Details

analyze1.8s (16.6%)

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)

sample2.7s (24.8%)

Results

1.7s	8256×	body	128	valid
922.0ms	4855×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

580×	`rules-6-rev_binary64`
559×	`fma-def_binary64`
302×	`rules-5_binary64`
287×	`rules-4_binary64`
260×	`rules-5-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	27	27
2	57	27
3	146	27
4	616	27
5	4509	27
6	4949	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

9.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.7b	(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 t l) 2)
✓	0.2b	(pow.f64 (/.f64 Om Omc) 2)
✓	0.2b	(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)))

series269.0ms (2.5%)

Counts

4 → 144

Calls

4 calls:

234.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
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))))
11.0ms	(pow.f64 (/.f64 Om Omc) 2)
9.0ms	(pow.f64 (/.f64 t l) 2)

rewrite93.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

441×	`prod-diff_binary64`
161×	`egg-rr`
155×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`

Counts

4 → 161

Calls

4 calls:

87.0ms	(pow.f64 (/.f64 t l) 2)
87.0ms	(pow.f64 (/.f64 Om Omc) 2)
87.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
87.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	66
1	368	66
2	4187	66
3	5058	66
0	0	0
1	0	0

simplify196.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

841×	`rules-13_binary64`
409×	`rules-20_binary64`
383×	`rules-21_binary64`
301×	`fma-neg_binary64`
102×	`rules-11_binary64`

Counts

305 → 231

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	11401
1	1447	10534
2	4961	10534
3	5278	10534

prune412.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	225	6	231
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	226	6	232

Error

2.1b

Counts

232 → 6

Alt Table

Status	Error	Program
	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (/.f64 l (/.f64 t l))) 1))))
	46.9b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
▶	9.7b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.9b	(pow.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))))) 3)
	49.9b	(asin.f64 (-.f64 (fma.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc))))) (/.f64 (.f64 (.f64 Om Om) (pow.f64 l 3)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 Omc Omc) (pow.f64 t 3))))) (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc))))) (/.f64 (pow.f64 l 3) (*.f64 (sqrt.f64 1/2) (pow.f64 t 3)))))))
	9.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1))))

Compiler

Compiled 15478 to 10764 computations (30.5% saved)

localize16.0ms (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)
	0.2b	(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)))

prune468.0ms (4.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	231	6	237

Error

2.1b

Counts

237 → 6

Alt Table

Status	Error	Program
	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (/.f64 l (/.f64 t l))) 1))))
	46.9b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.7b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.9b	(pow.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))))) 3)
	49.9b	(asin.f64 (-.f64 (fma.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc))))) (/.f64 (.f64 (.f64 Om Om) (pow.f64 l 3)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 Omc Omc) (pow.f64 t 3))))) (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc))))) (/.f64 (pow.f64 l 3) (*.f64 (sqrt.f64 1/2) (pow.f64 t 3)))))))
▶	9.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1))))

Compiler

Compiled 15916 to 11206 computations (29.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1))))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
✓	9.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1)))
✓	14.4b	(cbrt.f64 (/.f64 t l))

series985.0ms (9.1%)

Counts

4 → 144

Calls

4 calls:

371.0ms	(cbrt.f64 (/.f64 t l))
351.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
244.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1)))
19.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1))))

rewrite100.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

496×	`prod-diff_binary64`
180×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`
173×	`expm1-log1p-u_binary64`
170×	`add-cbrt-cube_binary64`

Counts

4 → 148

Calls

4 calls:

96.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1))))
96.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 2)
96.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1)))
96.0ms	(cbrt.f64 (/.f64 t l))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	73
1	437	65
2	4807	65
3	5782	65
0	0	0
1	0	0

simplify160.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

843×	`rules-13_binary64`
423×	`rules-20_binary64`
386×	`rules-21_binary64`
105×	`rules-11_binary64`
97×	`fma-def_binary64`

Counts

292 → 232

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	471	11993
1	1522	11126
2	5033	11126

prune420.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	275	6	281

Error

2.1b

Counts

281 → 6

Alt Table

Status	Error	Program
▶	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (/.f64 l (/.f64 t l))) 1))))
	46.9b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
✓	9.7b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.9b	(pow.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))))) 3)
	49.9b	(asin.f64 (-.f64 (fma.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc))))) (/.f64 (.f64 (.f64 Om Om) (pow.f64 l 3)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 Omc Omc) (pow.f64 t 3))))) (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc))))) (/.f64 (pow.f64 l 3) (*.f64 (sqrt.f64 1/2) (pow.f64 t 3)))))))
✓	9.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1))))

Compiler

Compiled 17624 to 11778 computations (33.2% 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	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (/.f64 l (/.f64 t l))) 1))))
✓	3.8b	(/.f64 t (/.f64 l (/.f64 t l)))
✓	9.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (/.f64 l (/.f64 t l))) 1)))

series270.0ms (2.5%)

Counts

3 → 120

Calls

3 calls:

226.0ms

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

24.0ms

(/.f64 t (/.f64 l (/.f64 t l)))

19.0ms

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

rewrite94.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

523×	`prod-diff_binary64`
166×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
155×	`add-log-exp_binary64`

Counts

3 → 122

Calls

3 calls:

91.0ms

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

91.0ms

(/.f64 t (/.f64 l (/.f64 t l)))

91.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	68
1	390	59
2	4551	59
3	5597	59
0	0	0
1	0	0

simplify191.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

841×	`rules-13_binary64`
408×	`rules-20_binary64`
382×	`rules-21_binary64`
102×	`rules-11_binary64`
97×	`fma-def_binary64`

Counts

242 → 190

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	434	11305
1	1441	10381
2	4991	10381
3	4996	10381

prune376.0ms (3.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	236	6	242

Error

2.1b

Counts

242 → 6

Alt Table

Status	Error	Program
✓	10.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (/.f64 t (/.f64 l (/.f64 t l))) 1))))
	46.9b	(asin.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t))))
	49.9b	(asin.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc)))) (/.f64 (.f64 l (sqrt.f64 1/2)) t)) (.f64 1/8 (-.f64 (.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc))))) (/.f64 (pow.f64 l 3) (.f64 (sqrt.f64 1/2) (pow.f64 t 3)))) (.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 Om Om) (.f64 Omc Omc))))) (/.f64 (.f64 (.f64 Om Om) (pow.f64 l 3)) (.f64 (sqrt.f64 1/2) (.f64 (*.f64 Omc Omc) (pow.f64 t 3)))))))))
✓	9.7b	(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
	10.9b	(pow.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))))) 3)
✓	9.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (.f64 (cbrt.f64 (/.f64 t l)) (.f64 (/.f64 t l) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))) 1))))

Compiler

Compiled 15509 to 10601 computations (31.6% saved)

regimes2.0s (18.4%)

Accuracy

Total 1.5b remaining (41.3%)

Threshold costs 0b (0%)

Counts

106 → 3

Compiler

Compiled 56597 to 42208 computations (25.4% saved)

bsearch7.0ms (0.1%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	196
1	57	196
2	56	196

end184.0ms (1.7%)

Compiler: Compiled 470 to 311 computations (33.8% saved)

Details

analyze1.8s (16.6%)

sample2.7s (24.8%)

simplify44.0ms (0.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series269.0ms (2.5%)

rewrite93.0ms (0.9%)

simplify196.0ms (1.8%)

prune412.0ms (3.8%)

localize16.0ms (0.1%)

prune468.0ms (4.3%)

localize17.0ms (0.2%)

series985.0ms (9.1%)

rewrite100.0ms (0.9%)

simplify160.0ms (1.5%)

prune420.0ms (3.9%)

localize13.0ms (0.1%)

series270.0ms (2.5%)

rewrite94.0ms (0.9%)

simplify191.0ms (1.8%)

prune376.0ms (3.5%)

regimes2.0s (18.4%)

bsearch7.0ms (0.1%)

simplify3.0ms (0%)

end184.0ms (1.7%)

Profiling