Details

analyze9.0ms

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

sample67.0ms

Algorithm

intervals

Results

52.0ms	256×	body	80	valid
3.0ms	259×	pre	80	true
1.0ms	3×	body	80	invalid

simplify165.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4938	55
1	4938	55

prune9.0ms

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: 2.3b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))
0.4b	(*.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)
2.3b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`
46×	`add-cube-cbrt_binary64`
22×	`associate-l_binary64`
18×	`frac-add_binary64`
15×	`unpow-prod-down_binary64`
13×	`add-exp-log_binary64` `sqrt-prod_binary64`
12×	`associate-/r*_binary64` `distribute-lft-out_binary64` `cube-prod_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-r_binary64` `exp-prod_binary64`
7×	`pow1_binary64` `associate-*r/_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
5×	`add-log-exp_binary64` `sqr-pow_binary64`
4×	`div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`unswap-sqr_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `unpow2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 157

Calls

4 calls:

6.0ms	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))
68.0ms	(*.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))))
1.0ms	(sqrt.f64 PI.f64)
3.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

series631.0ms

Counts

4 → 10

Calls

4 calls:

66.0ms	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))
519.0ms	(*.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)
46.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

simplify98.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4999	6077
1	4999	6077

prune343.0ms

Filtered

103 candidates to 167 candidates (-62.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	150	17	167
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	17	169

Merged error: 0.6b

Counts

169 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))
0.4b	(*.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))))
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac_binary64`
81×	`*-un-lft-identity_binary64`
80×	`add-sqr-sqrt_binary64`
61×	`add-cube-cbrt_binary64`
46×	`associate-l_binary64`
35×	`unpow-prod-down_binary64`
27×	`sqrt-prod_binary64`
18×	`frac-add_binary64` `add-exp-log_binary64`
13×	`sqr-pow_binary64`
12×	`associate-/r*_binary64` `distribute-lft-out_binary64` `cube-prod_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`associate-*r/_binary64` `unswap-sqr_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `prod-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-exp_binary64` `exp-prod_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 191

Calls

4 calls:

6.0ms	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))
69.0ms	(*.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))))
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)

series795.0ms

Counts

4 → 10

Calls

4 calls:

70.0ms	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))
602.0ms	(*.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))))
123.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify141.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4975	8242
1	4975	8242

prune419.0ms

Filtered

128 candidates to 201 candidates (-57.0%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	183	18	201
Fresh	14	2	16
Picked	0	1	1
Done	0	0	0
Total	197	21	218

Merged error: 0.2b

Counts

218 → 21

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (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	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

70.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (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))))
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series728.0ms

Counts

4 → 8

Calls

4 calls:

608.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (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))))
119.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify114.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4938	4891
1	4938	4891

prune247.0ms

Filtered

74 candidates to 113 candidates (-52.7%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	18	19
Picked	0	1	1
Done	0	1	1
Total	113	21	134

Merged error: 0.2b

Counts

134 → 21

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)
1.0b	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
1.0b	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
19×	`pow1_binary64`
14×	`*-un-lft-identity_binary64` `pow1/3_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-pow1_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `pow-prod-up_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `pow-sqr_binary64`
2×	`pow-plus_binary64` `pow2_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)
6.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
4.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
0.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))

simplify92.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4939	909
1	4939	909

prune139.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	18	18
Picked	0	1	1
Done	0	2	2
Total	83	23	106

Merged error: 0.2b

Counts

106 → 23

regimes174.0ms

Accuracy

0% (1.0b remaining)

Error of 1.3b against oracle of 0.3b and baseline of 1.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	67
1	34	67

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
92.0ms	8106×	pre	80	true
22.0ms	106×	body	80	invalid

Details

analyze9.0ms

sample67.0ms

simplify165.0ms

prune9.0ms

localize24.0ms

rewrite85.0ms

series631.0ms

simplify98.0ms

prune343.0ms

localize27.0ms

rewrite88.0ms

series795.0ms

simplify141.0ms

prune419.0ms

localize31.0ms

rewrite80.0ms

series728.0ms

simplify114.0ms

prune247.0ms

localize37.0ms

rewrite15.0ms

series0.0ms

simplify92.0ms

prune139.0ms

regimes174.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling