Details

analyze2.0s (11.4%)

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 (15.2%)

Results

1.6s	8256×	body	128	valid
966.0ms	4946×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify54.0ms (0.3%)

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

11.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.5b	(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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	10.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series416.0ms (2.4%)

Counts

4 → 144

Calls

4 calls:

373.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
21.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
12.0ms	(pow.f64 (/.f64 Om Omc) 2)
9.0ms	(pow.f64 (/.f64 t l) 2)

rewrite33.0ms (0.2%)

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:

13.0ms	(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 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))))

simplify196.0ms (1.1%)

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

prune451.0ms (2.6%)

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

0.8b

Counts

230 → 9

Alt Table

Status	Error	Program
	28.8b	(asin.f64 (-.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))) (.f64 1/2 (.f64 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1)))))))
	16.2b	(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))
	36.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (sqrt.f64 (/.f64 t l)) 2) (pow.f64 (sqrt.f64 (/.f64 t l)) 2)) 1))))
	41.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	44.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	12.0b	(*.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	25.0b	(-.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)))))
	12.5b	(.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))))))
▶	11.5b	(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))))

Compiler

Compiled 14812 to 11053 computations (25.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.3b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	0.7b	(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))))
✓	10.6b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series389.0ms (2.2%)

Counts

3 → 120

Calls

3 calls:

352.0ms

(/.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

(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))))

18.0ms

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

rewrite43.0ms (0.2%)

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:

15.0ms

(/.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))

1.0ms

(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))))

simplify310.0ms (1.8%)

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 (3.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	299	5	304
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	299	14	313

Error

0.7b

Counts

313 → 14

Alt Table

Status	Error	Program
	28.8b	(asin.f64 (-.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))) (.f64 1/2 (.f64 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1)))))))
	16.2b	(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))
	41.9b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	36.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (sqrt.f64 (/.f64 t l)) 2) (pow.f64 (sqrt.f64 (/.f64 t l)) 2)) 1))))
	41.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	12.5b	(.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))))))
	41.9b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	47.4b	(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)))))
	44.8b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	44.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
▶	12.0b	(*.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	25.0b	(-.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)))))
	44.8b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
✓	11.5b	(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))))

Compiler

Compiled 18333 to 13679 computations (25.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.f64 (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	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	7.3b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	10.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series78.0ms (0.4%)

Counts

2 → 96

Calls

2 calls:

58.0ms

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

20.0ms

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

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms

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

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

simplify220.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

546×	`unswap-sqr_binary64`
501×	`associate-/l/_binary64`
474×	`associate-/r*_binary64`
373×	`associate-/r/_binary64`
357×	`fma-def_binary64`

Counts

164 → 79

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	69	5750
1	113	5133
2	241	5005
3	594	4809
4	1612	4634
5	4219	4634
6	4600	4630
7	4956	4630
8	4878	4630

prune973.0ms (5.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	385	7	392
Fresh	3	9	12
Picked	1	0	1
Done	1	0	1
Total	390	16	406

Error

0.7b

Counts

406 → 16

Alt Table

Status	Error	Program
	28.8b	(asin.f64 (-.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))) (.f64 1/2 (.f64 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1)))))))
	13.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.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 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))) (.f64 (cbrt.f64 (sqrt.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 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))) (*.f64 (cbrt.f64 (sqrt.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 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	41.9b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	12.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (sqrt.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))) (*.f64 (sqrt.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (sqrt.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	36.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (sqrt.f64 (/.f64 t l)) 2) (pow.f64 (sqrt.f64 (/.f64 t l)) 2)) 1))))
	41.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	11.5b	(fabs.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	47.4b	(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)))))
	44.8b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	12.1b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	12.5b	(*.f64 (pow.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))))) 5/2) (sqrt.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)))))))
	41.9b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	12.0b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.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))))))))
	44.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	44.8b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
	12.3b	(.f64 (sqrt.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))))))) (*.f64 (sqrt.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)))))) (sqrt.f64 (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 36743 to 27388 computations (25.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
	0.3b	(pow.f64 (/.f64 t l) 2)
	0.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	10.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

prune484.0ms (2.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	229	16	245

Error

0.7b

Counts

245 → 16

Alt Table

Status	Error	Program
	13.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.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 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))) (.f64 (cbrt.f64 (sqrt.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 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))) (*.f64 (cbrt.f64 (sqrt.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 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	41.9b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	12.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (sqrt.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))) (*.f64 (sqrt.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (sqrt.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	36.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (sqrt.f64 (/.f64 t l)) 2) (pow.f64 (sqrt.f64 (/.f64 t l)) 2)) 1))))
	41.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	11.5b	(fabs.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	47.4b	(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)))))
	44.8b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	12.1b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	12.5b	(*.f64 (pow.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))))) 5/2) (sqrt.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)))))))
	41.9b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	25.6b	(fabs.f64 (asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1)))))
	12.0b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (sqrt.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))))))))
	44.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	44.8b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
	12.3b	(.f64 (sqrt.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))))))) (*.f64 (sqrt.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)))))) (sqrt.f64 (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 15158 to 11353 computations (25.1% saved)

regimes8.1s (46.4%)

Accuracy

Total 0.2b remaining (21.8%)

Threshold costs 0.2b (21.8%)

Counts

325 → 3

Compiler

Compiled 231287 to 178440 computations (22.8% saved)

bsearch21.0ms (0.1%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	36	101
1	51	101
2	72	101
3	87	101
4	97	101
5	100	101
6	99	101

end415.0ms (2.4%)

Compiler: Compiled 845 to 639 computations (24.4% saved)

Details

analyze2.0s (11.4%)

sample2.7s (15.2%)

simplify54.0ms (0.3%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series416.0ms (2.4%)

rewrite33.0ms (0.2%)

simplify196.0ms (1.1%)

prune451.0ms (2.6%)

localize12.0ms (0.1%)

series389.0ms (2.2%)

rewrite43.0ms (0.2%)

simplify310.0ms (1.8%)

prune568.0ms (3.2%)

localize15.0ms (0.1%)

series78.0ms (0.4%)

rewrite14.0ms (0.1%)

simplify220.0ms (1.3%)

prune973.0ms (5.6%)

localize14.0ms (0.1%)

prune484.0ms (2.8%)

regimes8.1s (46.4%)

bsearch21.0ms (0.1%)

simplify5.0ms (0%)

end415.0ms (2.4%)

Profiling