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

sample71.0ms

Algorithm

intervals

Results

22.0ms	117×	body	160	valid
20.0ms	178×	body	80	nan
13.0ms	139×	body	80	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4732	19
1	4732	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: 10.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 t l) 2.0)
0.4b	(/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
9.4b	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64`
65×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`
28×	`difference-of-squares_binary64`
27×	`unpow-prod-down_binary64`
9×	`add-exp-log_binary64`
8×	`sqr-pow_binary64` `associate-/l*_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 → 130

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 t l) 2.0)
13.0ms	(/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
13.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow.f64 (/.f64 t l) 2.0)
118.0ms	(/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
20.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
175.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5012	3362

prune260.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 10.5b

Counts

143 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2.0)
0.3b	(pow.f64 (/.f64 t l) 2.0)
0.6b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0))) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
9.8b	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64`
10×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `asin-acos_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 Om Omc) 2.0)
5.0ms	(pow.f64 (/.f64 t l) 2.0)
1.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0))) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
3.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow.f64 (/.f64 Om Omc) 2.0)
13.0ms	(pow.f64 (/.f64 t l) 2.0)
21.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0))) (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
58.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5100	1105

prune140.0ms

Filtered

70 candidates to 91 candidates (-30.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Merged error: 10.5b

Counts

99 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

5.7b	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
5.7b	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
9.8b	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
9.8b	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

rewrite17.0ms

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 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
3.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
3.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
76.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
59.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
59.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4954	1218
1	4954	1218

prune153.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 10.5b

Counts

91 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
2.2b	(sqrt.f64 (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
13.7b	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
13.7b	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `asin-acos_binary64`

Counts

4 → 54

Calls

4 calls:

1.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
4.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
3.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
3.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

series265.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))))
78.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
75.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
77.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5121	1329

prune122.0ms

Filtered

61 candidates to 66 candidates (-8.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	66	7	73

Merged error: 10.5b

Counts

73 → 7

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	33
1	31	33

end0.0ms

sample1.9s

Algorithm

intervals

Results

709.0ms	3823×	body	160	valid
463.0ms	4831×	body	80	nan
387.0ms	4177×	body	80	valid

Details

analyze1.5s

sample71.0ms

simplify63.0ms

prune4.0ms

localize13.0ms

rewrite36.0ms

series327.0ms

simplify58.0ms

prune260.0ms

localize16.0ms

rewrite15.0ms

series106.0ms

simplify55.0ms

prune140.0ms

localize17.0ms

rewrite17.0ms

series270.0ms

simplify58.0ms

prune153.0ms

localize20.0ms

rewrite12.0ms

series265.0ms

simplify37.0ms

prune122.0ms

regimes1.1s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling