Details

analyze216.0ms (1%)

Algorithm

1×	search
2×	egg-herbie

Rules

847×	`unswap-sqr_binary64_2433`
640×	`associate-*l/_binary64_2408`
462×	`associate-*r/_binary64_2407`
372×	`associate-/l*_binary64_2410`
366×	`distribute-rgt-out_binary64_2418`
344×	`distribute-rgt-in_binary64_2415`
324×	`distribute-lft-in_binary64_2414`
294×	`associate-+l+_binary64_2398`
262×	`distribute-lft-out_binary64_2416`
258×	`associate-+r+_binary64_2397`
240×	`*-commutative_binary64_2396`
183×	`associate-l_binary64_2406`
178×	`associate-r_binary64_2405`
126×	`associate-/l/_binary64_2412`
105×	`+-commutative_binary64_2395`
78×	`-rgt-identity_binary64_2455` `-lft-identity_binary64_2454`
73×	`associate-/r*_binary64_2409`
68×	`sqr-pow_binary64_2437`
61×	`associate-/r/_binary64_2411`
52×	`times-frac_binary64_2471`
31×	`pow-sqr_binary64_2438`
22×	`distribute-rgt1-in_binary64_2421`
14×	`distribute-lft1-in_binary64_2420`
12×	`pow-plus_binary64_2528`
7×	`cube-div_binary64_2494` `/-rgt-identity_binary64_2456`
4×	`unpow3_binary64_2531` `cube-unmult_binary64_2502`
2×	`unpow2_binary64_2530` `exp-prod_binary64_2517` `cube-prod_binary64_2493` `swap-sqr_binary64_2432`
1×	`unpow1/2_binary64_2529` `unpow1_binary64_2523` `1-exp_binary64_2509` `cube-mult_binary64_2495` `sqr-abs_binary64_2480`
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` `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` `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-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-neg_binary64_2479` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `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` `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` `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-rgt-out--_binary64_2419` `distribute-lft-out--_binary64_2417` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	86
2	261	60
3	1006	52
4	3215	49
5	3806	47
6	4565	47
7	5512	47
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample76.0ms (0.4%)

Algorithm

1×

intervals

Results

55.0ms	256×	body	128	valid
3.0ms	259×	pre	128	true
1.0ms	3×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

847×	`unswap-sqr_binary64_2433`
640×	`associate-*l/_binary64_2408`
462×	`associate-*r/_binary64_2407`
372×	`associate-/l*_binary64_2410`
366×	`distribute-rgt-out_binary64_2418`
344×	`distribute-rgt-in_binary64_2415`
324×	`distribute-lft-in_binary64_2414`
294×	`associate-+l+_binary64_2398`
262×	`distribute-lft-out_binary64_2416`
258×	`associate-+r+_binary64_2397`
240×	`*-commutative_binary64_2396`
183×	`associate-l_binary64_2406`
178×	`associate-r_binary64_2405`
126×	`associate-/l/_binary64_2412`
105×	`+-commutative_binary64_2395`
78×	`-rgt-identity_binary64_2455` `-lft-identity_binary64_2454`
73×	`associate-/r*_binary64_2409`
68×	`sqr-pow_binary64_2437`
61×	`associate-/r/_binary64_2411`
52×	`times-frac_binary64_2471`
31×	`pow-sqr_binary64_2438`
22×	`distribute-rgt1-in_binary64_2421`
14×	`distribute-lft1-in_binary64_2420`
12×	`pow-plus_binary64_2528`
7×	`cube-div_binary64_2494` `/-rgt-identity_binary64_2456`
4×	`unpow3_binary64_2531` `cube-unmult_binary64_2502`
2×	`unpow2_binary64_2530` `exp-prod_binary64_2517` `cube-prod_binary64_2493` `swap-sqr_binary64_2432`
1×	`unpow1/2_binary64_2529` `unpow1_binary64_2523` `1-exp_binary64_2509` `cube-mult_binary64_2495` `sqr-abs_binary64_2480`
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` `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` `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-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-neg_binary64_2479` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `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` `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` `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-rgt-out--_binary64_2419` `distribute-lft-out--_binary64_2417` `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`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	86
2	261	60
3	1006	52
4	3215	49
5	3806	47
6	4565	47
7	5512	47

prune10.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

2.5b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
1.0b	(sqrt.f64 PI.f64)
2.5b	(exp.f64 (*.f64 x x))

rewrite467.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

143×	`times-frac_binary64_2471`
97×	`add-sqr-sqrt_binary64_2487`
88×	`*-un-lft-identity_binary64_2465`
83×	`add-cube-cbrt_binary64_2500`
70×	`associate-l_binary64_2406`
43×	`sqrt-prod_binary64_2481`
15×	`add-cbrt-cube_binary64_2501`
13×	`add-exp-log_binary64_2503`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `associate-/r*_binary64_2409`
5×	`div-inv_binary64_2462` `associate-r_binary64_2405`
4×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `unswap-sqr_binary64_2433`
3×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `distribute-lft-out_binary64_2416` `associate-/l*_binary64_2410`
2×	`flip3-+_binary64_2468` `frac-times_binary64_2475` `flip-+_binary64_2439` `associate-*r/_binary64_2407`
1×	`exp-to-pow_binary64_2527` `exp-prod_binary64_2517` `rem-exp-log_binary64_2505` `pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-l/_binary64_2408` `-commutative_binary64_2396` `frac-2neg_binary64_2476` `clear-num_binary64_2464`

Counts

4 → 163

Calls

4 calls:

45.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
5.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 7337 to 3085 computations (58% saved)

series466.0ms (2.2%)

Error

2.3b

Counts

4 → 24

Calls

4 calls:

294.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
92.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
29.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1936 to 1445 computations (25.4% saved)

simplify180.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

428×	`distribute-rgt-in_binary64_2415`
425×	`distribute-lft-in_binary64_2414`
392×	`associate-+l+_binary64_2398`
374×	`associate-*l/_binary64_2408`
338×	`associate-/l/_binary64_2412`
329×	`associate-*r/_binary64_2407`
209×	`*-commutative_binary64_2396`
152×	`associate-l_binary64_2406`
131×	`associate-r_binary64_2405`
109×	`associate-/l*_binary64_2410`
104×	`*-rgt-identity_binary64_2455`
100×	`associate-/r*_binary64_2409`
92×	`distribute-rgt-out_binary64_2418`
86×	`*-lft-identity_binary64_2454` `associate-/r/_binary64_2411`
61×	`distribute-lft-out_binary64_2416`
52×	`+-commutative_binary64_2395`
45×	`times-frac_binary64_2471`
43×	`sub-neg_binary64_2458`
41×	`associate-+r+_binary64_2397`
30×	`associate-+l-_binary64_2400`
28×	`associate--l+_binary64_2402` `associate--r+_binary64_2401`
26×	`sqr-pow_binary64_2437`
25×	`cancel-sign-sub-inv_binary64_2431` `associate-+r-_binary64_2399`
24×	`exp-prod_binary64_2517` `unswap-sqr_binary64_2433`
21×	`log-div_binary64_2552`
16×	`distribute-rgt-neg-in_binary64_2423`
15×	`log-prod_binary64_2551` `exp-sum_binary64_2511` `swap-sqr_binary64_2432` `distribute-neg-in_binary64_2426`
14×	`cube-div_binary64_2494`
13×	`neg-mul-1_binary64_2461` `neg-sub0_binary64_2460`
12×	`cube-prod_binary64_2493` `distribute-neg-frac_binary64_2429`
10×	`distribute-rgt1-in_binary64_2421`
9×	`associate--l-_binary64_2403`
8×	`distribute-lft-neg-in_binary64_2422`
7×	`cube-unmult_binary64_2502` `distribute-lft-neg-out_binary64_2424`
6×	`distribute-rgt-neg-out_binary64_2425`
5×	`div-sub_binary64_2470` `unsub-neg_binary64_2459` `/-rgt-identity_binary64_2456` `distribute-rgt-out--_binary64_2419`
4×	`pow-sqr_binary64_2438` `distribute-lft1-in_binary64_2420`
3×	`prod-exp_binary64_2514` `rem-sqrt-square_binary64_2478`
2×	`log-pow_binary64_2554` `unpow3_binary64_2531` `rem-log-exp_binary64_2506` `cube-mult_binary64_2495` `count-2_binary64_2413` `associate--r-_binary64_2404`
1×	`log-rec_binary64_2553` `unpow2_binary64_2530` `unpow1/2_binary64_2529` `pow-plus_binary64_2528` `unpow1_binary64_2523` `exp-diff_binary64_2513` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `sqr-abs_binary64_2480` `rem-square-sqrt_binary64_2477` `distribute-neg-out_binary64_2427`
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` `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` `div-exp_binary64_2516` `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` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-neg_binary64_2479` `mul-1-neg_binary64_2457` `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` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-lft-out--_binary64_2417`

Counts

187 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	7760
1	1057	7135
2	3658	7072
3	5169	7072

prune415.0ms (1.9%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	115	28	143
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	28	145

Error

1.5b

Counts

145 → 28

Compiler

Compiled 7668 to 3462 computations (54.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 3/4 (*.f64 x x))
0.3b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
2.5b	(exp.f64 (*.f64 x x))

rewrite283.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

23×	`add-cbrt-cube_binary64_2501`
22×	`add-exp-log_binary64_2503`
20×	`*-un-lft-identity_binary64_2465`
13×	`add-sqr-sqrt_binary64_2487`
11×	`add-cube-cbrt_binary64_2500`
10×	`times-frac_binary64_2471`
7×	`associate-l_binary64_2406` `associate-/l*_binary64_2410`
6×	`add-log-exp_binary64_2504` `pow1_binary64_2526` `prod-exp_binary64_2514` `div-exp_binary64_2516` `cbrt-unprod_binary64_2498` `cbrt-undiv_binary64_2499`
5×	`associate-r_binary64_2405` `distribute-lft-out_binary64_2416`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `div-inv_binary64_2462`
2×	`frac-times_binary64_2475` `associate-r/_binary64_2407` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/l/_binary64_2412` `associate-/r_binary64_2409`
1×	`exp-to-pow_binary64_2527` `exp-prod_binary64_2517` `rem-exp-log_binary64_2505` `pow-prod-down_binary64_2536` `unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-l/_binary64_2408` `-commutative_binary64_2396`

Counts

4 → 91

Calls

4 calls:

35.0ms	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
5.0ms	(/.f64 3/4 (*.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 4105 to 2395 computations (41.7% saved)

series533.0ms (2.5%)

Error

1.5b

Counts

4 → 27

Calls

4 calls:

290.0ms	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
115.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
43.0ms	(/.f64 3/4 (*.f64 x x))
32.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 2204 to 1680 computations (23.8% saved)

