Details

analyze17.0ms (0%)

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)

sample144.0ms (0.1%)

Algorithm

1×

intervals

Results

113.0ms	256×	body	128	valid
7.0ms	258×	pre	128	true
1.0ms	2×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify636.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (264.0ms)

Iter	Nodes	Cost
0	5512	47

prune17.0ms (0%)

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: 2.7b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize63.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite107.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_4170`
23×	`add-sqr-sqrt_binary64_4192`
22×	`times-frac_binary64_4176` `add-cube-cbrt_binary64_4205`
15×	`sqrt-prod_binary64_4186`
11×	`add-cbrt-cube_binary64_4206`
10×	`add-exp-log_binary64_4208`
7×	`associate-/l_binary64_4115` `associate-/r_binary64_4114`
6×	`add-log-exp_binary64_4209`
5×	`pow1_binary64_4231`
3×	`cbrt-undiv_binary64_4204` `div-exp_binary64_4221`
2×	`frac-2neg_binary64_4181` `div-inv_binary64_4167` `associate-/l/_binary64_4117` `clear-num_binary64_4169` `distribute-lft-out_binary64_4121`
1×	`exp-prod_binary64_4222` `prod-exp_binary64_4219` `cbrt-unprod_binary64_4203` `flip-+_binary64_4144` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `exp-to-pow_binary64_4232` `rem-sqrt-square_binary64_4183` `rem-exp-log_binary64_4210`

Counts

4 → 87

Calls

4 calls:

40.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
23.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
13.0ms	(exp.f64 (*.f64 x x))
2.0ms	(sqrt.f64 PI.f64)

series458.0ms (0.4%)

Counts

4 → 10

Calls

4 calls:

254.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
132.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
71.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify136.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4914	1650
1	4914	1650

prune1.1s (1%)

Pruning

46 alts after pruning (46 fresh and 0 done)

	Pruned	Kept	Total
New	52	45	97
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	53	46	99

Merged error: 0.4b

Counts

99 → 46

Compiler

Compiled 5308 to 2863 computations (46.1% saved)

localize42.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (*.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x))
0.4b	(.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (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))
1.1b	(pow.f64 (exp.f64 x) x)

rewrite230.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary64_4208`
23×	`*-un-lft-identity_binary64_4170` `add-cbrt-cube_binary64_4206`
16×	`add-sqr-sqrt_binary64_4192`
14×	`add-cube-cbrt_binary64_4205`
12×	`prod-exp_binary64_4219`
10×	`times-frac_binary64_4176` `div-exp_binary64_4221`
7×	`pow1_binary64_4231` `associate-l_binary64_4111`
6×	`cbrt-unprod_binary64_4203` `cbrt-undiv_binary64_4204`
5×	`associate-r_binary64_4110` `associate-/l*_binary64_4115` `distribute-lft-out_binary64_4121`
4×	`pow-pow_binary64_4242` `add-log-exp_binary64_4209` `associate-/r*_binary64_4114`
3×	`pow-to-exp_binary64_4239` `exp-prod_binary64_4222` `pow-unpow_binary64_4247` `associate-*r/_binary64_4112` `flip-+_binary64_4144` `pow-exp_binary64_4238` `div-inv_binary64_4167` `unpow-prod-down_binary64_4249` `flip3-+_binary64_4173` `associate-/l/_binary64_4117`
2×	`frac-times_binary64_4180` `frac-2neg_binary64_4181` `clear-num_binary64_4169`
1×	`distribute-lft-in_binary64_4119` `distribute-rgt-in_binary64_4120` `sqrt-div_binary64_4187` `sqr-pow_binary64_4142` `associate-l/_binary64_4113` `-commutative_binary64_4101` `pow-prod-down_binary64_4241` `unswap-sqr_binary64_4138`

Counts

4 → 106

Calls

4 calls:

118.0ms	(.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (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)))))
36.0ms	(/.f64 (*.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x))
17.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
6.0ms	(pow.f64 (exp.f64 x) x)

series818.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

406.0ms	(.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (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)))))
182.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
145.0ms	(/.f64 (*.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x))
84.0ms	(pow.f64 (exp.f64 x) x)

simplify247.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4957	3520
1	4957	3520

prune3.2s (3%)

Pruning

105 alts after pruning (105 fresh and 0 done)

	Pruned	Kept	Total
New	55	63	118
Fresh	3	42	45
Picked	1	0	1
Done	0	0	0
Total	59	105	164

Merged error: 0.3b

Counts

164 → 105

Compiler

Compiled 9139 to 5814 computations (36.4% saved)

localize123.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
0.5b	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
0.5b	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
1.1b	(pow.f64 (exp.f64 x) x)

rewrite120.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_4170`
12×	`cbrt-prod_binary64_4201`
10×	`add-sqr-sqrt_binary64_4192` `add-cube-cbrt_binary64_4205`
6×	`cbrt-div_binary64_4202`
5×	`pow1_binary64_4231`
4×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206` `pow-pow_binary64_4242` `add-log-exp_binary64_4209`
3×	`exp-prod_binary64_4222` `pow-unpow_binary64_4247` `pow1/3_binary64_4252` `flip-+_binary64_4144` `unpow-prod-down_binary64_4249` `flip3-+_binary64_4173` `distribute-lft-out_binary64_4121`
1×	`pow-to-exp_binary64_4239` `sqr-pow_binary64_4142` `pow-exp_binary64_4238`

Counts

4 → 62

Calls

4 calls:

24.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
21.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
21.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
13.0ms	(pow.f64 (exp.f64 x) x)

series524.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
165.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
80.0ms	(pow.f64 (exp.f64 x) x)
79.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4981	1237
1	4981	1237

prune3.1s (2.9%)

Pruning

131 alts after pruning (130 fresh and 1 done)

	Pruned	Kept	Total
New	47	27	74
Fresh	1	103	104
Picked	0	1	1
Done	0	0	0
Total	48	131	179

Merged error: 0.2b

Counts

179 → 131

Compiler

Compiled 10254 to 6949 computations (32.2% saved)

localize231.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (pow.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) 1/3) (cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x)))))
0.5b	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
0.5b	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
1.1b	(pow.f64 (exp.f64 x) x)

rewrite187.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_4192`
21×	`*-un-lft-identity_binary64_4170`
15×	`cbrt-prod_binary64_4201`
13×	`add-cube-cbrt_binary64_4205`
9×	`add-exp-log_binary64_4208` `unpow-prod-down_binary64_4249`
8×	`associate-l_binary64_4111`
7×	`associate-r_binary64_4110`
6×	`cbrt-div_binary64_4202` `unswap-sqr_binary64_4138`
5×	`pow1_binary64_4231` `pow1/3_binary64_4252` `add-cbrt-cube_binary64_4206`
4×	`sqr-pow_binary64_4142` `pow-pow_binary64_4242` `add-log-exp_binary64_4209` `distribute-lft-out_binary64_4121`
3×	`exp-prod_binary64_4222` `pow-unpow_binary64_4247` `prod-exp_binary64_4219` `flip-+_binary64_4144` `flip3-+_binary64_4173`
2×	`pow-to-exp_binary64_4239` `associate-*r/_binary64_4112` `cbrt-unprod_binary64_4203` `pow-exp_binary64_4238`
1×	`unpow1/3_binary64_4237` `pow-prod-up_binary64_4240` `*-commutative_binary64_4101` `pow-prod-down_binary64_4241` `pow-sqr_binary64_4143`

Counts

4 → 87

Calls

4 calls:

69.0ms	(.f64 (pow.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) 1/3) (cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x)))))
23.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
22.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
14.0ms	(pow.f64 (exp.f64 x) x)

series586.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(.f64 (pow.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) 1/3) (cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x)))))
173.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
154.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))))
69.0ms	(pow.f64 (exp.f64 x) x)

simplify342.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	4915	1727
1	4915	1727

prune3.2s (3%)

Pruning

171 alts after pruning (169 fresh and 2 done)

	Pruned	Kept	Total
New	54	45	99
Fresh	5	124	129
Picked	0	1	1
Done	0	1	1
Total	59	171	230

Merged error: 0.2b

Counts

230 → 171

Compiler

Compiled 5571 to 3623 computations (35% saved)

regimes8.9s (8.3%)

Compiler: Compiled 38612 to 28041 computations (27.4% saved)

bsearch47.2s (44.2%)

simplify35.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	71
1	39	71

end0.0ms (0%)

sample34.9s (32.7%)

Algorithm

1×

intervals

Results

3.8s	8000×	body	128	valid
218.0ms	8126×	pre	128	true
89.0ms	126×	body	128	invalid

Compiler

Compiled 13262 to 9645 computations (27.3% saved)

Pareto

0.0006410200436082621

Details

analyze17.0ms (0%)

sample144.0ms (0.1%)

simplify636.0ms (0.6%)

prune17.0ms (0%)

localize63.0ms (0.1%)

rewrite107.0ms (0.1%)

series458.0ms (0.4%)

simplify136.0ms (0.1%)

prune1.1s (1%)

localize42.0ms (0%)

rewrite230.0ms (0.2%)

series818.0ms (0.8%)

simplify247.0ms (0.2%)

prune3.2s (3%)

localize123.0ms (0.1%)

rewrite120.0ms (0.1%)

series524.0ms (0.5%)

simplify102.0ms (0.1%)

prune3.1s (2.9%)

localize231.0ms (0.2%)

rewrite187.0ms (0.2%)

series586.0ms (0.5%)

simplify342.0ms (0.3%)

prune3.2s (3%)

regimes8.9s (8.3%)

bsearch47.2s (44.2%)

simplify35.0ms (0%)

end0.0ms (0%)

sample34.9s (32.7%)

Profiling