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

sample100.0ms

Algorithm

intervals

Results

38.0ms	399×	body	80	nan
28.0ms	256×	body	80	valid
4.0ms	42×	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: 30.4b

Counts

2 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

4.5b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
6.6b	(.f64 (/.f64 l Om) (-.f64 U U))
11.0b	(.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)))))))
18.0b	(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))))))))

rewrite61.0ms

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:

10.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
17.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
17.0ms	(.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)))))))
13.0ms	(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))))))))

series2.9s

Counts

4 → 12

Calls

4 calls:

92.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
55.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
435.0ms	(.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))))))))

simplify87.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5128	2913

prune128.0ms

Filtered

77 candidates to 121 candidates (-57.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 19.8b

Counts

123 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

4.5b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
5.4b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
6.6b	(.f64 (/.f64 l Om) (-.f64 U U))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1_binary64`
30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64` `add-sqr-sqrt_binary64`
17×	`associate-r/_binary64` `associate-l*_binary64`
15×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
13×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
7×	`associate-r_binary64`
6×	`sub-neg_binary64`
5×	`sqrt-pow1_binary64`
4×	`add-log-exp_binary64` `flip3--_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 → 113

Calls

4 calls:

10.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
10.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

series2.9s

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
423.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
56.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
2.3s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

simplify96.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5041	2989

prune116.0ms

Filtered

75 candidates to 125 candidates (-66.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	122	12	134

Merged error: 16.0b

Counts

134 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

18.0b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))) (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))))
19.1b	(cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
19.1b	(cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
19.1b	(cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

128×	`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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))) (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))))
10.0ms	(cbrt.f64 (.f64 (.f64 2 n) (.f64 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 2 n) (.f64 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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

series5.1s

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))) (cbrt.f64 (.f64 (.f64 2 n) (.f64 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 2 n) (.f64 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 2 n) (.f64 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 2 n) (.f64 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 (53.0ms)

Iter	Nodes	Cost
0	5035	8687

prune187.0ms

Filtered

58 candidates to 95 candidates (-63.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	95	12	107

Merged error: 16.0b

Counts

107 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

6.6b	(.f64 (/.f64 l Om) (-.f64 U U))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
9.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 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 2 n) (.f64 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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

series7.2s

Counts

4 → 12

Calls

4 calls:

59.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
2.4s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
2.3s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

simplify82.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4990	2645
1	4990	2645

prune225.0ms

Filtered

70 candidates to 100 candidates (-42.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	99	13	112

Merged error: 16.0b

Counts

112 → 13

regimes289.0ms

Accuracy

32% (8.1b remaining)

Error of 27.1b against oracle of 19.0b and baseline of 30.9b

bsearch74.0ms

Steps

Iters	Range		Point
10	-5.1195757377761044e-303	3.484811878656185e-303	-2.14366188283304e-310

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	86
1	48	86

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	12629×	body	80	nan
786.0ms	8000×	body	80	valid
117.0ms	1194×	body	80	invalid

Details

analyze2.6s

sample100.0ms

simplify76.0ms

prune5.0ms

localize30.0ms

rewrite61.0ms

series2.9s

simplify87.0ms

prune128.0ms

localize16.0ms

rewrite40.0ms

series2.9s

simplify96.0ms

prune116.0ms

localize26.0ms

rewrite47.0ms

series5.1s

simplify121.0ms

prune187.0ms

localize25.0ms

rewrite37.0ms

series7.2s

simplify82.0ms

prune225.0ms

regimes289.0ms

bsearch74.0ms

simplify4.0ms

end0.0ms

sample2.9s

Profiling