Details

analyze1.8s (8.1%)

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)

sample2.5s (11.2%)

Results

1.6s	8256×	body	128	valid
849.0ms	4773×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify53.0ms (0.2%)

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

9.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.8b	(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 Om Omc) 2)
✓	0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.6b	(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)))

series571.0ms (2.6%)

Counts

4 → 168

Calls

4 calls:

336.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
207.0ms	(/.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))))
10.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64`
108×	`times-frac_binary64`
98×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
49×	`add-cube-cbrt_binary64`

Counts

4 → 177

Calls

4 calls:

12.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
11.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
3.0ms	(pow.f64 (/.f64 Om Omc) 2)
0.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

simplify325.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-def_binary64`
483×	`times-frac_binary64`
368×	`associate-/l*_binary64`
208×	`*-commutative_binary64`
144×	`+-commutative_binary64`

Counts

345 → 309

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	775	21028
1	2091	17483
2	4849	17362
3	5175	17362

prune565.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	301	8	309
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	8	310

Error

0.7b

Counts

310 → 8

Alt Table

Status	Error	Program
	13.5b	(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))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	17.9b	(asin.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (/.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 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
	11.0b	(.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 (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 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	45.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	22.1b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	9.9b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 18408 to 13568 computations (26.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.3b	(/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
✓	0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
✓	8.8b	(sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))

series2.3s (10.5%)

Counts

3 → 144

Calls

3 calls:

1.8s

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

507.0ms

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

30.0ms

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

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-prod_binary64`
8×	`times-frac_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

3 → 63

Calls

3 calls:

19.0ms

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

15.0ms

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

0.0ms

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

simplify390.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

373×	`associate-r_binary64`
332×	`fma-def_binary64`
307×	`associate-+r+_binary64`
211×	`associate-/r*_binary64`
167×	`associate-/l*_binary64`

Counts

207 → 232

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1609	45491
1	5075	45491

prune1.2s (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	353	2	355
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	354	9	363

Error

0.7b

Counts

363 → 9

Alt Table

Status	Error	Program
	13.5b	(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))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	10.4b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
	17.9b	(asin.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	11.0b	(.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 (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 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	22.1b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
▶	9.8b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
	9.9b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 52474 to 36167 computations (31.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
✓	0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
✓	8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))

series2.3s (10.6%)

Counts

3 → 144

Calls

3 calls:

1.8s

(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))

546.0ms

(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))

27.0ms

(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64`
24×	`difference-of-squares_binary64`
18×	`sqrt-prod_binary64`

Counts

3 → 87

Calls

3 calls:

17.0ms

(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))

15.0ms

(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))

0.0ms

(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))

simplify401.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

372×	`associate-r_binary64`
332×	`fma-def_binary64`
307×	`associate-+r+_binary64`
211×	`associate-/r*_binary64`
169×	`associate-/l*_binary64`

Counts

231 → 230

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1640	46582
1	5117	46582

prune1.2s (5.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	271	9	280

Error

0.7b

Counts

280 → 9

Alt Table

Status	Error	Program
	13.5b	(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))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	10.4b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
	17.9b	(asin.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	11.0b	(.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 (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 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	22.1b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))))))
✓	9.8b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
▶	9.9b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 48519 to 33865 computations (30.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.6b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	8.8b	(sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	14.7b	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series441.0ms (2%)

Counts

3 → 120

Calls

3 calls:

380.0ms

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

39.0ms

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

22.0ms

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

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
140×	`add-sqr-sqrt_binary64`
112×	`sqrt-prod_binary64`
95×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`

Counts

3 → 152

Calls

3 calls:

18.0ms

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

1.0ms

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

0.0ms

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

simplify350.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-def_binary64`
436×	`associate-/r*_binary64`
435×	`times-frac_binary64`
313×	`associate-/l*_binary64`
203×	`*-commutative_binary64`

Counts

272 → 277

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	809	23483
1	2069	20848
2	5201	20848

prune954.0ms (4.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	407	1	408
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	408	9	417

Error

0.7b

Counts

417 → 9

Alt Table

Status	Error	Program
	13.5b	(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))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	10.4b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
	17.9b	(asin.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	11.0b	(.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 (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 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	22.1b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))))))
✓	9.8b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
	9.9b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 30443 to 22463 computations (26.2% saved)

regimes6.3s (28.5%)

Accuracy

Total 0.1b remaining (17.4%)

Threshold costs 0.1b (17.4%)

Counts

277 → 3

Compiler

Compiled 174360 to 134275 computations (23% saved)

bsearch17.0ms (0.1%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	121
1	60	121
2	81	121
3	96	121
4	106	121
5	109	121
6	107	121

end266.0ms (1.2%)

Compiler: Compiled 524 to 388 computations (26% saved)

Details

analyze1.8s (8.1%)

sample2.5s (11.2%)

simplify53.0ms (0.2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series571.0ms (2.6%)

rewrite46.0ms (0.2%)

simplify325.0ms (1.5%)

prune565.0ms (2.5%)

localize16.0ms (0.1%)

series2.3s (10.5%)

rewrite39.0ms (0.2%)

simplify390.0ms (1.8%)

prune1.2s (5.2%)

localize17.0ms (0.1%)

series2.3s (10.6%)

rewrite41.0ms (0.2%)

simplify401.0ms (1.8%)

prune1.2s (5.4%)

localize15.0ms (0.1%)

series441.0ms (2%)

rewrite57.0ms (0.3%)

simplify350.0ms (1.6%)

prune954.0ms (4.3%)

regimes6.3s (28.5%)

bsearch17.0ms (0.1%)

simplify6.0ms (0%)

end266.0ms (1.2%)

Profiling