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)

sample83.0ms (0.8%)

Algorithm

1×

intervals

Results

51.0ms	256×	body	128	valid
3.0ms	261×	pre	128	true
1.0ms	5×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify159.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5512	47

prune10.0ms (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

2.6b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize22.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))
0.2b	(/.f64 15/8 (pow.f64 x 6))
0.1b	(+.f64 1/2 (/.f64 3/4 (*.f64 x x)))
0.1b	(+.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 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 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))
1.0b	(sqrt.f64 PI.f64)
2.6b	(exp.f64 (*.f64 x x))

rewrite80.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`times-frac_binary64_3494`
84×	`add-sqr-sqrt_binary64_3510`
79×	`*-un-lft-identity_binary64_3488`
70×	`associate-l_binary64_3429` `add-cube-cbrt_binary64_3523`
31×	`sqrt-prod_binary64_3504`
18×	`add-cbrt-cube_binary64_3524`
17×	`add-exp-log_binary64_3526`
7×	`pow1_binary64_3549`
6×	`add-log-exp_binary64_3527`
5×	`distribute-lft-out_binary64_3439` `associate-r_binary64_3428` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`
4×	`unswap-sqr_binary64_3456` `associate-/l*_binary64_3433` `cbrt-unprod_binary64_3521` `prod-exp_binary64_3537`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
2×	`associate-/l/_binary64_3435` `frac-times_binary64_3498` `associate-*r/_binary64_3430`
1×	`distribute-lft-in_binary64_3437` `associate-l/_binary64_3431` `clear-num_binary64_3487` `distribute-rgt-in_binary64_3438` `associate-/r_binary64_3432` `exp-to-pow_binary64_3550` `rem-exp-log_binary64_3528` `exp-prod_binary64_3540` `pow-prod-down_binary64_3559` `frac-2neg_binary64_3499` `pow1/2_binary64_3568` `*-commutative_binary64_3419` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501`

Counts

4 → 149

Calls

8 calls:

46.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 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)))))
9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))))

series296.0ms (2.9%)

Counts

4 → 24

Calls

4 calls:

196.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 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)))))
74.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
26.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1010 to 815 computations (19.3% saved)

simplify137.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4943	6637
1	4943	6637

prune522.0ms (5.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	147	26	173
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	26	175

Error

0.3b

Counts

175 → 26

Compiler

Compiled 8486 to 4000 computations (52.9% saved)

localize28.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(+.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 1/2 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 3)))) (+.f64 (.f64 3/4 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 5))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))))
0.2b	(+.f64 (.f64 3/4 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 5))) (.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7))))
0.2b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
0.2b	(*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488` `pow-pow_binary64_3560`
12×	`exp-prod_binary64_3540` `unpow-prod-down_binary64_3567` `pow-unpow_binary64_3565`
8×	`pow1_binary64_3549`
4×	`pow-exp_binary64_3556` `add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `pow-to-exp_binary64_3557` `add-log-exp_binary64_3527` `sqr-pow_binary64_3460`

Counts

4 → 80

Calls

8 calls:

4.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))

series167.0ms (1.7%)

Counts

4 → 24

Calls

4 calls:

43.0ms	(pow.f64 (exp.f64 x) x)
43.0ms	(pow.f64 (exp.f64 x) x)
41.0ms	(pow.f64 (exp.f64 x) x)
40.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 1608 to 1008 computations (37.3% saved)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5177	940

prune288.0ms (2.9%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	5	20	25
Picked	1	0	1
Done	0	0	0
Total	104	26	130

Error

0.2b

Counts

130 → 26

Compiler

Compiled 6798 to 3367 computations (50.5% saved)

localize40.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.2b	(+.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 x (cbrt.f64 x))) (pow.f64 (fabs.f64 x) 3)))) (+.f64 (.f64 3/4 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 5))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))))
0.2b	(+.f64 (.f64 3/4 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 5))) (.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7))))
0.2b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
0.2b	(*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
2.7b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 x (cbrt.f64 x)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow-pow_binary64_3560`
14×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
12×	`unpow-prod-down_binary64_3567`
10×	`exp-prod_binary64_3540` `pow-unpow_binary64_3565`
8×	`pow1_binary64_3549`
5×	`add-log-exp_binary64_3527`
4×	`pow-exp_binary64_3556` `add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `pow-to-exp_binary64_3557` `sqr-pow_binary64_3460`
1×	`exp-to-pow_binary64_3550`

Counts

4 → 77

Calls

8 calls:

4.0ms	(pow.f64 (exp.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 x (cbrt.f64 x)))
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(+.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 x (cbrt.f64 x))) (pow.f64 (fabs.f64 x) 3)))) (+.f64 (.f64 3/4 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 5))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))))

series442.0ms (4.4%)

Counts

4 → 21

Calls

4 calls:

312.0ms	(pow.f64 (exp.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 x (cbrt.f64 x)))
44.0ms	(pow.f64 (exp.f64 x) x)
44.0ms	(pow.f64 (exp.f64 x) x)
42.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 1734 to 1128 computations (34.9% saved)

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4939	977
1	4939	977

prune318.0ms (3.2%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	2	23	25
Picked	1	0	1
Done	0	0	0
Total	95	29	124

Error

0.2b

Counts

124 → 29

Compiler

Compiled 7320 to 3489 computations (52.3% saved)

localize44.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.2b	(+.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 x 4/3)) (pow.f64 (fabs.f64 x) 3)))) (+.f64 (.f64 3/4 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 5))) (.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))))
0.2b	(+.f64 (.f64 3/4 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 5))) (.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7))))
0.2b	(/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x))
0.2b	(*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
2.7b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 x 4/3))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523` `pow-unpow_binary64_3565` `*-un-lft-identity_binary64_3488`
15×	`unpow-prod-down_binary64_3567` `pow-pow_binary64_3560`
10×	`exp-prod_binary64_3540`
8×	`pow1_binary64_3549`
5×	`add-log-exp_binary64_3527` `sqr-pow_binary64_3460`
4×	`pow-exp_binary64_3556` `add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `pow-to-exp_binary64_3557`
1×	`exp-to-pow_binary64_3550`

Counts

4 → 83

Calls

8 calls:

5.0ms	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 x 4/3))
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (fabs.f64 x) 7)))

series421.0ms (4.2%)

Counts

4 → 21

Calls

4 calls:

292.0ms	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 x 4/3))
46.0ms	(pow.f64 (exp.f64 x) x)
42.0ms	(pow.f64 (exp.f64 x) x)
41.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 1706 to 1148 computations (32.7% saved)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4953	1061
1	4953	1061

prune263.0ms (2.6%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	4	24	28
Picked	1	0	1
Done	0	0	0
Total	104	29	133

Error

0.2b

Counts

133 → 29

Compiler

Compiled 5973 to 2956 computations (50.5% saved)

simplify123.0ms (1.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	903	8541
1	903	8541

regimes373.0ms (3.7%)

Compiler: Compiled 4975 to 3174 computations (36.2% saved)

bsearch0.0ms (0%)

regimes202.0ms (2%)

Compiler: Compiled 2658 to 1776 computations (33.2% saved)

bsearch0.0ms (0%)

regimes96.0ms (1%)

Compiler: Compiled 1186 to 841 computations (29.1% saved)

bsearch0.0ms (0%)

regimes78.0ms (0.8%)

Compiler: Compiled 923 to 656 computations (28.9% saved)

bsearch0.0ms (0%)

regimes32.0ms (0.3%)

Compiler: Compiled 295 to 215 computations (27.1% saved)

bsearch0.0ms (0%)

regimes29.0ms (0.3%)

Compiler: Compiled 265 to 193 computations (27.2% saved)

bsearch0.0ms (0%)

regimes9.0ms (0.1%)

Accuracy

Total 1.0b remaining (82%)

Threshold costs 1.0b (82%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch12.0ms (0.1%)

Compiler: Compiled 279 to 194 computations (30.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	148	433
1	148	433

end0.0ms (0%)

sample5.5s (54.7%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
103.0ms	8132×	pre	128	true
26.0ms	132×	body	128	invalid

Compiler

Compiled 5358 to 3438 computations (35.8% saved)

Pareto

0.7119154839800841

Details

analyze9.0ms (0.1%)

sample83.0ms (0.8%)

simplify159.0ms (1.6%)

prune10.0ms (0.1%)

localize22.0ms (0.2%)

rewrite80.0ms (0.8%)

series296.0ms (2.9%)

simplify137.0ms (1.4%)

prune522.0ms (5.2%)

localize28.0ms (0.3%)

rewrite27.0ms (0.3%)

series167.0ms (1.7%)

simplify53.0ms (0.5%)

prune288.0ms (2.9%)

localize40.0ms (0.4%)

rewrite26.0ms (0.3%)

series442.0ms (4.4%)

simplify80.0ms (0.8%)

prune318.0ms (3.2%)

localize44.0ms (0.4%)

rewrite28.0ms (0.3%)

series421.0ms (4.2%)

simplify62.0ms (0.6%)

prune263.0ms (2.6%)

simplify123.0ms (1.2%)

regimes373.0ms (3.7%)

bsearch0.0ms (0%)

regimes202.0ms (2%)

bsearch0.0ms (0%)

regimes96.0ms (1%)

bsearch0.0ms (0%)

regimes78.0ms (0.8%)

bsearch0.0ms (0%)

regimes32.0ms (0.3%)

bsearch0.0ms (0%)

regimes29.0ms (0.3%)

bsearch0.0ms (0%)

regimes9.0ms (0.1%)

bsearch12.0ms (0.1%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample5.5s (54.7%)

Profiling