Metrics for Hyperbolic secant

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

sample1.0s (55.7%)

Memory

-2.2MiB live, 1 256.8MiB allocated; 305ms collecting garbage

Samples

781.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 493.0ms

ival-exp: 331.0ms (67.2% of total)

ival-div!: 101.0ms (20.5% of total)

ival-neg: 33.0ms (6.7% of total)

ival-add!: 26.0ms (5.3% of total)

adjust: 2.0ms (0.4% of total)

Bogosity

preprocess46.0ms (2.5%)

Memory

-37.4MiB live, 55.2MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	52	12
2	175	12
3	1155	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 14 to 14 computations (0% saved)

series3.0ms (0.2%)

Memory

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

((/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (exp x) x (exp (neg x)) (neg x))

1.0ms

-inf

((/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (exp x) x (exp (neg x)) (neg x))

1.0ms

((/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (exp x) x (exp (neg x)) (neg x))

rewrite289.0ms (15.7%)

Memory

51.4MiB live, 261.8MiB allocated; 65ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	329
0	100	288
1	616	265
2	5340	265
0	8099	243
1	25200	243

Stop Event

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

Counts

30 → 86

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

Outputs
(*.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)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (cosh.f64 x)))
(/.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 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (cosh.f64 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 (cosh.f64 x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cosh.f64 (/.f64 (+.f64 (neg.f64 x) (neg.f64 x)) #s(literal 2 binary64))) (cosh.f64 (/.f64 (-.f64 (neg.f64 x) (neg.f64 x)) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cosh.f64 (/.f64 (+.f64 (neg.f64 x) x) #s(literal 2 binary64))) (cosh.f64 (/.f64 (-.f64 (neg.f64 x) x) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cosh.f64 (/.f64 (+.f64 x (neg.f64 x)) #s(literal 2 binary64))) (cosh.f64 (/.f64 (-.f64 x (neg.f64 x)) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cosh.f64 (/.f64 (+.f64 x x) #s(literal 2 binary64))) (cosh.f64 (/.f64 (-.f64 x x) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
(neg.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)))
(fma.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)) (exp.f64 x))
(-.f64 (+.f64 (exp.f64 x) (cosh.f64 x)) (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 (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)))
(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 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(pow.f64 (exp.f64 #s(literal -1 binary64)) x)
(pow.f64 (exp.f64 x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (exp.f64 x)))
(neg.f64 (neg.f64 (exp.f64 (neg.f64 x))))
(sqrt.f64 (exp.f64 (*.f64 (neg.f64 x) #s(literal 2 binary64))))
(-.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 (-.f64 #s(literal 0 binary64) x))
(exp.f64 (neg.f64 x))
(+.f64 (cosh.f64 (-.f64 #s(literal 0 binary64) x)) (sinh.f64 (-.f64 #s(literal 0 binary64) x)))
(+.f64 (sinh.f64 (neg.f64 x)) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 (neg.f64 x)))
(*.f64 #s(literal -1 binary64) x)
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 x #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) #s(literal 2 binary64))
(neg.f64 x)
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (fma.f64 (fma.f64 #s(literal 5/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -61/720 binary64) (.f64 x x) #s(literal 5/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64)))
#s(approx (+ (exp x) (exp (neg x))) #s(literal 2 binary64))
#s(approx (+ (exp x) (exp (neg x))) (fma.f64 x x #s(literal 2 binary64)))
#s(approx (+ (exp x) (exp (neg x))) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 x x) #s(literal 2 binary64)))
#s(approx (+ (exp x) (exp (neg x))) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/360 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 2 binary64)))
#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx x x)
#s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))
#s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
#s(approx (neg x) (neg.f64 x))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
#s(approx (+ (exp x) (exp (neg x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
#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 1 binary64) (cosh.f64 x)))
#s(approx (+ (exp x) (exp (neg x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
#s(approx (exp (neg x)) (exp.f64 (neg.f64 x)))

eval40.0ms (2.2%)

Memory: -39.3MiB live, 25.3MiB allocated; 32ms collecting garbage
Compiler: Compiled 473 to 284 computations (40% saved)

prune4.0ms (0.2%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	4	78

Accuracy

100.0%

Counts

78 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.8%	(/.f64 #s(literal 2 binary64) #s(approx (+ (exp x) (exp (neg x))) (fma.f64 x x #s(literal 2 binary64))))
▶	100.0%	(/.f64 #s(literal 1 binary64) (cosh.f64 x))
▶	47.9%	#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	48.5%	#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))

Compiler

Compiled 34 to 34 computations (0% saved)

series12.0ms (0.6%)

