Details

analyze1.9s (14.1%)

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)

sample2.6s (18.9%)

Results

1.6s	8256×	body	128	valid
888.0ms	4861×	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

11.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.9b	(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	(pow.f64 (/.f64 Om Omc) 2)
✓	0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	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))))
✓	10.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series447.0ms (3.3%)

Counts

4 → 168

Calls

4 calls:

241.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
179.0ms	(/.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))))
9.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite103.0ms (0.8%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	82
1	350	82
2	4570	82

Stop Event

1×	node limit

Counts

4 → 177

Calls

4 calls:

96.0ms	(pow.f64 (/.f64 Om Omc) 2)
96.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
96.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
96.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

simplify137.0ms (1%)

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	12522

Stop Event

1×	node limit

Counts

345 → 273

prune565.0ms (4.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	262	11	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	263	11	274

Error

0.5b

Counts

274 → 11

Alt Table

Status	Error	Program
	41.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	12.4b	(pow.f64 (sqrt.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)
	24.2b	(-.f64 (exp.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)))))) 1)
	43.7b	(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)))))))
	13.0b	(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)
▶	11.9b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	15.8b	(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))
	12.0b	(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)))))))
	34.1b	(+.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)))
	43.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	45.1b	(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 20672 to 14646 computations (29.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
	0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.5b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
✓	10.9b	(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

series246.0ms (1.8%)

Counts

2 → 96

Calls

2 calls:

229.0ms

(sqrt.f64 (expm1.f64 (log1p.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 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

rewrite74.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`prod-diff_binary64`
178×	`add-sqr-sqrt_binary64`
173×	`expm1-log1p-u_binary64`
172×	`log1p-expm1-u_binary64`
167×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	370	52
2	4761	52

Stop Event

1×	node limit

Counts

2 → 62

Calls

2 calls:

72.0ms

(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

72.0ms

(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

simplify105.0ms (0.8%)

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	10909
1	1732	9795

Stop Event

1×	node limit

Counts

158 → 129

prune529.0ms (3.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	270	11	281

Error

0.5b

Counts

281 → 11

Alt Table

Status	Error	Program
	41.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	12.4b	(pow.f64 (sqrt.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)
	24.2b	(-.f64 (exp.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)))))) 1)
	43.7b	(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)))))))
	13.0b	(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)
✓	11.9b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	15.8b	(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))
▶	12.0b	(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)))))))
	34.1b	(+.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)))
	43.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	45.1b	(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 20867 to 14879 computations (28.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.4b	(cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	10.9b	(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))))))
	10.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	17.1b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series1.0s (7.6%)

Counts

3 → 144

Calls

3 calls:

398.0ms

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

394.0ms

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

232.0ms

(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))))))

rewrite36.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

193×	`add-sqr-sqrt_binary64`
190×	`log1p-expm1-u_binary64`
190×	`expm1-log1p-u_binary64`
188×	`add-cbrt-cube_binary64`
185×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	135
1	425	76

Stop Event

1×	node limit

Counts

3 → 87

Calls

3 calls:

34.0ms

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

34.0ms

(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))))))

34.0ms

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

simplify215.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

577×	`*-commutative_binary64`
345×	`fma-def_binary64`
283×	`associate-+r+_binary64`
214×	`associate-r_binary64`
164×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1404	35452

Stop Event

1×	node limit

Counts

231 → 292

prune1.6s (11.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	482	2	484
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	483	12	495

Error

0.5b

Counts

495 → 12

Alt Table

Status	Error	Program
	43.7b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (*.f64 Omc Omc)))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	41.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
▶	12.4b	(pow.f64 (sqrt.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)
	24.2b	(-.f64 (exp.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)))))) 1)
	45.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (*.f64 Omc Omc)))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
	43.7b	(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)))))))
	13.0b	(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)
✓	11.9b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
✓	12.0b	(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)))))))
	34.1b	(+.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)))
	43.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	45.1b	(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 79455 to 55347 computations (30.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))))
✓	0.6b	(pow.f64 (sqrt.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)
✓	8.5b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	10.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series164.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

116.0ms

(pow.f64 (sqrt.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)

47.0ms

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

rewrite72.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

341×	`prod-diff_binary64`
178×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
168×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	56
1	391	56
2	4805	56

Stop Event

1×	node limit

Counts

2 → 58

Calls

2 calls:

69.0ms

(pow.f64 (sqrt.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)

69.0ms

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

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

649×	`associate-/l*_binary64`
452×	`associate-/r*_binary64`
380×	`associate-l_binary64`
340×	`associate-r_binary64`
294×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	2976
1	37	2976
2	70	2976
3	195	2976
4	873	2976

Stop Event

1×	node limit

Counts

154 → 62

prune392.0ms (2.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	189	5	194
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	192	14	206

Error

0.5b

Counts

206 → 14

Alt Table

Status	Error	Program
	43.7b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (*.f64 Omc Omc)))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	41.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	45.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (*.f64 Omc Omc)))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
	43.7b	(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)))))))
	13.0b	(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)
✓	12.0b	(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)))))))
	12.4b	(pow.f64 (fabs.f64 (sqrt.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)
✓	11.9b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	43.8b	(pow.f64 (sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))) 2)
	13.3b	(pow.f64 (pow.f64 (cbrt.f64 (sqrt.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)
	41.9b	(pow.f64 (sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))) 2)
	34.1b	(+.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)))
	43.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	13.1b	(pow.f64 (sqrt.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)) 2)

Compiler

Compiled 16389 to 11994 computations (26.8% saved)

regimes2.9s (21.1%)

Accuracy

Total 0.1b remaining (20.3%)

Threshold costs 0.1b (20.3%)

Counts

107 → 3

Compiler

Compiled 78735 to 59651 computations (24.2% saved)

bsearch8.0ms (0.1%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
15×	`+-commutative_binary64`
15×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	109
1	64	109
2	97	109
3	120	109
4	133	109
5	136	109

Stop Event

1×

saturated

end314.0ms (2.3%)

Compiler: Compiled 585 to 433 computations (26% saved)

Details

analyze1.9s (14.1%)

sample2.6s (18.9%)

simplify20.0ms (0.1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series447.0ms (3.3%)

rewrite103.0ms (0.8%)

simplify137.0ms (1%)

prune565.0ms (4.2%)

localize16.0ms (0.1%)

series246.0ms (1.8%)

rewrite74.0ms (0.5%)

simplify105.0ms (0.8%)

prune529.0ms (3.9%)

localize18.0ms (0.1%)

series1.0s (7.6%)

rewrite36.0ms (0.3%)

simplify215.0ms (1.6%)

prune1.6s (11.9%)

localize16.0ms (0.1%)

series164.0ms (1.2%)

rewrite72.0ms (0.5%)

simplify65.0ms (0.5%)

prune392.0ms (2.9%)

regimes2.9s (21.1%)

bsearch8.0ms (0.1%)

simplify5.0ms (0%)

end314.0ms (2.3%)

Profiling