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

sample99.0ms

Algorithm

intervals

Results

38.0ms	413×	body	80	nan
27.0ms	256×	body	80	valid
3.0ms	35×	body	80	invalid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4939	26
1	4939	26

prune12.0ms

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: 34.1b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
6.8b	(.f64 (/.f64 l Om) (-.f64 U U))
11.2b	(.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)))))))
21.4b	(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))))))))

rewrite41.0ms

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))))))))

series939.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
14.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
144.0ms	(.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)))))))
756.0ms	(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))))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5104	1952

prune124.0ms

Filtered

77 candidates to 121 candidates (-57.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Merged error: 23.8b

Counts

123 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

5.0b	(.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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
6.8b	(.f64 (/.f64 l Om) (-.f64 U U))
21.4b	(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:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

121.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
162.0ms	(.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))))))))
27.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
766.0ms	(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)))))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4972	2275
1	4972	2275

prune113.0ms

Filtered

76 candidates to 118 candidates (-55.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Merged error: 19.6b

Counts

126 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

11.8b	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
11.8b	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
11.8b	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
21.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 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)))))))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1_binary64`
15×	`cbrt-div_binary64`
10×	`associate-*r/_binary64`
8×	`pow-prod-down_binary64`
6×	`flip3--_binary64` `flip--_binary64` `frac-times_binary64`
5×	`sqrt-pow1_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×	`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 → 58

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)))
9.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 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)))))))))))

series835.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
33.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
33.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (-.f64 U U)))
735.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 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)))))))))))

simplify24.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5126	1068

prune86.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	70	12	82

Merged error: 19.6b

Counts

82 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

6.8b	(.f64 (/.f64 l Om) (-.f64 U U))
6.8b	(.f64 (/.f64 l Om) (-.f64 U U))
21.4b	(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)))))))))
21.4b	(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)))))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1_binary64` `add-sqr-sqrt_binary64`
26×	`associate-l_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64` `times-frac_binary64`
18×	`pow-prod-down_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-*r/_binary64`
10×	`associate-r_binary64` `sqrt-pow1_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `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` `sqrt-prod_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
14.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
740.0ms	(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)))))))))
731.0ms	(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

124 → 124

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5366	1688

prune140.0ms

Filtered

88 candidates to 124 candidates (-40.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	124	12	136

Merged error: 19.6b

Counts

136 → 12

regimes947.0ms

Accuracy

33.1% (7.7b remaining)

Error of 27.0b against oracle of 19.2b and baseline of 30.8b

bsearch1.0ms

simplify16.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	683	230
1	683	230

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	13179×	body	80	nan
748.0ms	8000×	body	80	valid
119.0ms	1200×	body	80	invalid

Details

analyze2.6s

sample99.0ms

simplify73.0ms

prune12.0ms

localize20.0ms

rewrite41.0ms

series939.0ms

simplify50.0ms

prune124.0ms

localize19.0ms

rewrite37.0ms

series1.1s

simplify63.0ms

prune113.0ms

localize21.0ms

rewrite31.0ms

series835.0ms

simplify24.0ms

prune86.0ms

localize22.0ms

rewrite39.0ms

series1.5s

simplify30.0ms

prune140.0ms

regimes947.0ms

bsearch1.0ms

simplify16.0ms

end0.0ms

sample2.9s

Profiling