Details

analyze1.8s (15.4%)

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 (21.6%)

Results

1.7s	8256×	body	128	valid
869.0ms	4751×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify22.0ms (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

prune3.0ms (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

9.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.7b	(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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series432.0ms (3.6%)

Counts

4 → 168

Calls

4 calls:

234.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
170.0ms	(/.f64 (-.f64 1 (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 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
9.0ms	(pow.f64 (/.f64 t l) 2)

rewrite105.0ms (0.9%)

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:

99.0ms	(pow.f64 (/.f64 t l) 2)
99.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
99.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
99.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

simplify134.0ms (1.1%)

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	12450

Stop Event

1×	node limit

Counts

345 → 274

prune593.0ms (5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	265	9	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	266	9	275

Error

0.7b

Counts

275 → 9

Alt Table

Status	Error	Program
▶	9.8b	(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))))))
	9.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
	10.3b	(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)
	11.0b	(*.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))
	28.1b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (pow.f64 (/.f64 t l) 2) (.f64 (/.f64 Om Omc) (/.f64 Om Omc))) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	49.8b	(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)))))))
	46.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	49.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))

Compiler

Compiled 20486 to 14472 computations (29.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 t l) 2)
	0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.7b	(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))))))
✓	8.8b	(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)))))

series263.0ms (2.2%)

Counts

2 → 96

Calls

2 calls:

245.0ms

(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)))))

18.0ms

(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))))))

rewrite80.0ms (0.7%)

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:

75.0ms

(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))))))

75.0ms

(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)))))

simplify103.0ms (0.9%)

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

prune553.0ms (4.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	271	9	280

Error

0.7b

Counts

280 → 9

Alt Table

Status	Error	Program
✓	9.8b	(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))))))
▶	9.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
	10.3b	(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)
	11.0b	(*.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))
	28.1b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (pow.f64 (/.f64 t l) 2) (.f64 (/.f64 Om Omc) (/.f64 Om Omc))) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	49.8b	(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)))))))
	46.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	49.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))

Compiler

Compiled 20683 to 14707 computations (28.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
✓	0.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
✓	8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1)))
✓	13.8b	(cbrt.f64 (/.f64 t l))

series1.0s (8.6%)

Counts

4 → 144

Calls

4 calls:

376.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
366.0ms	(cbrt.f64 (/.f64 t l))
262.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1)))
20.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

195×	`add-sqr-sqrt_binary64`
188×	`log1p-expm1-u_binary64`
188×	`expm1-log1p-u_binary64`
186×	`add-cbrt-cube_binary64`
184×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	73
1	412	67

Stop Event

1×	node limit

Counts

4 → 103

Calls

4 calls:

38.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
38.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
38.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1)))
38.0ms	(cbrt.f64 (/.f64 t l))

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	471	11917
1	1822	11073

Stop Event

1×	node limit

Counts

247 → 186

prune336.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	224	9	233

Error

0.7b

Counts

233 → 9

Alt Table

Status	Error	Program
✓	9.8b	(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))))))
✓	9.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 2) (.f64 (cbrt.f64 (/.f64 t l)) (/.f64 t l))) 1))))
▶	10.3b	(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)
	11.0b	(*.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))
	28.1b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (pow.f64 (/.f64 t l) 2) (.f64 (/.f64 Om Omc) (/.f64 Om Omc))) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	49.8b	(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)))))))
	46.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	49.6b	(asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))

Compiler

Compiled 15284 to 10235 computations (33% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(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)
	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))))
✓	7.3b	(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)))))
	8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series160.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

113.0ms

(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)

48.0ms

(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)))))

rewrite73.0ms (0.6%)

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:

70.0ms

(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)

70.0ms

(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)))))

simplify70.0ms (0.6%)

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

prune346.0ms (2.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	193	10	203

Error

0.7b

Counts

203 → 10

Alt Table

Status	Error	Program
✓	9.8b	(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))))))
	49.9b	(pow.f64 (sqrt.f64 (asin.f64 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))) 2)
	46.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (*.f64 (/.f64 (sqrt.f64 1/2) t) l)))
	11.1b	(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)
✓	10.3b	(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)
	11.0b	(*.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))
	28.1b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (pow.f64 (/.f64 t l) 2) (.f64 (/.f64 Om Omc) (/.f64 Om Omc))) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (*.f64 (/.f64 Om Omc) (/.f64 Om Omc))))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 Om Omc) (/.f64 Om Omc)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 1/2) t) l))))
	49.8b	(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)))))))
	10.5b	(pow.f64 (*.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))))) (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))))))) 2)

Compiler

Compiled 16251 to 11883 computations (26.9% saved)

regimes2.8s (23.4%)

Accuracy

Total 0.1b remaining (14.3%)

Threshold costs 0.1b (14.3%)

Counts

159 → 3

Compiler

Compiled 70972 to 56458 computations (20.5% saved)

bsearch7.0ms (0.1%)

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

end209.0ms (1.7%)

Compiler: Compiled 445 to 320 computations (28.1% saved)

Details

analyze1.8s (15.4%)

sample2.6s (21.6%)

simplify22.0ms (0.2%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series432.0ms (3.6%)

rewrite105.0ms (0.9%)

simplify134.0ms (1.1%)

prune593.0ms (5%)

localize18.0ms (0.2%)

series263.0ms (2.2%)

rewrite80.0ms (0.7%)

simplify103.0ms (0.9%)

prune553.0ms (4.6%)

localize16.0ms (0.1%)

series1.0s (8.6%)

rewrite40.0ms (0.3%)

simplify118.0ms (1%)

prune336.0ms (2.8%)

localize13.0ms (0.1%)

series160.0ms (1.3%)

rewrite73.0ms (0.6%)

simplify70.0ms (0.6%)

prune346.0ms (2.9%)

regimes2.8s (23.4%)

bsearch7.0ms (0.1%)

simplify4.0ms (0%)

end209.0ms (1.7%)

Profiling