Details

analyze773.0ms (14.4%)

Algorithm

1×

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)

sample45.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	186×	body	128	valid
7.0ms	27×	body	2048	valid
5.0ms	7×	body	4096	valid
5.0ms	256×	pre	128	true
4.0ms	22×	body	1024	valid
2.0ms	11×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify99.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64_2396`
3×	`distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414`
2×	`associate-/l*_binary64_2410` `+-commutative_binary64_2395`
1×	`1-exp_binary64_2509` `-rgt-identity_binary64_2455` `-lft-identity_binary64_2454` `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` `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 → 3

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

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	0	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	1	4

Error

15.7b

Counts

4 → 1

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.2b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
10.5b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite189.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

15.3b

Rules

22×	`*-un-lft-identity_binary64_2465`
21×	`add-sqr-sqrt_binary64_2487`
20×	`add-cube-cbrt_binary64_2500`
18×	`times-frac_binary64_2471`
16×	`sqrt-prod_binary64_2481`
8×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482` `associate-/r*_binary64_2409`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
3×	`sqrt-pow1_binary64_2483` `associate-/l*_binary64_2410`
2×	`pow1/2_binary64_2545` `associate-/r/_binary64_2411` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `sum-log_binary64_2556` `distribute-lft-out_binary64_2416` `+-commutative_binary64_2395` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `pow-prod-down_binary64_2536`

Counts

4 → 81

Calls

4 calls:

17.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2495 to 1576 computations (36.8% saved)

series619.0ms (11.5%)

Error

3.7b

Counts

4 → 66

Calls

4 calls:

160.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
145.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
138.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
102.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2707 to 2351 computations (13.2% saved)

simplify232.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64_2410`
506×	`associate-/r*_binary64_2409`
284×	`cancel-sign-sub-inv_binary64_2431`
183×	`associate-/r/_binary64_2411`
162×	`distribute-rgt-neg-in_binary64_2423`
132×	`sub-neg_binary64_2458`
130×	`distribute-lft-neg-in_binary64_2422`
104×	`distribute-neg-frac_binary64_2429`
98×	`associate-/l/_binary64_2412`
97×	`associate-r_binary64_2405`
95×	`times-frac_binary64_2471`
86×	`distribute-rgt-in_binary64_2415`
78×	`sqr-pow_binary64_2437`
75×	`*-commutative_binary64_2396`
72×	`associate-l_binary64_2406`
71×	`+-commutative_binary64_2395`
69×	`neg-sub0_binary64_2460`
68×	`neg-mul-1_binary64_2461`
54×	`associate-*r/_binary64_2407`
53×	`distribute-lft-in_binary64_2414`
46×	`associate-*l/_binary64_2408`
40×	`associate--l+_binary64_2402`
37×	`pow-sqr_binary64_2438`
34×	`distribute-lft-neg-out_binary64_2424`
30×	`unswap-sqr_binary64_2433`
29×	`associate--r+_binary64_2401`
22×	`distribute-neg-in_binary64_2426`
18×	`unsub-neg_binary64_2459` `*-rgt-identity_binary64_2455`
17×	`cube-prod_binary64_2493`
13×	`pow-plus_binary64_2528` `associate-+l+_binary64_2398`
12×	`swap-sqr_binary64_2432`
11×	`unpow3_binary64_2531`
10×	`cube-mult_binary64_2495` `distribute-rgt-out--_binary64_2419`
7×	`cube-div_binary64_2494` `*-lft-identity_binary64_2454` `difference-of-squares_binary64_2434` `distribute-rgt-out_binary64_2418` `distribute-lft-out--_binary64_2417`
6×	`log-prod_binary64_2551` `associate-+r+_binary64_2397`
5×	`log-div_binary64_2552` `cube-unmult_binary64_2502` `/-rgt-identity_binary64_2456`
4×	`mul-1-neg_binary64_2457` `distribute-rgt1-in_binary64_2421`
3×	`pow-base-1_binary64_2525` `exp-prod_binary64_2517` `rem-sqrt-square_binary64_2478` `div-sub_binary64_2470` `distribute-rgt-neg-out_binary64_2425` `associate-+l-_binary64_2400` `associate-+r-_binary64_2399`
2×	`unpow2_binary64_2530` `unpow1_binary64_2523` `rem-square-sqrt_binary64_2477`
1×	`log-rec_binary64_2553` `prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `sub0-neg_binary64_2452` `+-rgt-identity_binary64_2450` `*-inverses_binary64_2445` `cancel-sign-sub_binary64_2430` `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-pow_binary64_2554` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow1/2_binary64_2529` `exp-to-pow_binary64_2527` `unpow0_binary64_2524` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `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-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` `remove-double-neg_binary64_2453` `--rgt-identity_binary64_2451` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `div0_binary64_2446` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `difference-of-sqr--1_binary64_2436` `difference-of-sqr-1_binary64_2435` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-lft1-in_binary64_2420` `count-2_binary64_2413` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

147 → 327

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	3778
1	632	3658
2	1944	3592

prune614.0ms (11.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	320	7	327
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	321	7	328

Error

3.1b

Counts

328 → 7

Compiler

Compiled 10583 to 6908 computations (34.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))
1.1b	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
10.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

rewrite174.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

26×	`*-un-lft-identity_binary64_2465`
23×	`add-sqr-sqrt_binary64_2487`
22×	`add-cube-cbrt_binary64_2500`
18×	`times-frac_binary64_2471`
15×	`sqrt-prod_binary64_2481`
6×	`pow1_binary64_2526` `add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `associate-/r*_binary64_2409`
5×	`log-pow_binary64_2554`
4×	`sqrt-div_binary64_2482` `exp-prod_binary64_2517` `log-prod_binary64_2551`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/l*_binary64_2410`
2×	`distribute-lft-out_binary64_2416` `associate-/r/_binary64_2411`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `sum-log_binary64_2556` `+-commutative_binary64_2395` `exp-sum_binary64_2511` `rem-log-exp_binary64_2506` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462`

Counts

4 → 85

Calls

4 calls:

14.0ms	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
12.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
7.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 2753 to 1804 computations (34.5% saved)

series750.0ms (13.9%)

Error

3.1b

Counts

4 → 66

Calls

4 calls:

238.0ms	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))))
166.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))
154.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
118.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 2878 to 2510 computations (12.8% saved)

simplify208.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

416×	`times-frac_binary64_2471`
388×	`associate-l_binary64_2406`
381×	`associate-/l*_binary64_2410`
357×	`associate-r_binary64_2405`
249×	`associate-/r*_binary64_2409`
222×	`cancel-sign-sub-inv_binary64_2431`
168×	`associate-*l/_binary64_2408`
146×	`associate-*r/_binary64_2407`
140×	`distribute-rgt-neg-in_binary64_2423`
110×	`distribute-lft-neg-in_binary64_2422`
100×	`sub-neg_binary64_2458`
84×	`associate-/l/_binary64_2412`
79×	`sqr-pow_binary64_2437`
72×	`associate-/r/_binary64_2411`
69×	`distribute-neg-frac_binary64_2429`
63×	`distribute-rgt-in_binary64_2415`
58×	`+-commutative_binary64_2395`
57×	`neg-mul-1_binary64_2461`
56×	`neg-sub0_binary64_2460`
53×	`*-commutative_binary64_2396`
38×	`pow-sqr_binary64_2438`
35×	`distribute-lft-in_binary64_2414`
32×	`unswap-sqr_binary64_2433`
29×	`distribute-lft-neg-out_binary64_2424` `associate--l+_binary64_2402`
19×	`associate--r+_binary64_2401`
18×	`distribute-neg-in_binary64_2426`
17×	`cube-prod_binary64_2493`
16×	`*-rgt-identity_binary64_2455`
14×	`distribute-rgt-out--_binary64_2419`
13×	`pow-plus_binary64_2528` `distribute-rgt-out_binary64_2418`
12×	`unsub-neg_binary64_2459`
11×	`unpow3_binary64_2531` `swap-sqr_binary64_2432` `associate-+l+_binary64_2398`
10×	`cube-mult_binary64_2495`
8×	`log-prod_binary64_2551`
7×	`rem-log-exp_binary64_2506` `cube-div_binary64_2494` `difference-of-squares_binary64_2434`
6×	`*-lft-identity_binary64_2454` `associate-+r+_binary64_2397`
5×	`log-div_binary64_2552` `/-rgt-identity_binary64_2456`
4×	`distribute-rgt1-in_binary64_2421`
3×	`pow-base-1_binary64_2525` `exp-prod_binary64_2517` `cube-unmult_binary64_2502` `distribute-lft-out--_binary64_2417` `associate-+l-_binary64_2400` `associate-+r-_binary64_2399`
2×	`unpow2_binary64_2530` `exp-to-pow_binary64_2527` `unpow1_binary64_2523` `rem-sqrt-square_binary64_2478` `div-sub_binary64_2470` `distribute-rgt-neg-out_binary64_2425`
1×	`log-pow_binary64_2554` `log-rec_binary64_2553` `prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-exp-log_binary64_2505` `rem-square-sqrt_binary64_2477` `sub0-neg_binary64_2452` `+-rgt-identity_binary64_2450` `*-inverses_binary64_2445` `cancel-sign-sub_binary64_2430` `distribute-lft-out_binary64_2416` `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` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow1/2_binary64_2529` `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` `exp-sum_binary64_2511` `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-abs_binary64_2480` `sqr-neg_binary64_2479` `mul-1-neg_binary64_2457` `remove-double-neg_binary64_2453` `--rgt-identity_binary64_2451` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `div0_binary64_2446` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `difference-of-sqr--1_binary64_2436` `difference-of-sqr-1_binary64_2435` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-lft1-in_binary64_2420` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Counts

151 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	3707
1	520	3564
2	1474	3552

prune313.0ms (5.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	183	7	190

Error

3.1b

Counts

190 → 7

Compiler

Compiled 5560 to 3837 computations (31% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
1.7b	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))
2.9b	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
10.5b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite261.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

42×	`add-sqr-sqrt_binary64_2487`
33×	`cancel-sign-sub-inv_binary64_2431`
31×	`*-un-lft-identity_binary64_2465`
30×	`times-frac_binary64_2471`
22×	`add-cube-cbrt_binary64_2500`
14×	`sqrt-prod_binary64_2481`
10×	`difference-of-squares_binary64_2434`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`add-log-exp_binary64_2504`
6×	`associate-/r/_binary64_2411`
5×	`pow1_binary64_2526`
4×	`flip3-+_binary64_2468` `sqrt-div_binary64_2482` `flip-+_binary64_2439`
3×	`div-inv_binary64_2462` `associate-/r*_binary64_2409`
2×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `diff-log_binary64_2557` `flip3--_binary64_2469` `sub-neg_binary64_2458` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/l*_binary64_2410`

Counts

4 → 105

Calls

4 calls:

17.0ms	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
10.0ms	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))
9.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 5057 to 2940 computations (41.9% saved)

series821.0ms (15.3%)

Error

3.1b

Counts

4 → 80

Calls

4 calls:

