Metrics for Hyperbolic secant

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

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 9 computations (10% saved)

sample583.0ms (74.1%)

Memory

3.4MiB live, 613.8MiB allocated; 85ms collecting garbage

Samples

377.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-exp: 122.0ms (52.1% of total)

ival-div!: 54.0ms (23.1% of total)

ival-neg: 36.0ms (15.4% of total)

ival-add!: 20.0ms (8.5% of total)

adjust: 2.0ms (0.9% of total)

Bogosity

preprocess42.0ms (5.3%)

Memory

1.7MiB live, 47.0MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	52	12
2	180	12
3	1390	12

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Symmetry

(abs x)

Compiler

Compiled 16 to 14 computations (12.5% saved)

series7.0ms (0.9%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	306

Stop Event

1×	iter-limit

Counts

7 → 23

Calls

Call 1

Inputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
#s(literal 2 binary64)
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)

Outputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))))
#s(approx (+ (exp x) (exp (neg x))) #s(literal 2 binary64))
#s(approx (+ (exp x) (exp (neg x))) (+.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
#s(approx (+ (exp x) (exp (neg x))) (+.f64 #s(literal 2 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/12 binary64) (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (+ (exp x) (exp (neg x))) (+.f64 #s(literal 2 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/12 binary64) (*.f64 #s(literal 1/360 binary64) (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x)))))))
#s(approx x x)
#s(approx (exp (neg x)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) x)))
#s(approx (exp (neg x)) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))))
#s(approx (exp (neg x)) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))) #s(literal 1 binary64)))))
#s(approx (neg x) (*.f64 #s(literal -1 binary64) x))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
#s(approx (+ (exp x) (exp (neg x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
#s(approx (exp x) (exp.f64 x))
#s(approx (exp (neg x)) (exp.f64 (neg.f64 x)))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x)))))
#s(approx (+ (exp x) (exp (neg x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
#s(approx (exp (neg x)) (exp.f64 (*.f64 #s(literal -1 binary64) x)))

Calls

3 calls:

Time	Variable	Point
1.0ms	x	inf
1.0ms	x	-inf
1.0ms	x	0

rewrite50.0ms (6.3%)

Memory

7.3MiB live, 53.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	12	19
1	52	17
0	467	17

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

7 → 109

Calls

Call 1

Inputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
#s(literal 2 binary64)
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)

Outputs
(.f64 (/.f64 #s(literal 2 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x)))) (.f64 #s(literal 2 binary64) (sinh.f64 x)))
(.f64 (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
(.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) (cosh.f64 x))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(pow.f64 (cosh.f64 x) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64))) (exp.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (cosh.f64 x)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (cosh.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (cosh.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (cosh.f64 x))
(/.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (cosh.f64 x))))
(neg.f64 (/.f64 #s(literal -2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x)))) (*.f64 #s(literal 2 binary64) (sinh.f64 x)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64))))) (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x))) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
#s(literal 2 binary64)
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (exp.f64 (neg.f64 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (exp.f64 (neg.f64 x))) (exp.f64 x))) (exp.f64 x))
(*.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (exp.f64 x))
(.f64 (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 x))))
(.f64 (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x)))))
(*.f64 (cosh.f64 x) #s(literal 2 binary64))
(*.f64 (exp.f64 x) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
(/.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x))) (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (pow.f64 (neg.f64 (exp.f64 (neg.f64 x))) #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) (.f64 (exp.f64 x) (neg.f64 (exp.f64 (neg.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x)))) (neg.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x))))
(/.f64 (neg.f64 (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64))))) (neg.f64 (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x)))))
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 x)))
(/.f64 (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) (expm1.f64 (+.f64 x x))))
(/.f64 (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(neg.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sinh.f64 (neg.f64 x)) (cosh.f64 x))) (cosh.f64 x) (exp.f64 x))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sinh.f64 x) (cosh.f64 x))) (cosh.f64 x) (exp.f64 (neg.f64 x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sinh.f64 x) (cosh.f64 x))) (cosh.f64 x) (exp.f64 x))
(fma.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (+.f64 (sinh.f64 (neg.f64 x)) (exp.f64 x)))
(fma.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (sinh.f64 x) (neg.f64 (exp.f64 (neg.f64 x)))))
(fma.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x))
(fma.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (cosh.f64 x) (*.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (sinh.f64 x)))
(fma.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)) (exp.f64 x))
(fma.f64 (cosh.f64 x) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (*.f64 (sinh.f64 x) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64))))
(fma.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) (+.f64 (sinh.f64 (neg.f64 x)) (exp.f64 x)))
(fma.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) (-.f64 (sinh.f64 x) (neg.f64 (exp.f64 (neg.f64 x)))))
(fma.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) (cosh.f64 x))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (+.f64 (sinh.f64 (neg.f64 x)) (exp.f64 x)))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (sinh.f64 x) (neg.f64 (exp.f64 (neg.f64 x)))))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (cosh.f64 x))
(-.f64 (+.f64 (exp.f64 x) (cosh.f64 x)) (sinh.f64 x))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (.f64 #s(literal 2 binary64) (sinh.f64 x))) (/.f64 (exp.f64 (-.f64 (neg.f64 x) x)) (.f64 #s(literal 2 binary64) (sinh.f64 x))))
(-.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) (exp.f64 x)))
(-.f64 (exp.f64 (neg.f64 x)) (neg.f64 (exp.f64 x)))
(-.f64 (exp.f64 x) (neg.f64 (exp.f64 (neg.f64 x))))
(+.f64 (+.f64 (exp.f64 (neg.f64 x)) (cosh.f64 x)) (sinh.f64 x))
(+.f64 (+.f64 (exp.f64 x) (cosh.f64 x)) (sinh.f64 (neg.f64 x)))
(+.f64 (.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (cosh.f64 x)) (.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (sinh.f64 x)))
(+.f64 (.f64 (cosh.f64 x) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64))) (.f64 (sinh.f64 x) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64))))
(+.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x)))) (/.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x)))))
(+.f64 (cosh.f64 x) (+.f64 (sinh.f64 (neg.f64 x)) (exp.f64 x)))
(+.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) (neg.f64 (exp.f64 (neg.f64 x)))))
(+.f64 (cosh.f64 x) (cosh.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sinh.f64 x) (cosh.f64 x))) (cosh.f64 x))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (.f64 (sinh.f64 x) (sinh.f64 x)) (.f64 (cosh.f64 x) (sinh.f64 x)))))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(fma.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (sinh.f64 x))
(fma.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) (sinh.f64 x))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (sinh.f64 x))
(sqrt.f64 (exp.f64 (+.f64 x x)))
(-.f64 (cosh.f64 x) (sinh.f64 (neg.f64 x)))
(fabs.f64 (neg.f64 (exp.f64 x)))
(fabs.f64 (exp.f64 x))
(exp.f64 x)
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
x
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sinh.f64 (neg.f64 x)) (cosh.f64 x))) (cosh.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sinh.f64 x) (cosh.f64 x))) (cosh.f64 x))
(*.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(pow.f64 (exp.f64 x) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 x) (cosh.f64 x)) (.f64 (sinh.f64 (neg.f64 x)) (sinh.f64 (neg.f64 x)))) (exp.f64 x))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (neg.f64 x)) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (.f64 (sinh.f64 (neg.f64 x)) (sinh.f64 (neg.f64 x))) (.f64 (cosh.f64 x) (sinh.f64 (neg.f64 x))))))
(/.f64 (-.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (fma.f64 (sinh.f64 x) (sinh.f64 x) (*.f64 (cosh.f64 x) (sinh.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(neg.f64 (neg.f64 (exp.f64 (neg.f64 x))))
(fma.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (sinh.f64 (neg.f64 x)))
(fma.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) (sinh.f64 (neg.f64 x)))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (sinh.f64 (neg.f64 x)))
(sqrt.f64 (exp.f64 (-.f64 (neg.f64 x) x)))
(-.f64 (cosh.f64 x) (neg.f64 (sinh.f64 (neg.f64 x))))
(-.f64 (cosh.f64 x) (sinh.f64 x))
(fabs.f64 (neg.f64 (exp.f64 (neg.f64 x))))
(fabs.f64 (exp.f64 (neg.f64 x)))
(exp.f64 (neg.f64 x))
(+.f64 (sinh.f64 (neg.f64 x)) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 (neg.f64 x)))
(neg.f64 x)

eval16.0ms (2.1%)

Memory: -27.7MiB live, 23.3MiB allocated; 8ms collecting garbage
Compiler: Compiled 1 824 to 440 computations (75.9% saved)

prune3.0ms (0.4%)

Memory

7.1MiB live, 7.1MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	2	127

Accuracy

100.0%

Counts

127 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 #s(literal 1 binary64) (cosh.f64 x))
▶	52.6%	#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))

Compiler

Compiled 14 to 13 computations (7.1% saved)

series6.0ms (0.8%)

Memory

9.2MiB live, 9.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	188

Stop Event

1×	iter-limit

Counts

5 → 12

Calls

Call 1

Inputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (cosh.f64 x))
(cosh.f64 x)
x

Outputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))))
#s(approx (cosh x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
#s(approx (cosh x) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (cosh x) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx x x)
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
#s(approx (/ 1 (cosh x)) (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))))
#s(approx (cosh x) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x)))))

Calls

3 calls:

Time	Variable	Point
2.0ms	x	inf
2.0ms	x	-inf
0.0ms	x	0

rewrite45.0ms (5.7%)

Memory

-19.9MiB live, 26.5MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
0	13	14
1	61	14
0	501	14

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

5 → 46

Calls

Call 1

Inputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (cosh.f64 x))
(cosh.f64 x)
x

Outputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 (/.f64 #s(literal 2 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x)))) (.f64 #s(literal 2 binary64) (sinh.f64 x)))
(.f64 (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x))))
(*.f64 (pow.f64 (cosh.f64 x) #s(literal -1/2 binary64)) (pow.f64 (cosh.f64 x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
(.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) (cosh.f64 x))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (cosh.f64 x))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (cosh.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(pow.f64 (cosh.f64 x) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64))) (exp.f64 x))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (cosh.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (cosh.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (cosh.f64 x))))
(/.f64 #s(literal 1 binary64) (pow.f64 (cosh.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (cosh.f64 x))
(/.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (cosh.f64 x))))
(neg.f64 (/.f64 #s(literal -2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (cosh.f64 x)))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (cosh.f64 x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x)))) (*.f64 #s(literal 2 binary64) (sinh.f64 x)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64))))) (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x))) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(exp.f64 (*.f64 (log.f64 (cosh.f64 x)) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(*.f64 (+.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)))
(*.f64 (cosh.f64 x) #s(literal 1 binary64))
(.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x))) (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64)))
(/.f64 (+.f64 (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64)))) (*.f64 (+.f64 (expm1.f64 (-.f64 (neg.f64 x) x)) (exp.f64 (+.f64 x x))) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)) #s(literal -2 binary64))
(/.f64 (neg.f64 (cosh.f64 x)) #s(literal -1 binary64))
(/.f64 (cosh.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
(/.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))
(cosh.f64 (neg.f64 (neg.f64 x)))
(cosh.f64 (neg.f64 x))
(cosh.f64 x)
(-.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (neg.f64 (exp.f64 (neg.f64 x))) #s(literal 2 binary64)))
(+.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)))
x

eval4.0ms (0.6%)

Memory: 9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 585 to 177 computations (69.7% saved)

prune2.0ms (0.2%)

Memory

3.7MiB live, 3.7MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	52	2	54

Accuracy

100.0%

Counts

54 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 #s(literal 1 binary64) (cosh.f64 x))
✓	52.6%	#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))

Compiler

Compiled 14 to 13 computations (7.1% saved)

regimes7.0ms (0.9%)

Memory

16.5MiB live, 16.5MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

3 → 1

Calls

Call 1

Inputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))

Outputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))

Call 2

Inputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (cosh.f64 x))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 #s(literal 1 binary64) (cosh.f64 x))

Calls

6 calls:

1.0ms	x
1.0ms	(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
1.0ms	x
1.0ms	(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Accuracy	Segments	Branch
52.6%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
52.6%	1	`(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
52.6%	1	`x`
100.0%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
100.0%	1	`(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
100.0%	1	`x`

Compiler

Compiled 52 to 43 computations (17.3% saved)

derivations7.0ms (0.8%)

Memory

-41.6MiB live, 4.5MiB allocated; 4ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 14 to 11 computations (21.4% saved)

preprocess14.0ms (1.8%)

Memory: 30.1MiB live, 30.1MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 50 to 44 computations (12% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample583.0ms (74.1%)

preprocess42.0ms (5.3%)

series7.0ms (0.9%)

rewrite50.0ms (6.3%)

eval16.0ms (2.1%)

prune3.0ms (0.4%)

series6.0ms (0.8%)

rewrite45.0ms (5.7%)

eval4.0ms (0.6%)

prune2.0ms (0.2%)

regimes7.0ms (0.9%)

derivations7.0ms (0.8%)

preprocess14.0ms (1.8%)

end0.0ms (0%)

Profiling