Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify218.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5050	41

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2487`
30×	`associate-r_binary64_2405`
23×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
20×	`times-frac_binary64_2471`
19×	`add-exp-log_binary64_2503`
16×	`add-cbrt-cube_binary64_2501`
13×	`sqrt-prod_binary64_2481`
12×	`pow1_binary64_2526`
9×	`associate-l_binary64_2406`
8×	`prod-exp_binary64_2514`
7×	`unswap-sqr_binary64_2433`
6×	`cbrt-unprod_binary64_2498`
4×	`add-log-exp_binary64_2504` `unpow-prod-down_binary64_2544` `pow-prod-down_binary64_2536`
3×	`*-commutative_binary64_2396`
2×	`sqr-pow_binary64_2437`
1×	`pow1/2_binary64_2545` `associate-*r/_binary64_2407` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

Counts

4 → 99

Calls

4 calls:

19.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
1.0ms	(sqrt.f64 PI.f64)

series113.0ms (2%)

Counts

4 → 10

Calls

4 calls:

65.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
30.0ms	(*.f64 1/5 (pow.f64 x 4))
17.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5588	2543

prune199.0ms (3.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	108	3	111

Merged error: 0.0b

Counts

111 → 3

Compiler

Compiled 3922 to 2612 computations (33.4% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite169.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`add-exp-log_binary64_2503`
128×	`prod-exp_binary64_2514`
107×	`add-cbrt-cube_binary64_2501`
70×	`cbrt-unprod_binary64_2498`
51×	`pow1_binary64_2526`
48×	`associate-l_binary64_2406`
46×	`add-sqr-sqrt_binary64_2487`
40×	`times-frac_binary64_2471`
35×	`*-un-lft-identity_binary64_2465` `pow-prod-down_binary64_2536`
33×	`add-cube-cbrt_binary64_2500`
19×	`div-exp_binary64_2516`
15×	`associate-*l/_binary64_2408`
14×	`sqrt-prod_binary64_2481`
12×	`frac-add_binary64_2473`
11×	`cbrt-undiv_binary64_2499`
8×	`rec-exp_binary64_2515` `1-exp_binary64_2509`
6×	`flip3-+_binary64_2468` `frac-times_binary64_2475` `flip-+_binary64_2439` `associate-*r/_binary64_2407`
5×	`unswap-sqr_binary64_2433` `associate-r_binary64_2405`
4×	`add-log-exp_binary64_2504`
3×	`*-commutative_binary64_2396` `div-inv_binary64_2462`
1×	`distribute-lft-in_binary64_2414` `pow1/2_binary64_2545` `distribute-rgt-in_binary64_2415` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

Counts

4 → 183

Calls

4 calls:

79.0ms	(.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
26.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	(sqrt.f64 PI.f64)

series418.0ms (7.6%)

Counts

4 → 10

Calls

4 calls:

312.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
69.0ms	(.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
36.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify126.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4923	5382
1	4923	5382

prune488.0ms (8.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	192	4	196

Merged error: 0b

Counts

196 → 4

Compiler

Compiled 11364 to 5255 computations (53.8% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 (pow.f64 (fabs.f64 x) 7) 21)))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite114.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-exp-log_binary64_2503`
76×	`prod-exp_binary64_2514`
75×	`add-cbrt-cube_binary64_2501`
48×	`associate-l_binary64_2406`
46×	`add-sqr-sqrt_binary64_2487`
44×	`cbrt-unprod_binary64_2498`
40×	`times-frac_binary64_2471`
37×	`*-un-lft-identity_binary64_2465`
36×	`pow1_binary64_2526`
33×	`add-cube-cbrt_binary64_2500`
22×	`pow-prod-down_binary64_2536`
15×	`div-exp_binary64_2516`
14×	`sqrt-prod_binary64_2481`
12×	`frac-add_binary64_2473`
9×	`cbrt-undiv_binary64_2499`
7×	`associate-*l/_binary64_2408`
6×	`flip3-+_binary64_2468` `frac-times_binary64_2475` `flip-+_binary64_2439` `associate-r/_binary64_2407` `rec-exp_binary64_2515` `associate-r*_binary64_2405` `1-exp_binary64_2509`
5×	`unswap-sqr_binary64_2433`
4×	`add-log-exp_binary64_2504`
3×	`*-commutative_binary64_2396` `div-inv_binary64_2462`
1×	`distribute-lft-in_binary64_2414` `pow1/2_binary64_2545` `distribute-rgt-in_binary64_2415` `rem-sqrt-square_binary64_2478` `distribute-lft-out_binary64_2416` `sqrt-pow1_binary64_2483`

Counts

4 → 170

Calls

4 calls:

32.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 (pow.f64 (fabs.f64 x) 7) 21)))
28.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	(sqrt.f64 PI.f64)

series385.0ms (7%)

Counts

4 → 10

Calls

4 calls:

293.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 (pow.f64 (fabs.f64 x) 7) 21)))
54.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
38.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4922	5254
1	4922	5254

prune472.0ms (8.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	180	4	184

Merged error: 0b

Counts

184 → 4

Compiler

Compiled 8759 to 4963 computations (43.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 4) 1/5)
0.2b	(.f64 2/3 (.f64 x x))
0.3b	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2487`
19×	`add-exp-log_binary64_2503`
16×	`add-cbrt-cube_binary64_2501`
13×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
10×	`pow1_binary64_2526` `associate-l_binary64_2406`
9×	`sqrt-prod_binary64_2481`
7×	`prod-exp_binary64_2514`
6×	`times-frac_binary64_2471` `associate-/r*_binary64_2409`
5×	`cbrt-unprod_binary64_2498`
4×	`add-log-exp_binary64_2504` `unswap-sqr_binary64_2433` `unpow-prod-down_binary64_2544` `associate-r_binary64_2405`
3×	`pow-prod-down_binary64_2536`
2×	`-commutative_binary64_2396` `associate-/l/_binary64_2412` `associate-r/_binary64_2407` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `sqr-pow_binary64_2437`
1×	`flip3-+_binary64_2468` `pow1/2_binary64_2545` `flip-+_binary64_2439` `clear-num_binary64_2464` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483` `associate-/l*_binary64_2410`

Counts

4 → 86

Calls

4 calls:

16.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 4) 1/5)
1.0ms	(sqrt.f64 PI.f64)

series112.0ms (2%)

Counts

4 → 10

Calls

4 calls:

72.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
24.0ms	(*.f64 (pow.f64 x 4) 1/5)
17.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	6505	1912

prune145.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	96	4	100

Merged error: 0b

Counts

100 → 4

Compiler

Compiled 2957 to 1966 computations (33.5% saved)

regimes362.0ms (6.5%)

Compiler: Compiled 5019 to 3613 computations (28% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	66
1	40	66

end0.0ms (0%)

sample1.8s (32.2%)

Algorithm

1×

intervals

Results

733.0ms	8000×	body	128	valid
98.0ms	8000×	pre	128	true

Compiler

Compiled 1036 to 746 computations (28% saved)

Details

analyze6.0ms (0.1%)

sample36.0ms (0.6%)

simplify218.0ms (3.9%)

prune7.0ms (0.1%)

localize18.0ms (0.3%)

rewrite44.0ms (0.8%)

series113.0ms (2%)

simplify64.0ms (1.2%)

prune199.0ms (3.6%)

localize26.0ms (0.5%)

rewrite169.0ms (3%)

series418.0ms (7.6%)

simplify126.0ms (2.3%)

prune488.0ms (8.8%)

localize23.0ms (0.4%)

rewrite114.0ms (2.1%)

series385.0ms (7%)

simplify100.0ms (1.8%)

prune472.0ms (8.5%)

localize18.0ms (0.3%)

rewrite38.0ms (0.7%)

series112.0ms (2%)

simplify50.0ms (0.9%)

prune145.0ms (2.6%)

regimes362.0ms (6.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (32.2%)

Profiling