Details

analyze235.0ms

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

sample17.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
0.0ms	8×	body	80	invalid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	110	11
1	110	11

prune5.0ms

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: 7.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.1b	(.f64 y (+.f64 1 (.f64 z z)))
4.8b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`div-exp_binary64`
6×	`cbrt-undiv_binary64`
5×	`prod-exp_binary64`
4×	`pow1_binary64` `associate-*r/_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `1-exp_binary64` `associate-/r/_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

2 → 74

Calls

2 calls:

6.0ms	(.f64 y (+.f64 1 (.f64 z z)))
9.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

series28.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(.f64 y (+.f64 1 (.f64 z z)))
18.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5072	883

prune69.0ms

Filtered

51 candidates to 80 candidates (-56.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Merged error: 4.6b

Counts

81 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 x)
0.8b	(/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z)))
3.2b	(/.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 y (/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z)))))
3.5b	(/.f64 y (/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z))))

rewrite549.0ms

Algorithm

rewrite-expression-head

Rules

10225×	`times-frac_binary64`
3971×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2523×	`cbrt-prod_binary64`
512×	`associate-/r*_binary64`
485×	`div-inv_binary64`
120×	`add-exp-log_binary64`
75×	`cbrt-undiv_binary64` `div-exp_binary64`
74×	`add-cbrt-cube_binary64`
54×	`associate-/r/_binary64`
48×	`associate-/l*_binary64`
23×	`flip3-+_binary64` `flip-+_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/l/_binary64`
1×	`pow1/3_binary64`

Counts

4 → 3070

Calls

4 calls:

1.0ms	(cbrt.f64 x)
13.0ms	(/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z)))
99.0ms	(/.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 y (/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z)))))
27.0ms	(/.f64 y (/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 x)
34.0ms	(/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z)))
21.0ms	(/.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 y (/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z)))))
45.0ms	(/.f64 y (/.f64 (/.f64 (cbrt.f64 1) (cbrt.f64 x)) (+.f64 1 (*.f64 z z))))

simplify813.0ms

Algorithm

egg-herbie

Counts

3082 → 3082

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5162	135259

prune25.0s

Filtered

2540 candidates to 3082 candidates (-21.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	3082	0	3082
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	3082	7	3089

Merged error: 4.6b

Counts

3089 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (/.f64 1 x))
0.8b	(/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z)))
3.2b	(/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 y (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (.f64 z z)))))
3.5b	(/.f64 y (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

1496×	`times-frac_binary64`
635×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
455×	`cbrt-prod_binary64`
224×	`associate-/r*_binary64`
50×	`div-inv_binary64`
32×	`add-exp-log_binary64`
26×	`associate-/r/_binary64`
22×	`add-cbrt-cube_binary64`
20×	`associate-/l*_binary64`
16×	`cbrt-undiv_binary64` `div-exp_binary64`
11×	`flip3-+_binary64` `flip-+_binary64`
6×	`cbrt-div_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64`
3×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`associate-r/_binary64` `pow1/3_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 699

Calls

4 calls:

3.0ms	(cbrt.f64 (/.f64 1 x))
8.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z)))
37.0ms	(/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 y (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (.f64 z z)))))
19.0ms	(/.f64 y (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 (/.f64 1 x))
30.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z)))
23.0ms	(/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 y (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (.f64 z z)))))
57.0ms	(/.f64 y (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z))))

simplify130.0ms

Algorithm

egg-herbie

Counts

711 → 711

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5267	17490

prune1.6s

Filtered

542 candidates to 711 candidates (-31.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	710	1	711
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	710	8	718

Merged error: 4.6b

Counts

718 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b	(/.f64 (cbrt.f64 y) (/.f64 (cbrt.f64 (/.f64 (cbrt.f64 1) x)) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
1.3b	(/.f64 (cbrt.f64 (/.f64 1 x)) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (sqrt.f64 (+.f64 1 (*.f64 z z))))))
14.1b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
14.1b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

4544×	`times-frac_binary64`
2343×	`cbrt-prod_binary64`
1827×	`add-sqr-sqrt_binary64`
1825×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
735×	`sqrt-prod_binary64`
191×	`associate-/r*_binary64`
121×	`div-inv_binary64`
67×	`associate-/r/_binary64`
52×	`sqrt-div_binary64`
27×	`add-exp-log_binary64`
26×	`flip3-+_binary64` `flip-+_binary64`
22×	`associate-/l*_binary64`
14×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`cbrt-div_binary64` `associate-/l/_binary64`

Counts

4 → 1776

Calls

4 calls:

48.0ms	(/.f64 (cbrt.f64 y) (/.f64 (cbrt.f64 (/.f64 (cbrt.f64 1) x)) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
28.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (sqrt.f64 (+.f64 1 (*.f64 z z))))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 (cbrt.f64 y) (/.f64 (cbrt.f64 (/.f64 (cbrt.f64 1) x)) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
54.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (sqrt.f64 (+.f64 1 (*.f64 z z))))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify428.0ms

Algorithm

egg-herbie

Counts

1788 → 1788

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5205	62754

prune9.4s

Filtered

1023 candidates to 1788 candidates (-74.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	1788	0	1788
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	1788	8	1796

Merged error: 4.6b

Counts

1796 → 8

regimes382.0ms

Accuracy

0% (1.0b remaining)

Error of 5.8b against oracle of 4.9b and baseline of 5.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	45
1	26	45

end0.0ms

sample513.0ms

Algorithm

intervals

Results

311.0ms	8000×	body	80	valid
17.0ms	453×	body	80	invalid

Details

analyze235.0ms

sample17.0ms

simplify7.0ms

prune5.0ms

localize7.0ms

rewrite17.0ms

series28.0ms

simplify49.0ms

prune69.0ms

localize14.0ms

rewrite549.0ms

series116.0ms

simplify813.0ms

prune25.0s

localize11.0ms

rewrite132.0ms

series125.0ms

simplify130.0ms

prune1.6s

localize28.0ms

rewrite294.0ms

series100.0ms

simplify428.0ms

prune9.4s

regimes382.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample513.0ms

Profiling