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

sample98.0ms

Algorithm

intervals

Results

40.0ms	368×	body	80	nan
24.0ms	256×	body	80	valid
4.0ms	37×	body	80	invalid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4939	26
1	4939	26

prune17.0ms

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: 30.7b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

4.8b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
6.0b	(.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)))))))
18.5b	(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))))))))

series929.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
16.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
145.0ms	(.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)))))))
745.0ms	(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))))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5104	1952

prune180.0ms

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: 21.6b

Counts

123 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

6.0b	(.f64 (/.f64 l Om) (-.f64 U U))
6.1b	(.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 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
18.5b	(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

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

Counts

4 → 106

Calls

4 calls:

10.0ms	(.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))))))))
6.0ms	(.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)))))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

16.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
142.0ms	(.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))))))))
115.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
736.0ms	(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)))))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4972	2275
1	4972	2275

prune169.0ms

Filtered

76 candidates to 118 candidates (-55.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 20.0b

Counts

129 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

4.8b	(.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))
6.1b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om))))))))))
6.6b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))))))
18.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-exp-log_binary64`
70×	`add-cbrt-cube_binary64`
62×	`cbrt-unprod_binary64` `prod-exp_binary64`
40×	`pow1_binary64`
28×	`associate-*r/_binary64`
23×	`pow-prod-down_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`add-sqr-sqrt_binary64` `frac-times_binary64`
7×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
5×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64`

Counts

4 → 124

Calls

4 calls:

25.0ms	(.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om))))))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))))))
9.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

26.0ms	(.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))
144.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om))))))))))
132.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))))))
738.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (.f64 (-.f64 U* U) (/.f64 (cbrt.f64 l) (cbrt.f64 Om)))))))))))

simplify87.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4950	2559
1	4950	2559

prune147.0ms

Filtered

68 candidates to 136 candidates (-100.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	135	14	149

Merged error: 20.0b

Counts

149 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

6.6b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
6.6b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
18.5b	(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)))))))))
18.5b	(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)))))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1_binary64`
18×	`pow-prod-down_binary64`
12×	`associate-*r/_binary64` `add-sqr-sqrt_binary64`
10×	`sqrt-pow1_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 76

Calls

4 calls:

6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
6.0ms	(.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)))))))))
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)))))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

116.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
117.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
716.0ms	(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)))))))))
720.0ms	(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)))))))))

simplify30.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5154	2128

prune111.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	88	14	102

Merged error: 20.0b

Counts

102 → 14

regimes1.3s

Accuracy

30.8% (8.7b remaining)

Error of 27.6b against oracle of 18.9b and baseline of 31.4b

bsearch1.0ms

simplify23.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	916	228
1	916	228

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	12829×	body	80	nan
780.0ms	8000×	body	80	valid
122.0ms	1210×	body	80	invalid

Details

analyze2.6s

sample98.0ms

simplify76.0ms

prune17.0ms

localize17.0ms

rewrite42.0ms

series929.0ms

simplify54.0ms

prune180.0ms

localize18.0ms

rewrite37.0ms

series1.0s

simplify68.0ms

prune169.0ms

localize27.0ms

rewrite56.0ms

series1.0s

simplify87.0ms

prune147.0ms

localize22.0ms

rewrite29.0ms

series1.7s

simplify30.0ms

prune111.0ms

regimes1.3s

bsearch1.0ms

simplify23.0ms

end0.0ms

sample2.9s

Profiling