Memory

21.4MiB live, 21.4MiB allocated; 0ms collecting garbage

Counts

13 → 22

Calls

Call 1

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

Outputs
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(hole binary64 1))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (cosh x) #s(hole binary64 (+ 1 (* 1/2 (pow x 2)))))
#s(approx (cosh x) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))))
#s(approx (cosh x) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))))
#s(approx (+ (exp x) (exp (neg x))) #s(hole binary64 2))
#s(approx (+ (exp x) (exp (neg x))) #s(hole binary64 (+ 2 (pow x 2))))
#s(approx (+ (exp x) (exp (neg x))) #s(hole binary64 (+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))))
#s(approx (+ (exp x) (exp (neg x))) #s(hole binary64 (+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(hole binary64 (/ 2 (+ (exp x) (exp (neg x))))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (/ 1 (cosh x)) #s(hole binary64 (/ 2 (+ (exp x) (/ 1 (exp x))))))
#s(approx (cosh x) #s(hole binary64 (* 1/2 (+ (exp x) (/ 1 (exp x))))))
#s(approx (+ (exp x) (exp (neg x))) #s(hole binary64 (+ (exp x) (exp (neg x)))))
#s(approx (+ (* x x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ 1 (pow x 2)))))))
#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(hole binary64 (/ 2 (+ (exp x) (exp (* -1 x))))))
#s(approx (+ (exp x) (exp (neg x))) #s(hole binary64 (+ (exp x) (exp (* -1 x)))))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((/ 2 (+ (exp x) (exp (neg x)))) 1 (/ 2 (+ (exp x) (exp (neg x)))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (/ 1 (cosh x)) (cosh x) (/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (+ (* x x) 2))
4.0ms	x	@	-inf	((/ 2 (+ (exp x) (exp (neg x)))) 1 (/ 2 (+ (exp x) (exp (neg x)))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (/ 1 (cosh x)) (cosh x) (/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (+ (* x x) 2))
3.0ms	x	@	0	((/ 2 (+ (exp x) (exp (neg x)))) 1 (/ 2 (+ (exp x) (exp (neg x)))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (/ 1 (cosh x)) (cosh x) (/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (+ (* x x) 2))

Time

Variable

Point

Expression

4.0ms

inf

((/ 2 (+ (exp x) (exp (neg x)))) 1 (/ 2 (+ (exp x) (exp (neg x)))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (/ 1 (cosh x)) (cosh x) (/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (+ (* x x) 2))

4.0ms

-inf

((/ 2 (+ (exp x) (exp (neg x)))) 1 (/ 2 (+ (exp x) (exp (neg x)))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (/ 1 (cosh x)) (cosh x) (/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (+ (* x x) 2))

3.0ms

((/ 2 (+ (exp x) (exp (neg x)))) 1 (/ 2 (+ (exp x) (exp (neg x)))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (/ 1 (cosh x)) (cosh x) (/ 2 (+ (exp x) (exp (neg x)))) 2 (+ (exp x) (exp (neg x))) (+ (* x x) 2))

rewrite199.0ms (10.8%)

Memory

-36.2MiB live, 248.3MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	408
0	109	356
1	650	322
2	5708	312
0	8111	298
1	25265	298

Stop Event

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

Counts

35 → 214

Calls

Call 1

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

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

eval21.0ms (1.1%)

Memory: 4.7MiB live, 50.8MiB allocated; 3ms collecting garbage
Compiler: Compiled 1 136 to 605 computations (46.7% saved)

prune5.0ms (0.3%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	197	4	201

Accuracy

100.0%

Counts

201 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.8%	(/.f64 #s(literal 2 binary64) #s(approx (+ (exp x) (exp (neg x))) (fma.f64 x x #s(literal 2 binary64))))
✓	100.0%	(/.f64 #s(literal 1 binary64) (cosh.f64 x))
✓	47.9%	#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	48.5%	#s(approx (/ 2 (+ (exp x) (exp (neg x)))) #s(literal 1 binary64))

Compiler

Compiled 67 to 58 computations (13.4% saved)

regimes5.0ms (0.3%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

3 calls:

2.0ms	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)))

Results

Accuracy	Segments	Branch
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 13 to 13 computations (0% saved)

regimes4.0ms (0.2%)

Memory

9.4MiB live, 9.4MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

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

#s(approx (/ 2 (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))

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

Outputs
(/.f64 #s(literal 2 binary64) #s(approx (+ (exp x) (exp (neg x))) (fma.f64 x x #s(literal 2 binary64))))

Calls

3 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)))

Results

Accuracy	Segments	Branch
76.8%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
76.8%	1	`(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
76.8%	1	`x`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes4.0ms (0.2%)

Memory

8.2MiB live, 8.2MiB allocated; 0ms collecting garbage

Accuracy

Total -0.4b remaining (-1.3%)

Threshold costs -0.4b (-1.3%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
48.5%	1	`x`
48.5%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
48.5%	1	`(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 13 to 13 computations (0% saved)

derivations161.0ms (8.7%)

Memory

-46.7MiB live, 57.3MiB allocated; 43ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 19 to 15 computations (21.1% saved)

preprocess23.0ms (1.2%)

Memory: 10.1MiB live, 54.7MiB allocated; 5ms collecting garbage
Remove: (abs x)
Compiler: Compiled 70 to 66 computations (5.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.0s (55.7%)

preprocess46.0ms (2.5%)

series3.0ms (0.2%)

rewrite289.0ms (15.7%)

eval40.0ms (2.2%)

prune4.0ms (0.2%)

series12.0ms (0.6%)

rewrite199.0ms (10.8%)

eval21.0ms (1.1%)

prune5.0ms (0.3%)

regimes5.0ms (0.3%)

regimes4.0ms (0.2%)

regimes4.0ms (0.2%)

derivations161.0ms (8.7%)

preprocess23.0ms (1.2%)

end0.0ms (0%)

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