Details

analyze1.8s (13.8%)

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)

sample119.0ms (0.9%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
13.0ms	128×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% 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

7.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.4b	(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 Om Omc) 2)
✓	0.2b	(pow.f64 (/.f64 t l) 2)
✓	0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	6.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series397.0ms (3%)

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)))
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 Om Omc) 2)
10.0ms	(pow.f64 (/.f64 t l) 2)

rewrite31.0ms (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:

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))))

simplify197.0ms (1.5%)

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

prune440.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	222	7	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	223	7	230

Error

0.6b

Counts

230 → 7

Alt Table

Status	Error	Program
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	21.0b	(-.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)))))
	8.6b	(.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))))))
	43.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	7.6b	(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))))
▶	7.4b	(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))))))
	11.2b	(asin.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 14718 to 10959 computations (25.5% saved)

localize17.0ms (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)
	0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	6.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

prune467.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	229	7	236

Error

0.6b

Counts

236 → 7

Alt Table

Status	Error	Program
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	21.0b	(-.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)))))
	8.6b	(.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))))))
	43.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	7.6b	(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))))
✓	7.4b	(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))))))
	11.2b	(asin.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 15152 to 11397 computations (24.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))
✓	0.6b	(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))))
✓	6.7b	(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)))
✓	16.1b	(cbrt.f64 (/.f64 t l))

series1.5s (11.7%)

Counts

4 → 144

Calls

4 calls:

696.0ms	(*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))
426.0ms	(cbrt.f64 (/.f64 t l))
378.0ms	(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)))
26.0ms	(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))))

rewrite53.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
100×	`times-frac_binary64`
82×	`*-un-lft-identity_binary64`
77×	`cbrt-prod_binary64`
61×	`add-cube-cbrt_binary64`

Counts

4 → 174

Calls

4 calls:

12.0ms	(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)))
11.0ms	(*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))
2.0ms	(cbrt.f64 (/.f64 t l))
0.0ms	(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))))

simplify242.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

542×	`fma-def_binary64`
401×	`times-frac_binary64`
354×	`associate-/r*_binary64`
283×	`associate-/l*_binary64`
224×	`*-commutative_binary64`

Counts

318 → 323

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	775	17618
1	1949	15431
2	4973	15431

prune698.0ms (5.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	393	2	395
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	394	8	402

Error

0.6b

Counts

402 → 8

Alt Table

Status	Error	Program
✓	7.6b	(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))))
	34.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 l))) (cbrt.f64 (/.f64 1 (sqrt.f64 l)))) (.f64 (cbrt.f64 (/.f64 t (sqrt.f64 l))) (cbrt.f64 (/.f64 t (sqrt.f64 l))))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	21.0b	(-.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)))))
	8.6b	(.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))))))
	43.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	7.4b	(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))))))
▶	7.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 t l) (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))

Compiler

Compiled 24012 to 14729 computations (38.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 t l) (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
✓	6.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 t l) (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1)))
	16.1b	(cbrt.f64 (/.f64 t l))
✓	26.4b	(cbrt.f64 (*.f64 (/.f64 t l) (/.f64 t l)))

series1.3s (10.1%)

Counts

3 → 120

Calls

3 calls:

672.0ms

(cbrt.f64 (*.f64 (/.f64 t l) (/.f64 t l)))

626.0ms

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

27.0ms

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

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
46×	`sqrt-prod_binary64`
42×	`*-un-lft-identity_binary64`
30×	`difference-of-squares_binary64`

Counts

3 → 84

Calls

3 calls:

11.0ms

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

5.0ms

(cbrt.f64 (*.f64 (/.f64 t l) (/.f64 t l)))

0.0ms

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

simplify305.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-def_binary64`
776×	`times-frac_binary64`
326×	`*-commutative_binary64`
154×	`associate-r_binary64`
148×	`+-commutative_binary64`

Counts

204 → 208

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	888	17609
1	2461	16205
2	4809	16169
3	4943	16169

prune531.0ms (4.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	244	8	252

Error

0.6b

Counts

252 → 8

Alt Table

Status	Error	Program
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	21.0b	(-.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)))))
	8.6b	(.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))))))
	34.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 t l) (/.f64 t l))) 2) (pow.f64 (*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 l))) (cbrt.f64 (/.f64 t (sqrt.f64 l)))) 2)) 1))))
	43.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	7.6b	(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))))
✓	7.4b	(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))))))
✓	7.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 t l) (/.f64 t l))) 2) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))

Compiler

Compiled 20249 to 13640 computations (32.6% saved)

regimes2.6s (20%)

Accuracy

Total 0.1b remaining (10.5%)

Threshold costs 0.1b (10.5%)

Counts

139 → 3

Compiler

Compiled 67441 to 49381 computations (26.8% saved)

bsearch6.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	34	97
1	48	97
2	66	97
3	79	97
4	88	97
5	91	97
6	90	97

end2.0ms (0%)

Compiler: Compiled 67 to 47 computations (29.9% saved)

sample2.2s (16.6%)

Algorithm

1×

intervals

Results

979.0ms	8000×	body	128	valid
521.0ms	4740×	body	128	nan

Compiler

Compiled 359 to 270 computations (24.8% saved)

Details

analyze1.8s (13.8%)

sample119.0ms (0.9%)

simplify52.0ms (0.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series397.0ms (3%)

rewrite31.0ms (0.2%)

simplify197.0ms (1.5%)

prune440.0ms (3.4%)

localize17.0ms (0.1%)

prune467.0ms (3.6%)

localize18.0ms (0.1%)

series1.5s (11.7%)

rewrite53.0ms (0.4%)

simplify242.0ms (1.8%)

prune698.0ms (5.3%)

localize18.0ms (0.1%)

series1.3s (10.1%)

rewrite33.0ms (0.3%)

simplify305.0ms (2.3%)

prune531.0ms (4.1%)

regimes2.6s (20%)

bsearch6.0ms (0%)

simplify5.0ms (0%)

end2.0ms (0%)

sample2.2s (16.6%)

Profiling