Details

analyze2.9s (18.4%)

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)

sample68.0ms (0.4%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
18.0ms	155×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify56.0ms (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

prune8.0ms (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

9.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.0b	(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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	8.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series621.0ms (4%)

Counts

4 → 168

Calls

4 calls:

368.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
222.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
20.0ms	(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 t l) 2)

rewrite53.0ms (0.3%)

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))
12.0ms	(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 t l) 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))))

simplify401.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

966×	`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	784	21028
1	2107	17327
2	4863	17206
3	5187	17206

prune641.0ms (4.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	300	9	309
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	9	310

Error

0.8b

Counts

310 → 9

Alt Table

Status	Error	Program
	9.0b	(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))))))
	35.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (sqrt.f64 (/.f64 t l)) 2) (pow.f64 (sqrt.f64 (/.f64 t l)) 2)) 1))))
	10.1b	(.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))))))
	49.2b	(asin.f64 (sqrt.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 l 2) (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))) (pow.f64 t 2)))))
▶	9.0b	(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))))))
	42.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	42.0b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	9.1b	(asin.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	9.1b	(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))))))

Compiler

Compiled 18356 to 13501 computations (26.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
	0.3b	(pow.f64 (/.f64 t l) 2)
	0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	8.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

prune602.0ms (3.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	307	2	309
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	309	9	318

Error

0.8b

Counts

318 → 9

Alt Table

Status	Error	Program
	9.9b	(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))))))))
	42.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
▶	9.0b	(expm1.f64 (log1p.f64 (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)))))))
	35.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (sqrt.f64 (/.f64 t l)) 2) (pow.f64 (sqrt.f64 (/.f64 t l)) 2)) 1))))
	10.1b	(.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))))))
	49.2b	(asin.f64 (sqrt.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 l 2) (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))) (pow.f64 t 2)))))
✓	9.0b	(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))))))
	42.0b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	9.1b	(asin.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 19002 to 14131 computations (25.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.8b	(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)))))
✓	8.0b	(sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series697.0ms (4.4%)

Counts

3 → 144

Calls

3 calls:

451.0ms

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

231.0ms

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

15.0ms

(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)))))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

176×	`add-sqr-sqrt_binary64`
113×	`times-frac_binary64`
89×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
46×	`sqrt-prod_binary64`

Counts

3 → 146

Calls

3 calls:

16.0ms

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

11.0ms

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

0.0ms

(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)))))

simplify308.0ms (2%)

Algorithm

1×	egg-herbie

Rules

533×	`fma-def_binary64`
298×	`associate-*r/_binary64`
289×	`times-frac_binary64`
275×	`associate-/l*_binary64`
233×	`associate-/r*_binary64`

Counts

290 → 231

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	580	17770
1	1560	16842
2	4943	16842
3	4960	16842

prune490.0ms (3.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	271	1	272
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	272	9	281

Error

0.8b

Counts

281 → 9

Alt Table

Status	Error	Program
✓	9.0b	(expm1.f64 (log1p.f64 (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)))))))
	42.5b	(expm1.f64 (log1p.f64 (asin.f64 (.f64 (sqrt.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc)))) (.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))))
	35.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (sqrt.f64 (/.f64 t l)) 2) (pow.f64 (sqrt.f64 (/.f64 t l)) 2)) 1))))
	10.1b	(.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))))))
	49.2b	(asin.f64 (sqrt.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 l 2) (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))) (pow.f64 t 2)))))
✓	9.0b	(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))))))
	9.9b	(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))))))))
	42.0b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	9.1b	(asin.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 18001 to 11396 computations (36.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.8b	(asin.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	8.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	9.3b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

series712.0ms (4.5%)

Counts

2 → 96

Calls

2 calls:

690.0ms

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

22.0ms

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

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`sqrt-prod_binary64`
64×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
30×	`difference-of-squares_binary64`

Counts

2 → 76

Calls

2 calls:

13.0ms

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

0.0ms

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

simplify248.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

694×	`associate-/l*_binary64`
681×	`associate-/r*_binary64`
614×	`fma-def_binary64`
228×	`*-commutative_binary64`
143×	`+-commutative_binary64`

Counts

172 → 162

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	788	18090
1	2400	17137
2	5805	17137

prune1.8s (11.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	652	2	654
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	653	10	663

Error

0.8b

Counts

663 → 10

Alt Table

Status	Error	Program
	9.5b	(.f64 (sqrt.f64 (asin.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.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 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
✓	9.0b	(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))))))
	10.2b	(.f64 (.f64 (cbrt.f64 (asin.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.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 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.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 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	9.9b	(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))))))))
✓	9.0b	(expm1.f64 (log1p.f64 (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)))))))
	42.5b	(expm1.f64 (log1p.f64 (asin.f64 (.f64 (sqrt.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc)))) (.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))))
	35.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (sqrt.f64 (/.f64 t l)) 2) (pow.f64 (sqrt.f64 (/.f64 t l)) 2)) 1))))
	42.0b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.1b	(asin.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	49.2b	(asin.f64 (sqrt.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 l 2) (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))) (pow.f64 t 2)))))

Compiler

Compiled 74715 to 52957 computations (29.1% saved)

regimes3.7s (23.2%)

Accuracy

Total 0.5b remaining (44.5%)

Threshold costs 0.5b (44.5%)

Counts

172 → 3

Compiler

Compiled 96456 to 75659 computations (21.6% saved)

bsearch8.0ms (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

end2.0ms (0%)

Compiler: Compiled 83 to 57 computations (31.3% saved)

sample2.3s (14.6%)

Algorithm

1×

intervals

Results

976.0ms	8000×	body	128	valid
528.0ms	4570×	body	128	nan

Compiler

Compiled 584 to 436 computations (25.3% saved)

Details

analyze2.9s (18.4%)

sample68.0ms (0.4%)

simplify56.0ms (0.4%)

prune8.0ms (0%)

localize13.0ms (0.1%)

series621.0ms (4%)

rewrite53.0ms (0.3%)

simplify401.0ms (2.6%)

prune641.0ms (4.1%)

localize18.0ms (0.1%)

prune602.0ms (3.8%)

localize19.0ms (0.1%)

series697.0ms (4.4%)

rewrite49.0ms (0.3%)

simplify308.0ms (2%)

prune490.0ms (3.1%)

localize15.0ms (0.1%)

series712.0ms (4.5%)

rewrite26.0ms (0.2%)

simplify248.0ms (1.6%)

prune1.8s (11.6%)

regimes3.7s (23.2%)

bsearch8.0ms (0.1%)

simplify6.0ms (0%)

end2.0ms (0%)

sample2.3s (14.6%)

Profiling