Details

analyze2.1s (19.3%)

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)

sample2.7s (24.6%)

Results

1.7s	8256×	body	128	valid
941.0ms	4701×	body	128	invalid

Compiler

Compiled 48 to 40 computations (16.7% saved)

preprocess37.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

297×	`associate-l_binary64`
292×	`fma-def_binary64`
258×	`associate-r_binary64`
230×	`cancel-sign-sub-inv_binary64`
219×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	203
1	143	189
2	313	189
3	952	189
4	3333	189
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify20.0ms (0.2%)

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

11.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.4b	(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
✓	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	0.7b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series389.0ms (3.6%)

Counts

4 → 168

Calls

42 calls:

29.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))	t	-inf
29.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))	t	inf
26.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))	l	-inf
26.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))	l	0
22.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))	l	inf

rewrite108.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

325×	`prod-diff_binary64`
175×	`add-sqr-sqrt_binary64`
172×	`pow1_binary64`
170×	`*-un-lft-identity_binary64`
163×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	82
1	351	82
2	4557	82
0	16	82

Stop Event

1×	saturated
1×	node limit

Counts

4 → 177

simplify152.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
471×	`times-frac_binary64`
399×	`associate-/r*_binary64`
321×	`associate-/l*_binary64`
203×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	14080
1	2097	12450

Stop Event

1×	node limit

Counts

345 → 274

prune573.0ms (5.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	264	10	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	10	275

Error

0.6b

Counts

275 → 10

Alt Table

Status	Error	Program
	12.6b	(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)
	11.5b	(asin.f64 (+.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))) -1/2)))
	12.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (*.f64 l (/.f64 l t))) 1))))
	47.4b	(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)))))))
▶	11.4b	(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))))))
	45.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	47.4b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	30.5b	(+.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)))
	12.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 t (.f64 (/.f64 1 l) (/.f64 t l))) 1))))
	45.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))

Compiler

Compiled 20596 to 14589 computations (29.2% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 t l) 2)
	0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	0.7b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
	10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

prune568.0ms (5.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	274	10	284

Error

0.6b

Counts

284 → 10

Alt Table

Status	Error	Program
	12.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (*.f64 l (/.f64 l t))) 1))))
	47.4b	(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)))))))
	12.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 t (.f64 (/.f64 1 l) (/.f64 t l))) 1))))
	12.4b	(expm1.f64 (log1p.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)))
✓	11.4b	(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))))))
	45.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	47.4b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
▶	11.5b	(asin.f64 (+.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))) -1/2)))
	30.5b	(+.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)))
	45.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))

Compiler

Compiled 21124 to 15121 computations (28.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.5b	(asin.f64 (+.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))) -1/2)))
✓	0.7b	(/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	10.0b	(sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series66.0ms (0.6%)

Counts

3 → 96

Calls

24 calls:

8.0ms	(sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))	t	-inf
5.0ms	(sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))	t	inf
5.0ms	(sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))	l	0
5.0ms	(/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))	t	-inf
4.0ms	(asin.f64 (+.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))) -1/2)))	Om	inf

rewrite39.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

207×	`add-sqr-sqrt_binary64`
200×	`pow1_binary64`
199×	`*-un-lft-identity_binary64`
192×	`add-log-exp_binary64`
192×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	78
1	416	69
0	19	81

Stop Event

1×	saturated
1×	node limit

Counts

3 → 69

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

894×	`times-frac_binary64`
435×	`associate-/r*_binary64`
417×	`associate-/l*_binary64`
278×	`fma-def_binary64`
209×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	4091
1	358	3971
2	1289	3061

Stop Event

1×	node limit

Counts

165 → 108

prune409.0ms (3.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	269	11	280

Error

0.6b

Counts

280 → 11

Alt Table

Status	Error	Program
	12.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 t (.f64 (/.f64 1 l) (/.f64 t l))) 1))))
	12.4b	(expm1.f64 (log1p.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)))
✓	11.4b	(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))))))
	45.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
▶	12.1b	(pow.f64 (sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 2)
	47.4b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	45.3b	(asin.f64 (+.f64 (/.f64 (neg.f64 (sqrt.f64 1/2)) (/.f64 t l)) (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))) -1/2)))
	30.5b	(+.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)))
	45.8b	(asin.f64 (+.f64 (.f64 (/.f64 l t) (sqrt.f64 1/2)) (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 (/.f64 Om Omc) (/.f64 Om Omc))) -1/2)))
	12.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (*.f64 l (/.f64 l t))) 1))))
	45.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))

Compiler

Compiled 11822 to 7714 computations (34.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 2)
✓	6.1b	(sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2))))
✓	10.8b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	10.8b	(pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)

series238.0ms (2.2%)

Counts

4 → 144

Calls

36 calls:

17.0ms	(pow.f64 (sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 2)	t	inf
12.0ms	(pow.f64 (sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 2)	Omc	inf
12.0ms	(pow.f64 (sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 2)	l	0
12.0ms	(pow.f64 (sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 2)	Om	0
11.0ms	(pow.f64 (sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 2)	t	-inf

rewrite98.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

203×	`prod-diff_binary64`
197×	`add-sqr-sqrt_binary64`
194×	`pow1_binary64`
190×	`*-un-lft-identity_binary64`
185×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	111
1	426	111
2	4893	111
0	20	116

Stop Event

1×	saturated
1×	node limit

Counts

4 → 104

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

604×	`associate-/l*_binary64`
522×	`associate-/r*_binary64`
263×	`fma-def_binary64`
198×	`associate-*r/_binary64`
191×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	6535
1	463	6412
2	1484	6256

Stop Event

1×	node limit

Counts

248 → 161

prune244.0ms (2.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	159	13	172

Error

0.6b

Counts

172 → 13

Alt Table

Status	Error	Program
	30.7b	(+.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 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2))) 1))) (fma.f64 (neg.f64 (acos.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 1 (.f64 (acos.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2))) 1)))
	45.3b	(asin.f64 (+.f64 (/.f64 (neg.f64 (sqrt.f64 1/2)) (/.f64 t l)) (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))) -1/2)))
	12.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 t (.f64 (/.f64 1 l) (/.f64 t l))) 1))))
	12.4b	(expm1.f64 (log1p.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)))
✓	11.4b	(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))))))
	45.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	13.0b	(pow.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2))))) 3) 2)
	47.4b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
	12.9b	(pow.f64 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))) 2)) (sqrt.f64 (cbrt.f64 (asin.f64 (fma.f64 (/.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) -1/2 (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) -1/2)))))) 2)
	30.5b	(+.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)))
	45.8b	(asin.f64 (+.f64 (.f64 (/.f64 l t) (sqrt.f64 1/2)) (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 (/.f64 Om Omc) (/.f64 Om Omc))) -1/2)))
	12.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (*.f64 l (/.f64 l t))) 1))))
	45.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))

Compiler

Compiled 9417 to 6845 computations (27.3% saved)

regimes2.5s (23.4%)

Accuracy

Total 0.3b remaining (33%)

Threshold costs 0.3b (33%)

Counts

124 → 3

Compiler

Compiled 61039 to 48823 computations (20% saved)

bsearch6.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 t l)
0.0ms	(/.f64 t l)

Steps

Iters	Point		Range
3.3013591093358795e+134	∈ [	3.3013591093358795e+134	,	2.5688981999892268e+138	]
-6.246144260202978e+156	∈ [	-6.246144260202978e+156	,	-5.7126092776386e+138	]

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
13×	`+-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	44	123
1	68	123
2	96	123
3	116	123
4	128	123
5	131	123

Stop Event

1×

saturated

end356.0ms (3.3%)

Stop Event

1×

fuel

Compiler

Compiled 702 to 517 computations (26.4% saved)

Details

analyze2.1s (19.3%)

sample2.7s (24.6%)

preprocess37.0ms (0.3%)

simplify20.0ms (0.2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series389.0ms (3.6%)

rewrite108.0ms (1%)

simplify152.0ms (1.4%)

prune573.0ms (5.3%)

localize18.0ms (0.2%)

prune568.0ms (5.2%)

localize17.0ms (0.2%)

series66.0ms (0.6%)

rewrite39.0ms (0.4%)

simplify64.0ms (0.6%)

prune409.0ms (3.8%)

localize20.0ms (0.2%)

series238.0ms (2.2%)

rewrite98.0ms (0.9%)

simplify101.0ms (0.9%)

prune244.0ms (2.2%)

regimes2.5s (23.4%)

bsearch6.0ms (0.1%)

simplify5.0ms (0%)

end356.0ms (3.3%)

Profiling