Details

analyze2.1s (18.3%)

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 24 to 20 computations (16.7% saved)

sample2.7s (22.9%)

Results

1.6s	8256×	body	128	valid
988.0ms	4920×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
527×	`associate-/r/_binary64`
522×	`fma-neg_binary64`
484×	`unswap-sqr_binary64`
458×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	33	27
2	63	27
3	165	27
4	492	27
5	1679	27
6	3655	27
7	4950	27
8	5043	27

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

13.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

Compiler

Compiled 85 to 67 computations (21.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 t l) 2)
✓	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	12.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series391.0ms (3.4%)

Counts

4 → 144

Calls

4 calls:

351.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
18.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
11.0ms	(pow.f64 (/.f64 t l) 2)
10.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
46×	`sqrt-prod_binary64`
38×	`unpow-prod-down_binary64`

Counts

4 → 132

Calls

4 calls:

10.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
4.0ms	(pow.f64 (/.f64 Om Omc) 2)
3.0ms	(pow.f64 (/.f64 t l) 2)
0.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

simplify193.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
399×	`times-frac_binary64`
353×	`associate-/r*_binary64`
282×	`associate-/l*_binary64`
223×	`associate-*l/_binary64`

Counts

276 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	708	15505
1	1879	12830
2	4964	12830

prune414.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	221	8	229
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	221	9	230

Error

0.9b

Counts

230 → 9

Alt Table

Status	Error	Program
	37.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (/.f64 1 (sqrt.f64 l)) 2) (pow.f64 (/.f64 t (sqrt.f64 l)) 2)) 1))))
	40.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	16.0b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
	43.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
▶	13.4b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	14.3b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	22.4b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	13.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	13.6b	(asin.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 14748 to 11001 computations (25.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.2b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	0.8b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	12.4b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series380.0ms (3.3%)

Counts

3 → 120

Calls

3 calls:

341.0ms

(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

21.0ms

(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

17.0ms

(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`sqrt-prod_binary64`
148×	`add-sqr-sqrt_binary64`
116×	`times-frac_binary64`
103×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`

Counts

3 → 168

Calls

3 calls:

19.0ms

(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

1.0ms

(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

0.0ms

(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

simplify308.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
433×	`times-frac_binary64`
377×	`associate-/r*_binary64`
291×	`associate-/l*_binary64`
202×	`associate-*l/_binary64`

Counts

288 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	645	19365
1	1761	16645
2	4923	16520
3	5188	16520

prune553.0ms (4.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	300	4	304
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	303	10	313

Error

0.8b

Counts

313 → 10

Alt Table

Status	Error	Program
	16.0b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
	43.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	44.0b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
✓	13.4b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	40.6b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	40.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	14.3b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	40.6b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	22.4b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
▶	13.4b	(asin.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (/.f64 Om Omc))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 18055 to 13446 computations (25.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	0.8b	(asin.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (/.f64 Om Omc))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
✓	2.0b	(sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	19.6b	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series257.0ms (2.2%)

Counts

4 → 132

Calls

4 calls:

149.0ms	(/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
43.0ms	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
38.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
26.0ms	(asin.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (/.f64 Om Omc))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
77×	`times-frac_binary64`
74×	`add-sqr-sqrt_binary64`
55×	`add-cube-cbrt_binary64`
54×	`sqrt-prod_binary64`

Counts

4 → 155

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
1.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
1.0ms	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
1.0ms	(asin.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (/.f64 Om Omc))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

simplify264.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

853×	`associate-/l*_binary64`
478×	`fma-def_binary64`
280×	`associate-/r/_binary64`
197×	`fma-neg_binary64`
164×	`cancel-sign-sub-inv_binary64`

Counts

287 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	13540
1	826	12255
2	2197	11749
3	4984	11749
4	5045	11749

prune544.0ms (4.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	316	1	317
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	317	10	327

Error

0.8b

Counts

327 → 10

Alt Table

Status	Error	Program
	16.0b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
	43.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	44.0b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
▶	13.4b	(expm1.f64 (log1p.f64 (asin.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (/.f64 Om Omc))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
✓	13.4b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	40.6b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	40.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	14.3b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	40.6b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	22.4b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 18272 to 12799 computations (30% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	0.8b	(asin.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (/.f64 Om Omc))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	2.0b	(sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
	19.6b	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

prune535.0ms (4.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	316	1	317
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	316	11	327

Error

0.8b

Counts

327 → 11

Alt Table

Status	Error	Program
	16.0b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
	43.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	44.0b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
✓	13.4b	(expm1.f64 (log1p.f64 (asin.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (/.f64 Om Omc))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
✓	13.4b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	40.6b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	40.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	14.8b	(expm1.f64 (log1p.f64 (.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (-.f64 1 (/.f64 Om Omc)))) (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/6) 3)))) (cbrt.f64 (asin.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (-.f64 1 (/.f64 Om Omc)))) (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/6) 3))))) (cbrt.f64 (asin.f64 (/.f64 (*.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (-.f64 1 (/.f64 Om Omc)))) (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/6) 3)))))))
	14.3b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	40.6b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	22.4b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 18739 to 13295 computations (29.1% saved)

regimes2.5s (21.5%)

Accuracy

Total 0.4b remaining (45.9%)

Threshold costs 0.4b (45.9%)

Counts

110 → 3

Compiler

Compiled 64251 to 50257 computations (21.8% saved)

bsearch6.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	105
1	57	105
2	74	105
3	88	105
4	96	105
5	98	105
6	97	105

end250.0ms (2.2%)

Compiler: Compiled 518 to 387 computations (25.3% saved)

Details

analyze2.1s (18.3%)

sample2.7s (22.9%)

simplify51.0ms (0.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series391.0ms (3.4%)

rewrite30.0ms (0.3%)

simplify193.0ms (1.7%)

prune414.0ms (3.6%)

localize14.0ms (0.1%)

series380.0ms (3.3%)

rewrite46.0ms (0.4%)

simplify308.0ms (2.7%)

prune553.0ms (4.8%)

localize17.0ms (0.1%)

series257.0ms (2.2%)

rewrite29.0ms (0.3%)

simplify264.0ms (2.3%)

prune544.0ms (4.7%)

localize24.0ms (0.2%)

prune535.0ms (4.6%)

regimes2.5s (21.5%)

bsearch6.0ms (0%)

simplify8.0ms (0.1%)

end250.0ms (2.2%)

Profiling