Details

analyze356.0ms (3.5%)

Algorithm

1×	search
2×	egg-herbie

Rules

511×	`unsub-neg_binary64_2459`
501×	`sub-neg_binary64_2458`
352×	`associate--l+_binary64_2402`
328×	`associate-+l+_binary64_2398`
312×	`neg-mul-1_binary64_2461`
308×	`neg-sub0_binary64_2460`
296×	`associate-+r+_binary64_2397`
251×	`associate-l_binary64_2406`
245×	`distribute-rgt-neg-in_binary64_2423`
243×	`distribute-rgt-in_binary64_2415`
232×	`distribute-rgt-out_binary64_2418`
217×	`associate-r_binary64_2405`
205×	`distribute-neg-in_binary64_2426`
185×	`distribute-lft-in_binary64_2414`
179×	`*-commutative_binary64_2396`
144×	`associate-+l-_binary64_2400`
131×	`+-commutative_binary64_2395`
101×	`distribute-lft-neg-out_binary64_2424`
92×	`associate-+r-_binary64_2399`
88×	`distribute-rgt-neg-out_binary64_2425`
84×	`unswap-sqr_binary64_2433`
81×	`cancel-sign-sub-inv_binary64_2431`
58×	`associate--r+_binary64_2401`
40×	`*-rgt-identity_binary64_2455`
36×	`cancel-sign-sub_binary64_2430`
28×	`distribute-lft-out_binary64_2416`
27×	`*-lft-identity_binary64_2454`
23×	`remove-double-neg_binary64_2453`
22×	`associate--r-_binary64_2404`
20×	`sub0-neg_binary64_2452` `sqr-pow_binary64_2437` `distribute-lft-neg-in_binary64_2422`
16×	`+-rgt-identity_binary64_2450`
10×	`pow-plus_binary64_2528`
8×	`mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `difference-of-sqr--1_binary64_2436`
6×	`cube-unmult_binary64_2502` `difference-of-squares_binary64_2434` `swap-sqr_binary64_2432` `distribute-lft1-in_binary64_2420`
5×	`unpow2_binary64_2530` `rem-sqrt-square_binary64_2478` `difference-of-sqr-1_binary64_2435`
3×	`unpow3_binary64_2531` `mul-1-neg_binary64_2457`
2×	`cube-prod_binary64_2493` `--rgt-identity_binary64_2451` `distribute-neg-out_binary64_2427` `distribute-rgt1-in_binary64_2421`
1×	`unpow1/2_binary64_2529` `unpow1_binary64_2523` `1-exp_binary64_2509` `pow-sqr_binary64_2438`
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` `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-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` `/-rgt-identity_binary64_2456` `+-lft-identity_binary64_2449` `div0_binary64_2446` `-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `distribute-neg-frac_binary64_2429` `distribute-frac-neg_binary64_2428` `distribute-rgt-out--_binary64_2419` `distribute-lft-out--_binary64_2417` `count-2_binary64_2413` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411` `associate-/l_binary64_2410` `associate-/r_binary64_2409` `associate-l/_binary64_2408` `associate-*r/_binary64_2407` `associate--l-_binary64_2403`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	86
1	90	86
2	258	86
3	660	86
4	1912	86
5	3405	86
6	4573	86
7	4994	86
8	5000	86
9	4923	86
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample25.0ms (0.2%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

