Details

analyze2.3s

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

sample87.0ms

Algorithm

intervals

Results

33.0ms	352×	body	128	nan
24.0ms	256×	body	128	valid
3.0ms	30×	body	128	invalid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5484	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: 28.4b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

4.9b	(.f64 (/.f64 l Om) (-.f64 U U))
6.8b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
8.7b	(.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)))))))
19.1b	(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))))))))

rewrite51.0ms

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 (/.f64 l Om) (-.f64 U U))
11.0ms	(.f64 n (.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)))))))
8.0ms	(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))))))))

series4.6s

Counts

4 → 12

Calls

4 calls:

119.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
194.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
777.0ms	(.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)))))))
3.5s	(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))))))))

simplify76.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5099	2919

prune143.0ms

Filtered

77 candidates to 121 candidates (-57.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 21.9b

Counts

123 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

6.6b	(*.f64 n (/.f64 l Om))
6.6b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
8.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
19.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

8.0ms	(*.f64 n (/.f64 l Om))
14.0ms	(.f64 (.f64 n (/.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 (.f64 n (/.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 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

series4.6s

Counts

4 → 12

Calls

4 calls:

33.0ms	(*.f64 n (/.f64 l Om))
209.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
809.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
3.6s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5015	2697

prune115.0ms

Filtered

69 candidates to 113 candidates (-63.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Merged error: 21.7b

Counts

124 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

19.1b	(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))))))))))
21.2b	(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))))))))
21.2b	(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))))))))
21.2b	(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))))))))

rewrite64.0ms

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:

15.0ms	(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))))))))
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))))))))
8.0ms	(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))))))))

series9.0s

Counts

4 → 12

Calls

4 calls:

3.4s	(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))))))))))
1.8s	(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))))))))
1.8s	(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))))))))
2.0s	(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))))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4978	8663
1	4978	8663

prune191.0ms

Filtered

59 candidates to 95 candidates (-61.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	95	12	107

Merged error: 21.7b

Counts

107 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

6.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U* U))
8.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U))))))
19.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U)))))))
27.1b	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 l Om)) 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1_binary64`
18×	`cbrt-prod_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`pow-prod-down_binary64`
12×	`associate-l_binary64`
11×	`*-un-lft-identity_binary64`
10×	`associate-*r/_binary64`
9×	`add-cube-cbrt_binary64`
8×	`associate-r_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `cube-div_binary64` `sqrt-pow1_binary64`
3×	`sqr-pow_binary64` `unswap-sqr_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `unpow3_binary64` `sqrt-div_binary64` `*-commutative_binary64` `cube-mult_binary64`
1×	`pow1/2_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 95

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U* U))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U)))))))
2.0ms	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 l Om)) 3))

series5.3s

Counts

4 → 12

Calls

4 calls:

236.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U* U))
896.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U))))))
4.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U)))))))
48.0ms	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 l Om)) 3))

simplify75.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5033	2842

prune106.0ms

Filtered

79 candidates to 107 candidates (-35.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	107	12	119

Merged error: 21.7b

Counts

119 → 12

regimes373.0ms

Accuracy

41.6% (5.4b remaining)

Error of 27.9b against oracle of 22.5b and baseline of 31.8b

bsearch2.0ms

simplify22.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	733	212
1	733	212

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	12412×	body	128	nan
757.0ms	8000×	body	128	valid
119.0ms	1203×	body	128	invalid

Details

analyze2.3s

sample87.0ms

simplify66.0ms

prune5.0ms

localize18.0ms

rewrite51.0ms

series4.6s

simplify76.0ms

prune143.0ms

localize18.0ms

rewrite51.0ms

series4.6s

simplify71.0ms

prune115.0ms

localize28.0ms

rewrite64.0ms

series9.0s

simplify111.0ms

prune191.0ms

localize21.0ms

rewrite42.0ms

series5.3s

simplify75.0ms

prune106.0ms

regimes373.0ms

bsearch2.0ms

simplify22.0ms

end0.0ms

sample2.9s

Profiling