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

sample68.0ms

Algorithm

intervals

Results

25.0ms	132×	body	160	valid
13.0ms	135×	body	80	nan
12.0ms	124×	body	80	valid

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

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: 7.8b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 t l) 2.0)
0.3b	(/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
0.4b	(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))))))
7.0b	(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)))))

rewrite38.0ms

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)))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow.f64 (/.f64 t l) 2.0)
123.0ms	(/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
21.0ms	(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))))))
187.0ms	(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)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5012	3362

prune251.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 7.7b

Counts

143 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))) (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))))
12.1b	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
12.1b	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
12.1b	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64` `sqrt-div_binary64`
2×	`sqrt-pow1_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-prod_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 53

Calls

4 calls:

26.0ms	(sqrt.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))) (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (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))))
5.0ms	(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))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))) (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))))
82.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
83.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
83.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4957	1131
1	4957	1131

prune164.0ms

Filtered

59 candidates to 65 candidates (-10.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	63	9	72

Merged error: 7.6b

Counts

72 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (fabs.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))))
1.5b	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
12.1b	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
12.1b	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
54×	`sqrt-prod_binary64`
41×	`*-un-lft-identity_binary64`
31×	`cbrt-prod_binary64`
29×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64`
12×	`unpow-prod-down_binary64`
6×	`cbrt-div_binary64` `sqr-pow_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
2×	`pow1/3_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `asin-acos_binary64` `sqrt-pow1_binary64` `div-inv_binary64` `sqrt-div_binary64`

Counts

4 → 101

Calls

4 calls:

1.0ms	(asin.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (fabs.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (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))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(asin.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))) (fabs.f64 (cbrt.f64 (+.f64 1.0 (.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))))
181.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 (pow.f64 (/.f64 Om Omc) 2.0)) (cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))))
82.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
81.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4975	3413
1	4975	3413

prune276.0ms

Filtered

100 candidates to 113 candidates (-13.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	114	8	122

Merged error: 7.6b

Counts

122 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

6.8b	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
7.4b	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
7.4b	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
12.1b	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series308.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
82.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
82.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
82.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4950	1200
1	4950	1200

prune151.0ms

Filtered

62 candidates to 72 candidates (-16.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 7.6b

Counts

80 → 8

regimes999.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample1.9s

Algorithm

intervals

Results

726.0ms	3815×	body	160	valid
442.0ms	4600×	body	80	nan
396.0ms	4185×	body	80	valid

Details

analyze1.5s

sample68.0ms

simplify62.0ms

prune4.0ms

localize14.0ms

rewrite38.0ms

series345.0ms

simplify57.0ms

prune251.0ms

localize20.0ms

rewrite39.0ms

series430.0ms

simplify33.0ms

prune164.0ms

localize17.0ms

rewrite30.0ms

series382.0ms

simplify63.0ms

prune276.0ms

localize21.0ms

rewrite16.0ms

series308.0ms

simplify70.0ms

prune151.0ms

regimes999.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling