Details

analyze3.4s (6%)

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)

sample4.6s (8.1%)

Results

2.8s	8256×	body	128	valid
1.7s	4968×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify87.0ms (0.2%)

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

prune7.0ms (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

11.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.3b	(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)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 t l) 2)
✓	0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	10.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series1.1s (2%)

Counts

4 → 168

Calls

4 calls:

663.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
402.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
36.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
19.0ms	(pow.f64 (/.f64 t l) 2)

rewrite211.0ms (0.4%)

Algorithm

2×	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`

Counts

4 → 177

Calls

4 calls:

198.0ms	(pow.f64 (/.f64 t l) 2)
198.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
198.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
198.0ms	(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
0	0	0
1	0	0

simplify346.0ms (0.6%)

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

345 → 274

Iterations

Useful iterations: 1 (0.0ms)

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

prune1.1s (2%)

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

1.8b

Counts

275 → 8

Alt Table

Status	Error	Program
	28.4b	(+.f64 (fma.f64 (PI.f64) 1/2 (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)))))) (fma.f64 (neg.f64 (sqrt.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (sqrt.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	47.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	13.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (*.f64 (/.f64 l t) l)) 1))))
▶	12.5b	(*.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))
	48.9b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	30.3b	(+.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)))
	15.2b	(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)))
✓	11.3b	(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 20608 to 14594 computations (29.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	0.8b	(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)
✓	5.5b	(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)))))
	10.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series13.7s (23.9%)

Counts

2 → 96

Calls

2 calls:

6.9s

(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)))))

6.8s

(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)

rewrite90.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

337×	`prod-diff_binary64`
186×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
175×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

88.0ms

(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)

88.0ms

(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)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	61
1	386	59
2	4604	59
3	5308	59
0	0	0
1	0	0

simplify253.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-/l*_binary64`
474×	`associate-l_binary64`
460×	`associate-/r*_binary64`
408×	`associate-r_binary64`
365×	`fma-def_binary64`

Counts

137 → 45

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	3216
1	51	3216
2	89	3216
3	230	3216
4	858	3216
5	4409	3216
6	4980	3216
7	4986	3216
8	4950	3216

prune1.7s (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	331	3	334
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	333	9	342

Error

1.8b

Counts

342 → 9

Alt Table

Status	Error	Program
	28.4b	(+.f64 (fma.f64 (PI.f64) 1/2 (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)))))) (fma.f64 (neg.f64 (sqrt.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (sqrt.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	47.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	13.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (*.f64 (/.f64 l t) l)) 1))))
▶	12.6b	(.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 (.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))))) 2) (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))
	48.9b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	24.6b	(*.f64 (cbrt.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))))))) (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))
	15.2b	(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)))
	13.4b	(*.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 (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) 2))
✓	11.3b	(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 35474 to 25859 computations (27.1% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(pow.f64 (cbrt.f64 (*.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))))) 2) (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)
	5.5b	(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)))))
✓	5.5b	(cbrt.f64 (*.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))))) 2) (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)))))))
	10.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series14.5s (25.2%)

Counts

2 → 96

Calls

2 calls:

7.4s

(pow.f64 (cbrt.f64 (*.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))))) 2) (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)

7.1s

(cbrt.f64 (*.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))))) 2) (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)))))))

rewrite109.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

353×	`prod-diff_binary64`
186×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
177×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

106.0ms

(pow.f64 (cbrt.f64 (*.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))))) 2) (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)

106.0ms

(cbrt.f64 (*.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))))) 2) (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)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	61
1	393	59
2	4625	59
3	5369	59
0	0	0
1	0	0

simplify272.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-/l*_binary64`
474×	`associate-l_binary64`
460×	`associate-/r*_binary64`
408×	`associate-r_binary64`
365×	`fma-def_binary64`

Counts

137 → 45

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	3216
1	51	3216
2	89	3216
3	230	3216
4	858	3216
5	4409	3216
6	4980	3216
7	4986	3216
8	4950	3216

prune2.5s (4.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	407	1	408
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	408	9	417

