Details

analyze2.7s (11.7%)

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)

sample2.8s (12.2%)

Results

1.7s	8256×	body	128	valid
971.0ms	4815×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify53.0ms (0.2%)

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

10.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.6b	(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)
✓	0.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	9.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series601.0ms (2.6%)

Counts

4 → 168

Calls

4 calls:

354.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
217.0ms	(/.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)

rewrite49.0ms (0.2%)

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))))

simplify471.0ms (2.1%)

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	4854	17362
3	5175	17362

prune531.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	302	7	309
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	302	8	310

Error

0.4b

Counts

310 → 8

Alt Table

Status	Error	Program
	48.9b	(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)))))
	40.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	14.1b	(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))
▶	10.7b	(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))))
	44.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	10.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	11.9b	(.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))))))
	10.8b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 18284 to 13484 computations (26.3% saved)

localize15.0ms (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)
✓	0.3b	(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))))
✓	10.3b	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series47.0ms (0.2%)

Counts

3 → 96

Calls

3 calls:

18.0ms	(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))))
17.0ms	(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
11.0ms	(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

prune213.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	134	9	143

Error

0.3b

Counts

143 → 9

Alt Table

Status	Error	Program
	48.9b	(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)))))
	40.3b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	40.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	44.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.0b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
✓	10.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	11.9b	(.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))))))
	14.1b	(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))
▶	10.8b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 4100 to 2881 computations (29.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
✓	0.7b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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))))
✓	9.9b	(sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
✓	15.5b	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series1.5s (6.4%)

Counts

4 → 168

Calls

4 calls:

1.0s	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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))))
380.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
40.0ms	(cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
21.0ms	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

rewrite88.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`times-frac_binary64`
169×	`add-sqr-sqrt_binary64`
112×	`sqrt-prod_binary64`
112×	`*-un-lft-identity_binary64`
80×	`difference-of-squares_binary64`

Counts

4 → 200

Calls

4 calls:

21.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
16.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

simplify489.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

948×	`fma-def_binary64`
658×	`times-frac_binary64`
271×	`*-commutative_binary64`
173×	`+-commutative_binary64`
168×	`sub-neg_binary64`

Counts

368 → 378

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1022	30216
1	2755	27341
2	4901	27337
3	5107	27337

prune957.0ms (4.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	468	0	468
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	468	9	477

Error

0.3b

Counts

477 → 9

Alt Table

Status	Error	Program
	48.9b	(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)))))
	40.3b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	40.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	44.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	45.0b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
✓	10.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
▶	11.9b	(.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))))))
	14.1b	(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))
✓	10.8b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 36133 to 26625 computations (26.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
✓	0.7b	(*.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))))))
✓	8.6b	(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)))))
	9.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series8.6s (37.7%)

Counts

2 → 96

Calls

2 calls:

4.5s

(*.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))))))

4.1s

(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)))))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

5.0ms

(*.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))))))

1.0ms

(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)))))

simplify206.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
514×	`associate-/l/_binary64`
485×	`associate-/r*_binary64`
386×	`associate-/r/_binary64`
341×	`unswap-sqr_binary64`

Counts

151 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	6090
1	125	5658
2	258	5102
3	732	5036
4	1860	4580
5	4454	4580
6	4996	4580
7	4928	4580

prune2.1s (9.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	872	3	875
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	873	11	884

Error

0.3b

Counts

884 → 11

Alt Table

Status	Error	Program
	48.9b	(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)))))
	40.3b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 t (sqrt.f64 2)) l)))
	40.2b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	44.9b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	11.9b	(.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 (.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))))))))
	12.6b	(.f64 (.f64 (pow.f64 (cbrt.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)))))) 5) (cbrt.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))))))
	45.0b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
✓	10.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	11.4b	(.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 (cbrt.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)))))) (cbrt.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))))))))
	14.1b	(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))
✓	10.8b	(asin.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (*.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)))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

Compiler

Compiled 89067 to 64704 computations (27.4% saved)

regimes966.0ms (4.3%)

Accuracy

Total 0.1b remaining (18.1%)

Threshold costs 0.1b (18.1%)

Counts

38 → 3

Compiler

Compiled 32002 to 24230 computations (24.3% saved)

bsearch3.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
9×	`+-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	34	99
1	49	99
2	67	99
3	80	99
4	89	99
5	92	99
6	91	99

end302.0ms (1.3%)

Compiler: Compiled 587 to 443 computations (24.5% saved)

Details

analyze2.7s (11.7%)

sample2.8s (12.2%)

simplify53.0ms (0.2%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series601.0ms (2.6%)

rewrite49.0ms (0.2%)

simplify471.0ms (2.1%)

prune531.0ms (2.3%)

localize15.0ms (0.1%)

series47.0ms (0.2%)

rewrite7.0ms (0%)

simplify108.0ms (0.5%)

prune213.0ms (0.9%)

localize17.0ms (0.1%)

series1.5s (6.4%)

rewrite88.0ms (0.4%)

simplify489.0ms (2.2%)

prune957.0ms (4.2%)

localize16.0ms (0.1%)

series8.6s (37.7%)

rewrite12.0ms (0.1%)

simplify206.0ms (0.9%)

prune2.1s (9.2%)

regimes966.0ms (4.3%)

bsearch3.0ms (0%)

simplify5.0ms (0%)

end302.0ms (1.3%)

Profiling