Details

analyze1.9s (14.1%)

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)

sample3.0s (22.6%)

Results

1.9s	8256×	body	128	valid
1.1s	4933×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify50.0ms (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

10.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.8b	(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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 t l) 2)
✓	0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	9.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series426.0ms (3.2%)

Counts

4 → 168

Calls

4 calls:

233.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
163.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
17.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
13.0ms	(pow.f64 (/.f64 t l) 2)

rewrite108.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

325×	`prod-diff_binary64`
181×	`egg-rr`
170×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`

Counts

4 → 181

Calls

4 calls:

102.0ms	(pow.f64 (/.f64 t l) 2)
102.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
102.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
102.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	82
1	348	82
2	4282	82
3	4971	82

simplify221.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
471×	`times-frac_binary64`
399×	`associate-/r*_binary64`
321×	`associate-/l*_binary64`
220×	`associate-*l/_binary64`

Counts

349 → 277

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	14080
1	1671	12450
2	4999	12450

prune586.0ms (4.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	268	9	277
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	268	10	278

Error

1.9b

Counts

278 → 10

Alt Table

Status	Error	Program
	10.9b	(asin.f64 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	46.0b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	10.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
▶	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))))
	45.4b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	34.2b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) 1 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1)))
✓	10.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	10.8b	(asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4) 2))
	11.8b	(*.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))))) (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))))) 2))
	26.6b	(-.f64 (exp.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)))))) 1)

Compiler

Compiled 20702 to 14662 computations (29.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 l t) (/.f64 l t))
✓	0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))
✓	0.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))))
✓	9.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1)))

series483.0ms (3.6%)

Counts

4 → 168

Calls

4 calls:

246.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1)))
191.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))
27.0ms	(*.f64 (/.f64 l t) (/.f64 l t))
18.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))))

rewrite111.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

344×	`prod-diff_binary64`
186×	`add-sqr-sqrt_binary64`
182×	`egg-rr`
177×	`log1p-expm1-u_binary64`
177×	`expm1-log1p-u_binary64`

Counts

4 → 182

Calls

4 calls:

105.0ms	(*.f64 (/.f64 l t) (/.f64 l t))
105.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))
105.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))))
105.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	91
1	379	82
2	4755	82
3	5485	82

simplify176.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
471×	`times-frac_binary64`
399×	`associate-/r*_binary64`
321×	`associate-/l*_binary64`
219×	`associate-*l/_binary64`

Counts

350 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	529	13936
1	1662	13086
2	4993	13086

prune1.3s (9.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	278	10	288

Error

1.9b

Counts

288 → 10

Alt Table

Status	Error	Program
	46.0b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	10.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
✓	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))))
	45.4b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	34.2b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) 1 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1)))
	10.9b	(asin.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 l t) -2) 1))) 3)))
✓	10.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
▶	10.8b	(asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4) 2))
	11.8b	(*.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))))) (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))))) 2))
	26.6b	(-.f64 (exp.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)))))) 1)

Compiler

Compiled 20901 to 14568 computations (30.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 t l) 2)
	0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.4b	(asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4) 2))
✓	15.7b	(pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4)

series430.0ms (3.2%)

Counts

2 → 96

Calls

2 calls:

411.0ms

(pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4)

18.0ms

(asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4) 2))

rewrite88.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

325×	`prod-diff_binary64`
186×	`add-sqr-sqrt_binary64`
185×	`log1p-expm1-u_binary64`
185×	`expm1-log1p-u_binary64`
178×	`add-cbrt-cube_binary64`

Counts

2 → 56

Calls

2 calls:

86.0ms

(asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4) 2))

86.0ms

(pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	54
1	398	53
2	4618	53
3	5253	53

simplify182.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

677×	`associate-/l*_binary64`
673×	`associate-/r*_binary64`
609×	`fma-def_binary64`
228×	`*-commutative_binary64`
138×	`+-commutative_binary64`

Counts

152 → 127

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	582	14677
1	2145	13928
2	5473	13928

prune652.0ms (4.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	270	10	280

Error

1.9b

Counts

280 → 10

Alt Table

Status	Error	Program
	46.0b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
▶	10.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
✓	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))))
	45.4b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	34.2b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) 1 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1)))
	10.9b	(asin.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 l t) -2) 1))) 3)))
✓	10.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	10.8b	(asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4) 2))
	11.8b	(*.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))))) (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))))) 2))
	26.6b	(-.f64 (exp.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)))))) 1)

Compiler

Compiled 26152 to 18066 computations (30.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
✓	9.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1)))
✓	13.4b	(cbrt.f64 (/.f64 t l))

series999.0ms (7.5%)

Counts

4 → 144

Calls

4 calls:

359.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
354.0ms	(cbrt.f64 (/.f64 t l))
263.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1)))
22.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))

rewrite93.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`prod-diff_binary64`
195×	`add-sqr-sqrt_binary64`
188×	`log1p-expm1-u_binary64`
188×	`expm1-log1p-u_binary64`
185×	`add-cbrt-cube_binary64`

Counts

4 → 119

Calls

4 calls:

90.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
90.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
90.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1)))
90.0ms	(cbrt.f64 (/.f64 t l))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	73
1	408	67
2	4692	67
3	5199	67

simplify156.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
396×	`times-frac_binary64`
338×	`associate-/r*_binary64`
334×	`associate-l_binary64`
254×	`associate-/l*_binary64`

Counts

263 → 202

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	471	11917
1	1478	11073
2	5323	11073

prune437.0ms (3.3%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	241	10	251

Error

1.9b

Counts

251 → 10

Alt Table

Status	Error	Program
	46.0b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
✓	10.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
✓	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 1 (*.f64 (/.f64 l t) (/.f64 l t))) 1))))
	45.4b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	34.2b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) 1 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1)))
	10.9b	(asin.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 l t) -2) 1))) 3)))
✓	10.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	10.8b	(asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4) 2))
	11.8b	(*.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))))) (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))))) 2))
	26.6b	(-.f64 (exp.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)))))) 1)

Compiler

Compiled 16656 to 11204 computations (32.7% saved)

regimes1.7s (12.5%)

Accuracy

Total 1.1b remaining (37.9%)

Threshold costs 0b (0%)

Counts

96 → 3

Compiler

Compiled 37497 to 30383 computations (19% saved)

bsearch4.0ms (0%)

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	106
1	61	106
2	84	106
3	110	106
4	127	106
5	136	106
6	139	106
7	138	106

end241.0ms (1.8%)

Compiler: Compiled 473 to 357 computations (24.5% saved)

Details

analyze1.9s (14.1%)

sample3.0s (22.6%)

simplify50.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series426.0ms (3.2%)

rewrite108.0ms (0.8%)

simplify221.0ms (1.7%)

prune586.0ms (4.4%)

localize14.0ms (0.1%)

series483.0ms (3.6%)

rewrite111.0ms (0.8%)

simplify176.0ms (1.3%)

prune1.3s (9.4%)

localize14.0ms (0.1%)

series430.0ms (3.2%)

rewrite88.0ms (0.7%)

simplify182.0ms (1.4%)

prune652.0ms (4.9%)

localize16.0ms (0.1%)

series999.0ms (7.5%)

rewrite93.0ms (0.7%)

simplify156.0ms (1.2%)

prune437.0ms (3.3%)

regimes1.7s (12.5%)

bsearch4.0ms (0%)

simplify7.0ms (0%)

end241.0ms (1.8%)

Profiling