Details

analyze219.0ms (4.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5050	41
0	1	1
1	1	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)

sample35.0ms (0.7%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify136.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

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

Error

0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (*.f64 (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)

rewrite88.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`pow1_binary64_3549`
43×	`add-exp-log_binary64_3526`
40×	`add-sqr-sqrt_binary64_3510`
39×	`add-cbrt-cube_binary64_3524`
36×	`associate-l_binary64_3429`
31×	`times-frac_binary64_3494`
29×	`*-un-lft-identity_binary64_3488`
27×	`add-cube-cbrt_binary64_3523`
22×	`prod-exp_binary64_3537`
21×	`pow-prod-up_binary64_3558` `pow-plus_binary64_3551`
20×	`cbrt-unprod_binary64_3521`
14×	`associate-*l/_binary64_3431` `sqrt-prod_binary64_3504`
13×	`pow-prod-down_binary64_3559`
12×	`frac-add_binary64_3496`
7×	`associate-r_binary64_3428`
6×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `frac-times_binary64_3498` `associate-*r/_binary64_3430`
5×	`unswap-sqr_binary64_3456` `div-exp_binary64_3539`
4×	`pow2_binary64_3569` `add-log-exp_binary64_3527` `cbrt-undiv_binary64_3522` `pow-sqr_binary64_3461`
3×	`*-commutative_binary64_3419`
2×	`pow3_binary64_3571` `div-inv_binary64_3485`
1×	`distribute-lft-in_binary64_3437` `1-exp_binary64_3532` `distribute-rgt-in_binary64_3438` `rec-exp_binary64_3538` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501`

Counts

4 → 150

Calls

4 calls:

27.0ms	(.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)))))
13.0ms	(.f64 (.f64 (*.f64 (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)))
2.0ms	(sqrt.f64 PI.f64)

series374.0ms (7.8%)

Counts

4 → 10

Calls

4 calls:

309.0ms	(.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)))))
37.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
28.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify103.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4958	4756
1	4958	4756

prune440.0ms (9.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	4	162

Error

Counts

162 → 4

Compiler

Compiled 9989 to 4588 computations (54.1% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_3510`
30×	`associate-r_binary64_3428`
23×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
20×	`times-frac_binary64_3494`
19×	`add-exp-log_binary64_3526`
16×	`add-cbrt-cube_binary64_3524`
13×	`sqrt-prod_binary64_3504`
12×	`pow1_binary64_3549`
9×	`associate-l_binary64_3429`
8×	`prod-exp_binary64_3537`
7×	`unswap-sqr_binary64_3456`
6×	`cbrt-unprod_binary64_3521`
4×	`unpow-prod-down_binary64_3567` `pow-prod-down_binary64_3559` `add-log-exp_binary64_3527`
3×	`*-commutative_binary64_3419`
2×	`sqr-pow_binary64_3460`
1×	`pow-exp_binary64_3556` `pow-to-exp_binary64_3557` `associate-*r/_binary64_3430` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485` `rem-sqrt-square_binary64_3501`

Counts

4 → 99

Calls

4 calls:

22.0ms	(.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 1/21 (pow.f64 x 6))
1.0ms	(sqrt.f64 PI.f64)

series114.0ms (2.4%)

Counts

4 → 10

Calls

4 calls:

64.0ms	(.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)))
32.0ms	(*.f64 1/21 (pow.f64 x 6))
18.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5054	2532

prune201.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	110	3	113

Error

Counts

113 → 3

Compiler

Compiled 3846 to 2599 computations (32.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite48.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64_3526`
29×	`add-sqr-sqrt_binary64_3510`
26×	`associate-r_binary64_3428`
23×	`add-cbrt-cube_binary64_3524`
22×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
18×	`times-frac_binary64_3494` `prod-exp_binary64_3537`
15×	`pow1_binary64_3549`
12×	`sqrt-prod_binary64_3504`
11×	`associate-l_binary64_3429`
10×	`cbrt-unprod_binary64_3521`
6×	`pow-prod-down_binary64_3559`
5×	`associate-*r/_binary64_3430`
4×	`unswap-sqr_binary64_3456` `unpow-prod-down_binary64_3567` `add-log-exp_binary64_3527` `div-exp_binary64_3539`
3×	`*-commutative_binary64_3419`
2×	`1-exp_binary64_3532` `associate-*l/_binary64_3431` `flip-+_binary64_3462` `flip3-+_binary64_3491` `rec-exp_binary64_3538` `frac-times_binary64_3498` `sqr-pow_binary64_3460` `cbrt-undiv_binary64_3522`
1×	`pow-exp_binary64_3556` `pow-to-exp_binary64_3557` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `un-div-inv_binary64_3486` `div-inv_binary64_3485` `rem-sqrt-square_binary64_3501`

Counts

4 → 108

Calls

4 calls:

20.0ms	(.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))))) (/.f64 1 (sqrt.f64 PI.f64)))
6.0ms	(.f64 2/3 (.f64 x x))
5.0ms	(*.f64 (pow.f64 x 6) 1/21)
2.0ms	(sqrt.f64 PI.f64)

series120.0ms (2.5%)

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))))) (/.f64 1 (sqrt.f64 PI.f64)))
29.0ms	(*.f64 (pow.f64 x 6) 1/21)
18.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify101.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4933	2891
1	4933	2891

prune206.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	118	3	121

Error

Counts

121 → 3

Compiler

Compiled 3928 to 2677 computations (31.8% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 6) 1/21)
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)

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_3510`
19×	`add-exp-log_binary64_3526`
16×	`add-cbrt-cube_binary64_3524`
13×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
10×	`associate-l_binary64_3429` `pow1_binary64_3549`
9×	`sqrt-prod_binary64_3504`
7×	`prod-exp_binary64_3537`
6×	`associate-/r*_binary64_3432` `times-frac_binary64_3494`
5×	`cbrt-unprod_binary64_3521`
4×	`unswap-sqr_binary64_3456` `unpow-prod-down_binary64_3567` `associate-r_binary64_3428` `add-log-exp_binary64_3527`
3×	`pow-prod-down_binary64_3559`
2×	`associate-/l/_binary64_3435` `associate-r/_binary64_3430` `sqr-pow_binary64_3460` `-commutative_binary64_3419` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
1×	`pow-exp_binary64_3556` `clear-num_binary64_3487` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/l*_binary64_3433` `pow-to-exp_binary64_3557` `frac-2neg_binary64_3499` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `div-inv_binary64_3485` `rem-sqrt-square_binary64_3501`

Counts

4 → 86

Calls

4 calls:

15.0ms	(/.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))
5.0ms	(*.f64 (pow.f64 x 6) 1/21)
1.0ms	(sqrt.f64 PI.f64)

series114.0ms (2.4%)

Counts

4 → 10

Calls

4 calls:

64.0ms	(/.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))
29.0ms	(*.f64 (pow.f64 x 6) 1/21)
21.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4995	1906
1	4995	1906

prune142.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	96	3	99

Error

Counts

99 → 3

Compiler

Compiled 2953 to 1977 computations (33.1% saved)

regimes341.0ms (7.1%)

Accuracy

Total 0.1b remaining (99.4%)

Threshold costs 0.1b (99.4%)

Compiler

Compiled 4709 to 3338 computations (29.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	44
1	34	44

end0.0ms (0%)

sample1.7s (35.4%)

Algorithm

1×

intervals

Results

754.0ms	8000×	body	128	valid
97.0ms	8000×	pre	128	true

Compiler

Compiled 929 to 672 computations (27.7% saved)

Details

analyze219.0ms (4.6%)

sample35.0ms (0.7%)

simplify136.0ms (2.8%)

prune7.0ms (0.1%)

localize26.0ms (0.5%)

rewrite88.0ms (1.8%)

series374.0ms (7.8%)

simplify103.0ms (2.2%)

prune440.0ms (9.2%)

localize19.0ms (0.4%)

rewrite45.0ms (0.9%)

series114.0ms (2.4%)

simplify71.0ms (1.5%)

prune201.0ms (4.2%)

localize18.0ms (0.4%)

rewrite48.0ms (1%)

series120.0ms (2.5%)

simplify101.0ms (2.1%)

prune206.0ms (4.3%)

localize17.0ms (0.4%)

rewrite35.0ms (0.7%)

series114.0ms (2.4%)

simplify68.0ms (1.4%)

prune142.0ms (3%)

regimes341.0ms (7.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.7s (35.4%)

Profiling