217.0ms	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))
212.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))
147.0ms	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
116.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 6175 to 4631 computations (25% saved)

simplify230.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

527×	`cancel-sign-sub-inv_binary64_2431`
234×	`sub-neg_binary64_2458`
176×	`neg-sub0_binary64_2460`
167×	`neg-mul-1_binary64_2461`
162×	`associate-r_binary64_2405`
160×	`*-commutative_binary64_2396`
157×	`associate-/l*_binary64_2410`
155×	`associate-*l/_binary64_2408`
152×	`associate-l_binary64_2406`
146×	`div-sub_binary64_2470`
144×	`associate-*r/_binary64_2407`
123×	`times-frac_binary64_2471`
120×	`unswap-sqr_binary64_2433`
99×	`+-commutative_binary64_2395`
89×	`sqr-pow_binary64_2437`
83×	`distribute-rgt-neg-in_binary64_2423`
80×	`associate-/r*_binary64_2409`
68×	`associate-/l/_binary64_2412`
67×	`exp-prod_binary64_2517` `distribute-lft-neg-out_binary64_2424`
59×	`distribute-neg-frac_binary64_2429`
44×	`distribute-lft-neg-in_binary64_2422`
43×	`cube-prod_binary64_2493`
42×	`associate--l+_binary64_2402`
41×	`pow-sqr_binary64_2438`
39×	`distribute-rgt-in_binary64_2415`
35×	`unsub-neg_binary64_2459`
30×	`associate-/r/_binary64_2411` `associate--r+_binary64_2401`
28×	`swap-sqr_binary64_2432`
27×	`log-prod_binary64_2551` `*-rgt-identity_binary64_2455` `distribute-lft-in_binary64_2414`
26×	`cube-div_binary64_2494`
25×	`distribute-rgt-neg-out_binary64_2425`
22×	`associate-+l+_binary64_2398`
20×	`difference-of-squares_binary64_2434`
19×	`log-div_binary64_2552` `distribute-neg-in_binary64_2426`
17×	`*-lft-identity_binary64_2454`
16×	`unpow3_binary64_2531`
14×	`cube-mult_binary64_2495`
13×	`pow-plus_binary64_2528` `/-rgt-identity_binary64_2456` `associate-+r-_binary64_2399`
11×	`div0_binary64_2446`
9×	`associate-+r+_binary64_2397`
8×	`exp-sum_binary64_2511` `cube-unmult_binary64_2502`
6×	`exp-diff_binary64_2513` `rem-sqrt-square_binary64_2478`
4×	`rem-square-sqrt_binary64_2477` `+-rgt-identity_binary64_2450` `distribute-rgt1-in_binary64_2421` `distribute-rgt-out--_binary64_2419` `associate-+l-_binary64_2400`
3×	`pow-base-1_binary64_2525` `rem-3cbrt-lft_binary64_2490`
2×	`log-pow_binary64_2554` `log-rec_binary64_2553` `unpow2_binary64_2530` `unpow1_binary64_2523` `div-exp_binary64_2516` `sub0-neg_binary64_2452` `distribute-rgt-out_binary64_2418` `distribute-lft-out--_binary64_2417`
1×	`1-exp_binary64_2509` `exp-1-e_binary64_2508` `mul-1-neg_binary64_2457` `*-inverses_binary64_2445` `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` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow1/2_binary64_2529` `exp-to-pow_binary64_2527` `unpow0_binary64_2524` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `rec-exp_binary64_2515` `prod-exp_binary64_2514` `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-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `remove-double-neg_binary64_2453` `--rgt-identity_binary64_2451` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `+-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` `distribute-lft-out_binary64_2416` `associate--r-_binary64_2404` `associate--l-_binary64_2403`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	5471
1	973	5342
2	3325	5035

Details

analyze773.0ms (14.4%)

sample45.0ms (0.8%)

simplify99.0ms (1.8%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite189.0ms (3.5%)

series619.0ms (11.5%)

simplify232.0ms (4.3%)

prune614.0ms (11.4%)

localize15.0ms (0.3%)

rewrite174.0ms (3.2%)

series750.0ms (13.9%)

simplify208.0ms (3.9%)

prune313.0ms (5.8%)

localize18.0ms (0.3%)

rewrite261.0ms (4.9%)

series821.0ms (15.3%)

simplify230.0ms (4.3%)

end0.0ms (0%)

Profiling