Details

analyze1.8s (10.3%)

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)

sample73.0ms (0.4%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
18.0ms	175×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

525×	`associate-/r/_binary64`
484×	`unswap-sqr_binary64`
458×	`associate-/l/_binary64`
422×	`associate-*l/_binary64`
301×	`*-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	33	29
2	61	29
3	158	29
4	476	29
5	1623	29
6	3429	29
7	4631	29
8	4950	29
9	4898	29

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

9.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 46 to 38 computations (17.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(pow.f64 (/.f64 t l) 2)
0.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite240.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

Rules

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

Counts

4 → 126

Calls

4 calls:

14.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
3.0ms	(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)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 3954 to 2735 computations (30.8% saved)

series296.0ms (1.7%)

Error

2.0b

Counts

4 → 43

Calls

4 calls:

198.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
36.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
18.0ms	(pow.f64 (/.f64 t l) 2)
18.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 4954 to 4164 computations (15.9% saved)

simplify175.0ms (1%)

Algorithm

1×	egg-herbie

Rules

227×	`associate-/r/_binary64`
226×	`associate-/l/_binary64`
224×	`unswap-sqr_binary64`
182×	`sqr-pow_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

169 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	415	6265
1	878	5409
2	2604	5284
3	4741	5281
4	4958	5281

prune72.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	8	122

Error

0.5b

Counts

122 → 8

Alt Table

Status	Error	Program
	20.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 1 (/.f64 (.f64 t t) (.f64 l l))))))))
	15.5b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
✓	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
	42.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	15.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (*.f64 t (cbrt.f64 t)) (pow.f64 (/.f64 (cbrt.f64 t) l) 2)))))))
	14.3b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
▶	9.8b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
	42.6b	(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 1996 to 1400 computations (29.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
2.6b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite469.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

180×	`add-sqr-sqrt_binary64`
146×	`cbrt-prod_binary64`
145×	`times-frac_binary64`
122×	`*-un-lft-identity_binary64`
90×	`difference-of-squares_binary64`

Counts

4 → 187

Calls

4 calls:

14.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
13.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
11.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 10907 to 7718 computations (29.2% saved)

series1.1s (6.4%)

Error

0.5b

Counts

4 → 69

Calls

4 calls:

330.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
327.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
319.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
61.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 21132 to 17339 computations (17.9% saved)

simplify316.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

526×	`times-frac_binary64`
329×	`associate-/l*_binary64`
315×	`associate-/r*_binary64`
277×	`associate-r_binary64`
191×	`associate-l_binary64`

Counts

256 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	17873
1	1221	15845
2	4913	15787
3	4960	15787

prune208.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	191	8	199

Error

0.5b

Counts

199 → 8

Alt Table

Status	Error	Program
✓	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
	42.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	20.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 1 (/.f64 (.f64 t t) (.f64 l l))))))))
	14.3b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
	42.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	10.2b	(.f64 (sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))) (sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))
	10.8b	(.f64 (.f64 (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))) (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))) (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))
▶	9.8b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))

Compiler

Compiled 8403 to 5725 computations (31.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite568.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

356×	`cbrt-prod_binary64`
299×	`add-sqr-sqrt_binary64`
241×	`times-frac_binary64`
205×	`*-un-lft-identity_binary64`
153×	`sqrt-prod_binary64`

Counts

4 → 303

Calls

4 calls:

22.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
14.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
13.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 15383 to 11147 computations (27.5% saved)

series1.5s (8.4%)

Error

0.5b

Counts

4 → 76

Calls

4 calls:

358.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
334.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
333.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
329.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 26780 to 21988 computations (17.9% saved)

simplify383.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

526×	`times-frac_binary64`
343×	`associate-r_binary64`
329×	`associate-/l*_binary64`
315×	`associate-/r*_binary64`
256×	`associate-l_binary64`

Counts

379 → 315

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	596	25720
1	1587	23404
2	5001	23404

prune349.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	315	0	315
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	315	8	323

Error

0.5b

Counts

323 → 8

Alt Table

Status	Error	Program
✓	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
	42.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	20.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 1 (/.f64 (.f64 t t) (.f64 l l))))))))
	14.3b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
	42.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	10.2b	(.f64 (sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))) (sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))
	10.8b	(.f64 (.f64 (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))) (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))) (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))
✓	9.8b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))

Compiler

Compiled 11955 to 8266 computations (30.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.7b	(sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))
8.7b	(sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite282.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

122×	`add-sqr-sqrt_binary64`
96×	`times-frac_binary64`
96×	`cbrt-prod_binary64`
84×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`

Counts

4 → 140

Calls

4 calls:

14.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))
1.0ms	(sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))

Compiler

Compiled 8922 to 6594 computations (26.1% saved)

series904.0ms (5.1%)

Error

0.5b

Counts

4 → 62

Calls

4 calls:

349.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
344.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
67.0ms	(sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))
66.0ms	(sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))

Compiler

Compiled 16596 to 13798 computations (16.9% saved)

simplify301.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

270×	`times-frac_binary64`
214×	`cancel-sign-sub-inv_binary64`
184×	`associate-/l*_binary64`
169×	`associate-r_binary64`
169×	`associate-/r*_binary64`

Counts

202 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	329	12642
1	826	11456
2	2944	10640
3	4847	10560
4	4963	10560

prune150.0ms (0.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	150	8	158

Error

0.5b

Counts

158 → 8

Alt Table

Status	Error	Program
	9.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
	42.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
	20.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 1 (/.f64 (.f64 t t) (.f64 l l))))))))
	14.3b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
	42.6b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	10.2b	(.f64 (sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))) (sqrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))
	10.8b	(.f64 (.f64 (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))) (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3)))) (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))
	9.8b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))))

Compiler

Compiled 5797 to 4091 computations (29.4% saved)

regimes6.0s (33.8%)

Accuracy

Total 0.1b remaining (15.3%)

Threshold costs 0.1b (15.3%)

Compiler

Compiled 160294 to 123972 computations (22.7% saved)

bsearch14.0ms (0.1%)

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
13×	`+-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	38	102
1	58	102
2	83	102
3	102	102
4	115	102
5	119	102
6	117	102

end1.0ms (0%)

Compiler: Compiled 70 to 47 computations (32.9% saved)

sample2.4s (13.2%)

Algorithm

1×

intervals

Results

966.0ms	8000×	body	128	valid
578.0ms	4818×	body	128	nan

Compiler

Compiled 388 to 303 computations (21.9% saved)

Details

analyze1.8s (10.3%)

sample73.0ms (0.4%)

simplify72.0ms (0.4%)

prune2.0ms (0%)

localize13.0ms (0.1%)

rewrite240.0ms (1.3%)

series296.0ms (1.7%)

simplify175.0ms (1%)

prune72.0ms (0.4%)

localize18.0ms (0.1%)

rewrite469.0ms (2.6%)

series1.1s (6.4%)

simplify316.0ms (1.8%)

prune208.0ms (1.2%)

localize23.0ms (0.1%)

rewrite568.0ms (3.2%)

series1.5s (8.4%)

simplify383.0ms (2.1%)

prune349.0ms (2%)

localize22.0ms (0.1%)

rewrite282.0ms (1.6%)

series904.0ms (5.1%)

simplify301.0ms (1.7%)

prune150.0ms (0.8%)

regimes6.0s (33.8%)

bsearch14.0ms (0.1%)

simplify7.0ms (0%)

end1.0ms (0%)

sample2.4s (13.2%)

Profiling