Details

analyze1.8s (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 24 to 20 computations (16.7% saved)

sample117.0ms (1.1%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
14.0ms	134×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify54.0ms (0.5%)

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

9.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.7b	(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)

localize17.0ms (0.2%)

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)
✓	1.0b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	8.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series392.0ms (3.7%)

Counts

4 → 144

Calls

4 calls:

352.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
19.0ms	(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)
9.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite31.0ms (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)))
3.0ms	(pow.f64 (/.f64 t l) 2)
3.0ms	(pow.f64 (/.f64 Om Omc) 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))))

simplify204.0ms (1.9%)

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

prune510.0ms (4.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	220	9	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	9	230

Error

1.1b

Counts

230 → 9

Alt Table

Status	Error	Program
	10.8b	(.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))))))
▶	9.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	9.7b	(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))))
	16.3b	(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))
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	9.8b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	9.7b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	9.8b	(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 14802 to 11043 computations (25.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	1.0b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	2.6b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
✓	8.4b	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series387.0ms (3.7%)

Counts

3 → 120

Calls

3 calls:

357.0ms

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

11.0ms

(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
25×	`sqrt-prod_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 81

Calls

3 calls:

11.0ms

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

5.0ms

(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))

0.0ms

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

simplify181.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-def_binary64`
398×	`times-frac_binary64`
345×	`associate-/r*_binary64`
267×	`associate-/l*_binary64`
266×	`associate-*r/_binary64`

Counts

201 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	606	13522
1	1647	11250
2	5066	11250

prune462.0ms (4.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	238	9	247

Error

1.1b

Counts

247 → 9

Alt Table

Status	Error	Program
	9.7b	(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))))
▶	9.6b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
✓	9.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	16.3b	(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))
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	9.8b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.8b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	9.8b	(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 15152 to 11382 computations (24.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
	1.0b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	2.6b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
	8.4b	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

prune503.0ms (4.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	237	10	247

Error

1.1b

Counts

247 → 10

Alt Table

Status	Error	Program
	10.6b	(expm1.f64 (log1p.f64 (.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))))))))
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	9.8b	(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))))))
▶	9.7b	(expm1.f64 (log1p.f64 (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))))))
✓	9.6b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
✓	9.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	16.3b	(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))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	9.8b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.8b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 15736 to 11938 computations (24.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.4b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	1.0b	(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))))
✓	8.3b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series383.0ms (3.6%)

Counts

3 → 120

Calls

3 calls:

345.0ms

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

19.0ms

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

18.0ms

(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))))

rewrite41.0ms (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:

14.0ms

(/.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))))

simplify309.0ms (2.9%)

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

prune568.0ms (5.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	300	4	304
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	302	12	314

Error

1.0b

Counts

314 → 12

Alt Table

Status	Error	Program
	10.6b	(expm1.f64 (log1p.f64 (.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))))))))
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.4b	(expm1.f64 (log1p.f64 (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))))
✓	9.6b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
✓	9.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	16.3b	(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))
	43.5b	(expm1.f64 (log1p.f64 (asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))))
	43.5b	(expm1.f64 (log1p.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	49.3b	(expm1.f64 (log1p.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (fma.f64 (/.f64 t l) (sqrt.f64 2) (.f64 (/.f64 (pow.f64 l 3) (.f64 (pow.f64 t 3) (.f64 2 (sqrt.f64 2)))) -1/8)))))))
	10.8b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	9.8b	(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 18532 to 13953 computations (24.7% saved)

regimes2.0s (19.3%)

Accuracy

Total 0.3b remaining (33.3%)

Threshold costs 0.3b (33.3%)

Counts

98 → 3

Compiler

Compiled 49991 to 39616 computations (20.8% saved)

bsearch5.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	109
1	59	109
2	80	109
3	96	109
4	106	109
5	109	109
6	108	109

end2.0ms (0%)

Compiler: Compiled 73 to 53 computations (27.4% saved)

sample2.5s (23.3%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
584.0ms	4780×	body	128	nan

Compiler

Compiled 507 to 401 computations (20.9% saved)

Details

analyze1.8s (17.2%)

sample117.0ms (1.1%)

simplify54.0ms (0.5%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series392.0ms (3.7%)

rewrite31.0ms (0.3%)

simplify204.0ms (1.9%)

prune510.0ms (4.8%)

localize23.0ms (0.2%)

series387.0ms (3.7%)

rewrite27.0ms (0.3%)

simplify181.0ms (1.7%)

prune462.0ms (4.4%)

localize20.0ms (0.2%)

prune503.0ms (4.8%)

localize16.0ms (0.2%)

series383.0ms (3.6%)

rewrite41.0ms (0.4%)

simplify309.0ms (2.9%)

prune568.0ms (5.4%)

regimes2.0s (19.3%)

bsearch5.0ms (0%)

simplify6.0ms (0.1%)

end2.0ms (0%)

sample2.5s (23.3%)

Profiling