Details

analyze1.3s (17.2%)

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

Compiler

Compiled 20 to 20 computations (0% saved)

sample55.0ms (0.7%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
13.0ms	149×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify141.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	29

prune3.0ms (0%)

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

Error

10.9b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64_441`
67×	`times-frac_binary64_425`
59×	`*-un-lft-identity_binary64_419`
48×	`sqrt-prod_binary64_435`
38×	`unpow-prod-down_binary64_498` `add-cube-cbrt_binary64_454`
30×	`difference-of-squares_binary64_388`
10×	`add-exp-log_binary64_457`
8×	`sqr-pow_binary64_391` `unpow2_binary64_484`
7×	`pow1_binary64_480`
6×	`pow-unpow_binary64_496`
4×	`add-log-exp_binary64_458` `pow-exp_binary64_487` `add-cbrt-cube_binary64_455`
3×	`div-inv_binary64_416` `distribute-lft-out--_binary64_371`
2×	`associate-/r/_binary64_365` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `rem-sqrt-square_binary64_432` `div-exp_binary64_470`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `asin-acos_binary64_599`

Counts

4 → 126

Calls

4 calls:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(pow.f64 (/.f64 t l) 2)
4.0ms	(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))))))

series443.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
32.0ms	(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	(pow.f64 (/.f64 Om Omc) 2)
14.0ms	(pow.f64 (/.f64 t l) 2)

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5089	3793

prune229.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	8	139

Error

10.8b

Counts

139 → 8

Compiler

Compiled 4035 to 2761 computations (31.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 t)
0.5b	(cbrt.f64 t)
0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l)))))))
10.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64_441`
49×	`times-frac_binary64_425`
48×	`sqrt-prod_binary64_435`
45×	`*-un-lft-identity_binary64_419`
30×	`difference-of-squares_binary64_388`
24×	`add-cube-cbrt_binary64_454`
12×	`unpow-prod-down_binary64_498`
6×	`cbrt-prod_binary64_450` `sqr-pow_binary64_391` `unpow2_binary64_484`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`distribute-lft-out--_binary64_371`
2×	`pow1/3_binary64_501` `associate-/r/_binary64_365` `rem-sqrt-square_binary64_432`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `pow1/2_binary64_499` `div-inv_binary64_416` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `asin-acos_binary64_599`

Counts

4 → 90

Calls

4 calls:

18.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l)))))))

series500.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

291.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))
85.0ms	(cbrt.f64 t)
81.0ms	(cbrt.f64 t)
43.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l)))))))

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5158	3629

prune166.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	101	9	110

Error

10.8b

Counts

110 → 9

Compiler

Compiled 3750 to 2013 computations (46.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)))))))
10.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))))))
13.5b	(cbrt.f64 (/.f64 t l))
13.5b	(cbrt.f64 (/.f64 t l))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64_441`
67×	`times-frac_binary64_425`
57×	`*-un-lft-identity_binary64_419`
48×	`sqrt-prod_binary64_435`
36×	`add-cube-cbrt_binary64_454`
30×	`difference-of-squares_binary64_388`
26×	`cbrt-prod_binary64_450`
12×	`unpow-prod-down_binary64_498`
6×	`sqr-pow_binary64_391` `unpow2_binary64_484`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`div-inv_binary64_416` `distribute-lft-out--_binary64_371`
2×	`pow1/3_binary64_501` `cbrt-div_binary64_451` `associate-/r/_binary64_365` `rem-sqrt-square_binary64_432`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `asin-acos_binary64_599`

Counts

4 → 112

Calls

4 calls:

20.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))))))
3.0ms	(cbrt.f64 (/.f64 t l))
3.0ms	(cbrt.f64 (/.f64 t l))
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)))))))

series322.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))))))
53.0ms	(cbrt.f64 (/.f64 t l))
53.0ms	(cbrt.f64 (/.f64 t l))
35.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)))))))

simplify174.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4916	3967
1	4916	3967

prune214.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	125	8	133

Error

10.8b

Counts

133 → 8

Compiler

Compiled 4332 to 2731 computations (37% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 l)
0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2)))))))
10.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2))))))
13.5b	(cbrt.f64 (/.f64 t l))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_441`
58×	`times-frac_binary64_425`
51×	`*-un-lft-identity_binary64_419`
48×	`sqrt-prod_binary64_435`
30×	`difference-of-squares_binary64_388` `add-cube-cbrt_binary64_454`
16×	`cbrt-prod_binary64_450`
12×	`unpow-prod-down_binary64_498`
6×	`sqr-pow_binary64_391` `unpow2_binary64_484`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`distribute-lft-out--_binary64_371`
2×	`pow1/3_binary64_501` `div-inv_binary64_416` `associate-/r/_binary64_365` `rem-sqrt-square_binary64_432`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `cbrt-div_binary64_451` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `asin-acos_binary64_599`

Counts

4 → 101

Calls

4 calls:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2))))))
3.0ms	(cbrt.f64 (/.f64 t l))
1.0ms	(cbrt.f64 l)
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2)))))))

series352.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2))))))
81.0ms	(cbrt.f64 l)
52.0ms	(cbrt.f64 (/.f64 t l))
35.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2)))))))

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4931	5204
1	4931	5204

prune218.0ms (2.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	113	8	121

Error

10.8b

Counts

121 → 8

Compiler

Compiled 4673 to 2719 computations (41.8% saved)

regimes814.0ms (10.4%)

Accuracy

Total 0.1b remaining (0.7%)

Threshold costs 0.1b (0.7%)

Compiler

Compiled 11324 to 9962 computations (12% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	29
1	29	29

end0.0ms (0%)

sample2.3s (29.5%)

Algorithm

1×

intervals

Results

729.0ms	8000×	body	128	valid
405.0ms	4775×	body	128	nan

Compiler

Compiled 834 to 737 computations (11.6% saved)

Details

analyze1.3s (17.2%)

sample55.0ms (0.7%)

simplify141.0ms (1.8%)

prune3.0ms (0%)

localize18.0ms (0.2%)

rewrite41.0ms (0.5%)

series443.0ms (5.7%)

simplify84.0ms (1.1%)

prune229.0ms (2.9%)

localize18.0ms (0.2%)

rewrite34.0ms (0.4%)

series500.0ms (6.4%)

simplify93.0ms (1.2%)

prune166.0ms (2.1%)

localize18.0ms (0.2%)

rewrite42.0ms (0.5%)

series322.0ms (4.1%)

simplify174.0ms (2.2%)

prune214.0ms (2.7%)

localize24.0ms (0.3%)

rewrite36.0ms (0.5%)

series352.0ms (4.5%)

simplify115.0ms (1.5%)

prune218.0ms (2.8%)

regimes814.0ms (10.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (29.5%)

Profiling