Details

analyze1.9s (15.5%)

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)

sample124.0ms (1%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
17.0ms	154×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify54.0ms (0.4%)

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

9.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.3b	(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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(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))
✓	1.0b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	7.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series603.0ms (5%)

Counts

4 → 168

Calls

4 calls:

358.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
214.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
19.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
11.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite48.0ms (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:

13.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
10.0ms	(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))))

simplify334.0ms (2.7%)

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

prune593.0ms (4.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	298	11	309
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	299	11	310

Error

1.0b

Counts

310 → 11

Alt Table

Status	Error	Program
	9.5b	(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)))))
	9.5b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (.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))))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	9.8b	(*.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))))) (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))))))
	23.0b	(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 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)))
	10.5b	(.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))))))
▶	9.3b	(expm1.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))))))
	9.3b	(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))))
	12.8b	(asin.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) 3)))
	9.4b	(asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc)))) (sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	44.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))

Compiler

Compiled 18534 to 13678 computations (26.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(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))
	1.0b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	7.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

prune635.0ms (5.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	308	1	309
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	308	12	320

Error

1.0b

Counts

320 → 12

Alt Table

Status	Error	Program
	9.5b	(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)))))
	9.5b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (.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))))) (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.3b	(expm1.f64 (log1p.f64 (.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))))))))
	9.8b	(*.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))))) (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))))))
	23.0b	(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 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)))
	10.5b	(.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))))))
✓	9.3b	(expm1.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))))))
▶	9.3b	(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))))
	12.8b	(asin.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) 3)))
	9.4b	(asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc)))) (sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	44.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))

Compiler

Compiled 19258 to 14374 computations (25.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.6b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	1.0b	(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))))
✓	7.8b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series387.0ms (3.2%)

Counts

3 → 120

Calls

3 calls:

351.0ms

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

19.0ms

(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))))

16.0ms

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

rewrite40.0ms (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:

13.0ms

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

1.0ms

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

0.0ms

(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))))

simplify323.0ms (2.7%)

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 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	645	19365
1	1761	16645
2	4923	16520
3	5188	16520

prune646.0ms (5.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	297	7	304
Fresh	4	6	10
Picked	1	0	1
Done	0	1	1
Total	302	14	316

Error

1.0b

Counts

316 → 14

Alt Table

Status	Error	Program
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	45.2b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	48.4b	(asin.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)))))
	10.3b	(expm1.f64 (log1p.f64 (.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))))))))
	9.5b	(asin.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	10.5b	(.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))))))
▶	9.4b	(asin.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	9.3b	(expm1.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))))))
	9.4b	(asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc)))) (sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	9.5b	(asin.f64 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	44.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.2b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	45.6b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	9.8b	(*.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))))) (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))))))

Compiler

Compiled 18446 to 13747 computations (25.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 Om Omc) 2)
✓	1.0b	(asin.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	6.9b	(sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
	7.8b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series63.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

43.0ms

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

19.0ms

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

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-prod_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`sqrt-pow1_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms

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

0.0ms

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

simplify191.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

843×	`fma-neg_binary64`
447×	`times-frac_binary64`
425×	`unswap-sqr_binary64`
298×	`associate-/l*_binary64`
274×	`sub-neg_binary64`

Counts

103 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	3480
1	360	3133
2	919	3013
3	3355	2803
4	4799	2803
5	4256	2803
6	4109	2803
7	4863	2803
8	4899	2803

prune396.0ms (3.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	226	15	241

Error

1.0b

Counts

241 → 15

Alt Table

Status	Error	Program
	45.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	45.2b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	48.4b	(asin.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)))))
	10.3b	(expm1.f64 (log1p.f64 (.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))))))))
	53.9b	(asin.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	9.5b	(asin.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	10.5b	(.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))))))
✓	9.4b	(asin.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	9.3b	(expm1.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))))))
	9.4b	(asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc)))) (sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
	9.5b	(asin.f64 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	44.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.2b	(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	45.6b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	9.8b	(*.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))))) (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))))))

Compiler

Compiled 10431 to 7731 computations (25.9% saved)

regimes3.3s (27.4%)

Accuracy

Total 0.4b remaining (36.4%)

Threshold costs 0.4b (36.4%)

Counts

154 → 3

Compiler

Compiled 75139 to 59815 computations (20.4% saved)

bsearch10.0ms (0.1%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	115
1	49	115
2	67	115
3	80	115
4	89	115
5	92	115
6	91	115

end1.0ms (0%)

Compiler: Compiled 78 to 55 computations (29.5% saved)

sample2.4s (19.9%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
543.0ms	4768×	body	128	nan

Compiler

Compiled 614 to 478 computations (22.1% saved)

Details

analyze1.9s (15.5%)

sample124.0ms (1%)

simplify54.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series603.0ms (5%)

rewrite48.0ms (0.4%)

simplify334.0ms (2.7%)

prune593.0ms (4.9%)

localize19.0ms (0.2%)

prune635.0ms (5.2%)

localize14.0ms (0.1%)

series387.0ms (3.2%)

rewrite40.0ms (0.3%)

simplify323.0ms (2.7%)

prune646.0ms (5.3%)

localize22.0ms (0.2%)

series63.0ms (0.5%)

rewrite3.0ms (0%)

simplify191.0ms (1.6%)

prune396.0ms (3.3%)

regimes3.3s (27.4%)

bsearch10.0ms (0.1%)

simplify5.0ms (0%)

end1.0ms (0%)

sample2.4s (19.9%)

Profiling