Details

analyze423.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample40.0ms

Algorithm

intervals

Results

11.0ms	29×	body	2560	valid
8.0ms	176×	body	80	valid
6.0ms	25×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	21×	body	80	nan
0.0ms	8×	body	80	invalid
0.0ms	2×	body	160	valid

simplify624.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	715	20
1	715	20

prune3.0ms

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: 32.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
30.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
56.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
85.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4936	2470
1	4936	2470

prune96.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 6.8b

Counts

102 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac_binary64`
130×	`add-sqr-sqrt_binary64`
129×	`*-un-lft-identity_binary64`
77×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 175

Calls

4 calls:

16.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
30.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
58.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5112	5825

prune108.0ms

Filtered

103 candidates to 187 candidates (-81.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	186	9	195

Merged error: 6.7b

Counts

195 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.3b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
14.6b	(/.f64 (*.f64 a c) a)
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(/.f64 (*.f64 a c) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series152.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
57.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
9.0ms	(/.f64 (*.f64 a c) a)
60.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify90.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4855	967
1	4855	967

prune55.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	73	10	83

Merged error: 6.7b

Counts

83 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.3b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `distribute-rgt-neg-in_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

12.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
30.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
54.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
52.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify95.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5693	1819

prune55.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	91	9	100

Merged error: 6.7b

Counts

100 → 9

regimes144.0ms

Accuracy

94.4% (1.3b remaining)

Error of 7.1b against oracle of 5.7b and baseline of 29.5b

bsearch88.0ms

Steps

Iters	Range	Point
9	8.503045764242374e+102	7.043841452833814e+109	5.6105067610822575e+109
7	-9.595061259999025e-284	-6.432522803495987e-286	-6.551604594892804e-286
9	-3.1849173062266785e+52	-1.883271180546939e+47	-3.1444647779955165e+52

Iters

Range

Point

8.503045764242374e+102

7.043841452833814e+109

5.6105067610822575e+109

-9.595061259999025e-284

-6.432522803495987e-286

-6.551604594892804e-286

-3.1849173062266785e+52

-1.883271180546939e+47

-3.1444647779955165e+52

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	87	76
1	87	76

end0.0ms

sample1.1s

Algorithm

intervals

Results

263.0ms	1027×	body	2560	valid
233.0ms	5175×	body	80	valid
191.0ms	915×	body	1280	valid
78.0ms	449×	body	640	valid
34.0ms	220×	body	320	valid
33.0ms	106×	body	5120	valid
32.0ms	734×	body	80	nan
11.0ms	261×	body	80	invalid
9.0ms	108×	body	160	valid

Details

analyze423.0ms

sample40.0ms

simplify624.0ms

prune3.0ms

localize11.0ms

rewrite36.0ms

series252.0ms

simplify101.0ms

prune96.0ms

localize11.0ms

rewrite43.0ms

series262.0ms

simplify106.0ms

prune108.0ms

localize11.0ms

rewrite22.0ms

series152.0ms

simplify90.0ms

prune55.0ms

localize9.0ms

rewrite31.0ms

series315.0ms

simplify95.0ms

prune55.0ms

regimes144.0ms

bsearch88.0ms

simplify5.0ms

end0.0ms

sample1.1s

Profiling