Details

analyze1.1s (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)

sample3.2s (21.2%)

Results

844.0ms	5478×	body	128	valid
626.0ms	1222×	body	1024	valid
449.0ms	850×	body	1024	invalid
392.0ms	928×	body	512	valid
255.0ms	539×	body	512	invalid
232.0ms	1522×	body	128	invalid
152.0ms	557×	body	256	valid
78.0ms	288×	body	256	invalid
49.0ms	71×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify53.0ms (0.4%)

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

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

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)

localize16.0ms (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)))

series1.9s (12.7%)

Counts

4 → 120

Calls

4 calls:

1.5s	(/.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))))
359.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
79.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
3.0ms	(*.f64 (sqrt.f64 2) t)

rewrite96.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

144× egg-rr

Counts

4 → 144

Calls

2 calls:

92.0ms

((sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (*.f64 t t) (*.f64 l l))) (*.f64 l l))) (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (*.f64 t t) (*.f64 l l))) (*.f64 l l)) (*.f64 (sqrt.f64 2) t) (/.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)))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	105
1	397	105
2	4687	105
3	5518	105
0	0	0
1	0	0

simplify250.0ms (1.7%)

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

264 → 301

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1507	28688
1	5075	28688

prune857.0ms (5.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	292	9	301
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	293	9	302

Error

3.5b

Counts

302 → 9

Alt Table

Status	Error	Program
▶	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)))))))
	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)))))))
	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))))))))
	40.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) (neg.f64 (.f64 l l)))))
	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)))))))))

Compiler

Compiled 43757 to 32117 computations (26.6% saved)

localize29.0ms (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)))))))))

series645.0ms (4.3%)

Counts

4 → 104

Calls

4 calls:

554.0ms	(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)))))))))
31.0ms	(/.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))

rewrite68.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

79× egg-rr

Counts

4 → 79

Calls

2 calls:

66.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	110
1	562	96
2	4778	96
3	5022	96
0	0	0
1	0	0

simplify140.0ms (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

183 → 140

Iterations

Useful iterations: 1 (0.0ms)

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

prune394.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	139	10	149

Error

0.5b

Counts

149 → 10

Alt Table

Status	Error	Program
	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))))))))
✓	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)))))))
	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))
	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))))))))
	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))))))))))))
▶	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))
	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)))))))))

Compiler

Compiled 20920 to 14062 computations (32.8% 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)))))))))

series595.0ms (3.9%)

Counts

3 → 80

Calls

3 calls:

550.0ms

(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)))))))))

33.0ms

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

12.0ms

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

rewrite35.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

55× egg-rr

Counts

3 → 55

Calls

2 calls:

34.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	89
1	558	89
2	4953	89
0	0	0
1	0	0

simplify134.0ms (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

135 → 114

Iterations

Useful iterations: 1 (0.0ms)

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

prune389.0ms (2.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	132	12	144

Error

0.4b

Counts

144 → 12

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))))))))
▶	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))
	36.7b	(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))))))))
	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))
	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)))))))
✓	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)))))))
	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))
	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))))))))))))
	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))
	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)))))))))

Compiler

Compiled 20944 to 14610 computations (30.2% saved)

localize36.0ms (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 (6.8%)

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)))))))))

rewrite30.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

19× egg-rr

Counts

1 → 19

Calls

2 calls:

29.0ms

((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))))))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify240.0ms (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

prune1.4s (9.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	237	12	249

Error

0.4b

Counts

249 → 12

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))))))))
✓	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))
	36.7b	(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))))))))
	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))
	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)))))))
✓	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)))))))
	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))
	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))))))))))))
	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))
	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)))))))))

Compiler

Compiled 65621 to 44868 computations (31.6% saved)

regimes1.6s (10.3%)

Accuracy

Total 11.1b remaining (96%)

Threshold costs 0b (0%)

Counts

83 → 5

Compiler

Compiled 26934 to 18935 computations (29.7% saved)

bsearch451.0ms (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)

simplify7.0ms (0%)

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	70	254
1	90	254
2	99	254
3	104	254
4	106	254
5	104	254

end399.0ms (2.6%)

Compiler: Compiled 930 to 642 computations (31% saved)

Details

analyze1.1s (7.3%)

sample3.2s (21.2%)

simplify53.0ms (0.4%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series1.9s (12.7%)

rewrite96.0ms (0.6%)

simplify250.0ms (1.7%)

prune857.0ms (5.7%)

localize29.0ms (0.2%)

series645.0ms (4.3%)

rewrite68.0ms (0.5%)

simplify140.0ms (0.9%)

prune394.0ms (2.6%)

localize33.0ms (0.2%)

series595.0ms (3.9%)

rewrite35.0ms (0.2%)

simplify134.0ms (0.9%)

prune389.0ms (2.6%)

localize36.0ms (0.2%)

series1.0s (6.8%)

rewrite30.0ms (0.2%)

simplify240.0ms (1.6%)

prune1.4s (9.3%)

regimes1.6s (10.3%)

bsearch451.0ms (3%)

simplify7.0ms (0%)

end399.0ms (2.6%)

Profiling