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

24.0ms	126×	body	160	valid
14.0ms	148×	body	80	nan
12.0ms	130×	body	80	valid

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4912	29
1	4912	29

prune2.0ms

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: 8.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))))))
0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite49.0ms

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)
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))))))
15.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
19.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow.f64 (/.f64 t l) 2)
42.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
100.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
192.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4971	6460
1	4971	6460

prune185.0ms

Filtered

101 candidates to 185 candidates (-83.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	177	8	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	177	9	186

Merged error: 8.5b

Counts

186 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))))))
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)))))
7.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite41.0ms

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:

7.0ms	(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))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(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))))))
185.0ms	(/.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))))

simplify141.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4941	7842
1	4941	7842

prune180.0ms

Filtered

96 candidates to 206 candidates (-114.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	206	9	215

Merged error: 4.1b

Counts

215 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64`
6×	`cbrt-prod_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`cbrt-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 61

Calls

4 calls:

7.0ms	(cbrt.f64 (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))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series225.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
38.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
38.0ms	(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))))

simplify202.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	4953	1409
1	4953	1409

prune151.0ms

Filtered

56 candidates to 73 candidates (-30.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	73	9	82

Merged error: 4.1b

Counts

82 → 9

localize21.0ms

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)))))))
7.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite43.0ms

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

series564.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(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)))))))
83.0ms	(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)))))))
180.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
192.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5097	6552

prune218.0ms

Filtered

80 candidates to 158 candidates (-97.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	1	4	5
Picked	1	0	1
Done	0	3	3
Total	158	9	167

Merged error: 4.1b

Counts

167 → 9

regimes685.0ms

Accuracy

98.7% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.4b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	63
1	40	63

end0.0ms

sample2.0s

Algorithm

intervals

Results

717.0ms	3779×	body	160	valid
468.0ms	4773×	body	80	nan
412.0ms	4221×	body	80	valid

Details

analyze1.5s

sample65.0ms

simplify92.0ms

prune2.0ms

localize14.0ms

rewrite49.0ms

series348.0ms

simplify117.0ms

prune185.0ms

localize15.0ms

rewrite41.0ms

series274.0ms

simplify141.0ms

prune180.0ms

localize21.0ms

rewrite18.0ms

series225.0ms

simplify202.0ms

prune151.0ms

localize21.0ms

rewrite43.0ms

series564.0ms

simplify86.0ms

prune218.0ms

regimes685.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample2.0s

Profiling