Details

analyze2.0s (16.1%)

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)

sample3.4s (27%)

Results

2.3s	8256×	body	128	valid
991.0ms	4992×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify50.0ms (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

8.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.9b	(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
✓	0.2b	(pow.f64 (/.f64 t l) 2)
✓	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	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))))
✓	8.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series378.0ms (3%)

Counts

4 → 144

Calls

4 calls:

341.0ms	(sqrt.f64 (/.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 t l) 2)
9.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
46×	`sqrt-prod_binary64`
38×	`unpow-prod-down_binary64`

Counts

4 → 132

Calls

4 calls:

10.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
4.0ms	(pow.f64 (/.f64 Om Omc) 2)
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))))

simplify210.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
399×	`times-frac_binary64`
353×	`associate-/r*_binary64`
282×	`associate-/l*_binary64`
223×	`associate-*l/_binary64`

Counts

276 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	708	15505
1	1879	12830
2	4964	12830

prune431.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	221	8	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	8	230

Error

0.6b

Counts

230 → 8

Alt Table

Status	Error	Program
	13.6b	(cbrt.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (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	(asin.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	21.6b	(-.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)))))
▶	8.9b	(asin.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	46.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	42.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	9.4b	(*.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))))))
	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))))))

Compiler

Compiled 14822 to 11047 computations (25.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.5b	(expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	0.6b	(asin.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	8.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series551.0ms (4.4%)

Counts

2 → 96

Calls

2 calls:

529.0ms

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

21.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 21

Calls

2 calls:

0.0ms

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

0.0ms

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

simplify182.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

535×	`times-frac_binary64`
481×	`fma-def_binary64`
353×	`associate-/l*_binary64`
315×	`associate-/r*_binary64`
296×	`associate-l_binary64`

Counts

117 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	435	13741
1	1445	11575
2	5223	11575

prune600.0ms (4.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	248	9	257

Error

0.6b

Counts

257 → 9

Alt Table

Status	Error	Program
	13.6b	(cbrt.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	21.6b	(-.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)))))
✓	8.9b	(asin.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	43.0b	(asin.f64 (log1p.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	46.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	46.3b	(asin.f64 (log1p.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l))))))
	42.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
▶	9.4b	(*.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))))))
	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))))))

Compiler

Compiled 23794 to 18145 computations (23.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))))
✓	0.7b	(*.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))))))
✓	7.9b	(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)))))
	8.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series75.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

54.0ms

(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)))))

21.0ms

(*.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))))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms

(*.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))))))

1.0ms

(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)))))

simplify218.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

546×	`unswap-sqr_binary64`
501×	`associate-/l/_binary64`
474×	`associate-/r*_binary64`
373×	`associate-/r/_binary64`
357×	`fma-def_binary64`

Counts

164 → 79

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	69	5750
1	113	5133
2	241	5005
3	594	4809
4	1612	4634
5	4219	4634
6	4600	4630
7	4956	4630
8	4878	4630

prune935.0ms (7.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	387	5	392
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	390	11	401

Error

0.5b

Counts

401 → 11

Alt Table

Status	Error	Program
	10.1b	(.f64 (.f64 (sqrt.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))))))) (sqrt.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)))))))) (*.f64 (sqrt.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)))))) (sqrt.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))))))))
✓	8.9b	(asin.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	9.4b	(*.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 (expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	9.4b	(.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 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	42.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	13.6b	(cbrt.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	43.0b	(asin.f64 (log1p.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	46.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	46.3b	(asin.f64 (log1p.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l))))))
	13.6b	(*.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 (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	(*.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 (/.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 36227 to 26990 computations (25.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.9b	(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)))))
✓	7.9b	(sqrt.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)))))
	8.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	8.2b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series72.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

55.0ms	(sqrt.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)))))
17.0ms	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

1.0ms	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
1.0ms	(sqrt.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)))))

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
394×	`distribute-neg-frac_binary64`
384×	`unswap-sqr_binary64`
295×	`associate-/l*_binary64`
259×	`associate-/r*_binary64`

Counts

102 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	2970
1	247	2761
2	663	2705
3	3716	2687
4	5102	2687

prune489.0ms (3.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	208	12	220

Error

0.5b

Counts

220 → 12

Alt Table

Status	Error	Program
	10.1b	(.f64 (.f64 (sqrt.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))))))) (sqrt.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)))))))) (*.f64 (sqrt.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)))))) (sqrt.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))))))))
✓	8.9b	(asin.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	9.0b	(.f64 (.f64 (sqrt.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 (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 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	46.3b	(asin.f64 (log1p.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l))))))
	9.4b	(*.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 (expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	9.4b	(.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 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	42.8b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	13.6b	(*.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 (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)))))
	9.8b	(.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))))) (.f64 (fabs.f64 (cbrt.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)))))) (sqrt.f64 (cbrt.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))))))))
	13.6b	(cbrt.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	43.0b	(asin.f64 (log1p.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
	46.3b	(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 19177 to 14337 computations (25.2% saved)

regimes2.4s (18.7%)

Accuracy

Total 0.2b remaining (21.7%)

Threshold costs 0.2b (21.7%)

Counts

107 → 3

Compiler

Compiled 62750 to 49448 computations (21.2% saved)

bsearch6.0ms (0%)

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

simplify6.0ms (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	41	169
1	55	169
2	73	169
3	86	169
4	95	169
5	98	169
6	97	169

end397.0ms (3.1%)

Compiler: Compiled 798 to 599 computations (24.9% saved)

Details

analyze2.0s (16.1%)

sample3.4s (27%)

simplify50.0ms (0.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series378.0ms (3%)

rewrite28.0ms (0.2%)

simplify210.0ms (1.7%)

prune431.0ms (3.4%)

localize17.0ms (0.1%)

series551.0ms (4.4%)

rewrite2.0ms (0%)

simplify182.0ms (1.4%)

prune600.0ms (4.8%)

localize16.0ms (0.1%)

series75.0ms (0.6%)

rewrite14.0ms (0.1%)

simplify218.0ms (1.7%)

prune935.0ms (7.4%)

localize22.0ms (0.2%)

series72.0ms (0.6%)

rewrite5.0ms (0%)

simplify91.0ms (0.7%)

prune489.0ms (3.9%)

regimes2.4s (18.7%)

bsearch6.0ms (0%)

simplify6.0ms (0%)

end397.0ms (3.1%)

Profiling