Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample70.0ms (0.6%)

Algorithm

1×

intervals

Results

54.0ms	256×	body	128	valid
3.0ms	260×	pre	128	true
1.0ms	4×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify158.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5512	47

prune8.0ms (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

3.0b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.5b	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
2.7b	(exp.f64 (*.f64 x x))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`times-frac_binary64_2471`
86×	`*-un-lft-identity_binary64_2465`
83×	`add-sqr-sqrt_binary64_2487`
82×	`add-cube-cbrt_binary64_2500`
39×	`sqrt-prod_binary64_2481`
26×	`associate-/l*_binary64_2410`
14×	`add-cbrt-cube_binary64_2501`
13×	`add-exp-log_binary64_2503`
6×	`add-log-exp_binary64_2504` `div-inv_binary64_2462`
5×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `pow1_binary64_2526`
4×	`associate-/r*_binary64_2409`
3×	`associate-/l/_binary64_2412`
2×	`clear-num_binary64_2464` `frac-2neg_binary64_2476` `distribute-lft-out_binary64_2416`
1×	`flip3-+_binary64_2468` `exp-to-pow_binary64_2527` `pow1/2_binary64_2545` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `rem-exp-log_binary64_2505` `exp-prod_binary64_2517` `sqrt-pow1_binary64_2483` `cbrt-unprod_binary64_2498`

Counts

4 → 154

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
9.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series186.0ms (1.5%)

Counts

4 → 18

Calls

4 calls:

92.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
73.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
22.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 856 to 680 computations (20.6% saved)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4940	4477
1	4940	4477

prune337.0ms (2.8%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	146	26	172
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	147	27	174

Error

0.4b

Counts

174 → 27

Compiler

Compiled 8095 to 3620 computations (55.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.5b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
1.1b	(pow.f64 (exp.f64 x) x)

rewrite68.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64_2465`
28×	`add-exp-log_binary64_2503`
26×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
25×	`times-frac_binary64_2471`
20×	`add-cbrt-cube_binary64_2501`
15×	`unpow-prod-down_binary64_2544`
11×	`associate-/l*_binary64_2410`
10×	`pow1_binary64_2526` `prod-exp_binary64_2514`
9×	`frac-times_binary64_2475`
8×	`div-exp_binary64_2516`
6×	`associate-*l/_binary64_2408` `sqrt-div_binary64_2482` `cbrt-unprod_binary64_2498`
5×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-r/_binary64_2407` `sqr-pow_binary64_2437` `associate-r*_binary64_2405` `distribute-lft-out_binary64_2416`
4×	`add-log-exp_binary64_2504` `associate-/r*_binary64_2409` `cbrt-undiv_binary64_2499` `pow-pow_binary64_2537`
3×	`pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `exp-prod_binary64_2517` `pow-prod-down_binary64_2536` `pow-unpow_binary64_2542`
2×	`associate-/l/_binary64_2412` `clear-num_binary64_2464` `div-inv_binary64_2462` `frac-2neg_binary64_2476`
1×	`distribute-lft-in_binary64_2414` `-commutative_binary64_2396` `distribute-rgt-in_binary64_2415` `associate-l*_binary64_2406`

Counts

4 → 127

Calls

4 calls:

36.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
5.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
3.0ms	(pow.f64 (exp.f64 x) x)

series401.0ms (3.3%)

Counts

4 → 30

Calls

4 calls:

213.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
77.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
73.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
37.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 1336 to 1019 computations (23.7% saved)

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4929	4589
1	4929	4589

prune378.0ms (3.1%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	140	17	157
Fresh	10	16	26
Picked	1	0	1
Done	0	0	0
Total	151	33	184

Error

0.2b

Counts

184 → 33

Compiler

Compiled 7908 to 4460 computations (43.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (/.f64 (fabs.f64 x) (pow.f64 (exp.f64 x) (/.f64 x 2))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.7b	(pow.f64 (exp.f64 x) (/.f64 x 2))
0.7b	(pow.f64 (exp.f64 x) (/.f64 x 2))

rewrite88.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-exp-log_binary64_2503`
34×	`*-un-lft-identity_binary64_2465`
28×	`prod-exp_binary64_2514`
26×	`pow-unpow_binary64_2542`
25×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
23×	`add-cbrt-cube_binary64_2501` `div-exp_binary64_2516`
22×	`times-frac_binary64_2471`
11×	`pow1_binary64_2526`
9×	`frac-times_binary64_2475` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534`
8×	`pow-pow_binary64_2537` `cbrt-unprod_binary64_2498`
6×	`associate-*l/_binary64_2408` `unpow-prod-down_binary64_2544` `exp-prod_binary64_2517` `sqrt-div_binary64_2482`
5×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-r/_binary64_2407` `cbrt-undiv_binary64_2499` `associate-r*_binary64_2405` `distribute-lft-out_binary64_2416`
4×	`add-log-exp_binary64_2504` `associate-/l*_binary64_2410`
3×	`div-inv_binary64_2462` `pow-prod-down_binary64_2536`
2×	`associate-/l/_binary64_2412` `sqr-pow_binary64_2437`
1×	`distribute-lft-in_binary64_2414` `-commutative_binary64_2396` `associate-/r_binary64_2409` `clear-num_binary64_2464` `distribute-rgt-in_binary64_2415` `frac-2neg_binary64_2476` `associate-l_binary64_2406`

Counts

4 → 132

Calls

4 calls:

51.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (/.f64 (fabs.f64 x) (pow.f64 (exp.f64 x) (/.f64 x 2))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
5.0ms	(pow.f64 (exp.f64 x) (/.f64 x 2))
4.0ms	(pow.f64 (exp.f64 x) (/.f64 x 2))

series552.0ms (4.6%)

Counts

4 → 30

Calls

4 calls:

379.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (/.f64 (fabs.f64 x) (pow.f64 (exp.f64 x) (/.f64 x 2))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
73.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
52.0ms	(pow.f64 (exp.f64 x) (/.f64 x 2))
47.0ms	(pow.f64 (exp.f64 x) (/.f64 x 2))

Compiler

Compiled 1675 to 1291 computations (22.9% saved)

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4989	4727
1	4989	4727

prune445.0ms (3.7%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	152	10	162
Fresh	7	25	32
Picked	1	0	1
Done	0	0	0
Total	160	35	195

Error

0.2b

Counts

195 → 35

Compiler

Compiled 9011 to 5462 computations (39.4% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (/.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.7b	(pow.f64 (exp.f64 x) (/.f64 x 2))
1.1b	(pow.f64 (sqrt.f64 (exp.f64 x)) x)

rewrite96.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-exp-log_binary64_2503`
29×	`*-un-lft-identity_binary64_2465`
28×	`prod-exp_binary64_2514`
23×	`add-cbrt-cube_binary64_2501` `div-exp_binary64_2516`
20×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
16×	`pow-unpow_binary64_2542`
13×	`times-frac_binary64_2471`
12×	`pow1_binary64_2526`
10×	`pow-pow_binary64_2537`
9×	`frac-times_binary64_2475` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `unpow-prod-down_binary64_2544`
8×	`cbrt-unprod_binary64_2498`
6×	`associate-*l/_binary64_2408` `exp-prod_binary64_2517` `sqrt-div_binary64_2482`
5×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-r/_binary64_2407` `cbrt-undiv_binary64_2499` `associate-r*_binary64_2405` `distribute-lft-out_binary64_2416`
4×	`add-log-exp_binary64_2504` `sqrt-pow1_binary64_2483` `associate-/l*_binary64_2410`
3×	`sqrt-prod_binary64_2481` `pow-prod-down_binary64_2536`
2×	`associate-/l/_binary64_2412` `div-inv_binary64_2462` `sqr-pow_binary64_2437`
1×	`distribute-lft-in_binary64_2414` `-commutative_binary64_2396` `associate-/r_binary64_2409` `sqrt-pow2_binary64_2484` `pow1/2_binary64_2545` `clear-num_binary64_2464` `distribute-rgt-in_binary64_2415` `frac-2neg_binary64_2476` `associate-l_binary64_2406`

Counts

4 → 128

Calls

4 calls:

60.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (/.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
4.0ms	(pow.f64 (exp.f64 x) (/.f64 x 2))
4.0ms	(pow.f64 (sqrt.f64 (exp.f64 x)) x)

series477.0ms (3.9%)

Counts

4 → 30

Calls

4 calls:

311.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (/.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
73.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
46.0ms	(pow.f64 (sqrt.f64 (exp.f64 x)) x)
46.0ms	(pow.f64 (exp.f64 x) (/.f64 x 2))

Compiler

Compiled 1726 to 1258 computations (27.1% saved)

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4934	4702
1	4934	4702

prune317.0ms (2.6%)

Pruning

36 alts after pruning (35 fresh and 1 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	4	30	34
Picked	0	1	1
Done	0	0	0
Total	157	36	193

Error

0.2b

Counts

193 → 36

Compiler

Compiled 6918 to 3840 computations (44.5% saved)

regimes1.3s (11.1%)

Accuracy

Total 1.1b remaining (90.4%)

Threshold costs 0b (0%)

Compiler

Compiled 20921 to 13692 computations (34.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	64
1	33	64

end0.0ms (0%)

sample6.6s (54.8%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
105.0ms	8111×	pre	128	true
22.0ms	111×	body	128	invalid

Compiler

Compiled 7050 to 4618 computations (34.5% saved)

Details

analyze9.0ms (0.1%)

sample70.0ms (0.6%)

simplify158.0ms (1.3%)

prune8.0ms (0.1%)

localize21.0ms (0.2%)

rewrite42.0ms (0.3%)

series186.0ms (1.5%)

simplify96.0ms (0.8%)

prune337.0ms (2.8%)

localize21.0ms (0.2%)

rewrite68.0ms (0.6%)

series401.0ms (3.3%)

simplify97.0ms (0.8%)

prune378.0ms (3.1%)

localize24.0ms (0.2%)

rewrite88.0ms (0.7%)

series552.0ms (4.6%)

simplify95.0ms (0.8%)

prune445.0ms (3.7%)

localize30.0ms (0.2%)

rewrite96.0ms (0.8%)

series477.0ms (3.9%)

simplify95.0ms (0.8%)

prune317.0ms (2.6%)

regimes1.3s (11.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.6s (54.8%)

Profiling