Error

1.8b

Counts

417 → 9

Alt Table

Status	Error	Program
	28.4b	(+.f64 (fma.f64 (PI.f64) 1/2 (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)))))) (fma.f64 (neg.f64 (sqrt.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (sqrt.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	47.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	13.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (*.f64 (/.f64 l t) l)) 1))))
✓	12.6b	(.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 (.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))))) 2) (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))
	48.9b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	24.6b	(.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 (.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))))) 2) (cbrt.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))
	15.2b	(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)))
▶	13.4b	(*.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 (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) 2))
✓	11.3b	(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 53177 to 38955 computations (26.7% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(pow.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) 2)
✓	0.9b	(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)
	5.5b	(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)))))
	10.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series10.2s (17.8%)

Counts

2 → 96

Calls

2 calls:

5.8s

(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)

4.4s

(pow.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) 2)

rewrite65.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

202×	`add-sqr-sqrt_binary64`
198×	`log1p-expm1-u_binary64`
198×	`expm1-log1p-u_binary64`
192×	`add-cbrt-cube_binary64`
191×	`add-log-exp_binary64`

Counts

2 → 36

Calls

2 calls:

63.0ms

(pow.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) 2)

63.0ms

(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)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	61
1	433	59
2	4658	59
3	5013	59
0	0	0
1	0	0

simplify151.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-/l*_binary64`
474×	`associate-l_binary64`
460×	`associate-/r*_binary64`
408×	`associate-r_binary64`
365×	`fma-def_binary64`

Counts

132 → 40

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	3216
1	51	3216
2	89	3216
3	230	3216
4	858	3216
5	4409	3216
6	4980	3216
7	4986	3216
8	4950	3216

prune629.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	282	9	291

Error

1.8b

Counts

291 → 9

Alt Table

Status	Error	Program
	28.4b	(+.f64 (fma.f64 (PI.f64) 1/2 (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)))))) (fma.f64 (neg.f64 (sqrt.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (sqrt.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	47.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	13.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (*.f64 (/.f64 l t) l)) 1))))
✓	12.6b	(.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 (.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))))) 2) (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))
	48.9b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	24.6b	(.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 (.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))))) 2) (cbrt.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))
	13.6b	(*.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) (pow.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) 2))
	15.2b	(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)))
✓	11.3b	(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 31055 to 22906 computations (26.2% saved)

regimes1.8s (3.2%)

Accuracy

Total 1.3b remaining (44.4%)

Threshold costs 0b (0%)

Counts

82 → 3

Compiler

Compiled 55873 to 44180 computations (20.9% saved)

bsearch5.0ms (0%)

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`+-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	45	105
1	63	105
2	86	105
3	112	105
4	129	105
5	138	105
6	141	105
7	140	105

end263.0ms (0.5%)

Compiler: Compiled 533 to 405 computations (24% saved)

Details

analyze3.4s (6%)

sample4.6s (8.1%)

simplify87.0ms (0.2%)

prune7.0ms (0%)

localize24.0ms (0%)

series1.1s (2%)

rewrite211.0ms (0.4%)

simplify346.0ms (0.6%)

prune1.1s (2%)

localize29.0ms (0.1%)

series13.7s (23.9%)

rewrite90.0ms (0.2%)

simplify253.0ms (0.4%)

prune1.7s (2.9%)

localize38.0ms (0.1%)

series14.5s (25.2%)

rewrite109.0ms (0.2%)

simplify272.0ms (0.5%)

prune2.5s (4.4%)

localize37.0ms (0.1%)

series10.2s (17.8%)

rewrite65.0ms (0.1%)

simplify151.0ms (0.3%)

prune629.0ms (1.1%)

regimes1.8s (3.2%)

bsearch5.0ms (0%)

simplify7.0ms (0%)

end263.0ms (0.5%)

Profiling