Details

analyze3.3s (13.7%)

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)

sample116.0ms (0.5%)

Algorithm

1×

intervals

Results

50.0ms	256×	body	128	valid
36.0ms	173×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify128.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

525×	`associate-/r/_binary64`
484×	`unswap-sqr_binary64`
458×	`associate-/l/_binary64`
422×	`associate-*l/_binary64`
301×	`*-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	33	29
2	61	29
3	158	29
4	476	29
5	1623	29
6	3429	29
7	4631	29
8	4950	29
9	4898	29

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

9.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	9.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 46 to 38 computations (17.4% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.3b	(pow.f64 (/.f64 t l) 2)
0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite659.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

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 → 173

Calls

4 calls:

24.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
23.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
10.0ms	(pow.f64 (/.f64 t l) 2)
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 5892 to 4086 computations (30.7% saved)

series782.0ms (3.3%)

Error

2.0b

Counts

4 → 71

Calls

4 calls:

349.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
281.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
61.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
29.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 6215 to 5167 computations (16.9% saved)

simplify384.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

300×	`associate-/r/_binary64`
255×	`cancel-sign-sub-inv_binary64`
228×	`associate-/l/_binary64`
187×	`unswap-sqr_binary64`
185×	`distribute-rgt-in_binary64`

Counts

244 → 182

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	408	10824
1	886	9234
2	2693	8929
3	4947	8929

prune206.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	8	183

Error

0.6b

Counts

183 → 8

Alt Table

Status	Error	Program
	9.8b	(asin.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	9.8b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	46.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	9.9b	(asin.f64 (.f64 (+.f64 (.f64 (pow.f64 (/.f64 Om Omc) 2) -1/2) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
	22.6b	(asin.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (-.f64 1 (.f64 4 (pow.f64 (/.f64 t l) 4)))) (-.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
	13.8b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
▶	9.7b	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 2892 to 1979 computations (31.6% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
8.6b	(sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite219.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
7×	`sqrt-div_binary64`
6×	`*-un-lft-identity_binary64`

Counts

4 → 52

Calls

4 calls:

37.0ms	(sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 2428 to 1650 computations (32% saved)

series692.0ms (2.9%)

Error

0.6b

Counts

4 → 84

Calls

4 calls:

361.0ms	(sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
92.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
88.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
62.0ms	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 7389 to 5582 computations (24.5% saved)

simplify248.0ms (1%)

Algorithm

1×	egg-herbie

Rules

887×	`associate-/l*_binary64`
481×	`associate-*l/_binary64`
194×	`cancel-sign-sub-inv_binary64`
124×	`distribute-rgt-neg-in_binary64`
118×	`associate-/r/_binary64`

Counts

136 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	5382
1	488	4434
2	1665	4172
3	4947	4172
4	4960	4172

prune179.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Error

0.6b

Counts

106 → 8

Alt Table

Status	Error	Program
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	21.6b	(asin.f64 (log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
▶	9.8b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	46.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	9.9b	(asin.f64 (.f64 (+.f64 (.f64 (pow.f64 (/.f64 Om Omc) 2) -1/2) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
	10.2b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	10.9b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
✓	9.7b	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 2804 to 1901 computations (32.2% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
1.7b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
12.9b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
12.9b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite757.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

180×	`add-sqr-sqrt_binary64`
146×	`cbrt-prod_binary64`
145×	`times-frac_binary64`
122×	`*-un-lft-identity_binary64`
90×	`difference-of-squares_binary64`

Counts

4 → 187

Calls

4 calls:

30.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
22.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
21.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 10907 to 7718 computations (29.2% saved)

series2.2s (9.1%)

Error

0.6b

Counts

4 → 92

Calls

4 calls:

663.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
644.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
572.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
119.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 18047 to 14945 computations (17.2% saved)

simplify704.0ms (3%)

Algorithm

1×	egg-herbie

Rules

408×	`cancel-sign-sub-inv_binary64`
242×	`unswap-sqr_binary64`
219×	`times-frac_binary64`
216×	`associate-r_binary64`
162×	`associate-/l*_binary64`

Counts

279 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	445	17551
1	1024	14874
2	3381	14079
3	4951	14079
4	4971	14079

prune389.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	229	9	238

Error

0.6b

Counts

238 → 9

Alt Table

Status	Error	Program
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	21.6b	(asin.f64 (log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
▶	9.9b	(asin.f64 (.f64 (+.f64 (.f64 (pow.f64 (/.f64 Om Omc) 2) -1/2) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
	11.7b	(.f64 (.f64 (cbrt.f64 (asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) 1/6) 3))) (cbrt.f64 (asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) 1/6) 3)))) (cbrt.f64 (asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) 1/6) 3))))
✓	9.8b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	46.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	10.2b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	10.9b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
✓	9.7b	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 7495 to 5220 computations (30.4% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.3b	(pow.f64 (/.f64 t l) 2)
0.5b	(asin.f64 (.f64 (+.f64 (.f64 (pow.f64 (/.f64 Om Omc) 2) -1/2) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.6b	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite348.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

31×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
15×	`sqrt-prod_binary64`

Counts

4 → 100

Calls

4 calls:

7.0ms	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
6.0ms	(pow.f64 (/.f64 t l) 2)
1.0ms	(asin.f64 (.f64 (+.f64 (.f64 (pow.f64 (/.f64 Om Omc) 2) -1/2) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 3227 to 2422 computations (24.9% saved)

series337.0ms (1.4%)

Error

0.6b

Counts

4 → 63

Calls

4 calls:

96.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
94.0ms	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
70.0ms	(asin.f64 (.f64 (+.f64 (.f64 (pow.f64 (/.f64 Om Omc) 2) -1/2) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
30.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 3450 to 2887 computations (16.3% saved)

simplify244.0ms (1%)

Algorithm

1×	egg-herbie

Rules

959×	`times-frac_binary64`
506×	`associate-/l*_binary64`
199×	`cancel-sign-sub-inv_binary64`
126×	`sqr-pow_binary64`
99×	`unswap-sqr_binary64`

Counts

163 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	4354
1	612	3889
2	1669	3741
3	4909	3741
4	4952	3741

prune177.0ms (0.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	121	9	130

Error

0.6b

Counts

130 → 9

Alt Table

Status	Error	Program
	9.9b	(asin.f64 (.f64 (+.f64 (.f64 (pow.f64 (/.f64 Om Omc) 2) -1/2) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
	11.7b	(.f64 (.f64 (cbrt.f64 (asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) 1/6) 3))) (cbrt.f64 (asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) 1/6) 3)))) (cbrt.f64 (asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) 1/6) 3))))
	9.8b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	46.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	10.0b	(asin.f64 (.f64 (+.f64 (.f64 (pow.f64 (/.f64 Om Omc) 2) -1/2) 1) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))))
	10.2b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	10.9b	(.f64 (.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 1 (/.f64 Om Omc)) (-.f64 1 (/.f64 Om Omc))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	9.7b	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 2135 to 1576 computations (26.2% saved)

regimes7.5s (31.7%)

Accuracy

Total 0.1b remaining (10.9%)

Threshold costs 0.1b (10.9%)

Compiler

Compiled 100838 to 79071 computations (21.6% saved)

bsearch17.0ms (0.1%)

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

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-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	39	120
1	60	120
2	81	120
3	96	120
4	106	120
5	109	120
6	107	120

end3.0ms (0%)

Compiler: Compiled 82 to 56 computations (31.7% saved)

sample4.0s (17%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	128	valid
1.0s	4917×	body	128	nan

Compiler

Compiled 509 to 383 computations (24.8% saved)

Details

analyze3.3s (13.7%)

sample116.0ms (0.5%)

simplify128.0ms (0.5%)

prune3.0ms (0%)

localize38.0ms (0.2%)

rewrite659.0ms (2.8%)

series782.0ms (3.3%)

simplify384.0ms (1.6%)

prune206.0ms (0.9%)

localize35.0ms (0.1%)

rewrite219.0ms (0.9%)

series692.0ms (2.9%)

simplify248.0ms (1%)

prune179.0ms (0.8%)

localize33.0ms (0.1%)

rewrite757.0ms (3.2%)

series2.2s (9.1%)

simplify704.0ms (3%)

prune389.0ms (1.6%)

localize34.0ms (0.1%)

rewrite348.0ms (1.5%)

series337.0ms (1.4%)

simplify244.0ms (1%)

prune177.0ms (0.7%)

regimes7.5s (31.7%)

bsearch17.0ms (0.1%)

simplify13.0ms (0.1%)

end3.0ms (0%)

sample4.0s (17%)

Profiling