Details

analyze1.8s (11.3%)

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)

sample109.0ms (0.7%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
15.0ms	126×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify47.0ms (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

9.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.8b	(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)
✓	0.3b	(pow.f64 (/.f64 t l) 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))))
✓	9.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series394.0ms (2.5%)

Counts

4 → 144

Calls

4 calls:

355.0ms	(sqrt.f64 (/.f64 (-.f64 1 (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 (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 (0.2%)

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)))
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))))

simplify187.0ms (1.2%)

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

prune449.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	219	10	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	220	10	230

Error

0.6b

Counts

230 → 10

Alt Table

Status	Error	Program
	9.9b	(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))))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	10.3b	(*.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))))))
	41.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	22.7b	(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))))
	23.4b	(-.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)))))
	13.7b	(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)))
	11.0b	(.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))))))
	14.1b	(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))
▶	9.8b	(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 14846 to 11083 computations (25.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.5b	(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))))
✓	2.5b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
✓	9.1b	(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)))

series381.0ms (2.4%)

Counts

3 → 120

Calls

3 calls:

351.0ms

(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)))

19.0ms

(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)))

rewrite23.0ms (0.1%)

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)))

4.0ms

(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))))

simplify164.0ms (1%)

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

prune451.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	238	10	248

Error

0.6b

Counts

248 → 10

Alt Table

Status	Error	Program
	22.7b	(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))))
	11.0b	(.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))))))
▶	9.9b	(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))))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	10.3b	(*.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))))))
	41.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	23.4b	(-.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)))))
	13.7b	(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)))
	14.1b	(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))
✓	9.8b	(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 15192 to 11441 computations (24.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(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))))))
✓	2.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	9.3b	(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)))))
✓	14.6b	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series348.0ms (2.2%)

Counts

4 → 144

Calls

4 calls:

230.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
54.0ms	(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)))))
43.0ms	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
21.0ms	(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))))))

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
103×	`times-frac_binary64`
95×	`sqrt-prod_binary64`
85×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`

Counts

4 → 158

Calls

4 calls:

16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
4.0ms	(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)))))
1.0ms	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.0ms	(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))))))

simplify348.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

461×	`fma-neg_binary64`
314×	`sub-neg_binary64`
221×	`*-commutative_binary64`
220×	`fma-def_binary64`
196×	`associate-r_binary64`

Counts

302 → 281

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	578	15791
1	1374	13566
2	4064	13072
3	4583	12670
4	4832	12670
5	4922	12670

prune686.0ms (4.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	363	0	363
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	363	10	373

Error

0.6b

Counts

373 → 10

Alt Table

Status	Error	Program
	22.7b	(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))))
	11.0b	(.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))))))
✓	9.9b	(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))))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	10.3b	(*.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))))))
	41.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	23.4b	(-.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)))))
	13.7b	(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)))
	14.1b	(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))
✓	9.8b	(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 23976 to 17810 computations (25.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))))
✓	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))))))
✓	7.9b	(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)))))
	9.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series82.0ms (0.5%)

Counts

2 → 96

Calls

2 calls:

61.0ms

(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))))))

rewrite15.0ms (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:

6.0ms

(*.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)))))

simplify201.0ms (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

prune1.0s (6.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	386	6	392
Fresh	3	4	7
Picked	1	0	1
Done	1	1	2
Total	391	11	402

Error

0.5b

Counts

402 → 11

Alt Table

Status	Error	Program
	22.7b	(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))))
	11.0b	(.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))))))
	10.3b	(*.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 (expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	11.0b	(*.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)))))))
	9.9b	(.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))))))))
	11.3b	(.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))))))) (pow.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)))))) 4))
	10.4b	(.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))))))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	10.3b	(.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 (fabs.f64 (/.f64 Om Omc))) (*.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 (fabs.f64 (/.f64 Om Omc))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	41.3b	(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 (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 35816 to 26677 computations (25.5% saved)

regimes6.4s (40.6%)

Accuracy

Total 0.1b remaining (14%)

Threshold costs 0.1b (14%)

Counts

246 → 3

Compiler

Compiled 161382 to 125115 computations (22.5% saved)

bsearch16.0ms (0.1%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
11×	`+-commutative_binary64`
11×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	118
1	53	118
2	76	118
3	94	118
4	106	118
5	110	118
6	109	118

end1.0ms (0%)

Compiler: Compiled 79 to 56 computations (29.1% saved)

sample2.5s (16%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
564.0ms	4599×	body	128	nan

Compiler

Compiled 642 to 491 computations (23.5% saved)

Details

analyze1.8s (11.3%)

sample109.0ms (0.7%)

simplify47.0ms (0.3%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series394.0ms (2.5%)

rewrite31.0ms (0.2%)

simplify187.0ms (1.2%)

prune449.0ms (2.9%)

localize14.0ms (0.1%)

series381.0ms (2.4%)

rewrite23.0ms (0.1%)

simplify164.0ms (1%)

prune451.0ms (2.9%)

localize17.0ms (0.1%)

series348.0ms (2.2%)

rewrite46.0ms (0.3%)

simplify348.0ms (2.2%)

prune686.0ms (4.4%)

localize14.0ms (0.1%)

series82.0ms (0.5%)

rewrite15.0ms (0.1%)

simplify201.0ms (1.3%)

prune1.0s (6.4%)

regimes6.4s (40.6%)

bsearch16.0ms (0.1%)

simplify6.0ms (0%)

end1.0ms (0%)

sample2.5s (16%)

Profiling