Details

analyze1.4s (7.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample3.9s (20.2%)

Results

1.3s	5478×	body	128	valid
731.0ms	1222×	body	1024	valid
544.0ms	928×	body	512	valid
502.0ms	850×	body	1024	invalid
249.0ms	1522×	body	128	invalid
219.0ms	539×	body	512	invalid
175.0ms	557×	body	256	valid
85.0ms	288×	body	256	invalid
47.0ms	71×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
506×	`fma-neg_binary64`
500×	`distribute-rgt-in_binary64`
420×	`distribute-lft-in_binary64`
403×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	48	39
2	103	39
3	222	39
4	455	39
5	975	39
6	2136	39
7	4390	39
8	4971	39

prune3.0ms (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

41.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))

Compiler

Compiled 114 to 72 computations (36.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	9.4b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	21.8b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series1.8s (9.1%)

Counts

4 → 120

Calls

4 calls:

1.4s	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
309.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
74.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
4.0ms	(*.f64 (sqrt.f64 2) t)

rewrite361.0ms (1.9%)

Algorithm

4×	egg-rewrite

Rules

92×	`egg`
59×	`egg`
53×	`egg`
25×	`egg`

Counts

4 → 229

Calls

4 calls:

114.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
89.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
81.0ms	(*.f64 (sqrt.f64 2) t)
71.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	331	31
2	4050	31
3	5108	31
0	14	29
1	312	29
2	3857	29
3	4986	29
4	4935	29
0	5	6
1	99	6
2	1029	6
3	4823	6
4	5948	6
0	18	39
1	397	39
2	4687	39
3	5518	39

simplify296.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

632×	`*-commutative_binary64`
385×	`fma-def_binary64`
342×	`associate-+r+_binary64`
278×	`associate-r_binary64`
225×	`associate-*r/_binary64`

Counts

349 → 385

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1507	28688
1	5075	28688

prune880.0ms (4.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	376	9	385
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	377	9	386

Error

3.5b

Counts

386 → 9

Alt Table

Status	Error	Program
	40.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (sqrt.f64 (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 (sqrt.f64 (fma.f64 2 (.f64 t t) (.f64 l l))) (/.f64 (+.f64 x 1) (-.f64 x 1))) (neg.f64 (*.f64 l l)))))
	38.3b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
▶	29.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	45.8b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	63.0b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1)))))
	63.1b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1))) (/.f64 (.f64 t (sqrt.f64 2)) l)))
	36.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
	36.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))

Compiler

Compiled 46401 to 33453 computations (27.9% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.5b	(/.f64 (.f64 l l) (.f64 x x))
✓	16.7b	(/.f64 (.f64 t t) (.f64 x x))
✓	20.0b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	26.2b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

series640.0ms (3.3%)

Counts

4 → 104

Calls

4 calls:

547.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))
33.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
30.0ms	(/.f64 (.f64 l l) (.f64 x x))
29.0ms	(/.f64 (.f64 t t) (.f64 x x))

rewrite258.0ms (1.3%)

Algorithm

4×	egg-rewrite

Rules

59×	`egg`
59×	`egg`
52×	`egg`
21×	`egg`

Counts

4 → 191

Calls

4 calls:

82.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
76.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))
49.0ms	(/.f64 (.f64 l l) (.f64 x x))
47.0ms	(/.f64 (.f64 t t) (.f64 x x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	562	72
2	4778	72
3	5022	72
0	7	10
1	150	10
2	1774	10
3	4985	10
4	5317	10
0	6	10
1	129	7
2	1647	7
3	5252	7
0	6	10
1	129	7
2	1647	7
3	5252	7

simplify167.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
410×	`associate-/r*_binary64`
315×	`times-frac_binary64`
291×	`associate-l_binary64`
246×	`associate-*r/_binary64`

Counts

295 → 249

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	533	11996
1	1714	9975
2	5319	9975

prune516.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	244	5	249
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	248	10	258

Error

0.5b

Counts

258 → 10

Alt Table

Status	Error	Program
	36.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
▶	29.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))))))) 2))
✓	29.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	45.8b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	55.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
	31.7b	(/.f64 (.f64 (sqrt.f64 2) t) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	36.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 3/2) 1/3))
	56.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))

Compiler

Compiled 27844 to 16998 computations (39% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.8b	(/.f64 (*.f64 l l) (pow.f64 x 3))
✓	9.9b	(/.f64 (*.f64 t t) x)
	20.0b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	26.2b	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

series631.0ms (3.2%)

Counts

3 → 80

Calls

3 calls:

543.0ms

(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 4 (/.f64 (*.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (*.f64 l l) (pow.f64 x 3)) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

78.0ms

(/.f64 (*.f64 l l) (pow.f64 x 3))

10.0ms

(/.f64 (*.f64 t t) x)

rewrite172.0ms (0.9%)

Algorithm

3×	egg-rewrite

Rules

83×	`egg`
52×	`egg`
19×	`egg`

Counts

3 → 154

Calls

3 calls:

80.0ms

(/.f64 (*.f64 l l) (pow.f64 x 3))

46.0ms

(/.f64 (*.f64 t t) x)

43.0ms

(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 4 (/.f64 (*.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (*.f64 l l) (pow.f64 x 3)) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	72
1	558	72
2	4953	72
0	5	7
1	106	7
2	1363	7
3	5319	7
0	7	10
1	150	10
2	1774	10
3	4985	10
4	5317	10

simplify162.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
410×	`associate-/r*_binary64`
315×	`times-frac_binary64`
291×	`associate-l_binary64`
246×	`associate-*r/_binary64`

Counts

234 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	533	11684
1	1714	9663
2	5319	9663

prune821.0ms (4.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	264	3	267
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	265	12	277

Error

0.4b

Counts

277 → 12

Alt Table

Status	Error	Program
	58.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))) 2))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 3/2) 1/3))
	56.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))) 2))
✓	29.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	45.8b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	55.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
	31.7b	(/.f64 (.f64 (sqrt.f64 2) t) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
▶	30.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))))))))) 2))
	36.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
	36.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))
	56.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))

Compiler

Compiled 29352 to 19153 computations (34.7% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	9.9b	(/.f64 (*.f64 t t) x)
	20.0b	(/.f64 (*.f64 t t) (pow.f64 x 3))
	26.2b	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))
✓	27.0b	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

series1.0s (5.2%)

Counts

1 → 36

Calls

1 calls:

1.0s

(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 4 (/.f64 (*.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (*.f64 l l) (pow.f64 x 3)) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

rewrite44.0ms (0.2%)

Algorithm

1×	egg-rewrite

Rules

19× egg

Counts

1 → 19

Calls

1 calls:

42.0ms

(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 4 (/.f64 (*.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (*.f64 l l) (pow.f64 x 3)) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	72
1	556	72
2	4948	72

simplify306.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

970×	`times-frac_binary64`
938×	`fma-def_binary64`
310×	`*-commutative_binary64`
220×	`+-commutative_binary64`
185×	`associate-+r+_binary64`

Counts

55 → 83

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	801	20834
1	2873	20802
2	4995	20802

prune2.1s (10.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	435	0	435
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	435	12	447

Error

0.4b

Counts

447 → 12

Alt Table

Status	Error	Program
	58.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))) 2))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 3/2) 1/3))
	56.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))) 2))
✓	29.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	45.8b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	55.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
	31.7b	(/.f64 (.f64 (sqrt.f64 2) t) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
✓	30.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))))))))) 2))
	36.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
	36.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))
	56.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))

Compiler

Compiled 88563 to 56644 computations (36% saved)

regimes2.5s (13.1%)

Accuracy

Total 11.1b remaining (96%)

Threshold costs 0b (0%)

Counts

98 → 5

Compiler

Compiled 32119 to 22405 computations (30.2% saved)

bsearch645.0ms (3.3%)

Steps

Iters	Range		Point
7	1.047081942949223e-41	2.4877840920365027e-39	2.4426192567774815e-39
8	4.158460835548421e-230	6.20592556137329e-226	4.26980358877847e-230
7	2.2361357653711518e-298	4.090616439001549e-296	4.0189218111892443e-296
3	-2.3610905839388477e-32	-2.0342246964884252e-32	-2.3406614659731964e-32

Compiler

Compiled 4 to 3 computations (25% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	252
1	88	252
2	97	252
3	102	252
4	104	252
5	102	252

end584.0ms (3%)

Compiler: Compiled 928 to 638 computations (31.3% saved)

Details

analyze1.4s (7.3%)

sample3.9s (20.2%)

simplify58.0ms (0.3%)

prune3.0ms (0%)

localize15.0ms (0.1%)

series1.8s (9.1%)

rewrite361.0ms (1.9%)

simplify296.0ms (1.5%)

prune880.0ms (4.5%)

localize30.0ms (0.2%)

series640.0ms (3.3%)

rewrite258.0ms (1.3%)

simplify167.0ms (0.9%)

prune516.0ms (2.7%)

localize33.0ms (0.2%)

series631.0ms (3.2%)

rewrite172.0ms (0.9%)

simplify162.0ms (0.8%)

prune821.0ms (4.2%)

localize37.0ms (0.2%)

series1.0s (5.2%)

rewrite44.0ms (0.2%)

simplify306.0ms (1.6%)

prune2.1s (10.8%)

regimes2.5s (13.1%)

bsearch645.0ms (3.3%)

simplify10.0ms (0.1%)

end584.0ms (3%)

Profiling