Details

analyze2.1s (9.4%)

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

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample2.7s (12.4%)

Results

1.7s	8256×	body	128	valid
955.0ms	4972×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify51.0ms (0.2%)

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

9.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.5b	(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)

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	(pow.f64 (/.f64 t l) 2)
✓	0.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	9.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series277.0ms (1.3%)

Counts

4 → 144

Calls

4 calls:

239.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
16.0ms	(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)

rewrite31.0ms (0.1%)

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:

11.0ms	(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 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))))

simplify190.0ms (0.9%)

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

prune412.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	223	6	229
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	223	7	230

Error

0.3b

Counts

230 → 7

Alt Table

Status	Error	Program
	9.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
	41.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
▶	9.5b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.7b	(.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))))))
	45.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	14.1b	(asin.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) 3)))

Compiler

Compiled 14644 to 10907 computations (25.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	7.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	7.1b	(sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	8.6b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series421.0ms (1.9%)

Counts

4 → 144

Calls

4 calls:

192.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
172.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
43.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
13.0ms	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

rewrite77.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

272×	`add-sqr-sqrt_binary64`
218×	`times-frac_binary64`
212×	`sqrt-prod_binary64`
183×	`*-un-lft-identity_binary64`
130×	`difference-of-squares_binary64`

Counts

4 → 282

Calls

4 calls:

15.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
15.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
3.0ms	(sqrt.f64 (/.f64 1 (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))

simplify371.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

367×	`fma-def_binary64`
340×	`times-frac_binary64`
295×	`associate-/l*_binary64`
285×	`associate-/r*_binary64`
194×	`associate-*r/_binary64`

Counts

426 → 438

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	678	22337
1	1798	19285
2	4962	19265
3	4990	19265

prune1.4s (6.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	475	1	476
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	475	8	483

Error

0.3b

Counts

483 → 8

Alt Table

Status	Error	Program
▶	9.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
	41.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
✓	9.5b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.7b	(.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))))))
	45.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	14.1b	(asin.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) 3)))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (.f64 (/.f64 (sqrt.f64 1/2) t) (*.f64 l (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))))

Compiler

Compiled 27054 to 19967 computations (26.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))
✓	9.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1)))
✓	14.6b	(cbrt.f64 (/.f64 t l))

series1.5s (7%)

Counts

4 → 120

Calls

4 calls:

577.0ms	(*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))
355.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
352.0ms	(cbrt.f64 (/.f64 t l))
254.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1)))

rewrite55.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`add-sqr-sqrt_binary64`
109×	`times-frac_binary64`
91×	`*-un-lft-identity_binary64`
90×	`cbrt-prod_binary64`
70×	`add-cube-cbrt_binary64`

Counts

4 → 198

Calls

4 calls:

13.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1)))
10.0ms	(*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))
3.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
2.0ms	(cbrt.f64 (/.f64 t l))

simplify289.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-def_binary64`
398×	`times-frac_binary64`
352×	`associate-/r*_binary64`
279×	`associate-/l*_binary64`
227×	`*-commutative_binary64`

Counts

318 → 343

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	799	16269
1	2017	14297
2	4878	14164
3	5135	14164

prune627.0ms (2.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	421	0	421
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	421	8	429

Error

0.3b

Counts

429 → 8

Alt Table

Status	Error	Program
✓	9.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
	41.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
✓	9.5b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
▶	10.7b	(.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))))))
	45.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	14.1b	(asin.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) 3)))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (.f64 (/.f64 (sqrt.f64 1/2) t) (*.f64 l (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))))

Compiler

Compiled 24942 to 15218 computations (39% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	0.7b	(*.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))))))
✓	7.8b	(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)))))
	9.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series6.1s (27.7%)

Counts

2 → 96

Calls

2 calls:

3.3s

(*.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))))))

2.8s

(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)))))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms

(*.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))))))

1.0ms

(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)))))

simplify197.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
514×	`associate-/l/_binary64`
485×	`associate-/r*_binary64`
386×	`associate-/r/_binary64`
341×	`unswap-sqr_binary64`

Counts

151 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	6090
1	125	5658
2	258	5238
3	732	5168
4	1860	4702
5	4454	4702
6	4996	4702
7	4928	4702

prune1.5s (6.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	548	3	551
Fresh	1	3	4
Picked	1	0	1
Done	0	3	3
Total	550	9	559

Error

0.3b

Counts

559 → 9

Alt Table

Status	Error	Program
✓	9.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
	41.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	10.1b	(.f64 (cbrt.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (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))))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (.f64 (/.f64 (sqrt.f64 1/2) t) (*.f64 l (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))))
	11.4b	(.f64 (.f64 (pow.f64 (cbrt.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)))))) 4) (pow.f64 (cbrt.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)))))) 2)) (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))))))
	45.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	10.7b	(.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 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
✓	9.5b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 63015 to 46468 computations (26.3% saved)

regimes3.3s (15.2%)

Accuracy

Total 0.2b remaining (21.7%)

Threshold costs 0.2b (21.7%)

Counts

121 → 3

Compiler

Compiled 98285 to 75381 computations (23.3% saved)

bsearch8.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	97
1	46	97
2	64	97
3	77	97
4	86	97
5	89	97
6	88	97

end260.0ms (1.2%)

Compiler: Compiled 515 to 384 computations (25.4% saved)

Details

analyze2.1s (9.4%)

sample2.7s (12.4%)

simplify51.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series277.0ms (1.3%)

rewrite31.0ms (0.1%)

simplify190.0ms (0.9%)

prune412.0ms (1.9%)

localize18.0ms (0.1%)

series421.0ms (1.9%)

rewrite77.0ms (0.3%)

simplify371.0ms (1.7%)

prune1.4s (6.4%)

localize18.0ms (0.1%)

series1.5s (7%)

rewrite55.0ms (0.3%)

simplify289.0ms (1.3%)

prune627.0ms (2.8%)

localize15.0ms (0.1%)

series6.1s (27.7%)

rewrite10.0ms (0%)

simplify197.0ms (0.9%)

prune1.5s (6.7%)

regimes3.3s (15.2%)

bsearch8.0ms (0%)

simplify5.0ms (0%)

end260.0ms (1.2%)

Profiling