Metrics for Hyperbolic secant

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample730.0ms (43.1%)

Results

720.0ms

8256×

body

256

valid

Bogosity

preprocess147.0ms (8.7%)

Algorithm

1×	egg-herbie

Rules

444×	`swap-sqr`
427×	`*-commutative`
422×	`fma-def`
408×	`sqr-pow`
361×	`associate-r`

Problems

256×

No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	93
1	27	93
2	46	93
3	77	93
4	147	93
5	337	93
6	883	93
7	2651	93
8	3615	93
9	4837	93
10	6321	93

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Symmetry

(abs x)

Compiler

Compiled 34 to 16 computations (52.9% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize29.0ms (1.7%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 25 to 9 computations (64% saved)

series2.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms	x	@	inf	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	0	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	0	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms	x	@	inf	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite119.0ms (7%)

Algorithm

1×	batch-egg-rewrite

Rules

58×	`*-un-lft-identity`
55×	`add-cbrt-cube`
53×	`add-exp-log`
53×	`pow1`
52×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	144	40
2	2151	40

Stop Event

1×

unsound

Counts

2 → 22

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Outputs
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4

simplify102.0ms (6%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-+r+`
487×	`distribute-lft-out`
363×	`+-commutative`
344×	`*-commutative`
331×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	464
1	96	459
2	213	453
3	500	449
4	1746	449
5	2885	449
6	3998	449
7	7076	449

Stop Event

1×	node limit

Counts

38 → 40

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
2
(+.f64 2 (pow.f64 x 2))
(+.f64 2 (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2)))
(+.f64 2 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (*.f64 5/24 (pow.f64 x 4))))
(fma.f64 5/24 (pow.f64 x 4) (fma.f64 -1/2 (pow.f64 x 2) 1))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) (*.f64 -61/720 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))
(fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 5/24 -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -61/720 (pow.f64 x 6) 1)))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -61/720 (pow.f64 x 6) (fma.f64 5/24 (pow.f64 x 4) 1)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2
(+.f64 2 (pow.f64 x 2))
(fma.f64 x x 2)
(+.f64 2 (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2)))
(+.f64 2 (fma.f64 1/12 (pow.f64 x 4) (pow.f64 x 2)))
(+.f64 2 (fma.f64 (pow.f64 x 4) 1/12 (pow.f64 x 2)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 2))
(+.f64 2 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))))
(+.f64 2 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (pow.f64 x 2))))
(+.f64 2 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (pow.f64 x 2))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 2)))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x 2)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 2)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4

eval11.0ms (0.7%)

Compiler: Compiled 388 to 310 computations (20.1% saved)

prune7.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	5	41

Accuracy

100.0%

Counts

41 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.9%	(/.f64 2 (fma.f64 x x 2))
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	53.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.8%	1
	48.9%	0
▶	76.9%	(/.f64 2 (fma.f64 x x 2))
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	53.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.8%	1
	48.9%	0

Compiler

Compiled 56 to 46 computations (17.9% saved)

localize47.0ms (2.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.3%	(/.f64 2 (fma.f64 x x 2))

Compiler

Compiled 33 to 24 computations (27.3% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/.f64 2 (fma.f64 x x 2))
0.0ms	x	@	-inf	(/.f64 2 (fma.f64 x x 2))
0.0ms	x	@	0	(/.f64 2 (fma.f64 x x 2))

rewrite64.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

580×	`associate-r`
412×	`associate-l`
353×	`frac-times`
254×	`add-cube-cbrt`
254×	`add-sqr-sqrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	74	21
2	862	21

Stop Event

1×	node limit

Counts

1 → 60

Calls

Call 1

Inputs
(/.f64 2 (fma.f64 x x 2))

Outputs
(+.f64 (exp.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2)))) -1)
(-.f64 (exp.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2)))) 1)
(*.f64 2 (/.f64 1 (fma.f64 x x 2)))
(*.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(*.f64 1 (/.f64 2 (fma.f64 x x 2)))
(*.f64 (/.f64 1 (fma.f64 x x 2)) 2)
(*.f64 (/.f64 1 (fma.f64 x x 2)) -2)
(*.f64 -2 (/.f64 1 (fma.f64 x x 2)))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (/.f64 2 (sqrt.f64 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2))
(*.f64 (/.f64 2 (pow.f64 (cbrt.f64 (fma.f64 x x 2)) 2)) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x x 2)) 2)) (/.f64 2 (cbrt.f64 (fma.f64 x x 2))))
(*.f64 -1 (/.f64 2 (fma.f64 x x 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (fma.f64 x x 2) -1/2) (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (pow.f64 (fma.f64 x x 2) -2) 2)))
(*.f64 (pow.f64 (fma.f64 x x 2) -1/2) (/.f64 2 (sqrt.f64 (fma.f64 x x 2))))
(.f64 (pow.f64 (fma.f64 x x 2) -1/2) (.f64 (pow.f64 (fma.f64 x x 2) -1/2) 2))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (sqrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2)))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 2) (.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2)) (.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) 2))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2))) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 2)) (pow.f64 (fma.f64 x x 2) -1/2))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4))
(.f64 (.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 2)) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (/.f64 2 (+.f64 (pow.f64 x 4) -4)) (+.f64 (pow.f64 x 2) -2))
(.f64 (/.f64 2 (+.f64 8 (pow.f64 x 6))) (-.f64 (+.f64 (pow.f64 x 4) 4) (.f64 2 (pow.f64 x 2))))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 1 (fma.f64 x x 2)))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4))
(*.f64 (sqrt.f64 (/.f64 4 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2))
(.f64 (sqrt.f64 (.f64 (/.f64 2 (fma.f64 x x 2)) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(*.f64 (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) 3) (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) 3))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) 3))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(*.f64 (cbrt.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 2))) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(.f64 (cbrt.f64 (.f64 (/.f64 2 (fma.f64 x x 2)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 6) (*.f64 4 (pow.f64 (fma.f64 x x 2) -2))))) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)
(pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)
(pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)
(pow.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 1/2)
(pow.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 3)) 1/3)
(sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))
(fabs.f64 (/.f64 2 (fma.f64 x x 2)))
(log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 2 (fma.f64 x x 2)))))
(cbrt.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 3)))
(expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))
(exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))
(log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))

simplify85.0ms (5%)

Algorithm

1×	egg-herbie

Rules

446×	`associate-/l/`
435×	`unswap-sqr`
423×	`*-commutative`
378×	`associate-/r/`
293×	`associate-+l+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2947
1	478	2838
2	1806	2760
3	6081	2760

Stop Event

1×	node limit

Counts

72 → 117

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 1/4 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/8 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 4)))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 4))) (.f64 16 (/.f64 1 (pow.f64 x 8)))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 4))) (.f64 16 (/.f64 1 (pow.f64 x 8)))))
(+.f64 (exp.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2)))) -1)
(-.f64 (exp.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2)))) 1)
(*.f64 2 (/.f64 1 (fma.f64 x x 2)))
(*.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(*.f64 1 (/.f64 2 (fma.f64 x x 2)))
(*.f64 (/.f64 1 (fma.f64 x x 2)) 2)
(*.f64 (/.f64 1 (fma.f64 x x 2)) -2)
(*.f64 -2 (/.f64 1 (fma.f64 x x 2)))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (/.f64 2 (sqrt.f64 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2))
(*.f64 (/.f64 2 (pow.f64 (cbrt.f64 (fma.f64 x x 2)) 2)) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x x 2)) 2)) (/.f64 2 (cbrt.f64 (fma.f64 x x 2))))
(*.f64 -1 (/.f64 2 (fma.f64 x x 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (fma.f64 x x 2) -1/2) (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (pow.f64 (fma.f64 x x 2) -2) 2)))
(*.f64 (pow.f64 (fma.f64 x x 2) -1/2) (/.f64 2 (sqrt.f64 (fma.f64 x x 2))))
(.f64 (pow.f64 (fma.f64 x x 2) -1/2) (.f64 (pow.f64 (fma.f64 x x 2) -1/2) 2))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (sqrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2)))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 2) (.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2)) (.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) 2))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2))) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 2)) (pow.f64 (fma.f64 x x 2) -1/2))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4))
(.f64 (.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 2)) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (/.f64 2 (+.f64 (pow.f64 x 4) -4)) (+.f64 (pow.f64 x 2) -2))
(.f64 (/.f64 2 (+.f64 8 (pow.f64 x 6))) (-.f64 (+.f64 (pow.f64 x 4) 4) (.f64 2 (pow.f64 x 2))))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 1 (fma.f64 x x 2)))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4))
(*.f64 (sqrt.f64 (/.f64 4 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2))
(.f64 (sqrt.f64 (.f64 (/.f64 2 (fma.f64 x x 2)) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(*.f64 (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) 3) (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) 3))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) 3))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(*.f64 (cbrt.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 2))) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(.f64 (cbrt.f64 (.f64 (/.f64 2 (fma.f64 x x 2)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 6) (*.f64 4 (pow.f64 (fma.f64 x x 2) -2))))) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)
(pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)
(pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)
(pow.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 1/2)
(pow.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 3)) 1/3)
(sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))
(fabs.f64 (/.f64 2 (fma.f64 x x 2)))
(log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 2 (fma.f64 x x 2)))))
(cbrt.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 3)))
(expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))
(exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))
(log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 1/4 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (*.f64 1/4 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (*.f64 1/4 (pow.f64 x 4)))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 1/4 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/8 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -1/8 (pow.f64 x 6) (*.f64 1/4 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 1/4 (pow.f64 x 4) (*.f64 -1/8 (pow.f64 x 6))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 4 (pow.f64 x 4)))
(+.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 -4 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 4 (pow.f64 x 4))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -4 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 4))) (.f64 16 (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8)))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (-.f64 (/.f64 8 (pow.f64 x 6)) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8)))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (/.f64 8 (pow.f64 x 6)) (+.f64 (/.f64 -4 (pow.f64 x 4)) (/.f64 -16 (pow.f64 x 8)))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 4 (pow.f64 x 4)))
(+.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 -4 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 4 (pow.f64 x 4))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -4 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 4))) (.f64 16 (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8)))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (-.f64 (/.f64 8 (pow.f64 x 6)) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8)))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (/.f64 8 (pow.f64 x 6)) (+.f64 (/.f64 -4 (pow.f64 x 4)) (/.f64 -16 (pow.f64 x 8)))))
(+.f64 (exp.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2)))) -1)
(/.f64 2 (fma.f64 x x 2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2)))) 1)
(/.f64 2 (fma.f64 x x 2))
(*.f64 2 (/.f64 1 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(/.f64 2 (fma.f64 x x 2))
(*.f64 1 (/.f64 2 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 1 (fma.f64 x x 2)) 2)
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 1 (fma.f64 x x 2)) -2)
(/.f64 -2 (fma.f64 x x 2))
(*.f64 -2 (/.f64 1 (fma.f64 x x 2)))
(/.f64 -2 (fma.f64 x x 2))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 2 (sqrt.f64 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x 2) -1/2) (sqrt.f64 (fma.f64 x x 2))) 2)
(*.f64 (/.f64 2 (pow.f64 (cbrt.f64 (fma.f64 x x 2)) 2)) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x x 2)) 2)) (/.f64 2 (cbrt.f64 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(*.f64 -1 (/.f64 2 (fma.f64 x x 2)))
(/.f64 -2 (fma.f64 x x 2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (fma.f64 x x 2) -1/2) (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2)))
(.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (.f64 (pow.f64 (fma.f64 x x 2) -1/2) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (pow.f64 (fma.f64 x x 2) -2) 2)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 2 (pow.f64 (fma.f64 x x 2) -2))))
(*.f64 (pow.f64 (fma.f64 x x 2) -1/2) (/.f64 2 (sqrt.f64 (fma.f64 x x 2))))
(*.f64 (/.f64 2 (sqrt.f64 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x 2) -1/2) (sqrt.f64 (fma.f64 x x 2))) 2)
(.f64 (pow.f64 (fma.f64 x x 2) -1/2) (.f64 (pow.f64 (fma.f64 x x 2) -1/2) 2))
(/.f64 2 (fma.f64 x x 2))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (sqrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2)))
(*.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/4))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(/.f64 2 (fma.f64 x x 2))
(.f64 (cbrt.f64 2) (.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 2) (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (/.f64 1 (cbrt.f64 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 2) (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (fma.f64 x x 2))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (/.f64 (cbrt.f64 2) (cbrt.f64 (fma.f64 x x 2))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))))
(*.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) 4))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 7))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4)) (.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))))
(.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4))))
(.f64 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2)) (.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) 2))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2)) (/.f64 2 (cbrt.f64 (fma.f64 x x 2))))
(/.f64 (*.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2))) (cbrt.f64 (fma.f64 x x 2)))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6)))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/12) 6))
(.f64 (.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2))) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2)) (/.f64 2 (cbrt.f64 (fma.f64 x x 2))))
(/.f64 (*.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x x 2) -2))) (cbrt.f64 (fma.f64 x x 2)))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 2)) (pow.f64 (fma.f64 x x 2) -1/2))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2)))
(.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (.f64 (pow.f64 (fma.f64 x x 2) -1/2) (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4))
(/.f64 2 (fma.f64 x x 2))
(.f64 (.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4)) (.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))))
(.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(/.f64 2 (fma.f64 x x 2))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 2)) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(.f64 (cbrt.f64 2) (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (/.f64 1 (cbrt.f64 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 2) (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (fma.f64 x x 2))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (/.f64 (cbrt.f64 2) (cbrt.f64 (fma.f64 x x 2))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))))
(*.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) 4))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 7))
(*.f64 (/.f64 2 (+.f64 (pow.f64 x 4) -4)) (+.f64 (pow.f64 x 2) -2))
(*.f64 (/.f64 2 (+.f64 (pow.f64 x 4) -4)) (fma.f64 x x -2))
(/.f64 (fma.f64 2 (pow.f64 x 2) -4) (+.f64 (pow.f64 x 4) -4))
(.f64 (/.f64 2 (+.f64 8 (pow.f64 x 6))) (-.f64 (+.f64 (pow.f64 x 4) 4) (.f64 2 (pow.f64 x 2))))
(.f64 (/.f64 2 (+.f64 (pow.f64 x 6) 8)) (-.f64 (+.f64 4 (pow.f64 x 4)) (.f64 2 (pow.f64 x 2))))
(.f64 (/.f64 2 (+.f64 (pow.f64 x 6) 8)) (+.f64 4 (+.f64 (pow.f64 x 4) (.f64 (pow.f64 x 2) -2))))
(*.f64 (/.f64 2 (+.f64 (pow.f64 x 6) 8)) (fma.f64 (pow.f64 x 2) -2 (+.f64 4 (pow.f64 x 4))))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 1 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4))
(*.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (sqrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2)))
(*.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/4) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/4))
(*.f64 (sqrt.f64 (/.f64 4 (fma.f64 x x 2))) (pow.f64 (fma.f64 x x 2) -1/2))
(*.f64 (pow.f64 (fma.f64 x x 2) -1/2) (sqrt.f64 (/.f64 4 (fma.f64 x x 2))))
(.f64 (sqrt.f64 (.f64 (/.f64 2 (fma.f64 x x 2)) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (sqrt.f64 (.f64 (/.f64 2 (fma.f64 x x 2)) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))))
(*.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 5)))
(*.f64 (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) 3) (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) 3))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) 3))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (cbrt.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 2))) (/.f64 1 (cbrt.f64 (fma.f64 x x 2))))
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 2))) (cbrt.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 2))))
(/.f64 (cbrt.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 2))) (cbrt.f64 (fma.f64 x x 2)))
(.f64 (cbrt.f64 (.f64 (/.f64 2 (fma.f64 x x 2)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2))) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6))
(.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (cbrt.f64 (.f64 (/.f64 2 (fma.f64 x x 2)) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3/2))))
(*.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 1/6) (cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 6) (*.f64 4 (pow.f64 (fma.f64 x x 2) -2))))) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 6) (*.f64 4 (pow.f64 (fma.f64 x x 2) -2))))))
(.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (cbrt.f64 (cbrt.f64 (.f64 4 (*.f64 (pow.f64 (fma.f64 x x 2) -2) (pow.f64 (/.f64 2 (fma.f64 x x 2)) 6))))))
(.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 6) (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -2)))))
(pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 1/2)
(sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))
(sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -2))
(pow.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 3)) 1/3)
(/.f64 2 (fma.f64 x x 2))
(sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))
(sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -2))
(fabs.f64 (/.f64 2 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 2 (fma.f64 x x 2)))))
(/.f64 2 (fma.f64 x x 2))
(cbrt.f64 (/.f64 8 (pow.f64 (fma.f64 x x 2) 3)))
(/.f64 2 (fma.f64 x x 2))
(expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))

eval50.0ms (2.9%)

Compiler: Compiled 1927 to 1519 computations (21.2% saved)

prune18.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	2	2
Done	0	1	1
Total	117	5	122

Accuracy

100.0%

Counts

122 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.9%	(/.f64 2 (fma.f64 x x 2))
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.8%	1
	48.9%	0
✓	76.9%	(/.f64 2 (fma.f64 x x 2))
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.8%	1
	48.9%	0

Compiler

Compiled 56 to 46 computations (17.9% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	3	3
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.9%	(/.f64 2 (fma.f64 x x 2))
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.8%	1
	48.9%	0
✓	76.9%	(/.f64 2 (fma.f64 x x 2))
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.8%	1
	48.9%	0

Compiler

Compiled 56 to 46 computations (17.9% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	3	3
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.9%	(/.f64 2 (fma.f64 x x 2))
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.8%	1
	48.9%	0

Compiler

Compiled 52 to 42 computations (19.2% saved)

regimes14.0ms (0.8%)

Counts

5 → 1

Calls

Call 1

Inputs
0
1
(/.f64 2 (fma.f64 x x 2))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Calls

3 calls:

6.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
4.0ms	x
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
100.0%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 42 to 32 computations (23.8% saved)

regimes8.0ms (0.5%)

Counts

4 → 2

Calls

Call 1

Inputs
0
1
(/.f64 2 (fma.f64 x x 2))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))

Outputs
(/.f64 2 (fma.f64 x x 2))
0

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
99.8%	2	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes7.0ms (0.4%)

Counts

2 → 2

Calls

Call 1

Inputs
0
1

Outputs
1
0

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
99.6%	2	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
0

Outputs
0

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
48.9%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch18.0ms (1.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	0.02401981349656457	1889.3051726669114

Results

16.0ms

144×

body

256

valid

Compiler

Compiled 112 to 91 computations (18.8% saved)

bsearch16.0ms (1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	0.02401981349656457	1889.3051726669114

Results

15.0ms

144×

body

256

valid

Compiler

Compiled 67 to 64 computations (4.5% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
2×	`+-commutative`
1×	`sub-neg`
1×	`neg-mul-1`
1×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	80
1	34	80
2	36	80
3	37	80

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 360) (/.f64 2 (fma.f64 x x 2)) 0)
(if (<=.f64 x 350) 1 0)
0

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 360) (/.f64 2 (fma.f64 x x 2)) 0)
(if (<=.f64 x 350) 1 0)
0

Compiler

Compiled 30 to 24 computations (20% saved)

soundness159.0ms (9.4%)

Rules

580×	`associate-+r+`
487×	`distribute-lft-out`
363×	`+-commutative`
344×	`*-commutative`
331×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	144	40
2	2151	40
0	46	464
1	96	459
2	213	453
3	500	449
4	1746	449
5	2885	449
6	3998	449
7	7076	449

Stop Event

1×	node limit
1×	unsound

Compiler

Compiled 28 to 22 computations (21.4% saved)

end0.0ms (0%)

preprocess42.0ms (2.5%)

Remove: (abs x)
Compiler: Compiled 90 to 70 computations (22.2% saved)

analyze0.0ms (0%)

sample730.0ms (43.1%)

preprocess147.0ms (8.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize29.0ms (1.7%)

series2.0ms (0.1%)

rewrite119.0ms (7%)

simplify102.0ms (6%)

eval11.0ms (0.7%)

prune7.0ms (0.4%)

localize47.0ms (2.8%)

series1.0ms (0.1%)

rewrite64.0ms (3.8%)

simplify85.0ms (5%)

eval50.0ms (2.9%)

prune18.0ms (1.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes14.0ms (0.8%)

regimes8.0ms (0.5%)

regimes7.0ms (0.4%)

regimes3.0ms (0.2%)

bsearch18.0ms (1.1%)

bsearch16.0ms (1%)

simplify5.0ms (0.3%)

soundness159.0ms (9.4%)

end0.0ms (0%)

preprocess42.0ms (2.5%)

Profiling