simplify160.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

228×	`associate-+l+_binary64_2398`
216×	`associate-/l/_binary64_2412`
207×	`associate-l_binary64_2406`
180×	`+-commutative_binary64_2395`
175×	`associate-+r+_binary64_2397`
167×	`distribute-rgt-in_binary64_2415`
166×	`associate-r_binary64_2405`
158×	`distribute-lft-in_binary64_2414`
156×	`associate-/r/_binary64_2411`
138×	`sub-neg_binary64_2458`
132×	`*-commutative_binary64_2396`
130×	`associate-*l/_binary64_2408`
115×	`associate-/r*_binary64_2409`
112×	`associate-*r/_binary64_2407`
109×	`exp-prod_binary64_2517`
107×	`times-frac_binary64_2471`
105×	`sqr-pow_binary64_2437`
104×	`associate-/l*_binary64_2410`
86×	`log-prod_binary64_2551`
75×	`distribute-lft-out_binary64_2416`
66×	`cube-prod_binary64_2493`
60×	`distribute-rgt-out_binary64_2418`
56×	`neg-mul-1_binary64_2461` `neg-sub0_binary64_2460`
50×	`unsub-neg_binary64_2459`
47×	`unswap-sqr_binary64_2433`
42×	`log-div_binary64_2552`
36×	`unpow3_binary64_2531`
35×	`exp-sum_binary64_2511`
34×	`cancel-sign-sub-inv_binary64_2431`
32×	`cube-div_binary64_2494` `associate--r+_binary64_2401`
29×	`*-lft-identity_binary64_2454`
27×	`*-rgt-identity_binary64_2455` `associate--l+_binary64_2402`
26×	`div-sub_binary64_2470`
25×	`swap-sqr_binary64_2432`
24×	`distribute-rgt-neg-in_binary64_2423`
22×	`associate-+l-_binary64_2400`
20×	`distribute-neg-frac_binary64_2429`
18×	`distribute-neg-in_binary64_2426`
17×	`cube-mult_binary64_2495` `associate-+r-_binary64_2399`
16×	`pow-sqr_binary64_2438`
15×	`log-pow_binary64_2554` `distribute-lft-neg-in_binary64_2422`
13×	`cube-unmult_binary64_2502`
11×	`+-rgt-identity_binary64_2450`
10×	`distribute-lft-neg-out_binary64_2424`
9×	`distribute-rgt-neg-out_binary64_2425`
8×	`distribute-rgt1-in_binary64_2421`
6×	`pow-plus_binary64_2528` `sub0-neg_binary64_2452` `distribute-rgt-out--_binary64_2419`
4×	`rem-sqrt-square_binary64_2478` `/-rgt-identity_binary64_2456` `count-2_binary64_2413`
3×	`log-rec_binary64_2553` `exp-to-pow_binary64_2527` `prod-exp_binary64_2514` `rem-log-exp_binary64_2506`
2×	`unpow1/2_binary64_2529` `distribute-lft1-in_binary64_2420` `associate--r-_binary64_2404`
1×	`log-E_binary64_2555` `unpow2_binary64_2530` `unpow1_binary64_2523` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `sqr-abs_binary64_2480` `rem-square-sqrt_binary64_2477` `remove-double-neg_binary64_2453` `+-lft-identity_binary64_2449`
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` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `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` `div-exp_binary64_2516` `rec-exp_binary64_2515` `exp-diff_binary64_2513` `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-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-neg_binary64_2479` `mul-1-neg_binary64_2457` `--rgt-identity_binary64_2451` `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` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-lft-out--_binary64_2417` `associate--l-_binary64_2403`

Counts

118 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4182
1	665	3465
2	2444	3391
3	4313	3352
4	4953	3352
5	4934	3352

prune252.0ms (1.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	7	20	27
Picked	1	0	1
Done	0	0	0
Total	82	26	108

Error

1.5b

Counts

108 → 26

Compiler

Compiled 4567 to 2643 computations (42.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x))))
0.4b	(.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)))
2.5b	(exp.f64 (*.f64 x x))

rewrite660.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

94×	`times-frac_binary64_2471`
70×	`add-sqr-sqrt_binary64_2487`
65×	`*-un-lft-identity_binary64_2465`
55×	`add-cube-cbrt_binary64_2500`
53×	`associate-r_binary64_2405`
42×	`sqrt-prod_binary64_2481`
38×	`add-exp-log_binary64_2503`
35×	`add-cbrt-cube_binary64_2501`
18×	`prod-exp_binary64_2514` `associate-l_binary64_2406`
13×	`cbrt-unprod_binary64_2498`
12×	`div-exp_binary64_2516`
11×	`pow1_binary64_2526` `frac-times_binary64_2475`
8×	`cbrt-undiv_binary64_2499` `associate-*r/_binary64_2407`
7×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-*l/_binary64_2408`
6×	`add-log-exp_binary64_2504` `div-inv_binary64_2462`
5×	`unswap-sqr_binary64_2433` `distribute-lft-out_binary64_2416`
4×	`pow-prod-down_binary64_2536` `associate-/l*_binary64_2410`
3×	`1-exp_binary64_2509`
2×	`*-commutative_binary64_2396` `associate-/l/_binary64_2412`
1×	`exp-to-pow_binary64_2527` `exp-prod_binary64_2517` `rem-exp-log_binary64_2505` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/r*_binary64_2409`

Counts

4 → 165

Calls

4 calls:

46.0ms	(.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)))
40.0ms	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x))))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 8510 to 5114 computations (39.9% saved)

series675.0ms (3.2%)

Error

1.5b

Counts

4 → 36

Calls

4 calls:

254.0ms	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x))))
221.0ms	(.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)))
99.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
32.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 2970 to 2266 computations (23.7% saved)

simplify355.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

268×	`associate-r_binary64_2405`
266×	`associate-l_binary64_2406`
219×	`distribute-rgt-in_binary64_2415`
210×	`distribute-lft-in_binary64_2414`
194×	`*-commutative_binary64_2396`
190×	`associate-/r/_binary64_2411`
171×	`associate-/l*_binary64_2410`
165×	`associate-*r/_binary64_2407`
154×	`div-sub_binary64_2470`
144×	`associate-/r*_binary64_2409`
140×	`associate-*l/_binary64_2408`
108×	`neg-mul-1_binary64_2461`
105×	`times-frac_binary64_2471`
104×	`distribute-lft-out_binary64_2416`
101×	`exp-prod_binary64_2517` `sub-neg_binary64_2458`
97×	`log-prod_binary64_2551`
72×	`+-commutative_binary64_2395`
68×	`associate-/l/_binary64_2412`
61×	`log-div_binary64_2552` `associate-+l+_binary64_2398`
60×	`cube-prod_binary64_2493` `associate-+r+_binary64_2397`
57×	`*-lft-identity_binary64_2454` `distribute-rgt-out_binary64_2418`
54×	`*-rgt-identity_binary64_2455`
52×	`exp-sum_binary64_2511`
51×	`cancel-sign-sub-inv_binary64_2431`
42×	`unswap-sqr_binary64_2433`
40×	`cube-div_binary64_2494`
37×	`/-rgt-identity_binary64_2456` `sqr-pow_binary64_2437`
33×	`swap-sqr_binary64_2432`
32×	`distribute-neg-in_binary64_2426`
25×	`distribute-rgt-neg-in_binary64_2423`
24×	`log-pow_binary64_2554`
23×	`associate-+l-_binary64_2400`
20×	`neg-sub0_binary64_2460` `distribute-neg-frac_binary64_2429` `distribute-lft-neg-out_binary64_2424`
18×	`unpow3_binary64_2531` `distribute-rgt-neg-out_binary64_2425`
17×	`distribute-lft-neg-in_binary64_2422`
16×	`associate--r+_binary64_2401`
15×	`exp-diff_binary64_2513`
14×	`cube-mult_binary64_2495` `associate-+r-_binary64_2399`
12×	`cube-unmult_binary64_2502`
11×	`distribute-rgt1-in_binary64_2421`
10×	`associate--l+_binary64_2402`
9×	`distribute-rgt-out--_binary64_2419`
8×	`unsub-neg_binary64_2459` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447`
7×	`log-rec_binary64_2553` `pow-plus_binary64_2528` `prod-exp_binary64_2514` `rem-sqrt-square_binary64_2478` `associate--l-_binary64_2403`
6×	`exp-to-pow_binary64_2527` `sub0-neg_binary64_2452` `+-lft-identity_binary64_2449` `pow-sqr_binary64_2438` `count-2_binary64_2413`
5×	`rec-exp_binary64_2515`
4×	`div-exp_binary64_2516`
3×	`unpow1/2_binary64_2529` `rem-log-exp_binary64_2506` `--rgt-identity_binary64_2451` `div0_binary64_2446` `associate--r-_binary64_2404`
2×	`sqr-neg_binary64_2479` `remove-double-neg_binary64_2453` `distribute-lft1-in_binary64_2420`
1×	`log-E_binary64_2555` `unpow2_binary64_2530` `unpow1_binary64_2523` `exp-neg_binary64_2512` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-exp-log_binary64_2505` `sqr-abs_binary64_2480` `rem-square-sqrt_binary64_2477` `remove-double-div_binary64_2441` `distribute-neg-out_binary64_2427`
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` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `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` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `mul-1-neg_binary64_2457` `+-rgt-identity_binary64_2450` `*-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `difference-of-sqr--1_binary64_2436` `difference-of-sqr-1_binary64_2435` `difference-of-squares_binary64_2434` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-lft-out--_binary64_2417`

Counts

201 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	343	9981
1	838	8513
2	3561	8411
3	4573	8333
4	4966	8333
5	4988	8333
6	4902	8333

prune452.0ms (2.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	146	8	154
Fresh	9	16	25
Picked	1	0	1
Done	0	0	0
Total	156	24	180

Error

1.4b

Counts

180 → 24

Compiler

Compiled 7768 to 4619 computations (40.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
0.4b	(exp.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))))
1.5b	(log.f64 (exp.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))))
2.5b	(exp.f64 (*.f64 x x))

rewrite454.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

81×	`times-frac_binary64_2471`
62×	`add-sqr-sqrt_binary64_2487`
53×	`*-un-lft-identity_binary64_2465`
52×	`associate-l_binary64_2406`
47×	`add-cube-cbrt_binary64_2500`
42×	`sqrt-prod_binary64_2481`
9×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
7×	`pow1_binary64_2526`
5×	`log-prod_binary64_2551` `unswap-sqr_binary64_2433` `associate-r_binary64_2405`
4×	`exp-sum_binary64_2511` `div-inv_binary64_2462`
3×	`exp-to-pow_binary64_2527` `exp-prod_binary64_2517` `log-pow_binary64_2554` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `distribute-lft-out_binary64_2416`
2×	`rem-exp-log_binary64_2505` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `flip3-+_binary64_2468` `frac-times_binary64_2475` `flip-+_binary64_2439` `associate-*r/_binary64_2407`
1×	`rem-log-exp_binary64_2506` `pow-prod-down_binary64_2536` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `associate-l/_binary64_2408` `-commutative_binary64_2396`

Counts

4 → 120

Calls

4 calls:

41.0ms	(.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
3.0ms	(exp.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))))
2.0ms	(log.f64 (exp.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))))
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 6250 to 3869 computations (38.1% saved)

series1.0s (4.8%)

Error

1.4b

Counts

4 → 36

Calls

4 calls:

417.0ms	(log.f64 (exp.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))))
251.0ms	(exp.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))))
232.0ms	(.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
34.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 3800 to 2861 computations (24.7% saved)

simplify173.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l*_binary64_2410`
482×	`associate-+l+_binary64_2398`
287×	`distribute-rgt-in_binary64_2415`
284×	`distribute-lft-in_binary64_2414`
169×	`associate-l_binary64_2406` `*-commutative_binary64_2396`
155×	`associate-*l/_binary64_2408`
150×	`associate-r_binary64_2405`
148×	`associate-*r/_binary64_2407`
93×	`distribute-rgt-out_binary64_2418`
80×	`associate-/r*_binary64_2409`
76×	`exp-prod_binary64_2517`
70×	`+-commutative_binary64_2395`
69×	`associate-+r+_binary64_2397`
68×	`associate-/l/_binary64_2412`
67×	`distribute-lft-out_binary64_2416`
66×	`unswap-sqr_binary64_2433`
58×	`*-lft-identity_binary64_2454`
53×	`*-rgt-identity_binary64_2455`
50×	`sqr-pow_binary64_2437`
39×	`cancel-sign-sub-inv_binary64_2431`
37×	`times-frac_binary64_2471`
35×	`log-prod_binary64_2551`
33×	`associate-/r/_binary64_2411`
28×	`sub-neg_binary64_2458`
25×	`swap-sqr_binary64_2432`
24×	`associate--r+_binary64_2401`
22×	`exp-sum_binary64_2511` `associate--l+_binary64_2402`
21×	`cube-prod_binary64_2493` `distribute-rgt-neg-in_binary64_2423`
14×	`distribute-neg-in_binary64_2426`
13×	`distribute-neg-frac_binary64_2429`
12×	`rem-log-exp_binary64_2506` `pow-sqr_binary64_2438` `distribute-lft-neg-in_binary64_2422`
11×	`log-pow_binary64_2554` `distribute-rgt1-in_binary64_2421`
10×	`neg-mul-1_binary64_2461` `neg-sub0_binary64_2460`
9×	`log-div_binary64_2552` `associate-+l-_binary64_2400`
7×	`cube-unmult_binary64_2502` `distribute-lft-neg-out_binary64_2424` `associate-+r-_binary64_2399`
6×	`prod-exp_binary64_2514`
5×	`exp-to-pow_binary64_2527` `cube-div_binary64_2494` `distribute-rgt-neg-out_binary64_2425` `distribute-rgt-out--_binary64_2419`
4×	`unpow3_binary64_2531` `cube-mult_binary64_2495` `rem-sqrt-square_binary64_2478` `unsub-neg_binary64_2459` `distribute-lft1-in_binary64_2420` `count-2_binary64_2413`
3×	`unpow1/2_binary64_2529`
2×	`log-rec_binary64_2553` `unpow2_binary64_2530` `unpow1_binary64_2523` `div-sub_binary64_2470`
1×	`log-E_binary64_2555` `pow-plus_binary64_2528` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-exp-log_binary64_2505` `sqr-abs_binary64_2480` `rem-square-sqrt_binary64_2477` `/-rgt-identity_binary64_2456`
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` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `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` `div-exp_binary64_2516` `rec-exp_binary64_2515` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `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-neg_binary64_2479` `mul-1-neg_binary64_2457` `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` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-lft-out--_binary64_2417` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

156 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	7810
1	824	7036
2	2752	6849
3	5124	6849

prune346.0ms (1.6%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	4	19	23
Picked	0	1	1
Done	0	0	0
Total	120	27	147

Error

1.2b

Counts

147 → 27

Compiler

Compiled 5784 to 3579 computations (38.1% saved)

regimes3.0s (13.9%)

Accuracy

Total 0.7b remaining (59.9%)

Threshold costs 0.7b (59.9%)

Compiler

Compiled 37760 to 24231 computations (35.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64_2395`
2×	`*-commutative_binary64_2396`
1×	`1-exp_binary64_2509`
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` `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` `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	24	50
1	31	50
2	30	50

end0.0ms (0%)

sample11.0s (51.5%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
97.0ms	8125×	pre	128	true
27.0ms	125×	body	128	invalid

Compiler

Compiled 12654 to 8125 computations (35.8% saved)

Details

analyze216.0ms (1%)

sample76.0ms (0.4%)

simplify75.0ms (0.4%)

prune10.0ms (0%)

localize22.0ms (0.1%)

rewrite467.0ms (2.2%)

series466.0ms (2.2%)

simplify180.0ms (0.8%)

prune415.0ms (1.9%)

localize22.0ms (0.1%)

rewrite283.0ms (1.3%)

series533.0ms (2.5%)

simplify160.0ms (0.8%)

prune252.0ms (1.2%)

localize21.0ms (0.1%)

rewrite660.0ms (3.1%)

series675.0ms (3.2%)

simplify355.0ms (1.7%)

prune452.0ms (2.1%)

localize26.0ms (0.1%)

rewrite454.0ms (2.1%)

series1.0s (4.8%)

simplify173.0ms (0.8%)

prune346.0ms (1.6%)

regimes3.0s (13.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample11.0s (51.5%)

Profiling