Details

analyze2.6s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

sample103.0ms

Algorithm

intervals

Results

46.0ms	447×	body	80	nan
24.0ms	256×	body	80	valid
3.0ms	35×	body	80	invalid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5485	39

prune5.0ms

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: 30.3b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

5.9b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
6.5b	(.f64 (/.f64 l Om) (-.f64 U U))
9.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
19.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
16×	`pow-prod-down_binary64` `*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
10×	`times-frac_binary64`
9×	`associate-r_binary64`
6×	`sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64` `frac-times_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

11.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
10.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series3.0s

Counts

4 → 12

Calls

4 calls:

92.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
54.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
439.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
2.4s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5128	2913

prune131.0ms

Filtered

77 candidates to 121 candidates (-57.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	8	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 22.5b

Counts

123 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
14.7b	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
14.7b	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
19.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U))) (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))) (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U))))))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-div_binary64`
14×	`pow1_binary64`
8×	`associate-*r/_binary64`
6×	`pow-prod-down_binary64` `flip3--_binary64` `flip--_binary64` `frac-times_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `add-sqr-sqrt_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64` `associate-*l/_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-prod_binary64` `flip-+_binary64`

Counts

4 → 57

Calls

4 calls:

7.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
7.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
7.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U))) (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))) (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U))))))))))

series2.8s

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
150.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
146.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
2.3s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U))) (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))) (cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U))))))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5018	1636

prune95.0ms

Filtered

59 candidates to 69 candidates (-16.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	69	9	78

Merged error: 22.5b

Counts

78 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

19.9b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
21.0b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
21.0b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
21.0b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

68×	`associate-*r/_binary64`
60×	`cbrt-div_binary64`
30×	`flip3-+_binary64` `flip-+_binary64`
28×	`frac-times_binary64`
26×	`sqrt-div_binary64`
24×	`pow1_binary64`
15×	`sqrt-pow1_binary64`
14×	`associate-*l/_binary64`
12×	`pow1/3_binary64`
9×	`pow-prod-up_binary64`
6×	`pow-plus_binary64`
5×	`pow-prod-down_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`pow-sqr_binary64` `cbrt-prod_binary64`
2×	`pow2_binary64`
1×	`pow1/2_binary64` `pow3_binary64` `sqrt-prod_binary64`

Counts

4 → 83

Calls

4 calls:

14.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
7.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
9.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
7.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series5.4s

Counts

4 → 12

Calls

4 calls:

2.2s	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
1.0s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.1s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.1s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4985	8687
1	4985	8687

prune184.0ms

Filtered

61 candidates to 95 candidates (-55.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	7	7
Picked	1	0	1
Done	1	0	1
Total	96	8	104

Merged error: 22.5b

Counts

104 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

9.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
9.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
21.0b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
21.0b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
8×	`associate-*r/_binary64`
6×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`cbrt-div_binary64` `flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
2×	`pow1/3_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `cbrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
12.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
7.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series3.0s

Counts

4 → 12

Calls

4 calls:

453.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
449.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
1.1s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.0s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify123.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4987	3628
1	4987	3628

prune126.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	84	8	92

Merged error: 22.5b

Counts

92 → 8

regimes300.0ms

Accuracy

50.2% (4.5b remaining)

Error of 26.5b against oracle of 22.0b and baseline of 31.0b

bsearch1.0ms

simplify21.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	616	302
1	616	302

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	12922×	body	80	nan
774.0ms	8000×	body	80	valid
127.0ms	1196×	body	80	invalid

Details

analyze2.6s

sample103.0ms

simplify76.0ms

prune5.0ms

localize17.0ms

rewrite42.0ms

series3.0s

simplify91.0ms

prune131.0ms

localize25.0ms

rewrite29.0ms

series2.8s

simplify45.0ms

prune95.0ms

localize25.0ms

rewrite43.0ms

series5.4s

simplify121.0ms

prune184.0ms

localize22.0ms

rewrite39.0ms

series3.0s

simplify123.0ms

prune126.0ms

regimes300.0ms

bsearch1.0ms

simplify21.0ms

end0.0ms

sample2.9s

Profiling