705×	`unsub-neg_binary64_2459`
556×	`cancel-sign-sub-inv_binary64_2431`
344×	`+-commutative_binary64_2395`
342×	`distribute-rgt-in_binary64_2415`
317×	`sub-neg_binary64_2458`
271×	`associate-l_binary64_2406`
266×	`distribute-rgt-neg-in_binary64_2423`
248×	`distribute-lft-in_binary64_2414`
233×	`neg-sub0_binary64_2460`
226×	`neg-mul-1_binary64_2461`
213×	`associate-r_binary64_2405`
206×	`distribute-lft-neg-in_binary64_2422`
185×	`associate--l+_binary64_2402`
173×	`associate-+l+_binary64_2398`
162×	`unswap-sqr_binary64_2433`
155×	`distribute-rgt-out_binary64_2418`
153×	`distribute-neg-in_binary64_2426`
151×	`associate-+r+_binary64_2397`
102×	`*-commutative_binary64_2396`
76×	`distribute-lft-out_binary64_2416`
73×	`associate-+l-_binary64_2400`
64×	`distribute-lft-neg-out_binary64_2424`
48×	`associate-+r-_binary64_2399`
45×	`difference-of-sqr--1_binary64_2436`
44×	`remove-double-neg_binary64_2453`
43×	`distribute-rgt-neg-out_binary64_2425`
41×	`*-rgt-identity_binary64_2455`
38×	`associate--r+_binary64_2401`
31×	`sqr-pow_binary64_2437`
29×	`*-lft-identity_binary64_2454`
16×	`cube-prod_binary64_2493`
13×	`pow-plus_binary64_2528`
11×	`sub0-neg_binary64_2452` `associate--r-_binary64_2404`
9×	`mul-1-neg_binary64_2457` `+-rgt-identity_binary64_2450` `distribute-rgt-out--_binary64_2419`
7×	`mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `distribute-lft1-in_binary64_2420`
6×	`unpow3_binary64_2531` `cube-unmult_binary64_2502` `swap-sqr_binary64_2432` `distribute-rgt1-in_binary64_2421`
5×	`unpow2_binary64_2530` `sqr-neg_binary64_2479` `difference-of-sqr-1_binary64_2435` `distribute-lft-out--_binary64_2417`
4×	`difference-of-squares_binary64_2434`
3×	`unpow1_binary64_2523` `cube-neg_binary64_2492` `rem-sqrt-square_binary64_2478` `pow-sqr_binary64_2438`
2×	`cube-mult_binary64_2495`
1×	`unpow1/2_binary64_2529` `1-exp_binary64_2509` `--rgt-identity_binary64_2451` `cancel-sign-sub_binary64_2430` `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` `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` `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-square-sqrt_binary64_2477` `times-frac_binary64_2471` `div-sub_binary64_2470` `/-rgt-identity_binary64_2456` `+-lft-identity_binary64_2449` `div0_binary64_2446` `-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `distribute-neg-frac_binary64_2429` `distribute-frac-neg_binary64_2428` `count-2_binary64_2413` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411` `associate-/l_binary64_2410` `associate-/r_binary64_2409` `associate-l/_binary64_2408` `associate-*r/_binary64_2407` `associate--l-_binary64_2403`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	43
1	55	43
2	150	43
3	389	43
4	1083	43
5	2231	43
6	4328	43
7	4714	43
8	4915	43

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.5b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite197.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
14×	`add-cbrt-cube_binary64_2501`
10×	`add-cube-cbrt_binary64_2500` `associate-r_binary64_2405`
6×	`pow-prod-down_binary64_2536` `prod-exp_binary64_2514` `add-log-exp_binary64_2504` `cbrt-unprod_binary64_2498` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `cancel-sign-sub-inv_binary64_2431`
4×	`associate-*r/_binary64_2407`
3×	`unpow-prod-down_binary64_2544` `pow-unpow_binary64_2542`
2×	`unswap-sqr_binary64_2433` `flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-l_binary64_2406` `*-commutative_binary64_2396` `sub-neg_binary64_2458` `difference-of-squares_binary64_2434` `associate-+r+_binary64_2397`
1×	`distribute-lft-out_binary64_2416` `pow-pow_binary64_2537` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `unpow2_binary64_2530` `sqr-pow_binary64_2437` `flip3--_binary64_2469` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `sum-log_binary64_2556` `+-commutative_binary64_2395`

Counts

4 → 87

Calls

4 calls:

9.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3356 to 1686 computations (49.8% saved)

series1.1s (10.8%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

568.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
257.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
122.0ms	(.f64 (.f64 b b) (+.f64 3 a))
76.0ms	(.f64 (.f64 a a) (-.f64 1 a))

Compiler

Compiled 3658 to 2730 computations (25.4% saved)

simplify147.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+l+_binary64_2398`
345×	`associate-+r+_binary64_2397`
267×	`associate-l_binary64_2406`
224×	`exp-prod_binary64_2517`
217×	`associate-r_binary64_2405` `+-commutative_binary64_2395`
212×	`cancel-sign-sub-inv_binary64_2431`
148×	`associate--l+_binary64_2402`
139×	`neg-mul-1_binary64_2461`
138×	`neg-sub0_binary64_2460`
136×	`*-commutative_binary64_2396`
117×	`distribute-rgt-out_binary64_2418`
107×	`distribute-rgt-in_binary64_2415`
106×	`exp-sum_binary64_2511`
101×	`distribute-lft-in_binary64_2414`
99×	`log-prod_binary64_2551`
97×	`unswap-sqr_binary64_2433`
69×	`distribute-rgt-neg-in_binary64_2423`
67×	`distribute-lft-out_binary64_2416`
66×	`sqr-pow_binary64_2437`
59×	`cube-prod_binary64_2493`
58×	`distribute-lft-neg-in_binary64_2422`
51×	`associate--r+_binary64_2401`
45×	`distribute-lft-neg-out_binary64_2424`
43×	`sub-neg_binary64_2458` `distribute-rgt-neg-out_binary64_2425`
39×	`distribute-neg-in_binary64_2426`
29×	`log-pow_binary64_2554`
28×	`associate-+r-_binary64_2399`
27×	`*-lft-identity_binary64_2454`
26×	`associate-+l-_binary64_2400`
22×	`exp-diff_binary64_2513` `*-rgt-identity_binary64_2455`
20×	`swap-sqr_binary64_2432` `distribute-rgt-out--_binary64_2419`
18×	`cube-unmult_binary64_2502`
17×	`pow-plus_binary64_2528`
16×	`unsub-neg_binary64_2459`
15×	`unpow3_binary64_2531` `rem-sqrt-square_binary64_2478`
13×	`exp-neg_binary64_2512`
12×	`pow-sqr_binary64_2438`
10×	`cube-mult_binary64_2495`
8×	`unpow1/2_binary64_2529`
7×	`unpow2_binary64_2530` `div-sub_binary64_2470` `distribute-lft-out--_binary64_2417`
6×	`unpow1_binary64_2523`
4×	`difference-of-squares_binary64_2434`
3×	`associate-/l/_binary64_2412` `associate-*r/_binary64_2407`
2×	`exp-lft-cube_binary64_2521` `rem-square-sqrt_binary64_2477` `count-2_binary64_2413`
1×	`prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `mul-1-neg_binary64_2457` `distribute-rgt1-in_binary64_2421` `associate-/r/_binary64_2411` `associate-/l*_binary64_2410`
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` `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-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `div-exp_binary64_2516` `rec-exp_binary64_2515` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-div_binary64_2494` `cube-neg_binary64_2492` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `times-frac_binary64_2471` `/-rgt-identity_binary64_2456` `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` `cancel-sign-sub_binary64_2430` `distribute-neg-frac_binary64_2429` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-lft1-in_binary64_2420` `associate-/r_binary64_2409` `associate-*l/_binary64_2408` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

141 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	215	2929
1	585	2618
2	1868	2522
3	4253	2518
4	4980	2518
5	4962	2518

prune191.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	3	117

Error

0.0b

Counts

117 → 3

Compiler

Compiled 3834 to 2002 computations (47.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.4b	(.f64 a (.f64 b b))
0.5b	(.f64 (.f64 b b) (+.f64 3 a))
0.9b	(.f64 a (.f64 a (*.f64 b b)))

rewrite229.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
16×	`add-sqr-sqrt_binary64_2487`
15×	`pow-prod-down_binary64_2536` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `*-un-lft-identity_binary64_2465`
12×	`associate-r_binary64_2405`
10×	`add-cube-cbrt_binary64_2500`
8×	`associate-l_binary64_2406`
6×	`cancel-sign-sub-inv_binary64_2431`
5×	`distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414`
4×	`add-log-exp_binary64_2504` `-commutative_binary64_2396` `associate-r/_binary64_2407`
3×	`unswap-sqr_binary64_2433`
2×	`sub-neg_binary64_2458` `difference-of-squares_binary64_2434`
1×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `distribute-lft-out_binary64_2416` `flip3--_binary64_2469` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417`

Counts

4 → 96

Calls

4 calls:

10.0ms	(.f64 (.f64 a a) (-.f64 1 a))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
8.0ms	(.f64 a (.f64 a (*.f64 b b)))
6.0ms	(.f64 a (.f64 b b))

Compiler

Compiled 4174 to 2266 computations (45.7% saved)

series452.0ms (4.4%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

121.0ms	(.f64 (.f64 b b) (+.f64 3 a))
115.0ms	(.f64 a (.f64 a (*.f64 b b)))
96.0ms	(.f64 a (.f64 b b))
75.0ms	(.f64 (.f64 a a) (-.f64 1 a))

Compiler

Compiled 2783 to 1984 computations (28.7% saved)

simplify129.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

415×	`distribute-rgt-in_binary64_2415`
398×	`distribute-lft-in_binary64_2414`
319×	`associate-l_binary64_2406`
267×	`exp-prod_binary64_2517` `associate-r_binary64_2405`
216×	`unsub-neg_binary64_2459`
214×	`distribute-rgt-neg-out_binary64_2425`
208×	`distribute-lft-neg-out_binary64_2424`
156×	`unswap-sqr_binary64_2433`
141×	`*-commutative_binary64_2396`
126×	`sqr-pow_binary64_2437`
122×	`log-prod_binary64_2551`
89×	`cube-prod_binary64_2493`
70×	`distribute-rgt-neg-in_binary64_2423`
68×	`*-lft-identity_binary64_2454`
65×	`swap-sqr_binary64_2432`
64×	`*-rgt-identity_binary64_2455`
60×	`distribute-lft-neg-in_binary64_2422`
54×	`exp-neg_binary64_2512`
53×	`neg-mul-1_binary64_2461` `neg-sub0_binary64_2460`
43×	`exp-sum_binary64_2511`
36×	`exp-diff_binary64_2513`
33×	`unpow3_binary64_2531`
31×	`sub-neg_binary64_2458`
29×	`pow-sqr_binary64_2438`
28×	`+-commutative_binary64_2395`
27×	`cube-mult_binary64_2495`
26×	`associate-+l+_binary64_2398`
25×	`cancel-sign-sub-inv_binary64_2431` `associate-+r+_binary64_2397`
17×	`pow-plus_binary64_2528`
15×	`cube-unmult_binary64_2502`
13×	`log-pow_binary64_2554`
12×	`mul0-rgt_binary64_2448` `mul0-lft_binary64_2447`
11×	`unpow1/2_binary64_2529` `distribute-rgt-out_binary64_2418`
7×	`difference-of-squares_binary64_2434` `associate-/l*_binary64_2410`
5×	`div-sub_binary64_2470` `sub0-neg_binary64_2452` `associate-+l-_binary64_2400`
4×	`rem-sqrt-square_binary64_2478` `distribute-neg-in_binary64_2426` `distribute-lft-out_binary64_2416`
3×	`difference-of-sqr-1_binary64_2435` `distribute-rgt-out--_binary64_2419` `associate-+r-_binary64_2399`
2×	`unpow2_binary64_2530` `unpow1_binary64_2523` `exp-lft-cube_binary64_2521` `+-rgt-identity_binary64_2450` `count-2_binary64_2413`
1×	`prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-3cbrt-lft_binary64_2490` `sqr-neg_binary64_2479` `rem-square-sqrt_binary64_2477` `mul-1-neg_binary64_2457` `distribute-rgt1-in_binary64_2421`
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` `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-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `div-exp_binary64_2516` `rec-exp_binary64_2515` `e-exp-1_binary64_2510` `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-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `times-frac_binary64_2471` `/-rgt-identity_binary64_2456` `remove-double-neg_binary64_2453` `--rgt-identity_binary64_2451` `+-lft-identity_binary64_2449` `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` `cancel-sign-sub_binary64_2430` `distribute-neg-frac_binary64_2429` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-lft1-in_binary64_2420` `distribute-lft-out--_binary64_2417` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411` `associate-/r_binary64_2409` `associate-l/_binary64_2408` `associate-r/_binary64_2407` `associate--r-_binary64_2404` `associate--l-_binary64_2403` `associate--l+_binary64_2402` `associate--r+_binary64_2401`

Counts

123 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	1537
1	392	1286
2	1326	1251
3	3314	1229
4	4565	1229
5	4989	1229
6	4929	1229

prune189.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	101	3	104

Error

0.0b

Counts

104 → 3

Compiler

Compiled 4009 to 2256 computations (43.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 a (+.f64 4 (.f64 2 a)))
0.0b	(+.f64 (.f64 4 (.f64 a a)) (.f64 (.f64 b b) (+.f64 (.f64 a (+.f64 4 (.f64 2 a))) (+.f64 (*.f64 b b) 12))))
0.0b	(.f64 4 (.f64 a a))
1.4b	(.f64 (.f64 b b) (+.f64 (.f64 a (+.f64 4 (.f64 2 a))) (+.f64 (*.f64 b b) 12)))

rewrite187.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
12×	`add-sqr-sqrt_binary64_2487` `associate-*r/_binary64_2407`
8×	`add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
7×	`pow-prod-down_binary64_2536` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-l_binary64_2406` `associate-r_binary64_2405`
6×	`add-log-exp_binary64_2504`
4×	`frac-add_binary64_2473`
3×	`unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `*-commutative_binary64_2396`
2×	`associate-+r+_binary64_2397`
1×	`sum-log_binary64_2556` `+-commutative_binary64_2395`

Counts

4 → 81

Calls

4 calls:

15.0ms	(.f64 (.f64 b b) (+.f64 (.f64 a (+.f64 4 (.f64 2 a))) (+.f64 (*.f64 b b) 12)))
7.0ms	(+.f64 (.f64 4 (.f64 a a)) (.f64 (.f64 b b) (+.f64 (.f64 a (+.f64 4 (.f64 2 a))) (+.f64 (*.f64 b b) 12))))
6.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
5.0ms	(.f64 4 (.f64 a a))

Compiler

Compiled 3124 to 1860 computations (40.5% saved)

series1.2s (11.4%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

645.0ms	(+.f64 (.f64 4 (.f64 a a)) (.f64 (.f64 b b) (+.f64 (.f64 a (+.f64 4 (.f64 2 a))) (+.f64 (*.f64 b b) 12))))
359.0ms	(.f64 (.f64 b b) (+.f64 (.f64 a (+.f64 4 (.f64 2 a))) (+.f64 (*.f64 b b) 12)))
68.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
38.0ms	(.f64 4 (.f64 a a))

Compiler

Compiled 2628 to 2087 computations (20.6% saved)

simplify125.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

515×	`associate-+l+_binary64_2398`
385×	`associate-l_binary64_2406`
345×	`associate-r_binary64_2405`
231×	`exp-prod_binary64_2517`
217×	`distribute-rgt-in_binary64_2415`
206×	`distribute-lft-in_binary64_2414`
187×	`cancel-sign-sub-inv_binary64_2431` `*-commutative_binary64_2396`
139×	`distribute-rgt-neg-in_binary64_2423`
128×	`unswap-sqr_binary64_2433`
123×	`distribute-rgt-out_binary64_2418`
111×	`distribute-lft-neg-in_binary64_2422`
90×	`associate--r+_binary64_2401`
81×	`+-commutative_binary64_2395`
70×	`associate--l+_binary64_2402`
68×	`distribute-neg-in_binary64_2426`
67×	`log-prod_binary64_2551`
65×	`distribute-lft-out_binary64_2416`
58×	`sqr-pow_binary64_2437`
56×	`associate-+r+_binary64_2397`
53×	`exp-sum_binary64_2511`
49×	`cube-prod_binary64_2493`
46×	`sub-neg_binary64_2458`
34×	`distribute-rgt-out--_binary64_2419`
33×	`distribute-lft-neg-out_binary64_2424`
32×	`*-lft-identity_binary64_2454`
31×	`*-rgt-identity_binary64_2455`
30×	`swap-sqr_binary64_2432`
27×	`neg-mul-1_binary64_2461` `neg-sub0_binary64_2460`
19×	`distribute-rgt-neg-out_binary64_2425`
16×	`unpow3_binary64_2531`
15×	`associate-+l-_binary64_2400` `associate-+r-_binary64_2399`
9×	`cube-mult_binary64_2495` `distribute-lft-out--_binary64_2417`
8×	`pow-plus_binary64_2528`
7×	`pow-sqr_binary64_2438`
5×	`exp-lft-sqr_binary64_2520` `unsub-neg_binary64_2459`
4×	`log-pow_binary64_2554` `unpow1/2_binary64_2529`
3×	`count-2_binary64_2413`
2×	`unpow2_binary64_2530` `unpow1_binary64_2523` `rem-sqrt-square_binary64_2478` `difference-of-squares_binary64_2434` `associate-/l*_binary64_2410`
1×	`prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `cube-unmult_binary64_2502`
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` `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-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-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` `mul-1-neg_binary64_2457` `/-rgt-identity_binary64_2456` `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` `cancel-sign-sub_binary64_2430` `distribute-neg-frac_binary64_2429` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-rgt1-in_binary64_2421` `distribute-lft1-in_binary64_2420` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411` `associate-/r_binary64_2409` `associate-l/_binary64_2408` `associate-r/_binary64_2407` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

123 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	3043
1	644	2638
2	2588	2614
3	4953	2614
4	5085	2614

prune160.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	99	3	102

Error

0.0b

Counts

102 → 3

Compiler

Compiled 3091 to 1932 computations (37.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 4 (.f64 a a))
0.3b	(.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2))))))
0.3b	(.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2))))))
0.3b	(.f64 (.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2)))))) (.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 a 2)))))))

rewrite842.0ms (8.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

166×	`associate-*r/_binary64_2407`
96×	`sqrt-div_binary64_2482`
80×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
64×	`frac-add_binary64_2473`
52×	`pow1_binary64_2526`
36×	`frac-times_binary64_2475`
25×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
22×	`pow-prod-down_binary64_2536`
20×	`add-sqr-sqrt_binary64_2487`
14×	`associate-r_binary64_2405`
13×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
11×	`add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
10×	`associate-l_binary64_2406`
8×	`sqrt-prod_binary64_2481`
6×	`associate-*l/_binary64_2408`
5×	`unswap-sqr_binary64_2433`
4×	`pow-prod-up_binary64_2535` `add-log-exp_binary64_2504` `pow-sqr_binary64_2438` `*-commutative_binary64_2396`
2×	`pow-plus_binary64_2528`
1×	`pow2_binary64_2546` `swap-sqr_binary64_2432`

Counts

4 → 157

Calls

4 calls:

20.0ms	(.f64 (.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2)))))) (.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 a 2)))))))
13.0ms	(.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2))))))
10.0ms	(.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2))))))
5.0ms	(.f64 4 (.f64 a a))

Compiler

Compiled 12462 to 8141 computations (34.7% saved)

series1.4s (13.3%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

414.0ms	(.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2))))))
408.0ms	(.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2))))))
375.0ms	(.f64 (.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 a 2)))))) (.f64 b (sqrt.f64 (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 a 2)))))))
40.0ms	(.f64 4 (.f64 a a))

Compiler

Compiled 6361 to 4938 computations (22.4% saved)

simplify306.0ms (3%)

Algorithm

1×	egg-herbie

Rules

537×	`associate-r_binary64_2405`
485×	`associate-l_binary64_2406`
355×	`cancel-sign-sub-inv_binary64_2431`
342×	`*-commutative_binary64_2396`
148×	`distribute-neg-in_binary64_2426`
147×	`sub-neg_binary64_2458`
131×	`+-commutative_binary64_2395`
121×	`associate-+r+_binary64_2397`
118×	`distribute-rgt-in_binary64_2415`
112×	`distribute-lft-in_binary64_2414`
111×	`associate-+l+_binary64_2398`
110×	`unswap-sqr_binary64_2433`
108×	`exp-prod_binary64_2517`
96×	`swap-sqr_binary64_2432`
70×	`sqr-pow_binary64_2437`
68×	`times-frac_binary64_2471`
60×	`associate-/r*_binary64_2409`
59×	`neg-sub0_binary64_2460`
58×	`log-prod_binary64_2551`
57×	`neg-mul-1_binary64_2461`
51×	`associate--l+_binary64_2402`
46×	`*-lft-identity_binary64_2454`
39×	`distribute-rgt-neg-in_binary64_2423`
37×	`associate--r+_binary64_2401`
33×	`associate-/l*_binary64_2410`
31×	`unsub-neg_binary64_2459` `distribute-lft-neg-in_binary64_2422`
26×	`cube-prod_binary64_2493`
23×	`*-rgt-identity_binary64_2455`
18×	`rem-sqrt-square_binary64_2478`
17×	`unpow3_binary64_2531` `distribute-neg-frac_binary64_2429`
15×	`exp-sum_binary64_2511`
13×	`rem-square-sqrt_binary64_2477` `associate-*r/_binary64_2407`
12×	`pow-plus_binary64_2528`
11×	`distribute-rgt-out_binary64_2418` `associate-*l/_binary64_2408`
9×	`cube-mult_binary64_2495`
8×	`cube-unmult_binary64_2502`
7×	`pow-sqr_binary64_2438` `distribute-lft-neg-out_binary64_2424` `distribute-rgt-out--_binary64_2419`
5×	`log-pow_binary64_2554` `exp-lft-sqr_binary64_2520`
3×	`unpow1/2_binary64_2529` `unpow1_binary64_2523` `distribute-lft-out_binary64_2416` `count-2_binary64_2413` `associate-+l-_binary64_2400` `associate-+r-_binary64_2399`
2×	`unpow2_binary64_2530` `mul-1-neg_binary64_2457`
1×	`prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `/-rgt-identity_binary64_2456` `difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`
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` `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-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-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` `div-sub_binary64_2470` `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` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-rgt-neg-out_binary64_2425` `distribute-rgt1-in_binary64_2421` `distribute-lft1-in_binary64_2420` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

211 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	11959
1	1091	10772
2	3750	10754
3	4972	10754
4	5004	10754

prune614.0ms (6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	157	3	160

Error

0.0b

Counts

160 → 3

Compiler

Compiled 9661 to 6434 computations (33.4% saved)

regimes593.0ms (5.8%)

Accuracy

Total 0.0b remaining (79.6%)

Threshold costs 0.0b (79.6%)

Compiler

Compiled 8550 to 5992 computations (29.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64_2395`
8×	`*-commutative_binary64_2396`
5×	`neg-mul-1_binary64_2461` `neg-sub0_binary64_2460`
4×	`sub-neg_binary64_2458`
3×	`unsub-neg_binary64_2459` `*-rgt-identity_binary64_2455`
2×	`distribute-rgt-neg-out_binary64_2425`
1×	`1-exp_binary64_2509` `*-lft-identity_binary64_2454` `distribute-lft-neg-out_binary64_2424` `distribute-rgt-neg-in_binary64_2423` `distribute-lft-neg-in_binary64_2422`
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` `mul-1-neg_binary64_2457` `/-rgt-identity_binary64_2456` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	55
1	41	55
2	48	55
3	52	55
4	60	55
5	59	55
6	57	55

end0.0ms (0%)

sample1.7s (16.8%)

Algorithm

1×

intervals

Results

449.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 1533 to 1089 computations (29% saved)

Details

analyze356.0ms (3.5%)

sample25.0ms (0.2%)

simplify81.0ms (0.8%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite197.0ms (1.9%)

series1.1s (10.8%)

simplify147.0ms (1.4%)

prune191.0ms (1.9%)

localize21.0ms (0.2%)

rewrite229.0ms (2.2%)

series452.0ms (4.4%)

simplify129.0ms (1.2%)

prune189.0ms (1.8%)

localize16.0ms (0.2%)

rewrite187.0ms (1.8%)

series1.2s (11.4%)

simplify125.0ms (1.2%)

prune160.0ms (1.6%)

localize17.0ms (0.2%)

rewrite842.0ms (8.2%)

series1.4s (13.3%)

simplify306.0ms (3%)

prune614.0ms (6%)

regimes593.0ms (5.8%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.7s (16.8%)

Profiling