Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 20 to 17 computations (15% saved)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify729.0ms (16.5%)

Algorithm

1×	egg-herbie

Rules

800×	`exp-prod_binary64_2517`
626×	`swap-sqr_binary64_2432`
517×	`associate-/l*_binary64_2410`
284×	`unsub-neg_binary64_2459`
214×	`exp-sum_binary64_2511` `distribute-rgt-neg-in_binary64_2423`
213×	`distribute-rgt-in_binary64_2415`
179×	`sub-neg_binary64_2458`
161×	`neg-mul-1_binary64_2461`
159×	`neg-sub0_binary64_2460`
157×	`*-commutative_binary64_2396`
130×	`distribute-lft-in_binary64_2414`
116×	`sqr-pow_binary64_2437`
108×	`associate-r_binary64_2405`
101×	`pow-sqr_binary64_2438`
100×	`associate-+l+_binary64_2398`
98×	`distribute-rgt-out_binary64_2418`
94×	`pow-plus_binary64_2528`
90×	`distribute-lft-neg-in_binary64_2422`
87×	`distribute-neg-frac_binary64_2429`
83×	`distribute-rgt1-in_binary64_2421`
74×	`associate--r+_binary64_2401` `associate-+r+_binary64_2397`
72×	`associate-l_binary64_2406`
69×	`cancel-sign-sub-inv_binary64_2431` `distribute-rgt-out--_binary64_2419`
62×	`associate--l+_binary64_2402`
51×	`+-commutative_binary64_2395`
48×	`exp-diff_binary64_2513`
44×	`distribute-lft-out_binary64_2416`
41×	`distribute-neg-in_binary64_2426`
40×	`distribute-lft-out--_binary64_2417`
39×	`associate-+l-_binary64_2400`
35×	`distribute-lft-neg-out_binary64_2424`
34×	`distribute-rgt-neg-out_binary64_2425`
31×	`remove-double-neg_binary64_2453`
21×	`sqr-neg_binary64_2479`
18×	`+-lft-identity_binary64_2449`
16×	`mul0-lft_binary64_2447`
14×	`mul0-rgt_binary64_2448`
13×	`sub0-neg_binary64_2452` `associate-*l/_binary64_2408`
12×	`exp-lft-sqr_binary64_2520` `div-sub_binary64_2470` `distribute-lft1-in_binary64_2420` `associate-*r/_binary64_2407` `associate-+r-_binary64_2399`
11×	`-rgt-identity_binary64_2455` `-lft-identity_binary64_2454`
10×	`exp-neg_binary64_2512` `+-rgt-identity_binary64_2450`
9×	`pow-base-1_binary64_2525` `cube-prod_binary64_2493`
8×	`+-inverses_binary64_2444` `count-2_binary64_2413`
7×	`distribute-neg-out_binary64_2427`
6×	`cube-unmult_binary64_2502` `associate--r-_binary64_2404`
5×	`--rgt-identity_binary64_2451`
4×	`difference-of-squares_binary64_2434`
3×	`div0_binary64_2446` `associate--l-_binary64_2403`
2×	`cube-neg_binary64_2492` `difference-of-sqr--1_binary64_2436` `unswap-sqr_binary64_2433` `associate-/r/_binary64_2411` `associate-/r*_binary64_2409`
1×	`exp-sqrt_binary64_2518` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `*-inverses_binary64_2445`
0×	`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` `unpow2_binary64_2530` `unpow1/2_binary64_2529` `exp-to-pow_binary64_2527` `unpow0_binary64_2524` `unpow1_binary64_2523` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-cbrt_binary64_2519` `div-exp_binary64_2516` `rec-exp_binary64_2515` `prod-exp_binary64_2514` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-mult_binary64_2495` `cube-div_binary64_2494` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `times-frac_binary64_2471` `mul-1-neg_binary64_2457` `/-rgt-identity_binary64_2456` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `difference-of-sqr-1_binary64_2435` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `associate-/l/_binary64_2412`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	34	28
2	53	28
3	76	28
4	104	28
5	137	28
6	243	28
7	967	28
8	2993	28

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

0.0b

Counts

1 → 1

Compiler

Compiled 19 to 16 computations (15.8% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
0.0b	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
15.0b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite225.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

27×	`add-sqr-sqrt_binary64_2487`
20×	`*-un-lft-identity_binary64_2465`
18×	`add-cube-cbrt_binary64_2500`
10×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `times-frac_binary64_2471`
9×	`associate-r_binary64_2405`
8×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `associate-l_binary64_2406` `cancel-sign-sub-inv_binary64_2431`
5×	`distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-*r/_binary64_2407`
3×	`associate-/l_binary64_2410` `associate-/r_binary64_2409`
2×	`associate-/l/_binary64_2412` `associate-/r/_binary64_2411` `pow-prod-down_binary64_2536` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `unswap-sqr_binary64_2433` `*-commutative_binary64_2396` `sub-neg_binary64_2458` `difference-of-squares_binary64_2434`
1×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `flip3--_binary64_2469` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `sum-log_binary64_2556` `+-commutative_binary64_2395`

Counts

4 → 95

Calls

4 calls:

14.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
6.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

Compiler

Compiled 2972 to 2376 computations (20.1% saved)

series302.0ms (6.8%)

Error

Counts

4 → 36

Calls

4 calls:

76.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
69.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
68.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
48.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

Compiler

Compiled 1268 to 1071 computations (15.5% saved)

simplify291.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

669×	`distribute-rgt-in_binary64_2415`
635×	`distribute-lft-in_binary64_2414`
279×	`times-frac_binary64_2471`
251×	`cancel-sign-sub-inv_binary64_2431`
216×	`associate-l_binary64_2406`
184×	`associate-r_binary64_2405`
128×	`distribute-rgt-neg-in_binary64_2423`
106×	`sub-neg_binary64_2458` `*-commutative_binary64_2396`
80×	`distribute-lft-neg-in_binary64_2422`
65×	`unswap-sqr_binary64_2433`
63×	`distribute-lft-neg-out_binary64_2424`
58×	`sqr-pow_binary64_2437`
57×	`neg-sub0_binary64_2460`
56×	`neg-mul-1_binary64_2461`
54×	`*-rgt-identity_binary64_2455`
52×	`+-commutative_binary64_2395`
42×	`*-lft-identity_binary64_2454`
39×	`distribute-rgt-out_binary64_2418`
38×	`exp-prod_binary64_2517`
36×	`distribute-neg-in_binary64_2426`
34×	`distribute-rgt-neg-out_binary64_2425` `associate-/l*_binary64_2410`
31×	`associate-/r*_binary64_2409`
27×	`unsub-neg_binary64_2459` `pow-sqr_binary64_2438` `distribute-rgt-out--_binary64_2419` `associate-*r/_binary64_2407`
26×	`associate-*l/_binary64_2408`
23×	`cube-prod_binary64_2493` `associate--l+_binary64_2402`
22×	`log-prod_binary64_2551` `associate--r+_binary64_2401`
20×	`associate-/l/_binary64_2412`
19×	`distribute-neg-frac_binary64_2429`
17×	`prod-exp_binary64_2514` `swap-sqr_binary64_2432`
16×	`div-exp_binary64_2516` `distribute-lft-out_binary64_2416`
10×	`unpow3_binary64_2531` `distribute-lft-out--_binary64_2417` `associate-/r/_binary64_2411`
9×	`associate-+l+_binary64_2398`
8×	`pow-plus_binary64_2528` `/-rgt-identity_binary64_2456`
7×	`log-div_binary64_2552` `cube-mult_binary64_2495` `div-sub_binary64_2470`
6×	`cube-unmult_binary64_2502` `cube-div_binary64_2494` `difference-of-squares_binary64_2434`
5×	`log-pow_binary64_2554` `exp-sum_binary64_2511`
4×	`rec-exp_binary64_2515` `distribute-neg-out_binary64_2427`
3×	`pow-base-1_binary64_2525` `associate-+l-_binary64_2400` `associate-+r-_binary64_2399`
2×	`exp-diff_binary64_2513` `distribute-rgt1-in_binary64_2421` `distribute-lft1-in_binary64_2420` `associate-+r+_binary64_2397`
1×	`log-rec_binary64_2553` `unpow2_binary64_2530` `unpow1_binary64_2523` `exp-sqrt_binary64_2518` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-log-exp_binary64_2506` `rem-3cbrt-lft_binary64_2490` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `sub0-neg_binary64_2452` `+-rgt-identity_binary64_2450` `*-inverses_binary64_2445` `cancel-sign-sub_binary64_2430`
0×	`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` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow1/2_binary64_2529` `exp-to-pow_binary64_2527` `unpow0_binary64_2524` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-neg_binary64_2512` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `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` `mul-1-neg_binary64_2457` `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_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` `distribute-frac-neg_binary64_2428` `count-2_binary64_2413` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

131 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3091
1	640	2870
2	2096	2858

prune265.0ms (6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	2	172

Error

Counts

172 → 2

Compiler

Compiled 3981 to 3082 computations (22.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x)
0.2b	(.f64 x (-.f64 (.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x) 12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))
0.2b	(*.f64 (pow.f64 x 3) 587893217913092678624467406457365636833467885051322882613974551606574556079145/463168356949264781694283940034751631413079938662562256157830336031652518559744)
9.6b	(-.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x (-.f64 (.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x) 12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))) (*.f64 (pow.f64 x 3) 587893217913092678624467406457365636833467885051322882613974551606574556079145/463168356949264781694283940034751631413079938662562256157830336031652518559744))

rewrite156.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`add-sqr-sqrt_binary64_2487`
18×	`associate-l_binary64_2406`
14×	`add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
13×	`add-exp-log_binary64_2503`
10×	`add-cbrt-cube_binary64_2501`
9×	`add-log-exp_binary64_2504` `associate-r_binary64_2405`
8×	`pow1_binary64_2526`
7×	`cancel-sign-sub-inv_binary64_2431`
6×	`unswap-sqr_binary64_2433`
5×	`prod-exp_binary64_2514`
4×	`unpow-prod-down_binary64_2544` `cube-prod_binary64_2493` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414`
3×	`sub-neg_binary64_2458` `cbrt-unprod_binary64_2498` `*-commutative_binary64_2396`
2×	`diff-log_binary64_2557` `flip3--_binary64_2469` `flip--_binary64_2440` `sqr-pow_binary64_2437` `pow-prod-down_binary64_2536` `associate-*r/_binary64_2407`
1×	`sum-log_binary64_2556` `associate--l+_binary64_2402` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `unpow3_binary64_2531` `cube-mult_binary64_2495`

Counts

4 → 91

Calls

4 calls:

7.0ms	(.f64 x (-.f64 (.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x) 12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))
6.0ms	(-.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x (-.f64 (.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x) 12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))) (*.f64 (pow.f64 x 3) 587893217913092678624467406457365636833467885051322882613974551606574556079145/463168356949264781694283940034751631413079938662562256157830336031652518559744))
6.0ms	(*.f64 (pow.f64 x 3) 587893217913092678624467406457365636833467885051322882613974551606574556079145/463168356949264781694283940034751631413079938662562256157830336031652518559744)
4.0ms	(*.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x)

Compiler

Compiled 2034 to 1625 computations (20.1% saved)

series231.0ms (5.2%)

Error

Counts

4 → 24

Calls

4 calls:

78.0ms	(.f64 x (-.f64 (.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x) 12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))
59.0ms	(-.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x (-.f64 (.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x) 12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))) (*.f64 (pow.f64 x 3) 587893217913092678624467406457365636833467885051322882613974551606574556079145/463168356949264781694283940034751631413079938662562256157830336031652518559744))
46.0ms	(*.f64 (pow.f64 x 3) 587893217913092678624467406457365636833467885051322882613974551606574556079145/463168356949264781694283940034751631413079938662562256157830336031652518559744)
26.0ms	(*.f64 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032 x)

Compiler

Compiled 757 to 650 computations (14.1% saved)

simplify554.0ms (12.5%)

Algorithm

1×	egg-herbie

Rules

451×	`distribute-rgt-in_binary64_2415`
449×	`distribute-lft-in_binary64_2414`
289×	`associate-l_binary64_2406`
260×	`associate-r_binary64_2405`
193×	`cancel-sign-sub-inv_binary64_2431`
185×	`unswap-sqr_binary64_2433`
130×	`distribute-rgt-neg-in_binary64_2423`
118×	`associate-+l+_binary64_2398`
116×	`distribute-lft-neg-in_binary64_2422`
104×	`exp-prod_binary64_2517`
94×	`log-prod_binary64_2551`
80×	`*-commutative_binary64_2396`
79×	`cube-prod_binary64_2493`
75×	`associate-l/_binary64_2408` `associate-r/_binary64_2407`
72×	`sqr-pow_binary64_2437`
46×	`swap-sqr_binary64_2432` `distribute-rgt-neg-out_binary64_2425`
42×	`sub-neg_binary64_2458`
40×	`distribute-lft-neg-out_binary64_2424`
38×	`distribute-rgt-out_binary64_2418`
34×	`pow-sqr_binary64_2438`
31×	`neg-sub0_binary64_2460` `associate-+l-_binary64_2400`
30×	`*-rgt-identity_binary64_2455` `+-commutative_binary64_2395`
28×	`neg-mul-1_binary64_2461` `*-lft-identity_binary64_2454` `associate--l+_binary64_2402`
26×	`associate-+r-_binary64_2399`
25×	`exp-sum_binary64_2511`
15×	`unpow3_binary64_2531`
13×	`distribute-rgt-out--_binary64_2419` `associate-/l*_binary64_2410`
12×	`exp-diff_binary64_2513` `unsub-neg_binary64_2459` `distribute-lft-out_binary64_2416`
11×	`log-pow_binary64_2554`
10×	`pow-plus_binary64_2528`
8×	`cube-mult_binary64_2495` `associate--r+_binary64_2401`
7×	`cube-unmult_binary64_2502`
6×	`difference-of-squares_binary64_2434` `associate-+r+_binary64_2397`
5×	`div-exp_binary64_2516` `rem-sqrt-square_binary64_2478`
4×	`+-rgt-identity_binary64_2450` `distribute-neg-out_binary64_2427` `distribute-lft-out--_binary64_2417` `associate-/l/_binary64_2412`
3×	`times-frac_binary64_2471` `associate-/r*_binary64_2409`
2×	`prod-exp_binary64_2514` `rem-square-sqrt_binary64_2477` `div-sub_binary64_2470` `distribute-neg-in_binary64_2426` `count-2_binary64_2413`
1×	`log-div_binary64_2552` `unpow2_binary64_2530` `pow-base-1_binary64_2525` `unpow1_binary64_2523` `exp-sqrt_binary64_2518` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-log-exp_binary64_2506` `cube-div_binary64_2494` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `*-inverses_binary64_2445` `distribute-neg-frac_binary64_2429` `associate-/r/_binary64_2411` `associate--r-_binary64_2404`
0×	`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` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow1/2_binary64_2529` `exp-to-pow_binary64_2527` `unpow0_binary64_2524` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `rec-exp_binary64_2515` `exp-neg_binary64_2512` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `rem-exp-log_binary64_2505` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `mul-1-neg_binary64_2457` `/-rgt-identity_binary64_2456` `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_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-frac-neg_binary64_2428` `distribute-rgt1-in_binary64_2421` `distribute-lft1-in_binary64_2420` `associate--l-_binary64_2403`

Counts

115 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	1608
1	392	1485
2	1635	1470

prune362.0ms (8.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	223	2	225

Error

Counts

225 → 2

Compiler

Compiled 5364 to 4240 computations (21% saved)

regimes169.0ms (3.8%)

Accuracy

Total 0.0b remaining (88.8%)

Threshold costs 0.0b (88.8%)

Compiler

Compiled 1646 to 1397 computations (15.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64_2396` `+-commutative_binary64_2395`
2×	`sub-neg_binary64_2458`
1×	`1-exp_binary64_2509` `neg-mul-1_binary64_2461` `neg-sub0_binary64_2460`
0×	`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` `exp-1-e_binary64_2508` `exp-0_binary64_2507` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `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` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	28	28
2	32	28
3	34	28
4	35	28

Proof

(* f64 6369080665019903/9007199254740992 (- f64 (/ f64 (+ f64 162377988252285/70368744177664 (* f64 h0 609359547581365/2251799813685248)) (+ f64 1 (* f64 h0 (+ f64 8937753748486939/9007199254740992 (* f64 h0 3228900788839551/72057594037927936))))) h0))

end0.0ms (0%)

sample1.1s (24.6%)

Algorithm

1×

intervals

Results

357.0ms

8000×

body

128

valid

Compiler

Compiled 563 to 479 computations (14.9% saved)

Details

analyze5.0ms (0.1%)

sample19.0ms (0.4%)

simplify729.0ms (16.5%)

prune2.0ms (0%)

localize16.0ms (0.4%)

rewrite225.0ms (5.1%)

series302.0ms (6.8%)

simplify291.0ms (6.6%)

prune265.0ms (6%)

localize9.0ms (0.2%)

rewrite156.0ms (3.5%)

series231.0ms (5.2%)

simplify554.0ms (12.5%)

prune362.0ms (8.2%)

regimes169.0ms (3.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (24.6%)

Profiling