Details

analyze2.1s (14.8%)

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)

sample2.6s (18.7%)

Results

1.7s	8256×	body	128	valid
886.0ms	4751×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify48.0ms (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`

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

Stop Event

1×	node limit

Counts

1 → 2

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

9.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.7b	(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	(/.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))))
✓	8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series405.0ms (2.9%)

Counts

4 → 168

Calls

4 calls:

220.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
160.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
15.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
10.0ms	(pow.f64 (/.f64 t l) 2)

rewrite95.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 177

Calls

4 calls:

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

simplify176.0ms (1.2%)

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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

345 → 274

prune539.0ms (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	267	7	274
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	267	8	275

Error

1.5b

Counts

275 → 8

Alt Table

Status	Error	Program
	11.0b	(*.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))
	49.8b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	9.8b	(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))
✓	9.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	16.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (sqrt.f64 (pow.f64 (/.f64 t l) 4)) 1))))
	10.3b	(pow.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))))) 2)
	30.8b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (pow.f64 (/.f64 t l) 2) (/.f64 (.f64 Om Om) (.f64 Omc Omc))) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (/.f64 (.f64 Om Om) (*.f64 Omc Omc))))))
	49.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))

Compiler

Compiled 20400 to 14430 computations (29.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 t l) 2)
	0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.7b	(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))
✓	16.0b	(pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4)

series423.0ms (3%)

Counts

2 → 96

Calls

2 calls:

405.0ms

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

17.0ms

(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))

rewrite67.0ms (0.5%)

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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 54

Calls

2 calls:

65.0ms

(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))

65.0ms

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

simplify184.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

150 → 125

prune619.0ms (4.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	267	8	275

Error

1.5b

Counts

275 → 8

Alt Table

Status	Error	Program
	11.0b	(*.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))
	49.8b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.8b	(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))
✓	9.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	16.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (sqrt.f64 (pow.f64 (/.f64 t l) 4)) 1))))
▶	10.3b	(pow.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))))) 2)
	30.8b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (pow.f64 (/.f64 t l) 2) (/.f64 (.f64 Om Om) (.f64 Omc Omc))) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (/.f64 (.f64 Om Om) (*.f64 Omc Omc))))))
	49.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))

Compiler

Compiled 25908 to 17873 computations (31% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.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))))) 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))))
✓	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)))))
	8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series160.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

115.0ms

(pow.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))))) 2)

45.0ms

(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)))))

rewrite76.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

341×	`prod-diff_binary64`
177×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
168×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	56
1	371	56
2	4450	56
3	5184	56

Stop Event

1×	node limit

Counts

2 → 58

Calls

2 calls:

73.0ms

(pow.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))))) 2)

73.0ms

(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)))))

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-/l*_binary64`
460×	`associate-/r*_binary64`
381×	`associate-l_binary64`
371×	`unswap-sqr_binary64`
365×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	2976
1	37	2976
2	67	2976
3	186	2976
4	758	2976
5	4157	2976
6	5148	2976

Stop Event

1×	node limit

Counts

154 → 62

prune370.0ms (2.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	191	11	202

Error

1.5b

Counts

202 → 11

Alt Table

Status	Error	Program
	11.0b	(*.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))
	49.8b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.8b	(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))
✓	9.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
▶	10.5b	(pow.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 (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))))))) 2)
✓	10.3b	(pow.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))))) 2)
	11.1b	(pow.f64 (sqrt.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))))) 3)) 2)
	30.8b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (pow.f64 (/.f64 t l) 2) (/.f64 (.f64 Om Om) (.f64 Omc Omc))) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (/.f64 (.f64 Om Om) (*.f64 Omc Omc))))))
	49.9b	(pow.f64 (sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))) 2)
	49.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	50.6b	(pow.f64 (sqrt.f64 (asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))) 2)

Compiler

Compiled 16528 to 12099 computations (26.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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)))))
✓	7.5b	(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)))))
	8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series2.8s (19.7%)

Counts

1 → 48

Calls

1 calls:

2.8s	(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)))))

rewrite58.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

337×	`prod-diff_binary64`
178×	`add-sqr-sqrt_binary64`
170×	`log1p-expm1-u_binary64`
170×	`expm1-log1p-u_binary64`
167×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	365	29
2	4466	29
3	5173	29

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

57.0ms

(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)))))

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-/l*_binary64`
460×	`associate-/r*_binary64`
437×	`unswap-sqr_binary64`
412×	`associate-l_binary64`
368×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1536
1	43	1536
2	78	1536
3	206	1536
4	798	1536
5	4248	1536
6	5353	1536

Stop Event

1×	node limit

Counts

69 → 23

prune735.0ms (5.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	308	4	312
Fresh	1	6	7
Picked	1	0	1
Done	1	2	3
Total	311	12	323

Error

1.5b

Counts

323 → 12

Alt Table

Status	Error	Program
	19.6b	(pow.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 (sqrt.f64 (asin.f64 (log.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))) 2)
	30.8b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (pow.f64 (/.f64 t l) 2) (/.f64 (.f64 Om Om) (.f64 Omc Omc))) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (/.f64 (.f64 Om Om) (*.f64 Omc Omc))))))
	11.0b	(*.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))
	49.8b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	49.9b	(pow.f64 (sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))) 2)
	15.6b	(pow.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 (sqrt.f64 (asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))))) 2)
	10.5b	(pow.f64 (*.f64 (cbrt.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))))))) (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))))))) 2)
	49.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
✓	9.8b	(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))
✓	9.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	50.6b	(pow.f64 (sqrt.f64 (asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))) 2)
	11.5b	(pow.f64 (*.f64 (pow.f64 (cbrt.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)))))) 3) (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))))))) 2)

Compiler

Compiled 34363 to 25139 computations (26.8% saved)

regimes2.1s (14.8%)

Accuracy

Total 0.5b remaining (20.3%)

Threshold costs 0.5b (20.3%)

Counts

95 → 5

Compiler

Compiled 61299 to 47341 computations (22.8% saved)

bsearch6.0ms (0%)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
16×	`+-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	72	250
1	92	250
2	115	250
3	141	250
4	158	250
5	167	250
6	170	250
7	169	250

Stop Event

1×

saturated

end320.0ms (2.3%)

Compiler: Compiled 750 to 562 computations (25.1% saved)

Details

analyze2.1s (14.8%)

sample2.6s (18.7%)

simplify48.0ms (0.3%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series405.0ms (2.9%)

rewrite95.0ms (0.7%)

simplify176.0ms (1.2%)

prune539.0ms (3.8%)

localize16.0ms (0.1%)

series423.0ms (3%)

rewrite67.0ms (0.5%)

simplify184.0ms (1.3%)

prune619.0ms (4.4%)

localize14.0ms (0.1%)

series160.0ms (1.1%)

rewrite76.0ms (0.5%)

simplify103.0ms (0.7%)

prune370.0ms (2.6%)

localize17.0ms (0.1%)

series2.8s (19.7%)

rewrite58.0ms (0.4%)

simplify72.0ms (0.5%)

prune735.0ms (5.2%)

regimes2.1s (14.8%)

bsearch6.0ms (0%)

simplify10.0ms (0.1%)

end320.0ms (2.3%)

Profiling