Details

analyze2.2s (20%)

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 (29.2%)

Results

1.7s	8256×	body	128	valid
1.5s	4779×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify53.0ms (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)

localize12.0ms (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)))

series611.0ms (5.5%)

Counts

4 → 168

Calls

4 calls:

353.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
225.0ms	(/.f64 (-.f64 1 (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 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
13.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite102.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

177× egg-rr

Counts

4 → 177

Calls

2 calls:

96.0ms

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

0.0ms

()

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

simplify181.0ms (1.6%)

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 → 273

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	14080
1	1671	12522
2	4999	12522

prune529.0ms (4.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	264	9	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	9	274

Error

1.9b

Counts

274 → 9

Alt Table

Status	Error	Program
	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)
	10.6b	(asin.f64 (sqrt.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	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)))
	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))))
	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 (*.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)))))
	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))))))
	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))))))

Compiler

Compiled 20620 to 14613 computations (29.1% saved)

localize16.0ms (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)))

series436.0ms (4%)

Counts

3 → 120

Calls

3 calls:

406.0ms

(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))))

11.0ms

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

rewrite79.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

106× egg-rr

Counts

3 → 106

Calls

2 calls:

76.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	59
1	364	59
2	4453	59
3	5141	59
0	0	0
1	0	0

simplify146.0ms (1.3%)

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

226 → 174

Iterations

Useful iterations: 1 (0.0ms)

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

prune382.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	211	9	220

Error

1.9b

Counts

220 → 9

Alt Table

Status	Error	Program
	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)
	10.6b	(asin.f64 (sqrt.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	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)))
	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))))
	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 (*.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)))))
	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))))))
	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))))))

Compiler

Compiled 15092 to 10806 computations (28.4% 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))

series81.0ms (0.7%)

Counts

3 → 96

Calls

3 calls:

41.0ms

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

21.0ms

(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)))))

18.0ms

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

rewrite84.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

86× egg-rr

Counts

3 → 86

Calls

2 calls:

79.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	58
1	386	54
2	4485	54
3	4986	54
0	0	0
1	0	0

simplify91.0ms (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

182 → 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

prune235.0ms (2.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	166	12	178

Error

0.8b

Counts

178 → 12

Alt Table

Status	Error	Program
	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)))
	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))
	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)))))
	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))))
	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))))
✓	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))))
✓	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)))))
	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))))
	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)))))

Compiler

Compiled 6657 to 4888 computations (26.6% 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	(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)

series70.0ms (0.6%)

Counts

3 → 96

Calls

3 calls:

39.0ms

(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))))

10.0ms

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

rewrite78.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

71× egg-rr

Counts

3 → 71

Calls

2 calls:

76.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	455	51
2	4643	51
3	5379	51
0	0	0
1	0	0

simplify196.0ms (1.8%)

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

167 → 98

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

prune311.0ms (2.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	199	12	211

Error

0.8b

Counts

211 → 12

Alt Table

Status	Error	Program
	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)))
	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))
	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)))))
	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))))
	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))))
✓	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))))
✓	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)))))
	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))))
	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)))))

Compiler

Compiled 10173 to 7596 computations (25.3% saved)

regimes1.6s (14.5%)

Accuracy

Total 0.1b remaining (17.6%)

Threshold costs 0.1b (17.6%)

Counts

82 → 3

Compiler

Compiled 35597 to 28893 computations (18.8% saved)

bsearch3.0ms (0%)

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

simplify11.0ms (0.1%)

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

end272.0ms (2.5%)

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

Details

analyze2.2s (20%)

sample3.2s (29.2%)

simplify53.0ms (0.5%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series611.0ms (5.5%)

rewrite102.0ms (0.9%)

simplify181.0ms (1.6%)

prune529.0ms (4.8%)

localize16.0ms (0.1%)

series436.0ms (4%)

rewrite79.0ms (0.7%)

simplify146.0ms (1.3%)

prune382.0ms (3.5%)

localize15.0ms (0.1%)

series81.0ms (0.7%)

rewrite84.0ms (0.8%)

simplify91.0ms (0.8%)

prune235.0ms (2.1%)

localize16.0ms (0.1%)

series70.0ms (0.6%)

rewrite78.0ms (0.7%)

simplify196.0ms (1.8%)

prune311.0ms (2.8%)

regimes1.6s (14.5%)

bsearch3.0ms (0%)

simplify11.0ms (0.1%)

end272.0ms (2.5%)

Profiling