Details

analyze930.0ms (11.7%)

Algorithm

1×	search
2×	egg-herbie

Rules

12×	`*-commutative_binary64_2396`
4×	`distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-/l*_binary64_2410` `+-commutative_binary64_2395`
2×	`associate-/r/_binary64_2411` `associate-l/_binary64_2408` `associate-r/_binary64_2407` `associate-l_binary64_2406` `associate-r_binary64_2405`
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` `erfc-erf_binary64_2728` `erf-erfc_binary64_2727` `erf-odd_binary64_2726` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `not-gte_binary64_2717` `not-lte_binary64_2716` `not-gt_binary64_2715` `not-lt_binary64_2714` `gte-same_binary64_2713` `lte-same_binary64_2712` `gt-same_binary64_2711` `lt-same_binary64_2710` `sinh---cosh_binary64_2657` `sinh-+-cosh_binary64_2656` `sinh-cosh_binary64_2655` `tanh-def-c_binary64_2654` `tanh-def-b_binary64_2653` `tanh-def-a_binary64_2652` `cosh-def_binary64_2651` `sinh-def_binary64_2650` `tan-neg_binary64_2597` `cos-neg_binary64_2596` `sin-neg_binary64_2595` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `hang-m-tan_binary64_2591` `hang-p-tan_binary64_2590` `hang-m0-tan_binary64_2589` `hang-p0-tan_binary64_2588` `hang-0m-tan_binary64_2587` `hang-0p-tan_binary64_2586` `tan-+PI/2_binary64_2585` `tan-+PI_binary64_2584` `tan-PI_binary64_2583` `tan-PI/3_binary64_2582` `tan-PI/4_binary64_2581` `tan-PI/6_binary64_2580` `cos-+PI/2_binary64_2579` `cos-+PI_binary64_2578` `cos-PI_binary64_2577` `cos-PI/2_binary64_2576` `cos-PI/3_binary64_2575` `cos-PI/4_binary64_2574` `cos-PI/6_binary64_2573` `sin-+PI/2_binary64_2572` `sin-+PI_binary64_2571` `sin-PI_binary64_2570` `sin-PI/2_binary64_2569` `sin-PI/3_binary64_2568` `sin-PI/4_binary64_2567` `sin-PI/6_binary64_2566` `sub-1-sin_binary64_2565` `sub-1-cos_binary64_2564` `-1-add-sin_binary64_2563` `-1-add-cos_binary64_2562` `1-sub-sin_binary64_2561` `1-sub-cos_binary64_2560` `cos-sin-sum_binary64_2559` `log-E_binary64_2555` `log-pow_binary64_2554` `log-rec_binary64_2553` `log-div_binary64_2552` `log-prod_binary64_2551` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow3_binary64_2531` `unpow2_binary64_2530` `unpow1/2_binary64_2529` `pow-plus_binary64_2528` `exp-to-pow_binary64_2527` `pow-base-1_binary64_2525` `unpow0_binary64_2524` `unpow1_binary64_2523` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `exp-prod_binary64_2517` `div-exp_binary64_2516` `rec-exp_binary64_2515` `prod-exp_binary64_2514` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `exp-sum_binary64_2511` `e-exp-1_binary64_2510` `exp-1-e_binary64_2508` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-unmult_binary64_2502` `cube-mult_binary64_2495` `cube-div_binary64_2494` `cube-prod_binary64_2493` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `times-frac_binary64_2471` `div-sub_binary64_2470` `neg-mul-1_binary64_2461` `neg-sub0_binary64_2460` `unsub-neg_binary64_2459` `sub-neg_binary64_2458` `mul-1-neg_binary64_2457` `/-rgt-identity_binary64_2456` `-rgt-identity_binary64_2455` `-lft-identity_binary64_2454` `remove-double-neg_binary64_2453` `sub0-neg_binary64_2452` `--rgt-identity_binary64_2451` `+-rgt-identity_binary64_2450` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `div0_binary64_2446` `-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `pow-sqr_binary64_2438` `sqr-pow_binary64_2437` `difference-of-sqr--1_binary64_2436` `difference-of-sqr-1_binary64_2435` `difference-of-squares_binary64_2434` `unswap-sqr_binary64_2433` `swap-sqr_binary64_2432` `cancel-sign-sub-inv_binary64_2431` `cancel-sign-sub_binary64_2430` `distribute-neg-frac_binary64_2429` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-neg-in_binary64_2426` `distribute-rgt-neg-out_binary64_2425` `distribute-lft-neg-out_binary64_2424` `distribute-rgt-neg-in_binary64_2423` `distribute-lft-neg-in_binary64_2422` `distribute-rgt1-in_binary64_2421` `distribute-lft1-in_binary64_2420` `distribute-rgt-out--_binary64_2419` `distribute-rgt-out_binary64_2418` `distribute-lft-out--_binary64_2417` `distribute-lft-out_binary64_2416` `count-2_binary64_2413` `associate-/l/_binary64_2412` `associate-/r_binary64_2409` `associate--r-_binary64_2404` `associate--l-_binary64_2403` `associate--l+_binary64_2402` `associate--r+_binary64_2401` `associate-+l-_binary64_2400` `associate-+r-_binary64_2399` `associate-+l+_binary64_2398` `associate-+r+_binary64_2397`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	52
1	48	52
2	58	52
3	64	52
4	68	52
5	70	52
6	67	52
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample42.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	193×	body	128	valid
7.0ms	26×	body	2048	valid
4.0ms	256×	pre	128	true
3.0ms	10×	body	4096	valid
3.0ms	15×	body	1024	valid
2.0ms	11×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64_2396`
2×	`distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-/l*_binary64_2410` `+-commutative_binary64_2395`
1×	`1-exp_binary64_2509` `associate-/r/_binary64_2411` `associate-l/_binary64_2408` `associate-r/_binary64_2407` `associate-l_binary64_2406` `associate-r_binary64_2405`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2728` `erf-erfc_binary64_2727` `erf-odd_binary64_2726` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `not-gte_binary64_2717` `not-lte_binary64_2716` `not-gt_binary64_2715` `not-lt_binary64_2714` `gte-same_binary64_2713` `lte-same_binary64_2712` `gt-same_binary64_2711` `lt-same_binary64_2710` `sinh---cosh_binary64_2657` `sinh-+-cosh_binary64_2656` `sinh-cosh_binary64_2655` `tanh-def-c_binary64_2654` `tanh-def-b_binary64_2653` `tanh-def-a_binary64_2652` `cosh-def_binary64_2651` `sinh-def_binary64_2650` `tan-neg_binary64_2597` `cos-neg_binary64_2596` `sin-neg_binary64_2595` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `hang-m-tan_binary64_2591` `hang-p-tan_binary64_2590` `hang-m0-tan_binary64_2589` `hang-p0-tan_binary64_2588` `hang-0m-tan_binary64_2587` `hang-0p-tan_binary64_2586` `tan-+PI/2_binary64_2585` `tan-+PI_binary64_2584` `tan-PI_binary64_2583` `tan-PI/3_binary64_2582` `tan-PI/4_binary64_2581` `tan-PI/6_binary64_2580` `cos-+PI/2_binary64_2579` `cos-+PI_binary64_2578` `cos-PI_binary64_2577` `cos-PI/2_binary64_2576` `cos-PI/3_binary64_2575` `cos-PI/4_binary64_2574` `cos-PI/6_binary64_2573` `sin-+PI/2_binary64_2572` `sin-+PI_binary64_2571` `sin-PI_binary64_2570` `sin-PI/2_binary64_2569` `sin-PI/3_binary64_2568` `sin-PI/4_binary64_2567` `sin-PI/6_binary64_2566` `sub-1-sin_binary64_2565` `sub-1-cos_binary64_2564` `-1-add-sin_binary64_2563` `-1-add-cos_binary64_2562` `1-sub-sin_binary64_2561` `1-sub-cos_binary64_2560` `cos-sin-sum_binary64_2559` `log-E_binary64_2555` `log-pow_binary64_2554` `log-rec_binary64_2553` `log-div_binary64_2552` `log-prod_binary64_2551` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow3_binary64_2531` `unpow2_binary64_2530` `unpow1/2_binary64_2529` `pow-plus_binary64_2528` `exp-to-pow_binary64_2527` `pow-base-1_binary64_2525` `unpow0_binary64_2524` `unpow1_binary64_2523` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `exp-prod_binary64_2517` `div-exp_binary64_2516` `rec-exp_binary64_2515` `prod-exp_binary64_2514` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `exp-sum_binary64_2511` `e-exp-1_binary64_2510` `exp-1-e_binary64_2508` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-unmult_binary64_2502` `cube-mult_binary64_2495` `cube-div_binary64_2494` `cube-prod_binary64_2493` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `times-frac_binary64_2471` `div-sub_binary64_2470` `neg-mul-1_binary64_2461` `neg-sub0_binary64_2460` `unsub-neg_binary64_2459` `sub-neg_binary64_2458` `mul-1-neg_binary64_2457` `/-rgt-identity_binary64_2456` `-rgt-identity_binary64_2455` `-lft-identity_binary64_2454` `remove-double-neg_binary64_2453` `sub0-neg_binary64_2452` `--rgt-identity_binary64_2451` `+-rgt-identity_binary64_2450` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `div0_binary64_2446` `-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `pow-sqr_binary64_2438` `sqr-pow_binary64_2437` `difference-of-sqr--1_binary64_2436` `difference-of-sqr-1_binary64_2435` `difference-of-squares_binary64_2434` `unswap-sqr_binary64_2433` `swap-sqr_binary64_2432` `cancel-sign-sub-inv_binary64_2431` `cancel-sign-sub_binary64_2430` `distribute-neg-frac_binary64_2429` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-neg-in_binary64_2426` `distribute-rgt-neg-out_binary64_2425` `distribute-lft-neg-out_binary64_2424` `distribute-rgt-neg-in_binary64_2423` `distribute-lft-neg-in_binary64_2422` `distribute-rgt1-in_binary64_2421` `distribute-lft1-in_binary64_2420` `distribute-rgt-out--_binary64_2419` `distribute-rgt-out_binary64_2418` `distribute-lft-out--_binary64_2417` `distribute-lft-out_binary64_2416` `count-2_binary64_2413` `associate-/l/_binary64_2412` `associate-/r_binary64_2409` `associate--r-_binary64_2404` `associate--l-_binary64_2403` `associate--l+_binary64_2402` `associate--r+_binary64_2401` `associate-+l-_binary64_2400` `associate-+r-_binary64_2399` `associate-+l+_binary64_2398` `associate-+r+_binary64_2397`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	30	26
2	35	26
3	38	26
4	40	26
5	41	26
6	38	26

prune3.0ms (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

13.0b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite135.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

12.8b

Rules

8×	`pow1_binary64_2526` `add-log-exp_binary64_2504`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-cube-cbrt_binary64_2500`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `flip3-+_binary64_2468` `sqrt-div_binary64_2482` `flip-+_binary64_2439` `sqrt-prod_binary64_2481`
3×	`sqrt-pow1_binary64_2483`
2×	`pow1/2_binary64_2545` `sum-log_binary64_2556` `+-commutative_binary64_2395` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `distribute-lft-out_binary64_2416` `pow-prod-down_binary64_2536`

Counts

4 → 51

Calls

4 calls:

13.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
5.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

Compiler

Compiled 1524 to 983 computations (35.5% saved)

series703.0ms (8.8%)

Error

2.9b

Counts

4 → 54

Calls

4 calls:

203.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
161.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
147.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
134.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2054 to 1825 computations (11.1% saved)

simplify94.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

772×	`times-frac_binary64_2471`
454×	`associate-/l*_binary64_2410`
373×	`associate-/r*_binary64_2409`
219×	`associate-*l/_binary64_2408`
169×	`cancel-sign-sub-inv_binary64_2431`
141×	`distribute-rgt-neg-in_binary64_2423`
126×	`distribute-lft-neg-in_binary64_2422`
118×	`distribute-rgt-in_binary64_2415`
108×	`associate-/r/_binary64_2411`
97×	`associate-r_binary64_2405`
92×	`distribute-lft-in_binary64_2414`
85×	`associate-l_binary64_2406`
74×	`distribute-neg-frac_binary64_2429`
67×	`*-commutative_binary64_2396`
63×	`unswap-sqr_binary64_2433`
58×	`sub-neg_binary64_2458`
48×	`sqr-pow_binary64_2437`
45×	`neg-sub0_binary64_2460`
42×	`neg-mul-1_binary64_2461`
39×	`+-commutative_binary64_2395`
37×	`associate-*r/_binary64_2407`
24×	`cube-prod_binary64_2493`
21×	`exp-prod_binary64_2517`
16×	`associate--l+_binary64_2402`
15×	`distribute-lft-out_binary64_2416`
14×	`distribute-rgt-out_binary64_2418`
13×	`cube-div_binary64_2494`
12×	`unpow3_binary64_2531`
11×	`unsub-neg_binary64_2459`
10×	`swap-sqr_binary64_2432` `distribute-lft-neg-out_binary64_2424` `associate-/l/_binary64_2412`
9×	`cube-unmult_binary64_2502` `distribute-rgt-out--_binary64_2419` `associate--r+_binary64_2401` `associate-+l+_binary64_2398`
8×	`cube-mult_binary64_2495` `distribute-neg-in_binary64_2426`
7×	`pow-plus_binary64_2528` `distribute-lft-out--_binary64_2417`
5×	`mul-1-neg_binary64_2457` `*-lft-identity_binary64_2454` `pow-sqr_binary64_2438`
4×	`unpow2_binary64_2530` `distribute-rgt1-in_binary64_2421`
3×	`log-prod_binary64_2551` `unpow1/2_binary64_2529` `rem-sqrt-square_binary64_2478`
2×	`unpow1_binary64_2523` `prod-exp_binary64_2514` `rem-square-sqrt_binary64_2477` `*-rgt-identity_binary64_2455` `distribute-rgt-neg-out_binary64_2425` `associate-+l-_binary64_2400` `associate-+r-_binary64_2399` `associate-+r+_binary64_2397`
1×	`exp-sum_binary64_2511` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `div-sub_binary64_2470` `difference-of-squares_binary64_2434` `count-2_binary64_2413`
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` `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-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-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` `/-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-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-lft1-in_binary64_2420` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

105 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	2232
1	442	2105
2	1385	2018
3	4966	2018
4	4952	2018

prune108.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	4	78

Error

2.6b

Counts

78 → 4

Compiler

Compiled 1794 to 1129 computations (37.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 p p) 4)
0.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
0.5b	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p p) 4))))))) 3)
14.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

rewrite173.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

14×	`pow1_binary64_2526`
11×	`add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
10×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
9×	`add-cube-cbrt_binary64_2500`
6×	`add-log-exp_binary64_2504`
5×	`sqrt-prod_binary64_2481`
4×	`sqrt-div_binary64_2482` `unpow-prod-down_binary64_2544` `pow-pow_binary64_2537` `pow-prod-down_binary64_2536` `cube-prod_binary64_2493`
3×	`sqrt-pow1_binary64_2483` `flip3-+_binary64_2468` `flip-+_binary64_2439` `pow-unpow_binary64_2542` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `associate-r_binary64_2405`
2×	`pow1/2_binary64_2545` `associate-*r/_binary64_2407` `cube-div_binary64_2494`
1×	`rem-sqrt-square_binary64_2478` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `unpow3_binary64_2531` `cube-mult_binary64_2495` `rem-cube-cbrt_binary64_2488` `sqrt-pow2_binary64_2484` `sqr-pow_binary64_2437` `sum-log_binary64_2556` `distribute-lft-out_binary64_2416` `+-commutative_binary64_2395` `unswap-sqr_binary64_2433` `associate-l_binary64_2406` `*-commutative_binary64_2396`

Counts

4 → 77

Calls

4 calls:

15.0ms	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p p) 4))))))) 3)
11.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
6.0ms	(.f64 (.f64 p p) 4)
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

Compiler

Compiled 2473 to 1603 computations (35.2% saved)

series762.0ms (9.6%)

Error

2.6b

Counts

4 → 45

Calls

4 calls:

376.0ms	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p p) 4))))))) 3)
150.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
131.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
43.0ms	(.f64 (.f64 p p) 4)

Compiler

Compiled 2202 to 1989 computations (9.7% saved)

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Rules

809×	`associate-/l*_binary64_2410`
354×	`unswap-sqr_binary64_2433`
185×	`distribute-rgt-neg-in_binary64_2423`
169×	`cancel-sign-sub-inv_binary64_2431`
165×	`associate-l_binary64_2406`
162×	`associate-r_binary64_2405`
161×	`distribute-lft-neg-in_binary64_2422`
136×	`associate-/r/_binary64_2411`
106×	`distribute-rgt-in_binary64_2415`
93×	`associate-/l/_binary64_2412`
92×	`sqr-pow_binary64_2437`
89×	`distribute-lft-in_binary64_2414`
86×	`times-frac_binary64_2471` `*-commutative_binary64_2396`
80×	`distribute-neg-frac_binary64_2429`
72×	`log-prod_binary64_2551`
68×	`exp-prod_binary64_2517`
50×	`cube-prod_binary64_2493`
48×	`sub-neg_binary64_2458`
43×	`neg-sub0_binary64_2460` `associate-/r*_binary64_2409`
42×	`+-commutative_binary64_2395`
40×	`neg-mul-1_binary64_2461`
38×	`swap-sqr_binary64_2432`
35×	`associate-*r/_binary64_2407`
26×	`associate-*l/_binary64_2408`
20×	`unpow3_binary64_2531` `rem-sqrt-square_binary64_2478`
17×	`cube-mult_binary64_2495`
16×	`associate--l+_binary64_2402`
14×	`pow-plus_binary64_2528`
13×	`pow-sqr_binary64_2438` `distribute-lft-neg-out_binary64_2424`
12×	`associate-+l+_binary64_2398`
10×	`log-pow_binary64_2554` `rem-square-sqrt_binary64_2477` `distribute-rgt-out--_binary64_2419`
9×	`cube-unmult_binary64_2502`
8×	`*-lft-identity_binary64_2454` `distribute-rgt-out_binary64_2418`
7×	`unsub-neg_binary64_2459` `*-rgt-identity_binary64_2455`
5×	`mul-1-neg_binary64_2457` `/-rgt-identity_binary64_2456` `associate-+r+_binary64_2397`
4×	`exp-sum_binary64_2511` `cube-div_binary64_2494` `distribute-neg-in_binary64_2426` `distribute-rgt1-in_binary64_2421` `distribute-lft-out--_binary64_2417` `count-2_binary64_2413`
3×	`unpow2_binary64_2530` `unpow1/2_binary64_2529` `unpow1_binary64_2523` `distribute-frac-neg_binary64_2428` `associate--r+_binary64_2401`
2×	`distribute-rgt-neg-out_binary64_2425` `associate-+l-_binary64_2400` `associate-+r-_binary64_2399`
1×	`prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `div-sub_binary64_2470` `difference-of-squares_binary64_2434` `distribute-lft-out_binary64_2416`
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-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-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `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-out_binary64_2427` `distribute-lft1-in_binary64_2420` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

122 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	2738
1	560	2633
2	1849	2559
3	5203	2559

prune147.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	96	5	101

Error

2.6b

Counts

101 → 5

Compiler

Compiled 2515 to 1728 computations (31.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
0.2b	(/.f64 (*.f64 x x) p)
21.2b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

rewrite108.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

36×	`times-frac_binary64_2471`
21×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
17×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
10×	`associate-/r*_binary64_2409`
9×	`pow1_binary64_2526`
7×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
6×	`div-inv_binary64_2462`
4×	`associate-/l*_binary64_2410`
3×	`add-log-exp_binary64_2504` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`
2×	`associate-*r/_binary64_2407` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-2neg_binary64_2476` `clear-num_binary64_2464`
1×	`pow1/2_binary64_2545` `sqrt-div_binary64_2482` `sqrt-prod_binary64_2481` `associate-/r/_binary64_2411`

Counts

3 → 82

Calls

3 calls:

8.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
6.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
4.0ms	(/.f64 (*.f64 x x) p)

Compiler

Compiled 1571 to 697 computations (55.6% saved)

series295.0ms (3.7%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

120.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
97.0ms	(/.f64 (*.f64 x x) p)
66.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

Compiler

Compiled 498 to 441 computations (11.4% saved)

simplify109.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-/l*_binary64_2410`
435×	`associate-l_binary64_2406`
423×	`associate-/l/_binary64_2412`
373×	`associate-/r/_binary64_2411`
367×	`associate-/r*_binary64_2409`
340×	`associate-*l/_binary64_2408`
306×	`log-div_binary64_2552`
304×	`associate-r_binary64_2405`
197×	`unswap-sqr_binary64_2433`
195×	`log-prod_binary64_2551`
181×	`cube-prod_binary64_2493`
173×	`associate-*r/_binary64_2407`
151×	`exp-prod_binary64_2517`
129×	`cube-div_binary64_2494`
127×	`*-commutative_binary64_2396`
54×	`times-frac_binary64_2471`
52×	`sub-neg_binary64_2458`
49×	`sqr-pow_binary64_2437`
33×	`log-rec_binary64_2553`
27×	`swap-sqr_binary64_2432`
25×	`div-sub_binary64_2470`
22×	`*-rgt-identity_binary64_2455`
19×	`neg-sub0_binary64_2460`
18×	`neg-mul-1_binary64_2461` `*-lft-identity_binary64_2454`
16×	`remove-double-div_binary64_2441`
13×	`log-pow_binary64_2554`
12×	`distribute-rgt-neg-in_binary64_2423` `distribute-lft-neg-in_binary64_2422`
11×	`unpow3_binary64_2531` `/-rgt-identity_binary64_2456`
10×	`cancel-sign-sub-inv_binary64_2431`
9×	`pow-plus_binary64_2528` `pow-sqr_binary64_2438`
8×	`distribute-neg-frac_binary64_2429` `associate--l-_binary64_2403` `associate-+l-_binary64_2400` `+-commutative_binary64_2395`
7×	`exp-lft-sqr_binary64_2520` `cube-unmult_binary64_2502` `cube-mult_binary64_2495` `unsub-neg_binary64_2459` `distribute-neg-in_binary64_2426` `associate--r+_binary64_2401`
6×	`div0_binary64_2446` `associate-+r-_binary64_2399`
4×	`rem-sqrt-square_binary64_2478` `distribute-rgt-in_binary64_2415` `associate--r-_binary64_2404`
3×	`unpow1/2_binary64_2529` `exp-sqrt_binary64_2518` `+-rgt-identity_binary64_2450` `associate-+l+_binary64_2398`
2×	`unpow2_binary64_2530` `unpow1_binary64_2523` `rem-square-sqrt_binary64_2477` `remove-double-neg_binary64_2453` `sub0-neg_binary64_2452` `associate-+r+_binary64_2397`
1×	`prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-3cbrt-rft_binary64_2491` `mul-1-neg_binary64_2457` `--rgt-identity_binary64_2451` `count-2_binary64_2413` `associate--l+_binary64_2402`
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-cbrt_binary64_2519` `div-exp_binary64_2516` `rec-exp_binary64_2515` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `exp-sum_binary64_2511` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-neg_binary64_2492` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `*-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-neg-out_binary64_2427` `distribute-rgt-neg-out_binary64_2425` `distribute-lft-neg-out_binary64_2424` `distribute-rgt1-in_binary64_2421` `distribute-lft1-in_binary64_2420` `distribute-rgt-out--_binary64_2419` `distribute-rgt-out_binary64_2418` `distribute-lft-out--_binary64_2417` `distribute-lft-out_binary64_2416` `distribute-lft-in_binary64_2414`

Counts

100 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1458
1	267	1284
2	828	1176
3	3586	1152
4	4926	1152
5	5049	1152

prune74.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	80	6	86

Error

0.0b

Counts

86 → 6

Compiler

Compiled 1291 to 581 computations (55% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.4b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))
8.1b	(sqrt.f64 (fabs.f64 (/.f64 p x)))
8.1b	(sqrt.f64 (fabs.f64 (/.f64 p x)))

rewrite72.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`add-sqr-sqrt_binary64_2487`
24×	`sqrt-prod_binary64_2481`
20×	`pow1_binary64_2526`
13×	`add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
10×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483`
8×	`swap-sqr_binary64_2432`
6×	`associate-l_binary64_2406` `associate-r_binary64_2405`
5×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow-prod-up_binary64_2535`
4×	`rem-sqrt-square_binary64_2478` `unswap-sqr_binary64_2433`
3×	`add-log-exp_binary64_2504` `pow-prod-down_binary64_2536` `pow-sqr_binary64_2438`
1×	`pow2_binary64_2546` `pow-plus_binary64_2528` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `sqrt-unprod_binary64_2485` `sqr-abs_binary64_2480` `rem-square-sqrt_binary64_2477` `*-commutative_binary64_2396`

Counts

3 → 76

Calls

3 calls:

7.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))

Compiler

Compiled 1360 to 191 computations (86% saved)

series162.0ms (2%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

64.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))
63.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))
25.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))

Compiler

Compiled 468 to 198 computations (57.7% saved)

