Details

analyze10.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample24.0ms

Algorithm

intervals

Results

9.0ms	66×	body	1280	valid
4.0ms	36×	body	640	valid
4.0ms	125×	body	80	valid
1.0ms	12×	body	320	valid
1.0ms	17×	body	160	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	1001	13
1	1001	13

prune2.0ms

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: 30.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 x 1.0) (-.f64 x 1.0))
3.8b	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
18×	`distribute-lft-out--_binary64`
14×	`distribute-lft-out_binary64`
13×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64`
5×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`

Counts

2 → 70

Calls

2 calls:

11.0ms	(/.f64 (+.f64 x 1.0) (-.f64 x 1.0))
32.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

series13.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(/.f64 (+.f64 x 1.0) (-.f64 x 1.0))
9.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

simplify35.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5024	1087

prune102.0ms

Filtered

50 candidates to 76 candidates (-52.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Merged error: 0.2b

Counts

77 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1.0 x) 3.0)
0.2b	(/.f64 3.0 (pow.f64 x 3))
0.2b	(*.f64 (/.f64 -1 x) (+.f64 (/.f64 1.0 x) 3.0))
8.8b	(-.f64 (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1.0 x) 3.0)) (/.f64 3.0 (pow.f64 x 3)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`
12×	`associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64`
5×	`flip3-+_binary64` `flip-+_binary64` `frac-sub_binary64`
4×	`associate-r_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-exp_binary64` `frac-times_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`associate-/l*_binary64`
2×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

7.0ms	(+.f64 (/.f64 1.0 x) 3.0)
8.0ms	(/.f64 3.0 (pow.f64 x 3))
13.0ms	(*.f64 (/.f64 -1 x) (+.f64 (/.f64 1.0 x) 3.0))
20.0ms	(-.f64 (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1.0 x) 3.0)) (/.f64 3.0 (pow.f64 x 3)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1.0 x) 3.0)
6.0ms	(/.f64 3.0 (pow.f64 x 3))
9.0ms	(*.f64 (/.f64 -1 x) (+.f64 (/.f64 1.0 x) 3.0))
5.0ms	(-.f64 (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1.0 x) 3.0)) (/.f64 3.0 (pow.f64 x 3)))

simplify42.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5256	1609

prune159.0ms

Filtered

95 candidates to 146 candidates (-53.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	144	5	149

Merged error: 0.1b

Counts

149 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1.0 x) 3.0)
0.1b	(/.f64 (neg.f64 (+.f64 (/.f64 1.0 x) 3.0)) x)
0.2b	(/.f64 3.0 (pow.f64 x 3))
8.8b	(-.f64 (/.f64 (neg.f64 (+.f64 (/.f64 1.0 x) 3.0)) x) (/.f64 3.0 (pow.f64 x 3)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac_binary64`
87×	`*-un-lft-identity_binary64`
85×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`distribute-rgt-neg-in_binary64`
16×	`distribute-lft-neg-in_binary64`
15×	`associate-/r_binary64` `associate-/l_binary64`
14×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-exp-log_binary64`
10×	`distribute-lft-out_binary64` `difference-of-squares_binary64`
8×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
6×	`sqr-pow_binary64`
4×	`pow1_binary64` `neg-mul-1_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `distribute-neg-frac_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `frac-sub_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 171

Calls

4 calls:

8.0ms	(+.f64 (/.f64 1.0 x) 3.0)
12.0ms	(/.f64 (neg.f64 (+.f64 (/.f64 1.0 x) 3.0)) x)
6.0ms	(/.f64 3.0 (pow.f64 x 3))
75.0ms	(-.f64 (/.f64 (neg.f64 (+.f64 (/.f64 1.0 x) 3.0)) x) (/.f64 3.0 (pow.f64 x 3)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1.0 x) 3.0)
9.0ms	(/.f64 (neg.f64 (+.f64 (/.f64 1.0 x) 3.0)) x)
5.0ms	(/.f64 3.0 (pow.f64 x 3))
5.0ms	(-.f64 (/.f64 (neg.f64 (+.f64 (/.f64 1.0 x) 3.0)) x) (/.f64 3.0 (pow.f64 x 3)))

simplify55.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4943	2284
1	4943	2284

prune156.0ms

Filtered

108 candidates to 183 candidates (-69.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	183	5	188

Merged error: 0.1b

Counts

188 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0))))
3.8b	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))
3.8b	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))
3.8b	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

189×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
52×	`distribute-lft-out--_binary64`
32×	`distribute-lft-out_binary64`
16×	`difference-of-squares_binary64` `cbrt-prod_binary64`
10×	`add-log-exp_binary64`
5×	`add-cube-cbrt_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `frac-sub_binary64`
3×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64`
1×	`pow1/3_binary64`

Counts

4 → 102

Calls

4 calls:

30.0ms	(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0))))
35.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))
32.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))
34.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0))))
9.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))
9.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))
12.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4989	2272
1	4989	2272

prune170.0ms

Filtered

74 candidates to 114 candidates (-54.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	114	5	119

Merged error: 0.0b

Counts

119 → 5

regimes76.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.0b

bsearch22.0ms

Steps

Iters	Range		Point
7	12302.25956354686	381651.6294982458	15314.37957646558
9	-30114.87532477197	-0.16605346141893446	-11903.191960040664

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	116	69
1	116	69

end0.0ms

sample680.0ms

Algorithm

intervals

Results

247.0ms	1698×	body	1280	valid
137.0ms	1201×	body	640	valid
126.0ms	4139×	body	80	valid
58.0ms	628×	body	320	valid
20.0ms	334×	body	160	valid

Details

analyze10.0ms

sample24.0ms

simplify98.0ms

prune2.0ms

localize6.0ms

rewrite46.0ms

series13.0ms

simplify35.0ms

prune102.0ms

localize10.0ms

rewrite53.0ms

series24.0ms

simplify42.0ms

prune159.0ms

localize9.0ms

rewrite108.0ms

series24.0ms

simplify55.0ms

prune156.0ms

localize10.0ms

rewrite138.0ms

series47.0ms

simplify49.0ms

prune170.0ms

regimes76.0ms

bsearch22.0ms

simplify3.0ms

end0.0ms

sample680.0ms

Profiling