binary64_2449 mul0-rgt_binary64_2448 mul0-lft_binary64_2447 div0_binary64_2446 *-inverses_binary64_2445 +-inverses_binary64_2444 lft-mult-inverse_binary64_2443 rgt-mult-inverse_binary64_2442 remove-double-div_binary64_2441 pow-sqr_binary64_2438 difference-of-sqr--1_binary64_2436 difference-of-sqr-1_binary64_2435 cancel-sign-sub_binary64_2430 distribute-neg-out_binary64_2427 distribute-rgt1-in_binary64_2421 distribute-lft1-in_binary64_2420 distribute-rgt-out--_binary64_2419 distribute-rgt-out_binary64_2418 distribute-lft-out--_binary64_2417 distribute-lft-out_binary64_2416 count-2_binary64_2413 associate--r-_binary64_2404 associate--l-_binary64_2403 associate--l+_binary64_2402 associate--r+_binary64_2401 associate-+l+_binary64_2398 associate-+r+_binary64_2397
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
040175
1103175
2310175
31387172
45232172

prune16.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
39.0b
Counts
2 → 2
Compiler

Compiled 323 to 229 computations (29.1% saved)

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.9b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))

rewrite403.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
34.5b
Rules
15×associate-*r/_binary64_2407
frac-sub_binary64_2474
associate-*l/_binary64_2408
add-log-exp_binary64_2504 frac-times_binary64_2475
pow1_binary64_2526 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487 *-un-lft-identity_binary64_2465
sub-div_binary64_2472
diff-log_binary64_2557 flip3--_binary64_2469 sub-neg_binary64_2458 flip--_binary64_2440 cancel-sign-sub-inv_binary64_2431
Counts
4 → 44
Calls

4 calls:

42.0ms
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
Compiler

Compiled 6110 to 4322 computations (29.3% saved)

series7.6s (10.6%)

Error
33.5b
Counts
4 → 24
Calls

4 calls:

7.4s
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))
43.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
43.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
40.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
Compiler

Compiled 6601 to 5084 computations (23% saved)

simplify204.0ms (0.3%)

Algorithm
egg-herbie
Rules
250×distribute-rgt-in_binary64_2415
242×distribute-lft-in_binary64_2414
216×associate-*r*_binary64_2405
193×unswap-sqr_binary64_2433
186×cancel-sign-sub-inv_binary64_2431
184×distribute-rgt-neg-in_binary64_2423
178×times-frac_binary64_2471
169×associate-*l*_binary64_2406
163×associate-/l*_binary64_2410
156×associate-*l/_binary64_2408
152×distribute-lft-neg-in_binary64_2422
148×*-commutative_binary64_2396
135×associate-*r/_binary64_2407
114×associate-/r*_binary64_2409
92×distribute-neg-frac_binary64_2429
81×unpow3_binary64_2531
67×sqr-pow_binary64_2437
53×distribute-lft-out_binary64_2416
52×neg-sub0_binary64_2460
51×cube-div_binary64_2494
44×+-commutative_binary64_2395
43×cube-prod_binary64_2493
42×sub-neg_binary64_2458
41×neg-mul-1_binary64_2461 distribute-rgt-out_binary64_2418
40×distribute-neg-in_binary64_2426
39×distribute-lft-neg-out_binary64_2424
35×swap-sqr_binary64_2432
33×mul-1-neg_binary64_2457
29×exp-prod_binary64_2517
17×associate-/r/_binary64_2411
16×cube-mult_binary64_2495
15×associate-/l/_binary64_2412
12×associate-+l+_binary64_2398 associate-+r+_binary64_2397
10×unpow2_binary64_2530 unpow1/2_binary64_2529 unpow1_binary64_2523
distribute-rgt-neg-out_binary64_2425
difference-of-squares_binary64_2434
cube-unmult_binary64_2502
pow-plus_binary64_2528 div-sub_binary64_2470
exp-sum_binary64_2511 unsub-neg_binary64_2459 pow-sqr_binary64_2438 distribute-rgt-out--_binary64_2419
exp-diff_binary64_2513 distribute-frac-neg_binary64_2428
div-exp_binary64_2516 1-exp_binary64_2509 +-rgt-identity_binary64_2450 distribute-lft-out--_binary64_2417 associate-+r-_binary64_2399
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_2728 erf-erfc_binary64_2727 erf-odd_binary64_2726 if-if-and-not_binary64_2725 if-if-and_binary64_2724 if-if-or-not_binary64_2723 if-if-or_binary64_2722 if-not_binary64_2721 if-same_binary64_2720 if-false_binary64_2719 if-true_binary64_2718 not-gte_binary64_2717 not-lte_binary64_2716 not-gt_binary64_2715 not-lt_binary64_2714 gte-same_binary64_2713 lte-same_binary64_2712 gt-same_binary64_2711 lt-same_binary64_2710 sinh---cosh_binary64_2657 sinh-+-cosh_binary64_2656 sinh-cosh_binary64_2655 tanh-def-c_binary64_2654 tanh-def-b_binary64_2653 tanh-def-a_binary64_2652 cosh-def_binary64_2651 sinh-def_binary64_2650 tan-neg_binary64_2597 cos-neg_binary64_2596 sin-neg_binary64_2595 tan-0_binary64_2594 cos-0_binary64_2593 sin-0_binary64_2592 hang-m-tan_binary64_2591 hang-p-tan_binary64_2590 hang-m0-tan_binary64_2589 hang-p0-tan_binary64_2588 hang-0m-tan_binary64_2587 hang-0p-tan_binary64_2586 tan-+PI/2_binary64_2585 tan-+PI_binary64_2584 tan-PI_binary64_2583 tan-PI/3_binary64_2582 tan-PI/4_binary64_2581 tan-PI/6_binary64_2580 cos-+PI/2_binary64_2579 cos-+PI_binary64_2578 cos-PI_binary64_2577 cos-PI/2_binary64_2576 cos-PI/3_binary64_2575 cos-PI/4_binary64_2574 cos-PI/6_binary64_2573 sin-+PI/2_binary64_2572 sin-+PI_binary64_2571 sin-PI_binary64_2570 sin-PI/2_binary64_2569 sin-PI/3_binary64_2568 sin-PI/4_binary64_2567 sin-PI/6_binary64_2566 sub-1-sin_binary64_2565 sub-1-cos_binary64_2564 -1-add-sin_binary64_2563 -1-add-cos_binary64_2562 1-sub-sin_binary64_2561 1-sub-cos_binary64_2560 cos-sin-sum_binary64_2559 log-E_binary64_2555 log-pow_binary64_2554 log-rec_binary64_2553 log-div_binary64_2552 log-prod_binary64_2551 pow-base-0_binary64_2549 unpow1/3_binary64_2532 exp-to-pow_binary64_2527 pow-base-1_binary64_2525 unpow0_binary64_2524 unpow-1_binary64_2522 exp-lft-cube_binary64_2521 exp-lft-sqr_binary64_2520 exp-cbrt_binary64_2519 exp-sqrt_binary64_2518 rec-exp_binary64_2515 prod-exp_binary64_2514 exp-neg_binary64_2512 e-exp-1_binary64_2510 exp-1-e_binary64_2508 exp-0_binary64_2507 rem-log-exp_binary64_2506 rem-exp-log_binary64_2505 cube-neg_binary64_2492 rem-3cbrt-rft_binary64_2491 rem-3cbrt-lft_binary64_2490 rem-cbrt-cube_binary64_2489 rem-cube-cbrt_binary64_2488 sqr-abs_binary64_2480 sqr-neg_binary64_2479 rem-sqrt-square_binary64_2478 rem-square-sqrt_binary64_2477 /-rgt-identity_binary64_2456 *-rgt-identity_binary64_2455 *-lft-identity_binary64_2454 remove-double-neg_binary64_2453 sub0-neg_binary64_2452 --rgt-identity_binary64_2451 +-lft-identity_binary64_2449 mul0-rgt_binary64_2448 mul0-lft_binary64_2447 div0_binary64_2446 *-inverses_binary64_2445 +-inverses_binary64_2444 lft-mult-inverse_binary64_2443 rgt-mult-inverse_binary64_2442 remove-double-div_binary64_2441 difference-of-sqr--1_binary64_2436 difference-of-sqr-1_binary64_2435 cancel-sign-sub_binary64_2430 distribute-neg-out_binary64_2427 distribute-rgt1-in_binary64_2421 distribute-lft1-in_binary64_2420 count-2_binary64_2413 associate--r-_binary64_2404 associate--l-_binary64_2403 associate--l+_binary64_2402 associate--r+_binary64_2401 associate-+l-_binary64_2400
Counts
68 → 51
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01937506
16036813
226826477
349916477
450676477

prune316.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New45651
Fresh101
Picked101
Done000
Total47653
Error
31.9b
Counts
53 → 6
Compiler

Compiled 6220 to 3881 computations (37.6% saved)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.2b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (*.f64 (*.f64 (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))) (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))) (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))))) 2)) y-scale) y-scale)))

rewrite501.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
31.2b
Rules
15×associate-*r/_binary64_2407
frac-sub_binary64_2474
associate-*l/_binary64_2408
add-log-exp_binary64_2504 frac-times_binary64_2475
pow1_binary64_2526 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487 *-un-lft-identity_binary64_2465
sub-div_binary64_2472
diff-log_binary64_2557 flip3--_binary64_2469 sub-neg_binary64_2458 flip--_binary64_2440 cancel-sign-sub-inv_binary64_2431
Counts
4 → 44
Calls

4 calls:

48.0ms
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (*.f64 (*.f64 (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))) (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))) (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))))) 2)) y-scale) y-scale)))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
Compiler

Compiled 7028 to 5024 computations (28.5% saved)

series7.6s (10.6%)

Error
31.9b
Counts
4 → 24
Calls

4 calls:

7.3s
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (*.f64 (*.f64 (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))) (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))) (cbrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))))) 2)) y-scale) y-scale)))
51.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
50.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
50.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
Compiler

Compiled 7060 to 5435 computations (23% saved)

simplify166.0ms (0.2%)

Algorithm
egg-herbie
Rules
254×distribute-rgt-in_binary64_2415
246×distribute-lft-in_binary64_2414
230×associate-*r*_binary64_2405
199×unswap-sqr_binary64_2433
186×cancel-sign-sub-inv_binary64_2431
184×distribute-rgt-neg-in_binary64_2423
183×associate-*l*_binary64_2406
178×times-frac_binary64_2471
163×associate-/l*_binary64_2410
156×associate-*l/_binary64_2408
152×distribute-lft-neg-in_binary64_2422
150×*-commutative_binary64_2396
136×associate-*r/_binary64_2407
114×associate-/r*_binary64_2409
92×distribute-neg-frac_binary64_2429
70×sqr-pow_binary64_2437
53×distribute-lft-out_binary64_2416
52×neg-sub0_binary64_2460
51×cube-div_binary64_2494
48×swap-sqr_binary64_2432
44×+-commutative_binary64_2395
43×cube-prod_binary64_2493
42×sub-neg_binary64_2458
41×neg-mul-1_binary64_2461 distribute-rgt-out_binary64_2418
40×distribute-neg-in_binary64_2426
39×distribute-lft-neg-out_binary64_2424
33×mul-1-neg_binary64_2457
32×exp-prod_binary64_2517
17×unpow3_binary64_2531 associate-/r/_binary64_2411
16×cube-mult_binary64_2495
15×associate-/l/_binary64_2412
12×associate-+l+_binary64_2398 associate-+r+_binary64_2397
10×unpow2_binary64_2530 unpow1/2_binary64_2529 unpow1_binary64_2523
distribute-rgt-neg-out_binary64_2425
cube-unmult_binary64_2502 difference-of-squares_binary64_2434
pow-plus_binary64_2528
div-sub_binary64_2470 pow-sqr_binary64_2438
log-prod_binary64_2551 exp-sum_binary64_2511 unsub-neg_binary64_2459 distribute-rgt-out--_binary64_2419
exp-diff_binary64_2513 distribute-frac-neg_binary64_2428
log-pow_binary64_2554 div-exp_binary64_2516 1-exp_binary64_2509 rem-3cbrt-lft_binary64_2490 +-rgt-identity_binary64_2450 distribute-lft-out--_binary64_2417 associate-+r-_binary64_2399
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_2728 erf-erfc_binary64_2727 erf-odd_binary64_2726 if-if-and-not_binary64_2725 if-if-and_binary64_2724 if-if-or-not_binary64_2723 if-if-or_binary64_2722 if-not_binary64_2721 if-same_binary64_2720 if-false_binary64_2719 if-true_binary64_2718 not-gte_binary64_2717 not-lte_binary64_2716 not-gt_binary64_2715 not-lt_binary64_2714 gte-same_binary64_2713 lte-same_binary64_2712 gt-same_binary64_2711 lt-same_binary64_2710 sinh---cosh_binary64_2657 sinh-+-cosh_binary64_2656 sinh-cosh_binary64_2655 tanh-def-c_binary64_2654 tanh-def-b_binary64_2653 tanh-def-a_binary64_2652 cosh-def_binary64_2651 sinh-def_binary64_2650 tan-neg_binary64_2597 cos-neg_binary64_2596 sin-neg_binary64_2595 tan-0_binary64_2594 cos-0_binary64_2593 sin-0_binary64_2592 hang-m-tan_binary64_2591 hang-p-tan_binary64_2590 hang-m0-tan_binary64_2589 hang-p0-tan_binary64_2588 hang-0m-tan_binary64_2587 hang-0p-tan_binary64_2586 tan-+PI/2_binary64_2585 tan-+PI_binary64_2584 tan-PI_binary64_2583 tan-PI/3_binary64_2582 tan-PI/4_binary64_2581 tan-PI/6_binary64_2580 cos-+PI/2_binary64_2579 cos-+PI_binary64_2578 cos-PI_binary64_2577 cos-PI/2_binary64_2576 cos-PI/3_binary64_2575 cos-PI/4_binary64_2574 cos-PI/6_binary64_2573 sin-+PI/2_binary64_2572 sin-+PI_binary64_2571 sin-PI_binary64_2570 sin-PI/2_binary64_2569 sin-PI/3_binary64_2568 sin-PI/4_binary64_2567 sin-PI/6_binary64_2566 sub-1-sin_binary64_2565 sub-1-cos_binary64_2564 -1-add-sin_binary64_2563 -1-add-cos_binary64_2562 1-sub-sin_binary64_2561 1-sub-cos_binary64_2560 cos-sin-sum_binary64_2559 log-E_binary64_2555 log-rec_binary64_2553 log-div_binary64_2552 pow-base-0_binary64_2549 unpow1/3_binary64_2532 exp-to-pow_binary64_2527 pow-base-1_binary64_2525 unpow0_binary64_2524 unpow-1_binary64_2522 exp-lft-cube_binary64_2521 exp-lft-sqr_binary64_2520 exp-cbrt_binary64_2519 exp-sqrt_binary64_2518 rec-exp_binary64_2515 prod-exp_binary64_2514 exp-neg_binary64_2512 e-exp-1_binary64_2510 exp-1-e_binary64_2508 exp-0_binary64_2507 rem-log-exp_binary64_2506 rem-exp-log_binary64_2505 cube-neg_binary64_2492 rem-3cbrt-rft_binary64_2491 rem-cbrt-cube_binary64_2489 rem-cube-cbrt_binary64_2488 sqr-abs_binary64_2480 sqr-neg_binary64_2479 rem-sqrt-square_binary64_2478 rem-square-sqrt_binary64_2477 /-rgt-identity_binary64_2456 *-rgt-identity_binary64_2455 *-lft-identity_binary64_2454 remove-double-neg_binary64_2453 sub0-neg_binary64_2452 --rgt-identity_binary64_2451 +-lft-identity_binary64_2449 mul0-rgt_binary64_2448 mul0-lft_binary64_2447 div0_binary64_2446 *-inverses_binary64_2445 +-inverses_binary64_2444 lft-mult-inverse_binary64_2443 rgt-mult-inverse_binary64_2442 remove-double-div_binary64_2441 difference-of-sqr--1_binary64_2436 difference-of-sqr-1_binary64_2435 cancel-sign-sub_binary64_2430 distribute-neg-out_binary64_2427 distribute-rgt1-in_binary64_2421 distribute-lft1-in_binary64_2420 count-2_binary64_2413 associate--r-_binary64_2404 associate--l-_binary64_2403 associate--l+_binary64_2402 associate--r+_binary64_2401 associate-+l-_binary64_2400
Counts
68 → 51
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01987506
16076813
227516389
350986389

prune340.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New51051
Fresh055
Picked011
Done000
Total51657
Error
31.9b
Counts
57 → 6
Compiler

Compiled 6305 to 3980 computations (36.9% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.5b
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite186.0ms (0.3%)

Algorithm
rewrite-expression-head
Error
31.7b
Rules
pow1_binary64_2526 add-log-exp_binary64_2504 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487 *-un-lft-identity_binary64_2465
Counts
4 → 28
Calls

4 calls:

2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
Compiler

Compiled 3304 to 2374 computations (28.1% saved)

series240.0ms (0.3%)

Error
31.9b
Counts
4 → 12
Calls

4 calls:

46.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
45.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
44.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
43.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
Compiler

Compiled 4024 to 3003 computations (25.4% saved)

simplify208.0ms (0.3%)

Algorithm
egg-herbie
Rules
1268×sqr-pow_binary64_2437
651×pow-sqr_binary64_2438
362×unswap-sqr_binary64_2433
265×cube-prod_binary64_2493
201×unpow3_binary64_2531
198×cube-mult_binary64_2495
159×associate-*l*_binary64_2406
142×*-commutative_binary64_2396
93×associate-*r*_binary64_2405
48×pow-plus_binary64_2528
16×rem-sqrt-square_binary64_2478
cube-unmult_binary64_2502
unpow2_binary64_2530 unpow1/2_binary64_2529 unpow1_binary64_2523
associate-/l*_binary64_2410
1-exp_binary64_2509 associate-/r/_binary64_2411 associate-*l/_binary64_2408 associate-*r/_binary64_2407
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_2728 erf-erfc_binary64_2727 erf-odd_binary64_2726 if-if-and-not_binary64_2725 if-if-and_binary64_2724 if-if-or-not_binary64_2723 if-if-or_binary64_2722 if-not_binary64_2721 if-same_binary64_2720 if-false_binary64_2719 if-true_binary64_2718 not-gte_binary64_2717 not-lte_binary64_2716 not-gt_binary64_2715 not-lt_binary64_2714 gte-same_binary64_2713 lte-same_binary64_2712 gt-same_binary64_2711 lt-same_binary64_2710 sinh---cosh_binary64_2657 sinh-+-cosh_binary64_2656 sinh-cosh_binary64_2655 tanh-def-c_binary64_2654 tanh-def-b_binary64_2653 tanh-def-a_binary64_2652 cosh-def_binary64_2651 sinh-def_binary64_2650 tan-neg_binary64_2597 cos-neg_binary64_2596 sin-neg_binary64_2595 tan-0_binary64_2594 cos-0_binary64_2593 sin-0_binary64_2592 hang-m-tan_binary64_2591 hang-p-tan_binary64_2590 hang-m0-tan_binary64_2589 hang-p0-tan_binary64_2588 hang-0m-tan_binary64_2587 hang-0p-tan_binary64_2586 tan-+PI/2_binary64_2585 tan-+PI_binary64_2584 tan-PI_binary64_2583 tan-PI/3_binary64_2582 tan-PI/4_binary64_2581 tan-PI/6_binary64_2580 cos-+PI/2_binary64_2579 cos-+PI_binary64_2578 cos-PI_binary64_2577 cos-PI/2_binary64_2576 cos-PI/3_binary64_2575 cos-PI/4_binary64_2574 cos-PI/6_binary64_2573 sin-+PI/2_binary64_2572 sin-+PI_binary64_2571 sin-PI_binary64_2570 sin-PI/2_binary64_2569 sin-PI/3_binary64_2568 sin-PI/4_binary64_2567 sin-PI/6_binary64_2566 sub-1-sin_binary64_2565 sub-1-cos_binary64_2564 -1-add-sin_binary64_2563 -1-add-cos_binary64_2562 1-sub-sin_binary64_2561 1-sub-cos_binary64_2560 cos-sin-sum_binary64_2559 log-E_binary64_2555 log-pow_binary64_2554 log-rec_binary64_2553 log-div_binary64_2552 log-prod_binary64_2551 pow-base-0_binary64_2549 unpow1/3_binary64_2532 exp-to-pow_binary64_2527 pow-base-1_binary64_2525 unpow0_binary64_2524 unpow-1_binary64_2522 exp-lft-cube_binary64_2521 exp-lft-sqr_binary64_2520 exp-cbrt_binary64_2519 exp-sqrt_binary64_2518 exp-prod_binary64_2517 div-exp_binary64_2516 rec-exp_binary64_2515 prod-exp_binary64_2514 exp-diff_binary64_2513 exp-neg_binary64_2512 exp-sum_binary64_2511 e-exp-1_binary64_2510 exp-1-e_binary64_2508 exp-0_binary64_2507 rem-log-exp_binary64_2506 rem-exp-log_binary64_2505 cube-div_binary64_2494 cube-neg_binary64_2492 rem-3cbrt-rft_binary64_2491 rem-3cbrt-lft_binary64_2490 rem-cbrt-cube_binary64_2489 rem-cube-cbrt_binary64_2488 sqr-abs_binary64_2480 sqr-neg_binary64_2479 rem-square-sqrt_binary64_2477 times-frac_binary64_2471 div-sub_binary64_2470 neg-mul-1_binary64_2461 neg-sub0_binary64_2460 unsub-neg_binary64_2459 sub-neg_binary64_2458 mul-1-neg_binary64_2457 /-rgt-identity_binary64_2456 *-rgt-identity_binary64_2455 *-lft-identity_binary64_2454 remove-double-neg_binary64_2453 sub0-neg_binary64_2452 --rgt-identity_binary64_2451 +-rgt-identity_binary64_2450 +-lft-identity_binary64_2449 mul0-rgt_binary64_2448 mul0-lft_binary64_2447 div0_binary64_2446 *-inverses_binary64_2445 +-inverses_binary64_2444 lft-mult-inverse_binary64_2443 rgt-mult-inverse_binary64_2442 remove-double-div_binary64_2441 difference-of-sqr--1_binary64_2436 difference-of-sqr-1_binary64_2435 difference-of-squares_binary64_2434 swap-sqr_binary64_2432 cancel-sign-sub-inv_binary64_2431 cancel-sign-sub_binary64_2430 distribute-neg-frac_binary64_2429 distribute-frac-neg_binary64_2428 distribute-neg-out_binary64_2427 distribute-neg-in_binary64_2426 distribute-rgt-neg-out_binary64_2425 distribute-lft-neg-out_binary64_2424 distribute-rgt-neg-in_binary64_2423 distribute-lft-neg-in_binary64_2422 distribute-rgt1-in_binary64_2421 distribute-lft1-in_binary64_2420 distribute-rgt-out--_binary64_2419 distribute-rgt-out_binary64_2418 distribute-lft-out--_binary64_2417 distribute-lft-out_binary64_2416 distribute-rgt-in_binary64_2415 distribute-lft-in_binary64_2414 count-2_binary64_2413 associate-/l/_binary64_2412 associate-/r*_binary64_2409 associate--r-_binary64_2404 associate--l-_binary64_2403 associate--l+_binary64_2402 associate--r+_binary64_2401 associate-+l-_binary64_2400 associate-+r-_binary64_2399 associate-+l+_binary64_2398 associate-+r+_binary64_2397 +-commutative_binary64_2395
Counts
40 → 16
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
027592
127508
239508
346508
452508
561508
681508
7135508
8312508
9617508
10621508
11751508
12905508
131122508
141420508
151793508
162236508
172759508
182979508
193049508
203059508
213061508
223061508
233630508
244271508
254741508

prune112.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New15116
Fresh044
Picked101
Done011
Total16622
Error
31.7b
Counts
22 → 6
Compiler

Compiled 2296 to 1652 computations (28% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.5b
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
28.5b
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite182.0ms (0.3%)

Algorithm
rewrite-expression-head
Error
31.7b
Rules
pow1_binary64_2526 add-log-exp_binary64_2504 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487 *-un-lft-identity_binary64_2465
Counts
4 → 28
Calls

4 calls:

2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
Compiler

Compiled 3360 to 2430 computations (27.7% saved)

series251.0ms (0.4%)

Error
31.7b
Counts
4 → 12
Calls

4 calls:

48.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
48.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
46.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
42.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
Compiler

Compiled 4096 to 3075 computations (24.9% saved)

simplify209.0ms (0.3%)

Algorithm
egg-herbie
Rules
1268×sqr-pow_binary64_2437
651×pow-sqr_binary64_2438
362×unswap-sqr_binary64_2433
265×cube-prod_binary64_2493
201×unpow3_binary64_2531
198×cube-mult_binary64_2495
159×associate-*l*_binary64_2406
142×*-commutative_binary64_2396
93×associate-*r*_binary64_2405
48×pow-plus_binary64_2528
16×rem-sqrt-square_binary64_2478
cube-unmult_binary64_2502
unpow2_binary64_2530 unpow1/2_binary64_2529 unpow1_binary64_2523
associate-/l*_binary64_2410
1-exp_binary64_2509 associate-/r/_binary64_2411 associate-*l/_binary64_2408 associate-*r/_binary64_2407
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_2728 erf-erfc_binary64_2727 erf-odd_binary64_2726 if-if-and-not_binary64_2725 if-if-and_binary64_2724 if-if-or-not_binary64_2723 if-if-or_binary64_2722 if-not_binary64_2721 if-same_binary64_2720 if-false_binary64_2719 if-true_binary64_2718 not-gte_binary64_2717 not-lte_binary64_2716 not-gt_binary64_2715 not-lt_binary64_2714 gte-same_binary64_2713 lte-same_binary64_2712 gt-same_binary64_2711 lt-same_binary64_2710 sinh---cosh_binary64_2657 sinh-+-cosh_binary64_2656 sinh-cosh_binary64_2655 tanh-def-c_binary64_2654 tanh-def-b_binary64_2653 tanh-def-a_binary64_2652 cosh-def_binary64_2651 sinh-def_binary64_2650 tan-neg_binary64_2597 cos-neg_binary64_2596 sin-neg_binary64_2595 tan-0_binary64_2594 cos-0_binary64_2593 sin-0_binary64_2592 hang-m-tan_binary64_2591 hang-p-tan_binary64_2590 hang-m0-tan_binary64_2589 hang-p0-tan_binary64_2588 hang-0m-tan_binary64_2587 hang-0p-tan_binary64_2586 tan-+PI/2_binary64_2585 tan-+PI_binary64_2584 tan-PI_binary64_2583 tan-PI/3_binary64_2582 tan-PI/4_binary64_2581 tan-PI/6_binary64_2580 cos-+PI/2_binary64_2579 cos-+PI_binary64_2578 cos-PI_binary64_2577 cos-PI/2_binary64_2576 cos-PI/3_binary64_2575 cos-PI/4_binary64_2574 cos-PI/6_binary64_2573 sin-+PI/2_binary64_2572 sin-+PI_binary64_2571 sin-PI_binary64_2570 sin-PI/2_binary64_2569 sin-PI/3_binary64_2568 sin-PI/4_binary64_2567 sin-PI/6_binary64_2566 sub-1-sin_binary64_2565 sub-1-cos_binary64_2564 -1-add-sin_binary64_2563 -1-add-cos_binary64_2562 1-sub-sin_binary64_2561 1-sub-cos_binary64_2560 cos-sin-sum_binary64_2559 log-E_binary64_2555 log-pow_binary64_2554 log-rec_binary64_2553 log-div_binary64_2552 log-prod_binary64_2551 pow-base-0_binary64_2549 unpow1/3_binary64_2532 exp-to-pow_binary64_2527 pow-base-1_binary64_2525 unpow0_binary64_2524 unpow-1_binary64_2522 exp-lft-cube_binary64_2521 exp-lft-sqr_binary64_2520 exp-cbrt_binary64_2519 exp-sqrt_binary64_2518 exp-prod_binary64_2517 div-exp_binary64_2516 rec-exp_binary64_2515 prod-exp_binary64_2514 exp-diff_binary64_2513 exp-neg_binary64_2512 exp-sum_binary64_2511 e-exp-1_binary64_2510 exp-1-e_binary64_2508 exp-0_binary64_2507 rem-log-exp_binary64_2506 rem-exp-log_binary64_2505 cube-div_binary64_2494 cube-neg_binary64_2492 rem-3cbrt-rft_binary64_2491 rem-3cbrt-lft_binary64_2490 rem-cbrt-cube_binary64_2489 rem-cube-cbrt_binary64_2488 sqr-abs_binary64_2480 sqr-neg_binary64_2479 rem-square-sqrt_binary64_2477 times-frac_binary64_2471 div-sub_binary64_2470 neg-mul-1_binary64_2461 neg-sub0_binary64_2460 unsub-neg_binary64_2459 sub-neg_binary64_2458 mul-1-neg_binary64_2457 /-rgt-identity_binary64_2456 *-rgt-identity_binary64_2455 *-lft-identity_binary64_2454 remove-double-neg_binary64_2453 sub0-neg_binary64_2452 --rgt-identity_binary64_2451 +-rgt-identity_binary64_2450 +-lft-identity_binary64_2449 mul0-rgt_binary64_2448 mul0-lft_binary64_2447 div0_binary64_2446 *-inverses_binary64_2445 +-inverses_binary64_2444 lft-mult-inverse_binary64_2443 rgt-mult-inverse_binary64_2442 remove-double-div_binary64_2441 difference-of-sqr--1_binary64_2436 difference-of-sqr-1_binary64_2435 difference-of-squares_binary64_2434 swap-sqr_binary64_2432 cancel-sign-sub-inv_binary64_2431 cancel-sign-sub_binary64_2430 distribute-neg-frac_binary64_2429 distribute-frac-neg_binary64_2428 distribute-neg-out_binary64_2427 distribute-neg-in_binary64_2426 distribute-rgt-neg-out_binary64_2425 distribute-lft-neg-out_binary64_2424 distribute-rgt-neg-in_binary64_2423 distribute-lft-neg-in_binary64_2422 distribute-rgt1-in_binary64_2421 distribute-lft1-in_binary64_2420 distribute-rgt-out--_binary64_2419 distribute-rgt-out_binary64_2418 distribute-lft-out--_binary64_2417 distribute-lft-out_binary64_2416 distribute-rgt-in_binary64_2415 distribute-lft-in_binary64_2414 count-2_binary64_2413 associate-/l/_binary64_2412 associate-/r*_binary64_2409 associate--r-_binary64_2404 associate--l-_binary64_2403 associate--l+_binary64_2402 associate--r+_binary64_2401 associate-+l-_binary64_2400 associate-+r-_binary64_2399 associate-+l+_binary64_2398 associate-+r+_binary64_2397 +-commutative_binary64_2395
Counts
40 → 12
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
027592
127508
239508
346508
452508
561508
681508
7135508
8312508
9617508
10621508
11751508
12905508
131122508
141420508
151793508
162236508
172759508
182979508
193049508
203059508
213061508
223061508
233630508
244271508
254741508

prune68.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New12012
Fresh044
Picked011
Done011
Total12618
Error
31.7b
Counts
18 → 6
Compiler

Compiled 1428 to 1038 computations (27.3% saved)

regimes3.2s (4.5%)

Accuracy

Total 5.1b remaining (13.9%)

Threshold costs 0b (0%)

Compiler

Compiled 50419 to 37606 computations (25.4% saved)

bsearch16.0ms (0%)

Compiler

Compiled 109 to 83 computations (23.9% saved)

simplify49.0ms (0.1%)

Algorithm
egg-herbie
Rules
65×*-commutative_binary64_2396
44×+-commutative_binary64_2395
40×sub-neg_binary64_2458
37×neg-sub0_binary64_2460
36×neg-mul-1_binary64_2461
26×distribute-rgt-neg-in_binary64_2423
24×distribute-lft-neg-in_binary64_2422
unsub-neg_binary64_2459 distribute-neg-in_binary64_2426
distribute-neg-frac_binary64_2429
cancel-sign-sub-inv_binary64_2431
distribute-lft-neg-out_binary64_2424
mul-1-neg_binary64_2457
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64_2725 if-if-and_binary64_2724 if-if-or-not_binary64_2723 if-if-or_binary64_2722 if-not_binary64_2721 if-same_binary64_2720 if-false_binary64_2719 if-true_binary64_2718 tan-0_binary64_2594 cos-0_binary64_2593 sin-0_binary64_2592 unpow1_binary64_2523 e-exp-1_binary64_2510 1-exp_binary64_2509 exp-1-e_binary64_2508 exp-0_binary64_2507 sqr-abs_binary64_2480 sqr-neg_binary64_2479 /-rgt-identity_binary64_2456 *-rgt-identity_binary64_2455 *-lft-identity_binary64_2454 remove-double-neg_binary64_2453 sub0-neg_binary64_2452 --rgt-identity_binary64_2451 +-rgt-identity_binary64_2450 +-lft-identity_binary64_2449 cancel-sign-sub_binary64_2430 distribute-frac-neg_binary64_2428 distribute-neg-out_binary64_2427 distribute-rgt-neg-out_binary64_2425
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
086852
1132852
2165852
3201852
4249852
5299852
6343852
7385852
8406852
9417852
10421852
11421852

end0.0ms (0%)

sample38.3s (53.5%)

Algorithm
intervals
Results
9.0s1424×body4096valid
6.4s1681×body2048valid
5.3s825×body4096invalid
4.4s1102×body2048invalid
2.2s893×body1024valid
1.8s3415×body128valid
1.5s608×body1024invalid
965.0ms67×body8192valid
534.0ms355×body512valid
482.0ms34×body8192invalid
424.0ms921×body128invalid
372.0ms244×body512invalid
165.0ms165×body256valid
108.0ms115×body256invalid
Compiler

Compiled 5899 to 4388 computations (25.6% saved)

Profiling

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