Details

analyze2.2s (16.8%)

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)

sample3.2s (25.1%)

Results

2.2s	8256×	body	128	valid
930.0ms	4779×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify63.0ms (0.5%)

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

10.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.5b	(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)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	9.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series917.0ms (7.1%)

Counts

4 → 168

Calls

4 calls:

504.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
385.0ms	(/.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))))
10.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite293.0ms (2.3%)

Algorithm

4×	egg-rewrite

Rules

90×	`egg`
67×	`egg`
34×	`egg`
31×	`egg`

Counts

4 → 222

Calls

4 calls:

85.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
82.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
76.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
44.0ms	(pow.f64 (/.f64 Om Omc) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	325	25
2	3995	25
3	5092	25
0	16	27
1	348	27
2	4282	27
3	4971	27
0	6	7
1	127	7
2	1435	7
3	5503	7
0	14	23
1	305	23
2	3779	23
3	5221	23

simplify192.0ms (1.5%)

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

390 → 318

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	13738
1	1671	12522
2	4999	12522

prune912.0ms (7.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	310	8	318
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	311	8	319

Error

2.0b

Counts

319 → 8

Alt Table

Status	Error	Program
	14.6b	(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))
	30.9b	(+.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)))
	11.6b	(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)
	47.5b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	10.6b	(asin.f64 (sqrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) 2) (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 2)) (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.5b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	46.1b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	10.5b	(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))))

Compiler

Compiled 21723 to 15347 computations (29.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.8b	(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))))
✓	3.2b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
✓	9.5b	(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)))

series462.0ms (3.6%)

Counts

3 → 120

Calls

3 calls:

433.0ms

(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)))

18.0ms

(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))))

10.0ms

(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))

rewrite231.0ms (1.8%)

Algorithm

3×	egg-rewrite

Rules

48×	`egg`
36×	`egg`
33×	`egg`

Counts

3 → 117

Calls

3 calls:

78.0ms

(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))))

76.0ms

(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))

74.0ms

(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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	25
1	341	25
2	4166	25
3	5286	25
0	8	7
1	143	7
2	1606	7
3	4971	7
4	5121	7
0	18	27
1	364	27
2	4453	27
3	5141	27

simplify157.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

237 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	11149
1	1400	10035
2	5174	10035

prune409.0ms (3.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	250	8	258

Error

2.0b

Counts

258 → 8

Alt Table

Status	Error	Program
	14.6b	(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))
	30.9b	(+.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)))
	11.6b	(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)
	47.5b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	10.6b	(asin.f64 (sqrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) 2) (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 2)) (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
▶	10.5b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	46.1b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	10.5b	(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))))

Compiler

Compiled 16030 to 11462 computations (28.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.4b	(/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	0.8b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	9.3b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series68.0ms (0.5%)

Counts

3 → 96

Calls

3 calls:

34.0ms

(/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

17.0ms

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

16.0ms

(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

rewrite174.0ms (1.3%)

Algorithm

3×	egg-rewrite

Rules

36×	`egg`
29×	`egg`
23×	`egg`

Counts

3 → 88

Calls

3 calls:

76.0ms

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

52.0ms

(/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

44.0ms

(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	180	13
2	1923	13
3	4929	13
0	18	29
1	386	27
2	4485	27
3	4986	27
0	10	16
1	206	14
2	2233	14
3	5187	14

simplify105.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-/l*_binary64`
518×	`associate-/r*_binary64`
308×	`fma-neg_binary64`
297×	`fma-def_binary64`
270×	`associate-l_binary64`

Counts

184 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	3069
1	372	2997
2	1333	2816
3	4995	2816
4	5155	2816

prune279.0ms (2.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	193	7	200
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	196	12	208

Error

0.8b

Counts

208 → 12

Alt Table

Status	Error	Program
	30.9b	(+.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)))
	43.2b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	14.6b	(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))
✓	10.5b	(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))))
	49.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) t) l (.f64 (/.f64 (pow.f64 l 5) (pow.f64 t 5)) (-.f64 (/.f64 1/16 (sqrt.f64 1/2)) (/.f64 1/64 (sqrt.f64 1/2))))) (.f64 (/.f64 (pow.f64 l 3) (.f64 (pow.f64 t 3) (sqrt.f64 1/2))) -1/8))))
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 -1 (/.f64 (*.f64 (sqrt.f64 1/2) l) t))))
	11.6b	(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)
	45.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 (sqrt.f64 1/2) l) t)))
✓	10.5b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	43.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (neg.f64 (/.f64 (.f64 t (sqrt.f64 2)) l)))))
	45.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (/.f64 (.f64 t (sqrt.f64 2)) l))))
▶	10.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/4) -1) (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/4) -1))))

Compiler

Compiled 7560 to 5522 computations (27% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 t l) 2)
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/4) -1) (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/4) -1))))
✓	17.6b	(pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/4)

series68.0ms (0.5%)

Counts

3 → 96

Calls

3 calls:

38.0ms

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

21.0ms

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

9.0ms

(pow.f64 (/.f64 t l) 2)

rewrite169.0ms (1.3%)

Algorithm

3×	egg-rewrite

Rules

67×	`egg`
34×	`egg`
22×	`egg`

Counts

3 → 123

Calls

3 calls:

77.0ms

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

46.0ms

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

43.0ms

(pow.f64 (/.f64 t l) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	208	14
2	2145	14
3	4963	14
0	21	33
1	455	30
2	4643	30
3	5379	30
0	6	7
1	127	7
2	1435	7
3	5503	7

simplify222.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1202×	`fma-def_binary64`
951×	`fma-neg_binary64`
445×	`times-frac_binary64`
409×	`unswap-sqr_binary64`
334×	`sub-neg_binary64`

Counts

219 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	2958
1	307	2754
2	861	2634
3	3266	2424
4	4696	2424
5	4213	2424
6	4272	2424
7	4399	2424
8	4927	2424
9	5792	2424

prune543.0ms (4.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	331	0	331
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	331	12	343

Error

0.8b

Counts

343 → 12

Alt Table

Status	Error	Program
	30.9b	(+.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)))
	43.2b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	14.6b	(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))
✓	10.5b	(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))))
	49.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) t) l (.f64 (/.f64 (pow.f64 l 5) (pow.f64 t 5)) (-.f64 (/.f64 1/16 (sqrt.f64 1/2)) (/.f64 1/64 (sqrt.f64 1/2))))) (.f64 (/.f64 (pow.f64 l 3) (.f64 (pow.f64 t 3) (sqrt.f64 1/2))) -1/8))))
	43.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 -1 (/.f64 (*.f64 (sqrt.f64 1/2) l) t))))
	11.6b	(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)
	45.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 (sqrt.f64 1/2) l) t)))
✓	10.5b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	43.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (neg.f64 (/.f64 (.f64 t (sqrt.f64 2)) l)))))
	45.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 1 (/.f64 (.f64 t (sqrt.f64 2)) l))))
✓	10.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/4) -1) (pow.f64 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/4) -1))))

Compiler

Compiled 15748 to 11608 computations (26.3% saved)

regimes1.9s (14.5%)

Accuracy

Total 0.1b remaining (17.6%)

Threshold costs 0.1b (17.6%)

Counts

88 → 3

Compiler

Compiled 37725 to 30733 computations (18.5% saved)

bsearch4.0ms (0%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	102
1	45	102
2	52	102
3	68	102
4	80	102
5	88	102
6	91	102
7	90	102

end294.0ms (2.3%)

Compiler: Compiled 517 to 408 computations (21.1% saved)

Details

analyze2.2s (16.8%)

sample3.2s (25.1%)

simplify63.0ms (0.5%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series917.0ms (7.1%)

rewrite293.0ms (2.3%)

simplify192.0ms (1.5%)

prune912.0ms (7.1%)

localize14.0ms (0.1%)

series462.0ms (3.6%)

rewrite231.0ms (1.8%)

simplify157.0ms (1.2%)

prune409.0ms (3.2%)

localize15.0ms (0.1%)

series68.0ms (0.5%)

rewrite174.0ms (1.3%)

simplify105.0ms (0.8%)

prune279.0ms (2.2%)

localize18.0ms (0.1%)

series68.0ms (0.5%)

rewrite169.0ms (1.3%)

simplify222.0ms (1.7%)

prune543.0ms (4.2%)

regimes1.9s (14.5%)

bsearch4.0ms (0%)

simplify6.0ms (0%)

end294.0ms (2.3%)

Profiling