Details

analyze1.9s (10.2%)

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)

sample2.5s (14%)

Results

1.6s	8256×	body	128	valid
866.0ms	4843×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

530×	`associate-/r/_binary64`
437×	`associate-/l/_binary64`
423×	`associate-*l/_binary64`
293×	`associate-l_binary64`
216×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	33	27
2	66	27
3	181	27
4	586	27
5	2362	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

9.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.5b	(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	(pow.f64 (/.f64 t l) 2)
✓	0.2b	(pow.f64 (/.f64 Om Omc) 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))))
✓	8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series274.0ms (1.5%)

Counts

4 → 144

Calls

4 calls:

235.0ms	(sqrt.f64 (/.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))))
11.0ms	(pow.f64 (/.f64 Om Omc) 2)
10.0ms	(pow.f64 (/.f64 t l) 2)

rewrite81.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

325×	`prod-diff_binary64`
170×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`
160×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	66
1	350	66
2	4570	66

Stop Event

1×	node limit

Counts

4 → 137

Calls

4 calls:

76.0ms	(pow.f64 (/.f64 t l) 2)
76.0ms	(pow.f64 (/.f64 Om Omc) 2)
76.0ms	(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)))

simplify112.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	11389
1	1732	10203

Stop Event

1×	node limit

Counts

281 → 207

prune394.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	199	8	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	200	8	208

Error

0.8b

Counts

208 → 8

Alt Table

Status	Error	Program
	10.7b	(*.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))
	28.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (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)))
	48.4b	(asin.f64 (.f64 -1 (.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
	45.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 (*.f64 t (/.f64 t l)) l) 1))))
	46.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	44.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
▶	9.5b	(expm1.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))))))

Compiler

Compiled 14811 to 10625 computations (28.3% 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	(pow.f64 (/.f64 Om Omc) 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))))
	8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

prune389.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	207	8	215

Error

0.8b

Counts

215 → 8

Alt Table

Status	Error	Program
▶	10.7b	(*.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))
	48.4b	(asin.f64 (.f64 -1 (.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
	45.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 (*.f64 t (/.f64 t l)) l) 1))))
	28.6b	(expm1.f64 (log1p.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (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)))))
	46.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	44.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
✓	9.5b	(expm1.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))))))

Compiler

Compiled 15205 to 11023 computations (27.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(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)
	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))))
✓	8.0b	(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)))

series5.8s (32%)

Counts

2 → 96

Calls

2 calls:

2.9s

(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)

2.9s

(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)))))

rewrite64.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	61
1	389	61
2	4984	61

Stop Event

1×	node limit

Counts

2 → 41

Calls

2 calls:

63.0ms

(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)

63.0ms

(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)))))

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

648×	`associate-/l*_binary64`
469×	`associate-l_binary64`
451×	`associate-/r*_binary64`
288×	`associate-/l/_binary64`
237×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	3216
1	51	3216
2	93	3216
3	240	3216
4	978	3216

Stop Event

1×	node limit

Counts

137 → 45

prune811.0ms (4.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	328	6	334
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	329	13	342

Error

0.7b

Counts

342 → 13

Alt Table

Status	Error	Program
	11.1b	(.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))))) (.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)))))) 2) (cbrt.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))))) 4))))
	28.6b	(expm1.f64 (log1p.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (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)))))
▶	10.7b	(*.f64 (cbrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (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))
	17.3b	(*.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 (-.f64 (exp.f64 (log1p.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))))))) 1) 2))
	45.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 (*.f64 t (/.f64 t l)) l) 1))))
	46.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	11.5b	(.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 (.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)))))) 2) (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))))))) 2))
	48.4b	(asin.f64 (.f64 -1 (.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
	44.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	12.1b	(*.f64 (cbrt.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)))) (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))
✓	9.5b	(expm1.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))))))
	10.7b	(*.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))))))) (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))

Compiler

Compiled 35867 to 26194 computations (27% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	8.0b	(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)))))
✓	8.0b	(cbrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	8.4b	(sqrt.f64 (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)))

series2.9s (16.1%)

Counts

2 → 72

Calls

2 calls:

2.9s	(cbrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
15.0ms	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

rewrite67.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

303×	`prod-diff_binary64`
184×	`add-sqr-sqrt_binary64`
177×	`log1p-expm1-u_binary64`
177×	`expm1-log1p-u_binary64`
175×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	42
1	386	42
2	4898	42

Stop Event

1×	node limit

Counts

2 → 44

Calls

2 calls:

66.0ms	(cbrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
66.0ms	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

simplify59.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
366×	`unswap-sqr_binary64`
291×	`associate-/l*_binary64`
253×	`associate-/r*_binary64`
187×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	2206
1	209	2179
2	649	2123
3	4233	2105

Stop Event

1×	node limit

Counts

116 → 69

prune444.0ms (2.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	190	13	203

Error

0.7b

Counts

203 → 13

Alt Table

Status	Error	Program
	11.1b	(.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))))) (.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)))))) 2) (cbrt.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))))) 4))))
	28.6b	(expm1.f64 (log1p.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (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)))))
✓	10.7b	(*.f64 (cbrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (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))
	17.3b	(*.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 (-.f64 (exp.f64 (log1p.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))))))) 1) 2))
	45.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 (*.f64 t (/.f64 t l)) l) 1))))
	46.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	11.5b	(.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 (.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)))))) 2) (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))))))) 2))
	48.4b	(asin.f64 (.f64 -1 (.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
	44.1b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	12.1b	(*.f64 (cbrt.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)))) (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))
✓	9.5b	(expm1.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))))))
	10.7b	(*.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))))))) (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))

Compiler

Compiled 18063 to 13279 computations (26.5% saved)

regimes1.8s (9.8%)

Accuracy

Total 0.1b remaining (16.9%)

Threshold costs 0.1b (16.9%)

Counts

83 → 3

Compiler

Compiled 46567 to 37087 computations (20.4% saved)

bsearch4.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	107
1	57	107
2	84	107
3	103	107
4	115	107
5	118	107

Stop Event

1×

saturated

end377.0ms (2.1%)

Compiler: Compiled 695 to 519 computations (25.3% saved)

Details

analyze1.9s (10.2%)

sample2.5s (14%)

simplify20.0ms (0.1%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series274.0ms (1.5%)

rewrite81.0ms (0.4%)

simplify112.0ms (0.6%)

prune394.0ms (2.2%)

localize16.0ms (0.1%)

prune389.0ms (2.1%)

localize17.0ms (0.1%)

series5.8s (32%)

rewrite64.0ms (0.4%)

simplify68.0ms (0.4%)

prune811.0ms (4.5%)

localize21.0ms (0.1%)

series2.9s (16.1%)

rewrite67.0ms (0.4%)

simplify59.0ms (0.3%)

prune444.0ms (2.4%)

regimes1.8s (9.8%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end377.0ms (2.1%)

Profiling