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

sample73.0ms

Algorithm

intervals

Results

28.0ms	139×	body	160	valid
15.0ms	151×	body	80	nan
12.0ms	117×	body	80	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4892	19
1	4892	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: 10.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite50.0ms

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

series128.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 t l) 2)
38.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
15.0ms	(asin.f64 (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)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4953	4274
1	4953	4274

prune234.0ms

Filtered

101 candidates to 185 candidates (-83.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	7	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	8	186

Merged error: 9.9b

Counts

186 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.5b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.9b	(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))))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite38.0ms

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)
18.0ms	(/.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))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 t l) 2)
66.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (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))))))
13.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify81.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4973	5066
1	4973	5066

prune209.0ms

Filtered

96 candidates to 206 candidates (-114.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	206	8	214

Merged error: 5.7b

Counts

214 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

5.3b	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
5.3b	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

26.0ms	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
23.0ms	(sqrt.f64 (/.f64 (cbrt.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))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
105.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
11.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify61.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5146	5601

prune381.0ms

Filtered

105 candidates to 190 candidates (-81.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	190	8	198

Merged error: 5.7b

Counts

198 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

5.8b	(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)))))))
5.8b	(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)))))))
8.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.7b	(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)))))))
18.0ms	(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)))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

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)))))))
30.0ms	(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)))))))
69.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
66.0ms	(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

prune212.0ms

Filtered

80 candidates to 158 candidates (-97.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	0	5	5
Picked	1	0	1
Done	2	0	2
Total	158	8	166

Merged error: 5.7b

Counts

166 → 8

regimes1.5s

Accuracy

88.6% (0.6b remaining)

Error of 6.4b against oracle of 5.8b and baseline of 10.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	64
1	44	64

end0.0ms

sample2.3s

Algorithm

intervals

Results

964.0ms	3840×	body	160	valid
496.0ms	4654×	body	80	nan
436.0ms	4160×	body	80	valid

Details

analyze1.6s

sample73.0ms

simplify41.0ms

prune4.0ms

localize16.0ms

rewrite50.0ms

series128.0ms

simplify70.0ms

prune234.0ms

localize17.0ms

rewrite38.0ms

series96.0ms

simplify81.0ms

prune209.0ms

localize27.0ms

rewrite69.0ms

series234.0ms

simplify61.0ms

prune381.0ms

localize20.0ms

rewrite46.0ms

series197.0ms

simplify78.0ms

prune212.0ms

regimes1.5s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling