Details

analyze1.9s (5.9%)

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)

sample64.0ms (0.2%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
16.0ms	146×	body	128	nan

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify60.0ms (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

10.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.4b	(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)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.4b	(/.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))))
✓	9.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

rewrite56.0ms (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:

24.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
11.0ms	(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))))

series602.0ms (1.9%)

Counts

4 → 168

Calls

4 calls:

332.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
221.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
33.0ms	(pow.f64 (/.f64 Om Omc) 2)
15.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

simplify542.0ms (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 → 618

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	775	21028
1	2091	17483
2	4849	17362
3	5175	17362

prune1.0s (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	612	6	618
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	613	6	619

Error

0.6b

Counts

619 → 6

Alt Table

Status	Error	Program
	44.0b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
▶	10.4b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	11.5b	(.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))))))
	15.1b	(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))
	10.6b	(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))))))
	43.5b	(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 18109 to 13348 computations (26.3% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 Om Omc) 2)
	0.4b	(/.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 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
✓	9.4b	(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

2.0ms

(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

1.0ms

(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

series5.4s (16.7%)

Counts

2 → 96

Calls

2 calls:

5.3s

(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

25.0ms

(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

simplify1.0s (3.1%)

Algorithm

1×	egg-herbie

Rules

667×	`*-commutative_binary64`
319×	`associate-r_binary64`
287×	`fma-def_binary64`
259×	`associate-+r+_binary64`
204×	`associate-/l*_binary64`

Counts

121 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1452	38733
1	4870	37194
2	4985	37194

prune2.5s (7.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	547	5	552
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	547	11	558

Error

0.5b

Counts

558 → 11

Alt Table

Status	Error	Program
	49.5b	(asin.f64 (.f64 l (sqrt.f64 (-.f64 (/.f64 1/2 (.f64 t t)) (.f64 1/2 (/.f64 (.f64 Om Om) (.f64 (.f64 t t) (*.f64 Omc Omc))))))))
	15.1b	(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))
	49.1b	(asin.f64 (.f64 (/.f64 1 t) (sqrt.f64 (.f64 1/2 (-.f64 (.f64 l l) (/.f64 (.f64 (.f64 l l) (.f64 Om Om)) (*.f64 Omc Omc)))))))
	15.1b	(cbrt.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))) (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	23.6b	(-.f64 (/.f64 PI.f64 2) (acos.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	43.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	44.0b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
✓	10.4b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	11.5b	(.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))))))
	49.8b	(asin.f64 (neg.f64 (.f64 (/.f64 1 t) (sqrt.f64 (.f64 1/2 (-.f64 (.f64 l l) (/.f64 (.f64 (.f64 l l) (.f64 Om Om)) (*.f64 Omc Omc))))))))
▶	10.6b	(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))))))

Compiler

Compiled 52929 to 36552 computations (30.9% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(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))))))
✓	1.6b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	15.0b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
✓	15.0b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

rewrite74.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-sqr-sqrt_binary64`
97×	`times-frac_binary64`
94×	`cbrt-prod_binary64`
82×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`

Counts

3 → 132

Calls

3 calls:

26.0ms

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

18.0ms

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

1.0ms

(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))))))

series2.2s (6.8%)

Counts

3 → 144

Calls

3 calls:

1.1s

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

1.1s

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

53.0ms

(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))))))

simplify1.0s (3.2%)

Algorithm

1×	egg-herbie

Rules

419×	`*-commutative_binary64`
275×	`+-commutative_binary64`
248×	`fma-def_binary64`
205×	`associate-+r+_binary64`
177×	`sub-neg_binary64`

Counts

276 → 500

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1266	35913
1	4166	34958
2	5027	34958

prune2.9s (9.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	686	1	687
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	687	11	698

Error

0.5b

Counts

698 → 11

Alt Table

Status	Error	Program
	49.5b	(asin.f64 (.f64 l (sqrt.f64 (-.f64 (/.f64 1/2 (.f64 t t)) (.f64 1/2 (/.f64 (.f64 Om Om) (.f64 (.f64 t t) (*.f64 Omc Omc))))))))
	15.1b	(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))
	49.1b	(asin.f64 (.f64 (/.f64 1 t) (sqrt.f64 (.f64 1/2 (-.f64 (.f64 l l) (/.f64 (.f64 (.f64 l l) (.f64 Om Om)) (*.f64 Omc Omc)))))))
	15.1b	(cbrt.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))) (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
	23.6b	(-.f64 (/.f64 PI.f64 2) (acos.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	43.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	44.0b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
✓	10.4b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	11.5b	(.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))))))
	49.8b	(asin.f64 (neg.f64 (.f64 (/.f64 1 t) (sqrt.f64 (.f64 1/2 (-.f64 (.f64 l l) (/.f64 (.f64 (.f64 l l) (.f64 Om Om)) (*.f64 Omc Omc))))))))
▶	10.6b	(expm1.f64 (log1p.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))))

Compiler

Compiled 62336 to 42562 computations (31.7% saved)

localize36.0ms (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))
✓	0.5b	(asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
	1.6b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
	15.0b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))

series26.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

25.0ms

(asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))

simplify223.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

680×	`associate-/r*_binary64`
545×	`div-sub_binary64`
472×	`associate-/l/_binary64`
458×	`unswap-sqr_binary64`
345×	`associate-/r/_binary64`

Counts

58 → 114

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	2077
1	83	1868
2	143	1868
3	354	1868
4	1436	1857
5	4201	1857
6	4733	1857
7	5246	1857

prune2.2s (6.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	1126	1	1127
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	1127	11	1138

Error

0.5b

Counts

1138 → 11

Alt Table

Status	Error	Program
	49.5b	(asin.f64 (.f64 l (sqrt.f64 (-.f64 (/.f64 1/2 (.f64 t t)) (.f64 1/2 (/.f64 (.f64 Om Om) (.f64 (.f64 t t) (*.f64 Omc Omc))))))))
	15.1b	(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))
	23.6b	(-.f64 (/.f64 PI.f64 2) (acos.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
	43.5b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	44.0b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)))
✓	10.4b	(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	11.5b	(.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))))))
	49.8b	(asin.f64 (neg.f64 (.f64 (/.f64 1 t) (sqrt.f64 (.f64 1/2 (-.f64 (.f64 l l) (/.f64 (.f64 (.f64 l l) (.f64 Om Om)) (*.f64 Omc Omc))))))))
	49.1b	(asin.f64 (.f64 (/.f64 1 t) (sqrt.f64 (.f64 1/2 (-.f64 (.f64 l l) (/.f64 (.f64 (.f64 l l) (.f64 Om Om)) (*.f64 Omc Omc)))))))
✓	10.6b	(expm1.f64 (log1p.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))))
	14.8b	(expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (.f64 (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3)) (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))) (asin.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))))))

Compiler

Compiled 42679 to 29737 computations (30.3% saved)

regimes6.0s (18.7%)

Accuracy

Total 0.1b remaining (14.9%)

Threshold costs 0.1b (14.9%)

Compiler

Compiled 72866 to 56952 computations (21.8% saved)

bsearch16.0ms (0.1%)

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

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
8×	`+-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	97
1	48	97
2	66	97
3	79	97
4	88	97
5	91	97
6	90	97

end3.0ms (0%)

Compiler: Compiled 67 to 47 computations (29.9% saved)

sample4.1s (12.9%)

Algorithm

1×

intervals

Results

1.8s	8000×	body	128	valid
988.0ms	4817×	body	128	nan

Compiler

Compiled 457 to 347 computations (24.1% saved)

Details

analyze1.9s (5.9%)

sample64.0ms (0.2%)

simplify60.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0%)

rewrite56.0ms (0.2%)

series602.0ms (1.9%)

simplify542.0ms (1.7%)

prune1.0s (3.2%)

localize32.0ms (0.1%)

rewrite5.0ms (0%)

series5.4s (16.7%)

simplify1.0s (3.1%)

prune2.5s (7.8%)

localize34.0ms (0.1%)

rewrite74.0ms (0.2%)

series2.2s (6.8%)

simplify1.0s (3.2%)

prune2.9s (9.2%)

localize36.0ms (0.1%)

rewrite2.0ms (0%)

series26.0ms (0.1%)

simplify223.0ms (0.7%)

prune2.2s (6.9%)

regimes6.0s (18.7%)

bsearch16.0ms (0.1%)

simplify11.0ms (0%)

end3.0ms (0%)

sample4.1s (12.9%)

Profiling