Details

analyze2.6s (13.3%)

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
0%	95.1%	4.9%	9
0%	95.1%	4.9%	10
0%	94.3%	5.7%	11
2.3%	89.3%	8.4%	12
3.5%	75.8%	20.7%	13
5.8%	73.5%	20.7%	14

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample2.7s (13.6%)

Results

1.7s	8256×	body	128	valid
953.0ms	4823×	body	128	invalid

Compiler

Compiled 47 to 39 computations (17% saved)

simplify53.0ms (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

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

11.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.8b	(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	(pow.f64 (/.f64 Om Omc) 2)
✓	0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	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))))
✓	11.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series618.0ms (3.1%)

Counts

4 → 168

Calls

4 calls:

367.0ms	(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))
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))))
10.0ms	(pow.f64 (/.f64 Om Omc) 2)

rewrite50.0ms (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:

12.0ms	(/.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 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))))

simplify335.0ms (1.7%)

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

prune761.0ms (3.8%)

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

0.6b

Counts

310 → 8

Alt Table

Status	Error	Program
	12.9b	(.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))))))
	14.7b	(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))))))
▶	11.8b	(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))))
	11.8b	(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))))))
	12.0b	(asin.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	31.0b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (*.f64 (pow.f64 (/.f64 t l) 2) (pow.f64 (/.f64 Om Omc) 2)) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (pow.f64 (/.f64 Om Omc) 2)))))
	45.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	44.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))

Compiler

Compiled 18470 to 13606 computations (26.3% saved)

localize13.0ms (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)
✓	0.5b	(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))))
✓	11.2b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series48.0ms (0.2%)

Counts

3 → 96

Calls

3 calls:

20.0ms	(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))))
18.0ms	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
10.0ms	(pow.f64 (/.f64 t l) 2)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

3.0ms	(pow.f64 (/.f64 t l) 2)
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))))

simplify108.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-neg_binary64`
715×	`times-frac_binary64`
356×	`associate-/l*_binary64`
297×	`associate-r_binary64`
288×	`associate-/r*_binary64`

Counts

152 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	3416
1	388	3018
2	989	2959
3	4909	2959
4	5648	2959

prune208.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	133	10	143

Error

0.5b

Counts

143 → 10

Alt Table

Status	Error	Program
	45.9b	(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 -1/16 (/.f64 (/.f64 (pow.f64 l 3) (pow.f64 t 3)) (sqrt.f64 2)))))))
	12.0b	(asin.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	12.9b	(.f64 (.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))))) (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)))))) (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))))))
	45.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	14.7b	(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))))))
	45.7b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
▶	11.8b	(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))))))
	44.2b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	31.0b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (*.f64 (pow.f64 (/.f64 t l) 2) (pow.f64 (/.f64 Om Omc) 2)) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (pow.f64 (/.f64 Om Omc) 2)))))
	44.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))

Compiler

Compiled 4372 to 3073 computations (29.7% saved)

localize15.0ms (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))
✓	0.5b	(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))))))
✓	7.3b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	11.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series794.0ms (4%)

Counts

2 → 96

Calls

2 calls:

771.0ms

(sqrt.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 (*.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 (0.1%)

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:

12.0ms

(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))))))

simplify243.0ms (1.2%)

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

prune2.1s (10.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	813	1	814
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	815	9	824

Error

0.5b

Counts

824 → 9

Alt Table

Status	Error	Program
	12.9b	(.f64 (.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))))) (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)))))) (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))))))
	45.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	14.7b	(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))))))
	45.7b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	45.9b	(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 -1/16 (/.f64 (/.f64 (pow.f64 l 3) (pow.f64 t 3)) (sqrt.f64 2)))))))
	44.2b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	31.0b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (*.f64 (pow.f64 (/.f64 t l) 2) (pow.f64 (/.f64 Om Omc) 2)) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (pow.f64 (/.f64 Om Omc) 2)))))
▶	11.8b	(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)))) (/.f64 (sqrt.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))))))
	44.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))

Compiler

Compiled 85388 to 60534 computations (29.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.3b	(sqrt.f64 (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
	7.3b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	11.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
	11.2b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series41.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

40.0ms

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 21

Calls

1 calls:

4.0ms

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

simplify158.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1259×	`fma-def_binary64`
976×	`fma-neg_binary64`
440×	`times-frac_binary64`
403×	`unswap-sqr_binary64`
289×	`associate-/l*_binary64`

Counts

45 → 45

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	127	1634
1	314	1490
2	852	1370
3	3176	1160
4	4757	1160
5	4191	1160
6	4259	1160
7	4273	1142
8	4762	1142
9	5752	1142

prune1.0s (5.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	359	0	359
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	359	9	368

Error

0.5b

Counts

368 → 9

Alt Table

Status	Error	Program
	12.9b	(.f64 (.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))))) (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)))))) (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))))))
	45.7b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	14.7b	(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))))))
	45.7b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
	45.9b	(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 -1/16 (/.f64 (/.f64 (pow.f64 l 3) (pow.f64 t 3)) (sqrt.f64 2)))))))
	44.2b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	31.0b	(asin.f64 (sqrt.f64 (-.f64 (fma.f64 2 (*.f64 (pow.f64 (/.f64 t l) 2) (pow.f64 (/.f64 Om Omc) 2)) 1) (fma.f64 2 (pow.f64 (/.f64 t l) 2) (pow.f64 (/.f64 Om Omc) 2)))))
✓	11.8b	(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)))) (/.f64 (sqrt.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))))))
	44.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))

Compiler

Compiled 40346 to 29009 computations (28.1% saved)

regimes7.5s (37.9%)

Accuracy

Total 0.1b remaining (17%)

Threshold costs 0.1b (17%)

Counts

313 → 3

Compiler

Compiled 171766 to 135392 computations (21.2% saved)

bsearch18.0ms (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

end276.0ms (1.4%)

Compiler: Compiled 492 to 364 computations (26% saved)

Details

analyze2.6s (13.3%)

sample2.7s (13.6%)

simplify53.0ms (0.3%)

prune8.0ms (0%)

localize13.0ms (0.1%)

series618.0ms (3.1%)

rewrite50.0ms (0.3%)

simplify335.0ms (1.7%)

prune761.0ms (3.8%)

localize13.0ms (0.1%)

series48.0ms (0.2%)

rewrite7.0ms (0%)

simplify108.0ms (0.5%)

prune208.0ms (1%)

localize15.0ms (0.1%)

series794.0ms (4%)

rewrite26.0ms (0.1%)

simplify243.0ms (1.2%)

prune2.1s (10.8%)

localize21.0ms (0.1%)

series41.0ms (0.2%)

rewrite5.0ms (0%)

simplify158.0ms (0.8%)

prune1.0s (5.2%)

regimes7.5s (37.9%)

bsearch18.0ms (0.1%)

simplify6.0ms (0%)

end276.0ms (1.4%)

Profiling