Details

analyze1.9s (12.3%)

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 (0.8%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
15.0ms	117×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify51.0ms (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

11.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.5b	(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 Om Omc) 2)
✓	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	10.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series418.0ms (2.7%)

Counts

4 → 144

Calls

4 calls:

372.0ms	(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 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
12.0ms	(pow.f64 (/.f64 t l) 2)
10.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite31.0ms (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)))
5.0ms	(pow.f64 (/.f64 t l) 2)
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))))

simplify206.0ms (1.3%)

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

prune460.0ms (3%)

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

1.0b

Counts

230 → 8

Alt Table

Status	Error	Program
	14.6b	(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))))))
	11.7b	(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))))))
▶	11.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	44.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	11.7b	(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))))))
	43.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	12.0b	(*.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))))))
	12.6b	(.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 14862 to 11075 computations (25.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 t l) 2)
✓	0.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	3.3b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
✓	10.3b	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series411.0ms (2.7%)

Counts

3 → 120

Calls

3 calls:

379.0ms

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

13.0ms

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

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
25×	`sqrt-prod_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 81

Calls

3 calls:

13.0ms

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

4.0ms

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

0.0ms

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

simplify181.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-def_binary64`
398×	`times-frac_binary64`
345×	`associate-/r*_binary64`
267×	`associate-/l*_binary64`
266×	`associate-*r/_binary64`

Counts

201 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	606	13522
1	1647	11250
2	5066	11250

prune445.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	239	7	246

Error

1.0b

Counts

246 → 7

Alt Table

Status	Error	Program
	12.0b	(*.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	12.6b	(.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))))))
	14.6b	(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))))))
	11.7b	(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))))))
	44.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	11.7b	(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))))))
	43.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))

Compiler

Compiled 15180 to 11409 computations (24.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(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))))))
✓	1.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	11.7b	(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)))))
✓	16.9b	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series366.0ms (2.4%)

Counts

4 → 144

Calls

4 calls:

245.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
54.0ms	(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)))))
42.0ms	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
23.0ms	(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))))))

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
103×	`times-frac_binary64`
95×	`sqrt-prod_binary64`
85×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`

Counts

4 → 158

Calls

4 calls:

16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
4.0ms	(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)))))
1.0ms	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.0ms	(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))))))

simplify396.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

461×	`fma-neg_binary64`
314×	`sub-neg_binary64`
221×	`*-commutative_binary64`
220×	`fma-def_binary64`
196×	`associate-r_binary64`

Counts

302 → 281

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	578	15791
1	1374	13566
2	4064	13072
3	4583	12670
4	4832	12670
5	4922	12670

prune700.0ms (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	361	2	363
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	363	7	370

Error

1.0b

Counts

370 → 7

Alt Table

Status	Error	Program
	12.0b	(*.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	12.6b	(.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))))))
▶	11.6b	(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))))) (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	44.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	43.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	13.4b	(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))))) (pow.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/6)))
	14.6b	(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))))))

Compiler

Compiled 24010 to 17818 computations (25.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.3b	(cbrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	10.3b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
	11.7b	(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)))))
	16.9b	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series58.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

41.0ms	(cbrt.f64 (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))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-prod_binary64`
6×	`sqrt-prod_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 31

Calls

2 calls:

1.0ms	(cbrt.f64 (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))

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

592×	`associate-/l*_binary64`
517×	`associate-/r*_binary64`
381×	`associate-l_binary64`
302×	`fma-def_binary64`
187×	`associate-*l/_binary64`

Counts

79 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	2523
1	455	2402
2	1355	2232
3	5050	2232

prune426.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	228	7	235

Error

1.0b

Counts

235 → 7

Alt Table

Status	Error	Program
	12.0b	(*.f64 (sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	12.6b	(.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))))))
✓	11.6b	(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))))) (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	44.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	43.4b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	13.4b	(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))))) (pow.f64 (/.f64 1 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/6)))
	14.6b	(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))))))

Compiler

Compiled 14429 to 10832 computations (24.9% saved)

regimes6.6s (43.4%)

Accuracy

Total 0.6b remaining (44.2%)

Threshold costs 0.6b (44.2%)

Counts

274 → 3

Compiler

Compiled 147684 to 116754 computations (20.9% saved)

bsearch14.0ms (0.1%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	121
1	56	121
2	84	121
3	103	121
4	116	121
5	120	121
6	119	121

end2.0ms (0%)

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

sample2.3s (14.9%)

Algorithm

1×

intervals

Results

984.0ms	8000×	body	128	valid
540.0ms	4835×	body	128	nan

Compiler

Compiled 410 to 312 computations (23.9% saved)

Details

analyze1.9s (12.3%)

sample116.0ms (0.8%)

simplify51.0ms (0.3%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series418.0ms (2.7%)

rewrite31.0ms (0.2%)

simplify206.0ms (1.3%)

prune460.0ms (3%)

localize16.0ms (0.1%)

series411.0ms (2.7%)

rewrite26.0ms (0.2%)

simplify181.0ms (1.2%)

prune445.0ms (2.9%)

localize17.0ms (0.1%)

series366.0ms (2.4%)

rewrite47.0ms (0.3%)

simplify396.0ms (2.6%)

prune700.0ms (4.6%)

localize23.0ms (0.2%)

series58.0ms (0.4%)

rewrite3.0ms (0%)

simplify66.0ms (0.4%)

prune426.0ms (2.8%)

regimes6.6s (43.4%)

bsearch14.0ms (0.1%)

simplify6.0ms (0%)

end2.0ms (0%)

sample2.3s (14.9%)

Profiling