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

sample63.0ms

Algorithm

intervals

Results

22.0ms	123×	body	160	valid
13.0ms	136×	body	80	nan
12.0ms	133×	body	80	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4892	19
1	4892	19

prune3.0ms

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: 11.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
11.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
48×	`sqrt-prod_binary64`
38×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
30×	`difference-of-squares_binary64`
10×	`add-exp-log_binary64`
8×	`unpow2_binary64` `sqr-pow_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
3×	`distribute-lft-out--_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `associate-/r/_binary64` `rem-sqrt-square_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `asin-acos_binary64` `sqrt-pow1_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 126

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 Om Omc) 2)
5.0ms	(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))))))
20.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 Om Omc) 2)
4.0ms	(pow.f64 (/.f64 t l) 2)
13.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
70.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4953	2498
1	4953	2498

prune122.0ms

Filtered

76 candidates to 138 candidates (-81.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	8	139

Merged error: 11.5b

Counts

139 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.5b	(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))))))
0.6b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.6b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite40.0ms

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:

5.0ms	(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))))))
19.0ms	(/.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))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 t l) 2)
13.0ms	(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))))))
68.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify84.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4973	5066
1	4973	5066

prune141.0ms

Filtered

96 candidates to 206 candidates (-114.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	206	8	214

Merged error: 6.1b

Counts

214 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 t)
0.5b	(cbrt.f64 t)
0.5b	(cbrt.f64 t)
11.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
48×	`sqrt-prod_binary64`
46×	`*-un-lft-identity_binary64`
30×	`difference-of-squares_binary64`
25×	`add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`
9×	`cbrt-prod_binary64`
6×	`unpow2_binary64` `sqr-pow_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `distribute-lft-out--_binary64`
2×	`associate-/r/_binary64` `rem-sqrt-square_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)
2.0ms	(cbrt.f64 t)
18.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt.f64 t)
14.0ms	(cbrt.f64 t)
15.0ms	(cbrt.f64 t)
78.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5006	2208

prune83.0ms

Filtered

70 candidates to 105 candidates (-50.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	105	8	113

Merged error: 6.1b

Counts

113 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

7.4b	(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)))))))
7.4b	(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)))))))
11.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
11.0b	(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)))))
18.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(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)))))))
32.0ms	(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)))))))
67.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
71.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify78.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4928	4274
1	4928	4274

prune163.0ms

Filtered

80 candidates to 158 candidates (-97.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	157	9	166

Merged error: 6.1b

Counts

166 → 9

regimes1.1s

Accuracy

98.5% (0.1b remaining)

Error of 5.6b against oracle of 5.6b and baseline of 10.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	41
1	37	41

end0.0ms

sample1.9s

Algorithm

intervals

Results

727.0ms	3829×	body	160	valid
443.0ms	4793×	body	80	nan
389.0ms	4171×	body	80	valid

Details

analyze1.5s

sample63.0ms

simplify43.0ms

prune3.0ms

localize14.0ms

rewrite37.0ms

series91.0ms

simplify53.0ms

prune122.0ms

localize14.0ms

rewrite40.0ms

series98.0ms

simplify84.0ms

prune141.0ms

localize20.0ms

rewrite27.0ms

series121.0ms

simplify72.0ms

prune83.0ms

localize17.0ms

rewrite46.0ms

series201.0ms

simplify78.0ms

prune163.0ms

regimes1.1s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling