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

sample69.0ms

Algorithm

intervals

Results

57.0ms	256×	body	80	valid
3.0ms	261×	pre	80	true
1.0ms	5×	body	80	invalid

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

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: 2.6b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
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)
2.5b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
22×	`associate-l_binary64`
18×	`frac-add_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`associate-r_binary64` `exp-prod_binary64`
7×	`pow1_binary64` `associate-*r/_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
5×	`add-log-exp_binary64`
3×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `unpow2_binary64` `sqr-pow_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` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 131

Calls

4 calls:

7.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
61.0ms	(*.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))

series131.0ms

Counts

4 → 10

Calls

4 calls:

14.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
104.0ms	(*.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)
12.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5616	3722

prune247.0ms

Filtered

97 candidates to 141 candidates (-45.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	124	17	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	17	143

Merged error: 0.8b

Counts

143 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

94×	`times-frac_binary64`
86×	`*-un-lft-identity_binary64`
85×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
51×	`sqrt-prod_binary64`
46×	`associate-l_binary64`
44×	`unpow-prod-down_binary64`
18×	`frac-add_binary64`
17×	`add-exp-log_binary64`
16×	`sqr-pow_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`associate-r/_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `associate-/r*_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` `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 → 195

Calls

4 calls:

6.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
67.0ms	(*.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))

series173.0ms

Counts

4 → 10

Calls

4 calls:

31.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
120.0ms	(*.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)
22.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify65.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5475	5571

prune318.0ms

Filtered

133 candidates to 205 candidates (-54.1%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	182	23	205
Fresh	10	6	16
Picked	1	0	1
Done	0	0	0
Total	193	29	222

Merged error: 0.3b

Counts

222 → 29

localize32.0ms

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

rewrite75.0ms

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:

65.0ms	(.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)
2.0ms	(sqrt.f64 PI.f64)
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series142.0ms

Counts

4 → 8

Calls

4 calls:

120.0ms	(.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))

simplify50.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5235	3058

prune188.0ms

Filtered

73 candidates to 113 candidates (-54.8%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	1	27	28
Picked	0	1	1
Done	0	0	0
Total	111	31	142

Merged error: 0.3b

Counts

142 → 31

localize30.0ms

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))

rewrite139.0ms

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:

55.0ms	(/.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))
67.0ms	(*.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))

series224.0ms

Counts

4 → 10

Calls

4 calls:

81.0ms	(/.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))
120.0ms	(*.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)
22.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify76.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4992	6022
1	4992	6022

prune201.0ms

Filtered

98 candidates to 209 candidates (-113.3%)

Pruning

35 alts after pruning (33 fresh and 2 done)

	Pruned	Kept	Total
New	194	15	209
Fresh	11	18	29
Picked	0	1	1
Done	0	1	1
Total	205	35	240

Merged error: 0.2b

Counts

240 → 35

regimes252.0ms

Accuracy

0% (1.0b remaining)

Error of 1.2b against oracle of 0.2b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	40
1	32	40

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
93.0ms	8124×	pre	80	true
27.0ms	124×	body	80	invalid

Details

analyze8.0ms

sample69.0ms

simplify103.0ms

prune8.0ms

localize24.0ms

rewrite79.0ms

series131.0ms

simplify67.0ms

prune247.0ms

localize27.0ms

rewrite86.0ms

series173.0ms

simplify65.0ms

prune318.0ms

localize32.0ms

rewrite75.0ms

series142.0ms

simplify50.0ms

prune188.0ms

localize30.0ms

rewrite139.0ms

series224.0ms

simplify76.0ms

prune201.0ms

regimes252.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling