Details

analyze1.4s (19.4%)

Algorithm

1×

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

sample69.0ms (0.9%)

Algorithm

1×

intervals

Results

24.0ms	132×	body	160	valid
16.0ms	124×	body	80	valid
12.0ms	135×	body	80	nan

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4732	19
1	4732	19

prune8.0ms (0.1%)

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

localize13.0ms (0.2%)

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)))))

rewrite41.0ms (0.6%)

Algorithm

1×	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:

14.0ms	(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)))))
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))))
5.0ms	(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))))))

series341.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(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)))))
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))))
19.0ms	(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))))))
14.0ms	(pow.f64 (/.f64 t l) 2.0)

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5012	3362

prune300.0ms (4.1%)

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 (0.3%)

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))))

rewrite41.0ms (0.6%)

Algorithm

1×	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:

30.0ms	(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))))
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))))

series425.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(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)))))))
84.0ms	(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))))
79.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4957	1131
1	4957	1131

prune181.0ms (2.5%)

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 (0.2%)

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))))

rewrite31.0ms (0.4%)

Algorithm

1×	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:

19.0ms	(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))))
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)))))))

series376.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(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))))
79.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
37.0ms	(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)))))))

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4975	3413
1	4975	3413

prune318.0ms (4.3%)

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

localize24.0ms (0.3%)

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))))

rewrite17.0ms (0.2%)

Algorithm

1×	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:

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	(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))))

series305.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(cbrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))
81.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
81.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0)))))
60.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 2.0 (pow.f64 (/.f64 t l) 2.0))))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4950	1200
1	4950	1200

prune179.0ms (2.4%)

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

regimes1.0s (14.2%)

Accuracy

Total 0.1b remaining (0.6%)

Threshold costs 0.1b (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms (0%)

sample1.9s (25.6%)

Algorithm

1×

intervals

Results

705.0ms	3815×	body	160	valid
423.0ms	4600×	body	80	nan
388.0ms	4185×	body	80	valid

Details

analyze1.4s (19.4%)

sample69.0ms (0.9%)

simplify64.0ms (0.9%)

prune8.0ms (0.1%)

localize13.0ms (0.2%)

rewrite41.0ms (0.6%)

series341.0ms (4.6%)

simplify60.0ms (0.8%)

prune300.0ms (4.1%)

localize20.0ms (0.3%)

rewrite41.0ms (0.6%)

series425.0ms (5.8%)

simplify39.0ms (0.5%)

prune181.0ms (2.5%)

localize17.0ms (0.2%)

rewrite31.0ms (0.4%)

series376.0ms (5.1%)

simplify63.0ms (0.9%)

prune318.0ms (4.3%)

localize24.0ms (0.3%)

rewrite17.0ms (0.2%)

series305.0ms (4.1%)

simplify73.0ms (1%)

prune179.0ms (2.4%)

regimes1.0s (14.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (25.6%)

Profiling