Details

analyze1.9s (10.6%)

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)

sample2.6s (15%)

Results

1.6s	8256×	body	128	valid
935.0ms	4930×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify52.0ms (0.3%)

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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	0.8b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	7.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series609.0ms (3.5%)

Counts

4 → 168

Calls

4 calls:

365.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
215.0ms	(/.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))))
11.0ms	(pow.f64 (/.f64 t l) 2)

rewrite48.0ms (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))))

simplify319.0ms (1.8%)

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	4868	17206
3	5187	17206

prune560.0ms (3.2%)

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

0.5b

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))
	9.5b	(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))))))
	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 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))))
	43.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	9.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	9.3b	(asin.f64 (sqrt.f64 (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

Compiler

Compiled 18328 to 13471 computations (26.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
✓	0.8b	(/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
✓	7.9b	(sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))

series2.4s (13.8%)

Counts

3 → 144

Calls

3 calls:

1.9s

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

532.0ms

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

28.0ms

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

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-prod_binary64`
8×	`times-frac_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

3 → 63

Calls

3 calls:

18.0ms

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

17.0ms

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

0.0ms

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

simplify376.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

373×	`associate-r_binary64`
332×	`fma-def_binary64`
307×	`associate-+r+_binary64`
211×	`associate-/r*_binary64`
167×	`associate-/l*_binary64`

Counts

207 → 232

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1609	45491
1	5075	45491

prune1.1s (6.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	270	3	273
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	271	10	281

Error

0.5b

Counts

281 → 10

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))
	22.2b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))))
	9.5b	(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))))))
▶	9.3b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (sqrt.f64 (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
	9.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (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))))))
	9.8b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
	43.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))

Compiler

Compiled 49188 to 34117 computations (30.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 Om Omc) 2)
	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.5b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (sqrt.f64 (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
✓	8.7b	(sqrt.f64 (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))

series269.0ms (1.5%)

Counts

3 → 120

Calls

3 calls:

230.0ms

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

28.0ms

(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (sqrt.f64 (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))

11.0ms

(pow.f64 (/.f64 Om Omc) 2)

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`unpow-prod-down_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`

Counts

3 → 56

Calls

3 calls:

8.0ms

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

4.0ms

(pow.f64 (/.f64 Om Omc) 2)

0.0ms

(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (sqrt.f64 (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))

simplify175.0ms (1%)

Algorithm

1×	egg-herbie

Rules

950×	`fma-def_binary64`
343×	`times-frac_binary64`
275×	`associate-l_binary64`
271×	`associate-/r*_binary64`
266×	`associate-r_binary64`

Counts

176 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	427	10962
1	1233	8472
2	4855	8314
3	5553	8314

prune353.0ms (2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	183	11	194

Error

0.5b

Counts

194 → 11

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))
	22.2b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))))
✓	9.3b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (sqrt.f64 (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
▶	9.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))))
	43.4b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (.f64 (hypot.f64 1 (/.f64 Om Omc)) (neg.f64 (/.f64 (.f64 t (sqrt.f64 2)) l)))))
✓	9.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
	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))))))
	9.8b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
	43.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	46.5b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (.f64 (hypot.f64 1 (/.f64 Om Omc)) (/.f64 (.f64 t (sqrt.f64 2)) l))))

Compiler

Compiled 10866 to 7832 computations (27.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))))
✓	0.8b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))
✓	7.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1)))
✓	30.2b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

series1.3s (7.3%)

Counts

4 → 168

Calls

4 calls:

644.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
367.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1)))
255.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))
25.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))))

rewrite65.0ms (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 → 174

Calls

4 calls:

13.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1)))
13.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))
3.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
0.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))))

simplify275.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

633×	`fma-def_binary64`
483×	`times-frac_binary64`
367×	`associate-/l*_binary64`
218×	`*-commutative_binary64`
147×	`+-commutative_binary64`

Counts

342 → 358

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	836	21206
1	2209	17824
2	4952	17824

prune821.0ms (4.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	446	0	446
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	446	11	457

Error

0.5b

Counts

457 → 11

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))
	22.2b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))))
✓	9.3b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (sqrt.f64 (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
✓	9.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) 1))))
	43.4b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (.f64 (hypot.f64 1 (/.f64 Om Omc)) (neg.f64 (/.f64 (.f64 t (sqrt.f64 2)) l)))))
✓	9.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
	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))))))
	9.8b	(.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))) (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4)) (*.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))))
	43.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	46.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	46.5b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 4))) (.f64 (hypot.f64 1 (/.f64 Om Omc)) (/.f64 (.f64 t (sqrt.f64 2)) l))))

Compiler

Compiled 27835 to 19505 computations (29.9% saved)

regimes3.9s (22.3%)

Accuracy

Total 0.3b remaining (38.7%)

Threshold costs 0.3b (38.7%)

Counts

191 → 3

Compiler

Compiled 98777 to 77152 computations (21.9% saved)

bsearch9.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
11×	`+-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	46	122
1	65	122
2	86	122
3	102	122
4	112	122
5	115	122
6	114	122

end298.0ms (1.7%)

Compiler: Compiled 547 to 403 computations (26.3% saved)

Details

analyze1.9s (10.6%)

sample2.6s (15%)

simplify52.0ms (0.3%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series609.0ms (3.5%)

rewrite48.0ms (0.3%)

simplify319.0ms (1.8%)

prune560.0ms (3.2%)

localize17.0ms (0.1%)

series2.4s (13.8%)

rewrite43.0ms (0.2%)

simplify376.0ms (2.1%)

prune1.1s (6.3%)

localize17.0ms (0.1%)

series269.0ms (1.5%)

rewrite15.0ms (0.1%)

simplify175.0ms (1%)

prune353.0ms (2%)

localize15.0ms (0.1%)

series1.3s (7.3%)

rewrite65.0ms (0.4%)

simplify275.0ms (1.6%)

prune821.0ms (4.7%)

regimes3.9s (22.3%)

bsearch9.0ms (0%)

simplify5.0ms (0%)

end298.0ms (1.7%)

Profiling