Metrics for Hyperbolic tangent

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

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 15 to 9 computations (40% saved)

sample4.4s (48%)

Memory

11.8MiB live, 4 493.5MiB allocated

Samples

1.7s	3 038×	2	valid
1.2s	4 640×	1	valid
733.0ms	7 984×	0	exit
66.0ms	578×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.0s

ival-exp: 1.8s (59% of total)

ival-sub: 318.0ms (10.7% of total)

ival-add: 294.0ms (9.9% of total)

adjust: 267.0ms (9% of total)

ival-div: 210.0ms (7.1% of total)

ival-neg: 109.0ms (3.7% of total)

ival-true: 12.0ms (0.4% of total)

ival-assert: 7.0ms (0.2% of total)

Bogosity

explain265.0ms (2.9%)

Memory

-10.7MiB live, 347.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
249	-	-	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
5	-	-	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0	-	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	-	-	`(exp.f64 x)`
0	-	-	`(exp.f64 (neg.f64 x))`
0	-	-	`(neg.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	cancellation	249	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	5	0
↳	`(exp.f64 x)`	overflow	5
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	5
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	5
↳	`(exp.f64 x)`	overflow	5

Confusion

	Predicted +	Predicted -
+	254	0
-	0	2

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	0	0
-	0	0	2

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

80.0ms	194×	2	valid
75.0ms	282×	1	valid
2.0ms	36×	0	valid

Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-exp: 74.0ms (66.9% of total)

adjust: 12.0ms (10.8% of total)

ival-sub: 8.0ms (7.2% of total)

ival-div: 7.0ms (6.3% of total)

ival-add: 5.0ms (4.5% of total)

ival-neg: 2.0ms (1.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess160.0ms (1.8%)

Memory

27.6MiB live, 162.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	34	27
2	87	27
3	351	27
4	3679	19
0	7	13
0	13	13
1	26	13
2	66	13
3	258	13
4	1659	9
0	8837	9

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) (.f64 #s(literal 2 binary64) (cosh.f64 x)))

Symmetry

(negabs x)

Compiler

Compiled 13 to 7 computations (46.2% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 13 to 7 computations (46.2% saved)

simplify109.0ms (1.2%)

Memory

-7.4MiB live, 134.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f64 x)
cost-diff	0	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
cost-diff	2	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
cost-diff	2	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	13	33
1	26	33
2	66	33
3	258	33
4	1659	25
0	8837	25

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) (.f64 #s(literal 2 binary64) (cosh.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(*.f64 #s(literal 2 binary64) (sinh.f64 x))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(*.f64 #s(literal 2 binary64) (cosh.f64 x))

localize85.0ms (0.9%)

Memory

-12.9MiB live, 134.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	1.230482505254126	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	56.81421522843766	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

43.0ms	97×	2	valid
34.0ms	141×	1	valid
1.0ms	18×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-exp: 36.0ms (53.9% of total)

ival-div: 12.0ms (18% of total)

ival-sub: 7.0ms (10.5% of total)

adjust: 5.0ms (7.5% of total)

ival-add: 4.0ms (6% of total)

ival-neg: 1.0ms (1.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series3.0ms (0%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

4 → 23

Calls

Call 1

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

Outputs
(* 2 x)
(* x (+ 2 (* 1/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
2
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(- (exp x) (exp (neg x)))
(+ (exp x) (exp (neg x)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(exp x)
(- (exp x) (exp (* -1 x)))
(+ (exp x) (exp (* -1 x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

((- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (exp x))

1.0ms

inf

((- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (exp x))

1.0ms

-inf

((- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (exp x))

simplify181.0ms (2%)

Memory

28.9MiB live, 169.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	210
1	292	210
2	958	200
3	3882	200
0	8155	179

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 22

Calls

Call 1

Inputs
(* 2 x)
(* x (+ 2 (* 1/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
2
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(- (exp x) (exp (neg x)))
(+ (exp x) (exp (neg x)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(exp x)
(- (exp x) (exp (* -1 x)))
(+ (exp x) (exp (* -1 x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))

Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 1/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/60 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2520 binary64) (.f64 x x) #s(literal 1/60 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (pow x 2))
(fma.f64 x x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/12 binary64) x) x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/360 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x) x #s(literal 2 binary64))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 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))
(- (exp x) (exp (neg x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+ (exp x) (exp (neg x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(exp x)
(exp.f64 x)
(- (exp x) (exp (* -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+ (exp x) (exp (* -1 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))

rewrite250.0ms (2.7%)

Memory

-2.7MiB live, 231.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
0	13	12
1	50	12
2	395	12
3	6196	12
0	9201	12

Stop Event

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

Counts

4 → 636

Calls

Call 1

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

Outputs
(.f64 (/.f64 (neg.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal -3 binary64) x)))) (neg.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (sinh.f64 x))
(.f64 (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (neg.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal -3 binary64) x))))) (neg.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 3 binary64) x))) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)))) (fma.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))) (+.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (pow.f64 (exp.f64 x) #s(literal 4 binary64))))
(.f64 (/.f64 (neg.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (sinh.f64 x)))
(.f64 (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (neg.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (sinh.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal -3 binary64) x))))) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 3 binary64) x))))) (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) (sinh.f64 x))
(.f64 (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal -3 binary64) x)))) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(*.f64 #s(literal -2 binary64) (sinh.f64 (neg.f64 x)))
(.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))
(.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal -3 binary64) x)))))
(.f64 #s(literal 1 binary64) (.f64 (sinh.f64 x) #s(literal 2 binary64)))
(.f64 (cosh.f64 x) (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (cosh.f64 x)))
(*.f64 (sinh.f64 x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sinh.f64 (/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (sinh.f64 x))
(.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (tanh.f64 x))
(.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(/.f64 (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 3 binary64) x))))) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))
(/.f64 (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (cosh.f64 x)) #s(literal 2 binary64))
(/.f64 (sinh.f64 (*.f64 #s(literal -2 binary64) x)) (neg.f64 (cosh.f64 x)))
(/.f64 (.f64 (/.f64 (.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal -3 binary64) x)))) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 2 binary64)))) (fma.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64) #s(literal 1 binary64)))
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(exp.f64 (*.f64 x #s(literal 1 binary64)))
(exp.f64 x)
(+.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (cosh.f64 x) (sinh.f64 x)))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (cosh.f64 x) (sinh.f64 x)))))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(+.f64 (sinh.f64 x) (cosh.f64 x))

eval144.0ms (1.6%)

Memory: -6.9MiB live, 135.3MiB allocated
Compiler: Compiled 19 340 to 1 974 computations (89.8% saved)

prune24.0ms (0.3%)

Memory

-12.5MiB live, 33.5MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	697	4	701
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	698	4	702

Accuracy

100.0%

Counts

702 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.0%	(/.f64 (sinh.f64 x) (cosh.f64 x))
▶	98.0%	(.f64 (sinh.f64 x) (/.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64))))
▶	100.0%	(tanh.f64 x)
▶	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Compiler

Compiled 36 to 25 computations (30.6% saved)

simplify126.0ms (1.4%)

Memory

21.4MiB live, 111.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(cosh.f64 x)
cost-diff	0	(sinh.f64 x)
cost-diff	3	(/.f64 (sinh.f64 x) (cosh.f64 x))
cost-diff	0	(*.f64 (cosh.f64 x) #s(literal 2 binary64))
cost-diff	0	(sinh.f64 x)
cost-diff	2	(/.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
cost-diff	5	(.f64 (sinh.f64 x) (/.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64))))
cost-diff	0	(tanh.f64 x)
cost-diff	0	(pow.f64 x #s(literal 3 binary64))
cost-diff	0	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	70
0	30	49
1	66	47
2	179	47
3	719	47
4	5558	47
0	8619	47

Stop Event

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

Calls

Call 1

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

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

localize146.0ms (1.6%)

Memory

-30.8MiB live, 118.4MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(cosh.f64 x)
accuracy	0.0078125	(sinh.f64 x)
accuracy	1.230482505254126	(/.f64 (sinh.f64 x) (cosh.f64 x))
accuracy	0.0	(cosh.f64 x)
accuracy	0.0078125	(sinh.f64 x)
accuracy	0.015625	(/.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
accuracy	1.218763755254126	(.f64 (sinh.f64 x) (/.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64))))
accuracy	0.0234375	(tanh.f64 x)
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.0078125	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	1.5236132308839734	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Samples

73.0ms	97×	2	valid
52.0ms	141×	1	valid
3.0ms	18×	0	valid

Compiler

Compiled 66 to 22 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-exp: 36.0ms (32.5% of total)

adjust: 29.0ms (26.2% of total)

ival-div: 21.0ms (18.9% of total)

const: 4.0ms (3.6% of total)

ival-add: 4.0ms (3.6% of total)

ival-mult: 4.0ms (3.6% of total)

ival-sub: 3.0ms (2.7% of total)

ival-pow: 3.0ms (2.7% of total)

ival-cosh: 2.0ms (1.8% of total)

ival-tanh: 1.0ms (0.9% of total)

ival-sinh: 1.0ms (0.9% of total)

ival-neg: 1.0ms (0.9% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series12.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

10 → 29

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 3)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
2
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ 2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(+ (exp x) (/ 1 (exp x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (* (sinh x) (/ 2 (* (cosh x) 2))) (/ 2 (* (cosh x) 2)) (sinh x) (* (cosh x) 2) (/ (sinh x) (cosh x)) (cosh x))
4.0ms	x	@	-inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (* (sinh x) (/ 2 (* (cosh x) 2))) (/ 2 (* (cosh x) 2)) (sinh x) (* (cosh x) 2) (/ (sinh x) (cosh x)) (cosh x))
2.0ms	x	@	0	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (* (sinh x) (/ 2 (* (cosh x) 2))) (/ 2 (* (cosh x) 2)) (sinh x) (* (cosh x) 2) (/ (sinh x) (cosh x)) (cosh x))

Time

Variable

Point

Expression

6.0ms

inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (* (sinh x) (/ 2 (* (cosh x) 2))) (/ 2 (* (cosh x) 2)) (sinh x) (* (cosh x) 2) (/ (sinh x) (cosh x)) (cosh x))

4.0ms

-inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (* (sinh x) (/ 2 (* (cosh x) 2))) (/ 2 (* (cosh x) 2)) (sinh x) (* (cosh x) 2) (/ (sinh x) (cosh x)) (cosh x))

2.0ms

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (* (sinh x) (/ 2 (* (cosh x) 2))) (/ 2 (* (cosh x) 2)) (sinh x) (* (cosh x) 2) (/ (sinh x) (cosh x)) (cosh x))

simplify166.0ms (1.8%)

Memory

4.5MiB live, 98.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	308
1	375	296
2	1183	292
3	3996	292
0	8028	266

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 3)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
2
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ 2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(+ (exp x) (/ 1 (exp x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64))) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -61/720 binary64) (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(* x (+ 1 (* 1/6 (pow x 2))))
(fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (pow x 2))
(fma.f64 x x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/360 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 2 binary64))
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(fma.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)) (*.f64 x x) #s(literal 1 binary64))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/ 2 (+ (exp x) (/ 1 (exp x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #s(literal 1/2 binary64))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(fma.f64 #s(literal 1/2 binary64) (exp.f64 x) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))

rewrite226.0ms (2.5%)

Memory

20.7MiB live, 153.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	59
0	30	38
1	113	36
2	762	36
0	8547	36

Stop Event

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

Counts

10 → 998

Calls

Call 1

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

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))) (.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))) (+.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))))
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(/.f64 (-.f64 (.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))) (.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)))) (sinh.f64 (neg.f64 x)))
(/.f64 (+.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.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 (pow.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.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 (fma.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (exp.f64 x))) #s(literal 4 binary64))
(/.f64 (fma.f64 (exp.f64 x) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (exp.f64 (neg.f64 x)))) #s(literal 4 binary64))
(/.f64 (*.f64 (cosh.f64 x) (sinh.f64 x)) (sinh.f64 x))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))) (neg.f64 (*.f64 #s(literal 4 binary64) (sinh.f64 x))))
(/.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (*.f64 #s(literal 4 binary64) (sinh.f64 x)))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)) #s(literal -2 binary64))
(/.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))
(neg.f64 (neg.f64 (cosh.f64 x)))
(cosh.f64 (neg.f64 x))
(cosh.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (sinh.f64 x))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (.f64 #s(literal 4 binary64) (sinh.f64 x))))
(-.f64 (/.f64 (+.f64 (cosh.f64 x) (exp.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 x) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64)))
(-.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (-.f64 (sinh.f64 x) (exp.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))))
(+.f64 (/.f64 (+.f64 (cosh.f64 x) (exp.f64 (neg.f64 x))) #s(literal 2 binary64)) (/.f64 (sinh.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x)))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x)))) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (sinh.f64 x))) (/.f64 (neg.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64))) (.f64 #s(literal 4 binary64) (sinh.f64 x))))
(+.f64 (/.f64 (+.f64 (cosh.f64 x) (exp.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 (neg.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 (sinh.f64 (neg.f64 x)) (exp.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (-.f64 (exp.f64 x) (sinh.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (cosh.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)))

eval191.0ms (2.1%)

Memory: -6.0MiB live, 149.2MiB allocated
Compiler: Compiled 18 588 to 2 431 computations (86.9% saved)

prune24.0ms (0.3%)

Memory

-11.4MiB live, 32.1MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	698	3	701
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	700	5	705

Accuracy

100.0%

Counts

705 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.0%	(/.f64 (sinh.f64 x) (cosh.f64 x))
▶	98.0%	(*.f64 (sinh.f64 x) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
✓	100.0%	(tanh.f64 x)
▶	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
▶	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))

Compiler

Compiled 58 to 37 computations (36.2% saved)

simplify121.0ms (1.3%)

Memory

25.8MiB live, 122.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(cosh.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (cosh.f64 x))
cost-diff	0	(sinh.f64 x)
cost-diff	2	(*.f64 (sinh.f64 x) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
cost-diff	2	(.f64 (.f64 x x) x)
cost-diff	0	(*.f64 #s(literal -1/3 binary64) x)
cost-diff	0	(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
cost-diff	2	(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	99
0	33	99
1	64	95
2	177	87
3	716	71
4	4934	71
0	8722	71

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
x
#s(literal 1 binary64)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(.f64 (.f64 x x) x)
(*.f64 x x)
x
#s(literal -1/3 binary64)
(*.f64 (sinh.f64 x) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
(sinh.f64 x)
x
(/.f64 #s(literal 1 binary64) (cosh.f64 x))
#s(literal 1 binary64)
(cosh.f64 x)

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

localize162.0ms (1.8%)

Memory

-26.3MiB live, 123.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(cosh.f64 x)
accuracy	0.0078125	(sinh.f64 x)
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (cosh.f64 x))
accuracy	1.218763755254126	(*.f64 (sinh.f64 x) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
accuracy	0.06640625	(.f64 (.f64 x x) x)
accuracy	1.5236132308839734	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
accuracy	0.00390625	(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
accuracy	0.0078125	(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
accuracy	0.3203125	(*.f64 #s(literal -1/3 binary64) x)
accuracy	1.5236132308839734	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))

Samples

85.0ms	97×	2	valid
60.0ms	141×	1	valid
3.0ms	18×	0	valid

Compiler

Compiled 86 to 23 computations (73.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-exp: 69.0ms (57.3% of total)

ival-mult: 16.0ms (13.3% of total)

adjust: 12.0ms (10% of total)

ival-add: 7.0ms (5.8% of total)

ival-div: 5.0ms (4.2% of total)

const: 4.0ms (3.3% of total)

ival-sub: 3.0ms (2.5% of total)

ival-cosh: 2.0ms (1.7% of total)

ival-sinh: 1.0ms (0.8% of total)

ival-neg: 1.0ms (0.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

12 → 29

Calls

Call 1

Inputs
(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) x)
(.f64 (.f64 x x) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(*.f64 x x)
(*.f64 (sinh.f64 x) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
(sinh.f64 x)
(/.f64 #s(literal 1 binary64) (cosh.f64 x))
(cosh.f64 x)

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/3 (pow x 2)))
(* -1/3 x)
(pow x 3)
(pow x 2)
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(/ 2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

((* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x) (* (* x x) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* (* x x) x) -1/3) x) (* x x) (* (sinh x) (/ 1 (cosh x))) (sinh x) (/ 1 (cosh x)) (cosh x))

3.0ms

inf

((* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x) (* (* x x) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* (* x x) x) -1/3) x) (* x x) (* (sinh x) (/ 1 (cosh x))) (sinh x) (/ 1 (cosh x)) (cosh x))

1.0ms

((* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x) (* (* x x) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* (* x x) x) -1/3) x) (* x x) (* (sinh x) (/ 1 (cosh x))) (sinh x) (/ 1 (cosh x)) (cosh x))

simplify215.0ms (2.4%)

Memory

8.6MiB live, 196.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	293
1	326	281
2	971	281
3	3966	281
0	8031	260

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/3 (pow x 2)))
(* -1/3 x)
(pow x 3)
(pow x 2)
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(/ 2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/3 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 2)
(*.f64 x x)
(* x (+ 1 (* 1/6 (pow x 2))))
(fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -61/720 binary64) (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(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))
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) x) x)
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #s(literal 1/2 binary64))
(/ 2 (+ (exp x) (/ 1 (exp x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(fma.f64 #s(literal 1/2 binary64) (exp.f64 x) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))

rewrite175.0ms (1.9%)

Memory

-4.6MiB live, 237.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	92
0	33	64
1	117	59
2	845	59
0	8215	59

Stop Event

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

Counts

12 → 401

Calls

Call 1

Inputs
(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) x)
(.f64 (.f64 x x) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(*.f64 x x)
(*.f64 (sinh.f64 x) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
(sinh.f64 x)
(/.f64 #s(literal 1 binary64) (cosh.f64 x))
(cosh.f64 x)

Outputs
(.f64 (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)) x)
(.f64 x (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64))) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (.f64 x #s(literal 1 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) (.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) (.f64 x #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64))) (fma.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)) (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x #s(literal 1 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) (*.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x)) (neg.f64 (-.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (neg.f64 (-.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/3 binary64))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x) (-.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/3 binary64)))))
(/.f64 (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (-.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/3 binary64)))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) x (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) x (*.f64 x #s(literal 1 binary64)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (*.f64 x #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) (.f64 x #s(literal -1/3 binary64))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) (.f64 x #s(literal -1/3 binary64))) (*.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 (.f64 x #s(literal -1/3 binary64)) (.f64 x x) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 x #s(literal -1/3 binary64)) (.f64 x x) (*.f64 x #s(literal 1 binary64)))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/3 binary64)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 x #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(+.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) (.f64 #s(literal 1 binary64) x))
(+.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) (.f64 x #s(literal 1 binary64)))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)) x))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)))) (.f64 (pow.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (neg.f64 (.f64 x #s(literal -1/3 binary64))) x) (.f64 (neg.f64 (.f64 x #s(literal -1/3 binary64))) x))) (+.f64 #s(literal 1 binary64) (.f64 (neg.f64 (*.f64 x #s(literal -1/3 binary64))) x)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64))))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64)))))) (.f64 (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64)))) #s(literal -1 binary64)))) (-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64))))) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/3 binary64)))) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (.f64 x #s(literal -1/3 binary64))) x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (.f64 x #s(literal -1/3 binary64))) x) (.f64 (neg.f64 (.f64 x #s(literal -1/3 binary64))) x) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (*.f64 x #s(literal -1/3 binary64))) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 x) (.f64 x #s(literal -1/3 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) (*.f64 x #s(literal -1/3 binary64)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/3 binary64) (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64))))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64)))) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64))))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64))))) (-.f64 (.f64 (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64)))) #s(literal -1 binary64))) (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64))))) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64)))) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/3 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1 binary64))))
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(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 (neg.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)) #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
(cosh.f64 (neg.f64 x))
(cosh.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (+.f64 (exp.f64 x) (cosh.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 x) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64)))
(-.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (-.f64 (sinh.f64 x) (exp.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 (neg.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 (neg.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 (neg.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 (neg.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))))
(+.f64 (/.f64 (+.f64 (exp.f64 (neg.f64 x)) (cosh.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 (neg.f64 x) #s(literal 2 binary64))))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 (neg.f64 x) #s(literal 2 binary64))))) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))) (/.f64 (.f64 (neg.f64 (exp.f64 (neg.f64 x))) (exp.f64 (neg.f64 x))) (.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))))
(+.f64 (/.f64 (+.f64 (exp.f64 x) (cosh.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 (neg.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 (sinh.f64 (neg.f64 x)) (exp.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (cosh.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)))

eval91.0ms (1%)

Memory: -30.6MiB live, 112.7MiB allocated
Compiler: Compiled 11 638 to 1 510 computations (87% saved)

prune7.0ms (0.1%)

Memory

33.2MiB live, 33.2MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	426	2	428
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	426	7	433

Accuracy

100.0%

Counts

433 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.0%	(/.f64 (sinh.f64 x) (cosh.f64 x))
✓	98.0%	(*.f64 (sinh.f64 x) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
✓	100.0%	(tanh.f64 x)
✓	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
▶	52.9%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))))
✓	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
▶	97.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 129 to 70 computations (45.7% saved)

simplify130.0ms (1.4%)

Memory

-13.8MiB live, 121.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	1	(-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64)))))
cost-diff	3	(.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))
cost-diff	5	(.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))
cost-diff	8	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))))
cost-diff	0	#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	193
0	33	187
1	85	174
2	359	161
3	1870	119
4	7128	119
0	9063	112

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
x
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))))
(-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64)))))
(*.f64 x x)
x
(.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))
(.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))
(neg.f64 (*.f64 x x))
(*.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
(+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
x
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) #s(literal 1 binary64))
(-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64)))))
(fma.f64 #s(literal -1/9 binary64) (pow.f64 (neg.f64 x) #s(literal 6 binary64)) (*.f64 x x))
(*.f64 x x)
x
(.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))
(*.f64 #s(literal 1/9 binary64) (pow.f64 (neg.f64 x) #s(literal 6 binary64)))
(.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64))
(neg.f64 (*.f64 x x))
(*.f64 (neg.f64 x) x)
(*.f64 x #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
(+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)

localize187.0ms (2.1%)

Memory

-11.5MiB live, 182.2MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.10613251953688403	(.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))
accuracy	0.3203125	(*.f64 x #s(literal -1/3 binary64))
accuracy	1.5236132308839734	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))))
accuracy	28.63806227459873	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))))
accuracy	0.0078125	(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
accuracy	1.5236132308839734	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
accuracy	1.8931903371339411	#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))

Samples

100.0ms	141×	1	valid
51.0ms	97×	2	valid
3.0ms	18×	0	valid

Compiler

Compiled 146 to 23 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-exp: 57.0ms (52.6% of total)

ival-mult: 19.0ms (17.5% of total)

adjust: 12.0ms (11.1% of total)

ival-div: 5.0ms (4.6% of total)

ival-add: 5.0ms (4.6% of total)

ival-sub: 4.0ms (3.7% of total)

const: 4.0ms (3.7% of total)

ival-neg: 2.0ms (1.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

9 → 20

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))))
(.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))
(.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))
(-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64)))))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))))
(*.f64 x #s(literal -1/3 binary64))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/3 (pow x 2)))
(* 1/9 (pow x 6))
(* 1/3 (pow x 3))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/9 (pow x 4))))
(* -1/3 x)
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* -1/9 (pow x 6))
(* (pow x 6) (- (/ 1 (pow x 4)) 1/9))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* -1/3 x) x) 1) x) (+ (* (* -1/3 x) x) 1) (/ (- (* x x) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3)))) (+ x (* (neg (* x x)) (* x -1/3)))) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3))) (* (neg (* x x)) (* x -1/3)) (- (* x x) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3)))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x -1/3))

3.0ms

inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* -1/3 x) x) 1) x) (+ (* (* -1/3 x) x) 1) (/ (- (* x x) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3)))) (+ x (* (neg (* x x)) (* x -1/3)))) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3))) (* (neg (* x x)) (* x -1/3)) (- (* x x) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3)))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x -1/3))

2.0ms

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* -1/3 x) x) 1) x) (+ (* (* -1/3 x) x) 1) (/ (- (* x x) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3)))) (+ x (* (neg (* x x)) (* x -1/3)))) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3))) (* (neg (* x x)) (* x -1/3)) (- (* x x) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3)))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x -1/3))

simplify167.0ms (1.8%)

Memory

-17.8MiB live, 128.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	167
1	161	161
2	395	161
3	1462	159
4	4418	159
0	8245	153

