Details

analyze1.5s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	76.4%	4.9%	9
18.7%	76.4%	4.9%	10
21.8%	72.5%	5.7%	11
21.8%	69.8%	8.4%	12
32.7%	46.6%	20.7%	13
32.7%	46.6%	20.7%	14

sample65.0ms

Algorithm

intervals

Results

22.0ms	119×	body	160	valid
14.0ms	149×	body	80	nan
13.0ms	137×	body	80	valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4732	19
1	4732	19

prune4.0ms

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: 9.7b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 Om Omc) 2.0)
0.4b	(/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
0.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
8.5b	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64`
65×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`
28×	`difference-of-squares_binary64`
27×	`unpow-prod-down_binary64`
9×	`add-exp-log_binary64`
8×	`sqr-pow_binary64` `associate-/l*_binary64`
7×	`distribute-lft-out--_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `asin-acos_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

4 → 130

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 Om Omc) 2.0)
13.0ms	(/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
13.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow.f64 (/.f64 Om Omc) 2.0)
127.0ms	(/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
21.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
190.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5039	3354

prune244.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 9.6b

Counts

143 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

7.7b	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
7.7b	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
8.7b	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
8.7b	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

120×	`sqrt-prod_binary64`
104×	`add-sqr-sqrt_binary64`
78×	`times-frac_binary64`
56×	`*-un-lft-identity_binary64`
42×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64`
12×	`unpow-prod-down_binary64`
10×	`pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
9×	`sqrt-pow1_binary64`
6×	`sqr-pow_binary64` `distribute-lft-out--_binary64`
5×	`pow1/2_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip-+_binary64`
3×	`pow-flip_binary64`
2×	`div-inv_binary64`
1×	`inv-pow_binary64`

Counts

4 → 140

Calls

4 calls:

7.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
20.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
3.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
3.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
187.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
75.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
77.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify82.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4946	3646
1	4946	3646

prune268.0ms

Filtered

101 candidates to 152 candidates (-50.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	152	9	161

Merged error: 9.6b

Counts

161 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin.f64 (.f64 (pow.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0))) -1/4) (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
7.7b	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
8.7b	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
17.0b	(pow.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))) -1/4)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt_binary64`
82×	`sqrt-prod_binary64`
56×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64`
15×	`unpow-prod-down_binary64`
7×	`pow1_binary64` `sqr-pow_binary64`
6×	`distribute-lft-out--_binary64`
5×	`add-exp-log_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `rem-sqrt-square_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `asin-acos_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 107

Calls

4 calls:

1.0ms	(asin.f64 (.f64 (pow.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0))) -1/4) (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
4.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
5.0ms	(pow.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))) -1/4)

series380.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(asin.f64 (.f64 (pow.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0))) -1/4) (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
185.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
76.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
98.0ms	(pow.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))) -1/4)

simplify58.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5893	3263

prune216.0ms

Filtered

85 candidates to 119 candidates (-40.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	119	9	128

Merged error: 9.6b

Counts

128 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
1.4b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
15.0b	(cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
15.0b	(cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt_binary64`
92×	`cbrt-prod_binary64`
82×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
36×	`difference-of-squares_binary64`
33×	`sqrt-prod_binary64`
18×	`unpow-prod-down_binary64`
9×	`sqr-pow_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r/_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-div_binary64` `flip3-+_binary64` `pow1/3_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64`
1×	`pow1/2_binary64` `asin-acos_binary64` `sqrt-div_binary64`

Counts

4 → 133

Calls

4 calls:

1.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
15.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
18.0ms	(cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
21.0ms	(cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
205.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
202.0ms	(cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
205.0ms	(cbrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4965	4796
1	4965	4796

prune383.0ms

Filtered

128 candidates to 145 candidates (-13.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	5	5
Picked	1	0	1
Done	0	3	3
Total	145	9	154

Merged error: 9.6b

Counts

154 → 9

regimes1.0s

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.4b and baseline of 10.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample2.0s

Algorithm

intervals

Results

745.0ms	3788×	body	160	valid
456.0ms	4752×	body	80	nan
402.0ms	4212×	body	80	valid

Details

analyze1.5s

sample65.0ms

simplify66.0ms

prune4.0ms

localize14.0ms

rewrite38.0ms

series353.0ms

simplify57.0ms

prune244.0ms

localize20.0ms

rewrite41.0ms

series488.0ms

simplify82.0ms

prune268.0ms

localize23.0ms

rewrite31.0ms

series380.0ms

simplify58.0ms

prune216.0ms

localize22.0ms

rewrite62.0ms

series652.0ms

simplify59.0ms

prune383.0ms

regimes1.0s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling