Details

analyze10.0ms

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

53.0ms	256×	body	80	valid
3.0ms	262×	pre	80	true
1.0ms	6×	body	80	invalid

simplify157.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (144.0ms)

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: 2.8b

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))
0.6b	(*.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)
2.6b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite82.0ms

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))
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))

series640.0ms

Counts

4 → 10

Calls

4 calls:

72.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
515.0ms	(*.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)
53.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

simplify140.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4925	6085
1	4925	6085

prune330.0ms

Filtered

97 candidates to 141 candidates (-45.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	122	19	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	19	143

Merged error: 0.7b

Counts

143 → 19

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))
0.6b	(*.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)
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite88.0ms

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))
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)
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series864.0ms

Counts

4 → 10

Calls

4 calls:

151.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
591.0ms	(*.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)
123.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify126.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5472	9229

prune416.0ms

Filtered

132 candidates to 205 candidates (-55.3%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	182	23	205
Fresh	12	6	18
Picked	1	0	1
Done	0	0	0
Total	195	29	224

Merged error: 0.2b

Counts

224 → 29

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
27×	`unpow-prod-down_binary64` `sqrt-prod_binary64`
26×	`pow-unpow_binary64`
9×	`sqr-pow_binary64`
8×	`pow-pow_binary64` `add-exp-log_binary64`
7×	`pow1_binary64` `associate-/l*_binary64`
6×	`associate-/r*_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 142

Calls

4 calls:

6.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0ms	(sqrt.f64 PI.f64)

series435.0ms

Counts

4 → 10

Calls

4 calls:

166.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
131.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
137.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)

simplify75.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5361	3335

prune392.0ms

Filtered

109 candidates to 152 candidates (-39.4%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	140	12	152
Fresh	10	18	28
Picked	1	0	1
Done	0	0	0
Total	151	30	181

Merged error: 0.2b

Counts

181 → 30

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow_binary64` `add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`pow1_binary64` `pow-pow_binary64`
6×	`unpow-prod-down_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 86

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series266.0ms

Counts

4 → 8

Calls

4 calls:

133.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
132.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify131.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4917	1144
1	4917	1144

prune182.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	3	26	29
Picked	0	1	1
Done	0	0	0
Total	93	31	124

Merged error: 0.1b

Counts

124 → 31

regimes222.0ms

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	39	85
1	39	85

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
87.0ms	8124×	pre	80	true
27.0ms	124×	body	80	invalid

Details

analyze10.0ms

sample67.0ms

simplify157.0ms

prune9.0ms

localize24.0ms

rewrite82.0ms

series640.0ms

simplify140.0ms

prune330.0ms

localize27.0ms

rewrite88.0ms

series864.0ms

simplify126.0ms

prune416.0ms

localize31.0ms

rewrite22.0ms

series435.0ms

simplify75.0ms

prune392.0ms

localize34.0ms

rewrite14.0ms

series266.0ms

simplify131.0ms

prune182.0ms

regimes222.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling