Details

analyze8.0ms

Algorithm

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

sample70.0ms

Algorithm

intervals

Results

58.0ms	256×	body	80	valid
3.0ms	258×	pre	80	true
0.0ms	2×	body	80	invalid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5067	34

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 2.1b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))
0.3b	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
2.1b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
22×	`associate-l_binary64`
21×	`add-cube-cbrt_binary64`
19×	`frac-add_binary64`
15×	`distribute-lft-out_binary64`
13×	`sqrt-prod_binary64`
9×	`add-cbrt-cube_binary64`
8×	`associate-r_binary64` `add-exp-log_binary64` `exp-prod_binary64`
7×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-*r/_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

29.0ms	(+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))
67.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
2.0ms	(sqrt.f64 PI.f64)
6.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

series138.0ms

Counts

4 → 10

Calls

4 calls:

21.0ms	(+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))
106.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.0ms	(sqrt.f64 PI.f64)
11.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5859	3416

prune293.0ms

Filtered

82 candidates to 117 candidates (-42.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	97	20	117
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	99	20	119

Merged error: 0.6b

Counts

119 → 20

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))
0.3b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.9b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
46×	`associate-l_binary64`
36×	`add-cube-cbrt_binary64`
27×	`sqrt-prod_binary64`
23×	`unpow-prod-down_binary64`
19×	`frac-add_binary64`
15×	`distribute-lft-out_binary64`
13×	`add-exp-log_binary64`
9×	`sqr-pow_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64`
6×	`add-log-exp_binary64`
4×	`pow-pow_binary64` `prod-exp_binary64`
3×	`pow-unpow_binary64` `div-inv_binary64` `div-exp_binary64` `exp-prod_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 141

Calls

4 calls:

27.0ms	(+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))
71.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

series165.0ms

Counts

4 → 10

Calls

4 calls:

20.0ms	(+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))
122.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
23.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify57.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5194	4712

prune325.0ms

Filtered

99 candidates to 151 candidates (-52.5%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	127	24	151
Fresh	15	4	19
Picked	0	1	1
Done	0	0	0
Total	142	29	171

Merged error: 0.2b

Counts

171 → 29

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp.f64 (log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))))
0.5b	(log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
0.9b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
12×	`log-prod_binary64` `add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
7×	`exp-prod_binary64`
6×	`distribute-lft-out_binary64` `exp-sum_binary64` `log-div_binary64`
5×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
3×	`pow-unpow_binary64` `exp-diff_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `log-pow_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `pow-exp_binary64`

Counts

4 → 72

Calls

4 calls:

28.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))))
27.0ms	(log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

series87.0ms

Counts

4 → 10

Calls

4 calls:

21.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3)))))
42.0ms	(log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
25.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify57.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5138	889

prune186.0ms

Filtered

48 candidates to 82 candidates (-70.8%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	8	19	27
Picked	1	0	1
Done	1	0	1
Total	84	27	111

Merged error: 0.1b

Counts

111 → 27

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
0.9b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`log-prod_binary64` `sqrt-prod_binary64`
5×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `distribute-lft-out_binary64` `unpow-prod-down_binary64` `log-div_binary64` `exp-prod_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `times-frac_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `rem-log-exp_binary64` `frac-add_binary64` `log-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 64

Calls

4 calls:

29.0ms	(log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series66.0ms

Counts

4 → 8

Calls

4 calls:

43.0ms	(log.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
23.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify73.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4968	597
1	4968	597

prune91.0ms

Filtered

47 candidates to 72 candidates (-53.2%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	25	26
Picked	0	1	1
Done	0	0	0
Total	70	29	99

Merged error: 0.1b

Counts

99 → 29

regimes281.0ms

Accuracy

0% (1.1b remaining)

Error of 1.3b against oracle of 0.2b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	42
1	34	42

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
92.0ms	8112×	pre	80	true
23.0ms	112×	body	80	invalid

Details

analyze8.0ms

sample70.0ms

simplify101.0ms

prune11.0ms

localize22.0ms

rewrite108.0ms

series138.0ms

simplify67.0ms

prune293.0ms

localize27.0ms

rewrite111.0ms

series165.0ms

simplify57.0ms

prune325.0ms

localize31.0ms

rewrite65.0ms

series87.0ms

simplify57.0ms

prune186.0ms

localize33.0ms

rewrite38.0ms

series66.0ms

simplify73.0ms

prune91.0ms

regimes281.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling