Details

analyze2.4s

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

39.0ms	414×	body	128	nan
27.0ms	256×	body	128	valid
4.0ms	37×	body	128	invalid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5484	39

prune8.0ms

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: 27.7b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

5.7b	(.f64 (/.f64 l Om) (-.f64 U U))
6.0b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
9.4b	(.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)))))))
17.3b	(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))))))))

rewrite55.0ms

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))
12.0ms	(.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))))))))

series4.9s

Counts

4 → 12

Calls

4 calls:

122.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
214.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
779.0ms	(.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)))))))
3.8s	(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))))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5099	2919

prune140.0ms

Filtered

77 candidates to 121 candidates (-57.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 19.6b

Counts

123 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(.f64 (/.f64 l Om) (-.f64 U U))
6.0b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
6.5b	(.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))))))))
17.3b	(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)))))))))

rewrite58.0ms

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:

15.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
12.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
10.0ms	(.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))))))))
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)))))))))

series4.8s

Counts

4 → 12

Calls

4 calls:

126.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
212.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
814.0ms	(.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))))))))
3.6s	(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)))))))))

simplify76.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5154	3001

prune124.0ms

Filtered

75 candidates to 125 candidates (-66.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	122	13	135

Merged error: 16.3b

Counts

135 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

6.5b	(.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))))))))
6.5b	(.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))))))))
17.3b	(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)))))))))
17.3b	(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)))))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(.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))))))))
11.0ms	(.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))))))))
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)))))))))
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)))))))))

series8.7s

Counts

4 → 12

Calls

4 calls:

766.0ms	(.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))))))))
773.0ms	(.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))))))))
3.5s	(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)))))))))
3.7s	(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)))))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5063	3848

prune142.0ms

Filtered

56 candidates to 100 candidates (-78.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	100	13	113

Merged error: 16.3b

Counts

113 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

17.3b	(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))))))))))
18.8b	(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))))))))
18.8b	(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))))))))
18.8b	(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))))))))

rewrite72.0ms

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:

20.0ms	(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))))))))))
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))))))))
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))))))))
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))))))))

series8.8s

Counts

4 → 12

Calls

4 calls:

3.5s	(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))))))))
1.7s	(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))))))))
1.7s	(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))))))))

simplify112.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4978	8663
1	4978	8663

prune187.0ms

Filtered

61 candidates to 95 candidates (-55.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	95	13	108

Merged error: 16.3b

Counts

108 → 13

regimes459.0ms

Accuracy

30.7% (8.4b remaining)

Error of 27.3b against oracle of 18.8b and baseline of 31.0b

bsearch2.0ms

simplify20.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	676	216
1	676	216

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	13385×	body	128	nan
770.0ms	8000×	body	128	valid
121.0ms	1177×	body	128	invalid

Details

analyze2.4s

sample98.0ms

simplify60.0ms

prune8.0ms

localize17.0ms

rewrite55.0ms

series4.9s

simplify71.0ms

prune140.0ms

localize19.0ms

rewrite58.0ms

series4.8s

simplify76.0ms

prune124.0ms

localize22.0ms

rewrite56.0ms

series8.7s

simplify56.0ms

prune142.0ms

localize25.0ms

rewrite72.0ms

series8.8s

simplify112.0ms

prune187.0ms

regimes459.0ms

bsearch2.0ms

simplify20.0ms

end0.0ms

sample3.0s

Profiling