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

sample67.0ms

Algorithm

intervals

Results

55.0ms	256×	body	80	valid
3.0ms	263×	pre	80	true
1.0ms	7×	body	80	invalid

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	5067	34

prune8.0ms

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: 2.5b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 3/4 (pow.f64 (fabs.f64 x) 5))
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)
2.5b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
45×	`times-frac_binary64`
37×	`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×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-r_binary64` `exp-prod_binary64`
7×	`associate-/r_binary64` `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`
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 → 137

Calls

4 calls:

5.0ms	(/.f64 3/4 (pow.f64 (fabs.f64 x) 5))
65.0ms	(*.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))

series134.0ms

Counts

4 → 10

Calls

4 calls:

19.0ms	(/.f64 3/4 (pow.f64 (fabs.f64 x) 5))
107.0ms	(*.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)
8.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4935	3583
1	4935	3583

prune280.0ms

Filtered

104 candidates to 147 candidates (-41.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	126	21	147
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	21	149

Merged error: 0.7b

Counts

149 → 21

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 3/4 (pow.f64 (fabs.f64 x) 5))
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))))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac_binary64`
72×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
52×	`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×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`associate-/r_binary64` `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`
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 → 171

Calls

4 calls:

5.0ms	(/.f64 3/4 (pow.f64 (fabs.f64 x) 5))
68.0ms	(*.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))))
1.0ms	(sqrt.f64 PI.f64)
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series168.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(/.f64 3/4 (pow.f64 (fabs.f64 x) 5))
126.0ms	(*.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))))
0.0ms	(sqrt.f64 PI.f64)
23.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify61.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5488	4966

prune280.0ms

Filtered

123 candidates to 181 candidates (-47.2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	164	17	181
Fresh	14	6	20
Picked	1	0	1
Done	0	0	0
Total	179	23	202

Merged error: 0.3b

Counts

202 → 23

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(.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	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite76.0ms

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:

66.0ms	(.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))))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series144.0ms

Counts

4 → 8

Calls

4 calls:

122.0ms	(.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))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)
22.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify51.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5235	3058

prune171.0ms

Filtered

71 candidates to 113 candidates (-59.2%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	3	19	22
Picked	0	1	1
Done	0	0	0
Total	112	24	136

Merged error: 0.3b

Counts

136 → 24

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.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))) (sqrt.f64 PI.f64))
0.3b	(*.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.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))) (sqrt.f64 PI.f64)))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

318×	`*-un-lft-identity_binary64`
156×	`distribute-lft-out_binary64`
154×	`times-frac_binary64`
80×	`add-sqr-sqrt_binary64`
58×	`add-cube-cbrt_binary64`
57×	`sqrt-prod_binary64`
52×	`associate-r_binary64`
17×	`add-exp-log_binary64`
15×	`div-inv_binary64`
11×	`add-cbrt-cube_binary64`
9×	`frac-add_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
8×	`associate-/l*_binary64`
7×	`associate-/l/_binary64` `associate-l_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `prod-exp_binary64`
5×	`sqr-pow_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `div-exp_binary64`
3×	`pow-to-exp_binary64` `flip3-+_binary64` `pow-unpow_binary64` `flip-+_binary64` `pow-exp_binary64` `exp-prod_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64`
1×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 199

Calls

4 calls:

59.0ms	(/.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))) (sqrt.f64 PI.f64))
72.0ms	(*.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.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))) (sqrt.f64 PI.f64)))
1.0ms	(sqrt.f64 PI.f64)
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series230.0ms

Counts

4 → 10

Calls

4 calls:

82.0ms	(/.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))) (sqrt.f64 PI.f64))
125.0ms	(*.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.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))) (sqrt.f64 PI.f64)))
0.0ms	(sqrt.f64 PI.f64)
23.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify79.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4992	6022
1	4992	6022

prune203.0ms

Filtered

97 candidates to 209 candidates (-115.5%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	201	8	209
Fresh	6	16	22
Picked	0	1	1
Done	1	0	1
Total	208	25	233

Merged error: 0.2b

Counts

233 → 25

regimes201.0ms

Accuracy

0% (1.0b 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	32	40
1	32	40

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
90.0ms	8119×	pre	80	true
23.0ms	119×	body	80	invalid

Details

analyze8.0ms

sample67.0ms

simplify109.0ms

prune8.0ms

localize23.0ms

rewrite85.0ms

series134.0ms

simplify56.0ms

prune280.0ms

localize27.0ms

rewrite85.0ms

series168.0ms

simplify61.0ms

prune280.0ms

localize28.0ms

rewrite76.0ms

series144.0ms

simplify51.0ms

prune171.0ms

localize29.0ms

rewrite148.0ms

series230.0ms

simplify79.0ms

prune203.0ms

regimes201.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling