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

sample76.0ms

Algorithm

intervals

Results

24.0ms	119×	body	160	valid
21.0ms	167×	body	80	nan
14.0ms	137×	body	80	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

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: 11.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite32.0ms

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 t l) 2)
5.0ms	(pow.f64 (/.f64 Om Omc) 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)))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 t l) 2)
4.0ms	(pow.f64 (/.f64 Om Omc) 2)
14.0ms	(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)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4953	2498
1	4953	2498

prune176.0ms

Filtered

76 candidates to 138 candidates (-81.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	8	139

Merged error: 11.5b

Counts

139 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.6b	(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))))))
0.7b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.3b	(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:

5.0ms	(pow.f64 (/.f64 Om Omc) 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))))))
20.0ms	(/.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))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 Om Omc) 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))))))
70.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (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))))

simplify64.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5349	5066

prune209.0ms

Filtered

97 candidates to 206 candidates (-112.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	205	9	214

Merged error: 6.8b

Counts

214 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

6.0b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
6.0b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
10.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
28.0ms	(sqrt.f64 (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))))
10.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4884	998
1	4884	998

prune147.0ms

Filtered

60 candidates to 84 candidates (-40.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Merged error: 6.8b

Counts

93 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
1.5b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
14.8b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.8b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

180×	`add-sqr-sqrt_binary64`
146×	`cbrt-prod_binary64`
145×	`times-frac_binary64`
122×	`*-un-lft-identity_binary64`
90×	`difference-of-squares_binary64`
59×	`add-cube-cbrt_binary64`
51×	`sqrt-prod_binary64`
36×	`unpow-prod-down_binary64`
18×	`unpow2_binary64` `sqr-pow_binary64`
9×	`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 → 187

Calls

4 calls:

1.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
21.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
14.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
96.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
96.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
98.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4963	6331
1	4963	6331

prune294.0ms

Filtered

107 candidates to 199 candidates (-86.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	198	10	208

Merged error: 6.8b

Counts

208 → 10

regimes1.6s

Accuracy

98% (0.1b remaining)

Error of 5.6b against oracle of 5.6b and baseline of 10.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	42
1	37	42

end0.0ms

sample2.1s

Algorithm

intervals

Results

803.0ms	3852×	body	160	valid
479.0ms	4625×	body	80	nan
427.0ms	4148×	body	80	valid

Details

analyze1.6s

sample76.0ms

simplify44.0ms

prune4.0ms

localize15.0ms

rewrite32.0ms

series92.0ms

simplify58.0ms

prune176.0ms

localize16.0ms

rewrite41.0ms

series97.0ms

simplify64.0ms

prune209.0ms

localize18.0ms

rewrite18.0ms

series75.0ms

simplify58.0ms

prune147.0ms

localize19.0ms

rewrite63.0ms

series317.0ms

simplify74.0ms

prune294.0ms

regimes1.6s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling