Details

analyze1.6s

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

sample72.0ms

Algorithm

intervals

Results

23.0ms	116×	body	160	valid
14.0ms	140×	body	80	valid
12.0ms	126×	body	80	nan

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5024	29

prune8.0ms

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: 9.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64`
108×	`times-frac_binary64`
98×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
49×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`
41×	`unpow-prod-down_binary64`
15×	`unpow2_binary64` `sqr-pow_binary64`
14×	`associate-/l*_binary64`
9×	`add-exp-log_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 → 173

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 Om Omc) 2)
15.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow.f64 (/.f64 Om Omc) 2)
101.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
32.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
197.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify111.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5210	6677

prune617.0ms

Filtered

108 candidates to 185 candidates (-71.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	5	186

Merged error: 9.8b

Counts

186 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.4b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.2b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
125×	`times-frac_binary64`
112×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
63×	`add-cube-cbrt_binary64`
41×	`unpow-prod-down_binary64`
17×	`associate-/l*_binary64`
15×	`unpow2_binary64` `sqr-pow_binary64`
9×	`add-exp-log_binary64`
7×	`distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `div-inv_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-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 194

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 Om Omc) 2)
24.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow.f64 (/.f64 Om Omc) 2)
196.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
32.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
42.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify143.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4941	7859
1	4941	7859

prune576.0ms

Filtered

97 candidates to 206 candidates (-112.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	205	6	211

Merged error: 5.6b

Counts

211 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.2b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
9.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

128×	`add-sqr-sqrt_binary64`
102×	`sqrt-prod_binary64`
98×	`times-frac_binary64`
84×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`
42×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`
12×	`unpow2_binary64` `sqr-pow_binary64`
8×	`pow1_binary64`
6×	`rem-sqrt-square_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 146

Calls

4 calls:

1.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
1.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series565.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
88.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
194.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
187.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5001	6552

prune581.0ms

Filtered

80 candidates to 158 candidates (-97.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	154	4	158
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	156	8	164

Merged error: 5.6b

Counts

164 → 8

localize47.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.2b	(sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
9.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.0b	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt_binary64`
84×	`sqrt-prod_binary64`
80×	`times-frac_binary64`
69×	`*-un-lft-identity_binary64`
42×	`difference-of-squares_binary64`
36×	`add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`
8×	`pow1_binary64`
6×	`unpow2_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 128

Calls

4 calls:

1.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
1.0ms	(sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
87.0ms	(sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
188.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
133.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4939	5690
1	4939	5690

prune755.0ms

Filtered

82 candidates to 140 candidates (-70.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	139	9	148

Merged error: 5.6b

Counts

148 → 9

regimes2.2s

Accuracy

98.1% (0.1b remaining)

Error of 5.8b against oracle of 5.7b and baseline of 10.2b

bsearch56.0ms

Steps

Iters	Range	Point
9	2425385830759457280967212541510049006313472260635598196454399490852112402967284152962416469143248827592449253149936836871463781441470464	302687982389943060257549018876832100652145152986236562857556023280892002225584810750713112783628901299750942407549253882910734110501474664448	1.916588774785655e+137

Iters

Range

Point

2425385830759457280967212541510049006313472260635598196454399490852112402967284152962416469143248827592449253149936836871463781441470464

302687982389943060257549018876832100652145152986236562857556023280892002225584810750713112783628901299750942407549253882910734110501474664448

1.916588774785655e+137

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	65
1	39	65

end0.0ms

sample2.1s

Algorithm

intervals

Results

763.0ms	3793×	body	160	valid
469.0ms	4662×	body	80	nan
427.0ms	4207×	body	80	valid

Details

analyze1.6s

sample72.0ms

simplify76.0ms

prune8.0ms

localize24.0ms

rewrite47.0ms

series345.0ms

simplify111.0ms

prune617.0ms

localize24.0ms

rewrite44.0ms

series287.0ms

simplify143.0ms

prune576.0ms

localize28.0ms

rewrite46.0ms

series565.0ms

simplify112.0ms

prune581.0ms

localize47.0ms

rewrite38.0ms

series492.0ms

simplify91.0ms

prune755.0ms

regimes2.2s

bsearch56.0ms

simplify4.0ms

end0.0ms

sample2.1s

Profiling