Details

analyze1.8s (15.7%)

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)

sample2.8s (23.7%)

Results

1.7s	8256×	body	128	valid
979.0ms	4752×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify52.0ms (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

8.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.3b	(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)
✓	0.5b	(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	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series398.0ms (3.4%)

Counts

4 → 144

Calls

4 calls:

357.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
20.0ms	(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)))
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))))

simplify191.0ms (1.6%)

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

prune511.0ms (4.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	222	7	229
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	222	8	230

Error

0.5b

Counts

230 → 8

Alt Table

Status	Error	Program
	9.5b	(.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))))))
▶	8.4b	(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))))
	8.8b	(*.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))))))
	12.4b	(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))
	40.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	43.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
✓	8.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	8.5b	(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))))))

Compiler

Compiled 14710 to 10963 computations (25.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.2b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	0.5b	(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))))
✓	7.7b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series404.0ms (3.4%)

Counts

3 → 120

Calls

3 calls:

367.0ms

(/.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))

rewrite40.0ms (0.3%)

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:

13.0ms

(/.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))))

simplify369.0ms (3.1%)

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

prune583.0ms (5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	300	4	304
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	301	11	312

Error

0.5b

Counts

312 → 11

Alt Table

Status	Error	Program
	9.5b	(.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))))))
✓	8.4b	(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))))
	45.5b	(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)))))
	8.8b	(*.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))))))
	12.4b	(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))
	39.7b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (/.f64 (.f64 t (sqrt.f64 2)) l)))))
	40.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	41.1b	(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	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
✓	8.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
▶	8.5b	(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))))))

Compiler

Compiled 18167 to 13530 computations (25.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(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))))))
	7.7b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	9.2b	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	9.2b	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

series405.0ms (3.4%)

Counts

3 → 120

Calls

3 calls:

206.0ms

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

182.0ms

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

16.0ms

(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))))))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`sqrt-prod_binary64`
99×	`add-sqr-sqrt_binary64`
88×	`times-frac_binary64`
77×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`

Counts

3 → 120

Calls

3 calls:

10.0ms

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

7.0ms

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

0.0ms

(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))))))

simplify355.0ms (3%)

Algorithm

1×	egg-herbie

Rules

933×	`times-frac_binary64`
613×	`cancel-sign-sub-inv_binary64`
489×	`fma-neg_binary64`
176×	`fma-def_binary64`
161×	`*-commutative_binary64`

Counts

240 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	380	12421
1	905	11307
2	2729	10848
3	4629	10728
4	4965	10728
5	4996	10728
6	4816	10728

prune472.0ms (4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	268	11	279

Error

0.5b

Counts

279 → 11

Alt Table

Status	Error	Program
	9.5b	(.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))))))
✓	8.4b	(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))))
	45.5b	(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)))))
	8.8b	(*.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))))))
	12.4b	(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))
	39.7b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (/.f64 (.f64 t (sqrt.f64 2)) l)))))
	40.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	8.5b	(expm1.f64 (log1p.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))))))))
	41.1b	(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	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
✓	8.3b	(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 15197 to 10492 computations (31% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(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))))))
	7.7b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
	9.2b	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	9.2b	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

prune479.0ms (4.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	268	11	279

Error

0.5b

Counts

279 → 11

Alt Table

Status	Error	Program
	9.5b	(.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))))))
✓	8.4b	(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))))
	45.5b	(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)))))
	8.8b	(*.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))))))
	12.4b	(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))
	39.7b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (/.f64 (.f64 t (sqrt.f64 2)) l)))))
	40.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	8.5b	(expm1.f64 (log1p.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))))))))
	41.1b	(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	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
✓	8.3b	(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 15429 to 10790 computations (30.1% saved)

regimes2.5s (21.1%)

Accuracy

Total 0.8b remaining (53.7%)

Threshold costs 0.8b (53.7%)

Counts

92 → 3

Compiler

Compiled 46438 to 36362 computations (21.7% saved)

bsearch6.0ms (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

end251.0ms (2.1%)

Compiler: Compiled 487 to 373 computations (23.4% saved)

Details

analyze1.8s (15.7%)

sample2.8s (23.7%)

simplify52.0ms (0.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series398.0ms (3.4%)

rewrite30.0ms (0.3%)

simplify191.0ms (1.6%)

prune511.0ms (4.3%)

localize13.0ms (0.1%)

series404.0ms (3.4%)

rewrite40.0ms (0.3%)

simplify369.0ms (3.1%)

prune583.0ms (5%)

localize17.0ms (0.1%)

series405.0ms (3.4%)

rewrite34.0ms (0.3%)

simplify355.0ms (3%)

prune472.0ms (4%)

localize22.0ms (0.2%)

prune479.0ms (4.1%)

regimes2.5s (21.1%)

bsearch6.0ms (0.1%)

simplify5.0ms (0%)

end251.0ms (2.1%)

Profiling