Details

analyze3.5s (12.7%)

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)

sample196.0ms (0.7%)

Algorithm

1×

intervals

Results

56.0ms	256×	body	128	valid
28.0ms	146×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify62.0ms (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

prune7.0ms (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

11.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.0b	(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)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(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))))
✓	9.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series1.2s (4.4%)

Counts

4 → 168

Calls

4 calls:

708.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
432.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
34.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
23.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite115.0ms (0.4%)

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:

35.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
24.0ms	(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)
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

simplify696.0ms (2.6%)

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

prune1.3s (4.6%)

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
	14.4b	(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))))
	24.2b	(-.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)))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	11.1b	(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)))))
	11.1b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	12.1b	(.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))))))
▶	11.0b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 18338 to 13528 computations (26.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.4b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	0.6b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	10.1b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series760.0ms (2.8%)

Counts

3 → 120

Calls

3 calls:

690.0ms

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

36.0ms

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

33.0ms

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

rewrite90.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`sqrt-prod_binary64`
148×	`add-sqr-sqrt_binary64`
116×	`times-frac_binary64`
103×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`

Counts

3 → 168

Calls

3 calls:

29.0ms

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

2.0ms

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

1.0ms

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

simplify663.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
433×	`times-frac_binary64`
377×	`associate-/r*_binary64`
291×	`associate-/l*_binary64`
202×	`associate-*l/_binary64`

Counts

288 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	647	19487
1	1766	16741
2	4926	16616
3	5190	16616

prune1.2s (4.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	306	5	311
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	309	10	319

Error

0.6b

Counts

319 → 10

Alt Table

Status	Error	Program
	32.1b	(asin.f64 (fabs.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	12.1b	(.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))))))
▶	11.0b	(asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	14.4b	(cbrt.f64 (pow.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)))) 3))
	24.2b	(-.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)))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	30.5b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (/.f64 (.f64 t (sqrt.f64 2)) l)))))
	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))))
	11.1b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	38.8b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (fma.f64 (/.f64 t l) (sqrt.f64 2) (.f64 (/.f64 (pow.f64 l 3) (.f64 (pow.f64 t 3) (.f64 2 (sqrt.f64 2)))) -1/8))))))

Compiler

Compiled 18658 to 13978 computations (25.1% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
	0.4b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	0.6b	(asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	10.1b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series36.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

36.0ms

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

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

2.0ms

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

simplify163.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-/r*_binary64`
632×	`distribute-neg-frac_binary64`
419×	`associate-/l/_binary64`
379×	`associate-*l/_binary64`
364×	`associate-*r/_binary64`

Counts

58 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	1968
1	65	1761
2	103	1761
3	254	1761
4	1081	1761
5	3802	1761
6	4956	1761

prune1.4s (5.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	309	2	311
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	311	10	321

Error

0.6b

Counts

321 → 10

Alt Table

Status	Error	Program
	30.5b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (/.f64 (.f64 t (sqrt.f64 2)) l)))))
	12.1b	(.f64 (.f64 (cbrt.f64 (asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))) (cbrt.f64 (asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))) (cbrt.f64 (asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))))
	32.1b	(asin.f64 (fabs.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	11.3b	(asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 1/2 (.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))))
	12.1b	(.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))))))
	14.4b	(cbrt.f64 (pow.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)))) 3))
	24.2b	(-.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)))))
	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))))
▶	11.1b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	38.8b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (fma.f64 (/.f64 t l) (sqrt.f64 2) (.f64 (/.f64 (pow.f64 l 3) (.f64 (pow.f64 t 3) (.f64 2 (sqrt.f64 2)))) -1/8))))))

Compiler

Compiled 19417 to 14707 computations (24.3% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
✓	5.8b	(sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	5.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	10.1b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series398.0ms (1.5%)

Counts

3 → 120

Calls

3 calls:

319.0ms

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

56.0ms

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

22.0ms

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

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

164×	`sqrt-prod_binary64`
141×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
95×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`

Counts

3 → 156

Calls

3 calls:

16.0ms

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

3.0ms

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

0.0ms

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

simplify379.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

642×	`cancel-sign-sub-inv_binary64`
391×	`fma-neg_binary64`
266×	`neg-mul-1_binary64`
214×	`distribute-neg-frac_binary64`
191×	`sub-neg_binary64`

Counts

276 → 247

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	445	14137
1	1035	12069
2	3023	11583
3	4546	11479
4	4954	11479
5	4812	11479

prune556.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	323	10	333

Error

0.6b

Counts

333 → 10

Alt Table

Status	Error	Program
	30.5b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (/.f64 (.f64 t (sqrt.f64 2)) l)))))
	12.1b	(.f64 (.f64 (cbrt.f64 (asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))) (cbrt.f64 (asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))) (cbrt.f64 (asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))))
	32.1b	(asin.f64 (fabs.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	11.3b	(asin.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (.f64 1/2 (.f64 (pow.f64 (/.f64 Om Omc) 2) (sqrt.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))))
	12.1b	(.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))))))
	14.4b	(cbrt.f64 (pow.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)))) 3))
	24.2b	(-.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)))))
	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))))
✓	11.1b	(asin.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	38.8b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (.f64 t (sqrt.f64 2))) (fma.f64 (/.f64 t l) (sqrt.f64 2) (.f64 (/.f64 (pow.f64 l 3) (.f64 (pow.f64 t 3) (.f64 2 (sqrt.f64 2)))) -1/8))))))

Compiler

Compiled 17308 to 12947 computations (25.2% saved)

regimes12.0s (44.1%)

Accuracy

Total 0.2b remaining (22.7%)

Threshold costs 0.2b (22.7%)

Counts

326 → 3

Compiler

Compiled 182401 to 146431 computations (19.7% saved)

bsearch20.0ms (0.1%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
12×	`+-commutative_binary64`
11×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	117
1	63	117
2	86	117
3	104	117
4	116	117
5	120	117
6	119	117

end2.0ms (0%)

Compiler: Compiled 80 to 55 computations (31.3% saved)

sample2.4s (8.9%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
563.0ms	4580×	body	128	nan

Compiler

Compiled 487 to 382 computations (21.6% saved)

Details

analyze3.5s (12.7%)

sample196.0ms (0.7%)

simplify62.0ms (0.2%)

prune7.0ms (0%)

localize25.0ms (0.1%)

series1.2s (4.4%)

rewrite115.0ms (0.4%)

simplify696.0ms (2.6%)

prune1.3s (4.6%)

localize29.0ms (0.1%)

series760.0ms (2.8%)

rewrite90.0ms (0.3%)

simplify663.0ms (2.4%)

prune1.2s (4.3%)

localize36.0ms (0.1%)

series36.0ms (0.1%)

rewrite3.0ms (0%)

simplify163.0ms (0.6%)

prune1.4s (5.1%)

localize32.0ms (0.1%)

series398.0ms (1.5%)

rewrite45.0ms (0.2%)

simplify379.0ms (1.4%)

prune556.0ms (2%)

regimes12.0s (44.1%)

bsearch20.0ms (0.1%)

simplify6.0ms (0%)

end2.0ms (0%)

sample2.4s (8.9%)

Profiling