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-/r*_binary64_2409`
513×	`unswap-sqr_binary64_2433`
497×	`times-frac_binary64_2471`
361×	`sqr-pow_binary64_2437`
298×	`associate-*l/_binary64_2408`
293×	`associate-*r/_binary64_2407`
243×	`associate-/l*_binary64_2410`
218×	`associate-+l+_binary64_2398`
183×	`*-commutative_binary64_2396`
152×	`log-prod_binary64_2551`
141×	`pow-sqr_binary64_2438` `associate-l_binary64_2406`
136×	`exp-prod_binary64_2517`
123×	`associate-+r+_binary64_2397`
111×	`cube-prod_binary64_2493`
109×	`distribute-rgt-in_binary64_2415`
97×	`distribute-lft-in_binary64_2414`
83×	`associate-r_binary64_2405`
78×	`swap-sqr_binary64_2432`
61×	`log-div_binary64_2552` `cube-div_binary64_2494`
53×	`+-commutative_binary64_2395`
51×	`rem-sqrt-square_binary64_2478` `associate-/r/_binary64_2411`
47×	`associate-/l/_binary64_2412`
37×	`unpow3_binary64_2531`
33×	`-rgt-identity_binary64_2455` `-lft-identity_binary64_2454`
30×	`pow-plus_binary64_2528`
29×	`cube-mult_binary64_2495`
21×	`log-pow_binary64_2554`
20×	`distribute-rgt-out_binary64_2418`
15×	`distribute-lft-out_binary64_2416`
13×	`unpow1/2_binary64_2529`
12×	`cube-unmult_binary64_2502`
10×	`count-2_binary64_2413`
6×	`unpow2_binary64_2530` `sub-neg_binary64_2458`
5×	`unpow1_binary64_2523` `exp-sqrt_binary64_2518` `distribute-rgt1-in_binary64_2421`
4×	`exp-lft-sqr_binary64_2520` `rem-square-sqrt_binary64_2477` `/-rgt-identity_binary64_2456` `distribute-lft1-in_binary64_2420`
2×	`log-rec_binary64_2553` `sqr-abs_binary64_2480`
1×	`prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489`
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-cbrt_binary64_2519` `div-exp_binary64_2516` `rec-exp_binary64_2515` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `exp-sum_binary64_2511` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-neg_binary64_2492` `rem-cube-cbrt_binary64_2488` `sqr-neg_binary64_2479` `div-sub_binary64_2470` `neg-mul-1_binary64_2461` `neg-sub0_binary64_2460` `unsub-neg_binary64_2459` `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` `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

94 → 54

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	48	989
1	69	933
2	185	926
3	462	894
4	1017	824
5	2563	824
6	4293	816
7	5185	816

prune34.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	56	4	60

Error

0.0b

Counts

60 → 4

Compiler

Compiled 600 to 118 computations (80.3% saved)

regimes1.2s (14.9%)

Accuracy

Total 0.1b remaining (53.5%)

Threshold costs 0.1b (53.5%)

Compiler

Compiled 10316 to 8159 computations (20.9% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64_2396`
2×	`+-commutative_binary64_2395`
1×	`unpow1_binary64_2523` `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` `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	22	55
1	29	55
2	28	55

end0.0ms (0%)

sample2.6s (32.4%)

Algorithm

1×

intervals

Results

309.0ms	6010×	body	128	valid
221.0ms	813×	body	2048	valid
135.0ms	8000×	pre	128	true
102.0ms	502×	body	1024	valid
86.0ms	274×	body	4096	valid
41.0ms	282×	body	512	valid
11.0ms	119×	body	256	valid

Compiler

Compiled 1322 to 1034 computations (21.8% saved)

Details

analyze930.0ms (11.7%)

sample42.0ms (0.5%)

simplify10.0ms (0.1%)

prune3.0ms (0%)

localize15.0ms (0.2%)

rewrite135.0ms (1.7%)

series703.0ms (8.8%)

simplify94.0ms (1.2%)

prune108.0ms (1.4%)

localize16.0ms (0.2%)

rewrite173.0ms (2.2%)

series762.0ms (9.6%)

simplify81.0ms (1%)

prune147.0ms (1.8%)

localize8.0ms (0.1%)

rewrite108.0ms (1.4%)

series295.0ms (3.7%)

simplify109.0ms (1.4%)

prune74.0ms (0.9%)

localize5.0ms (0.1%)

rewrite72.0ms (0.9%)

series162.0ms (2%)

simplify95.0ms (1.2%)

prune34.0ms (0.4%)

regimes1.2s (14.9%)

bsearch5.0ms (0.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (32.4%)

Profiling