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/3 (pow x 2)))
(* 1/9 (pow x 6))
(* 1/3 (pow x 3))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/9 (pow x 4))))
(* -1/3 x)
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* -1/9 (pow x 6))
(* (pow x 6) (- (/ 1 (pow x 4)) 1/9))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 2/15 binary64) x) x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64)) #s(literal 1/3 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/3 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* 1/9 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/9 binary64))
(* 1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/9 (pow x 4))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/9 binary64) (*.f64 x x))
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) x) x)
(* -1/9 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/9 binary64))
(* (pow x 6) (- (/ 1 (pow x 4)) 1/9))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/9 binary64)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(.f64 (neg.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (pow.f64 x #s(literal 3 binary64)))

rewrite259.0ms (2.8%)

Memory

39.4MiB live, 232.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	172
0	33	120
1	147	78
2	1259	73
0	9013	67

Stop Event

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

Counts

9 → 555

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))))
(.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))
(.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64)))
(-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64)))))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))))
(*.f64 x #s(literal -1/3 binary64))

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
(.f64 x #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)))
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
(.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (-.f64 (neg.f64 x) (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)))) (/.f64 (-.f64 (neg.f64 x) (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)))) (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(.f64 (/.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (*.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (-.f64 (neg.f64 x) (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (/.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 x x))) (neg.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x))) (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 2 binary64)) (/.f64 (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64)))) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64)))) (.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64)))) (.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64)) (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 x x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(/.f64 (.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (*.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (-.f64 (pow.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 3 binary64)))) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x))) (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 2 binary64)) (/.f64 (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64)))) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64)))) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (*.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))) (.f64 (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))) (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64)))) (.f64 (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))) (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 (fma.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)))
(/.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)))
(/.f64 (-.f64 (.f64 (neg.f64 x) x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))
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(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64)))) (.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x))) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64)))) (.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64)))) (.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (-.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64)) (*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64)))) (neg.f64 (neg.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64)))) (neg.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64)))) (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64))) (neg.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64))) (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64))))
(neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)))
(fma.f64 (neg.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))) (pow.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 2 binary64)))
(fma.f64 (fabs.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))) (fabs.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))) (pow.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 2 binary64)))
(fma.f64 (fabs.f64 (.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/3 binary64))) x (.f64 x x))
(fma.f64 (fabs.f64 (.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 x #s(literal 4 binary64))) x)) #s(literal 1/3 binary64) (.f64 x x))
(fma.f64 (fabs.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1/3 binary64) x))) (.f64 #s(literal 1/3 binary64) x) (.f64 x x))
(fma.f64 (fabs.f64 (.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/3 binary64) (*.f64 x x))
(fma.f64 (fabs.f64 (pow.f64 x #s(literal 6 binary64))) #s(literal 1/9 binary64) (*.f64 x x))
(fma.f64 (fabs.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/3 binary64) x) (.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/9 binary64) (*.f64 x x))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))
(fma.f64 (exp.f64 (log.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) (exp.f64 (log.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 x x))
(fma.f64 (pow.f64 (.f64 (.f64 (neg.f64 x) x) #s(literal -1/3 binary64)) #s(literal 2 binary64)) (.f64 x x) (.f64 x x))
(fma.f64 (.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/3 binary64)) x (.f64 x x))
(fma.f64 (.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 x #s(literal 4 binary64))) x) #s(literal -1/3 binary64) (.f64 x x))
(fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1/3 binary64) x)) (.f64 #s(literal -1/3 binary64) x) (.f64 x x))
(fma.f64 (.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64))) #s(literal -1/3 binary64) (*.f64 x x))
(fma.f64 (.f64 #s(literal 1/3 binary64) x) (fabs.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x))
(fma.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (neg.f64 x) x) (*.f64 x x))
(fma.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 x x) (*.f64 x x))
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) x) (.f64 x x))
(fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (pow.f64 x #s(literal 4 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 x x)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/9 binary64) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fabs.f64 (.f64 #s(literal -1/3 binary64) (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal -1/3 binary64) (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 x x))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (pow.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 2 binary64)))
(fma.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 x x))
(fma.f64 (.f64 #s(literal -1/3 binary64) x) (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 x #s(literal 4 binary64))) (.f64 x x))
(fma.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (neg.f64 x) x) (.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 x x))
(fma.f64 (.f64 (neg.f64 x) x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 x x))
(fma.f64 (.f64 x x) (fabs.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 #s(literal 1/9 binary64) (.f64 x x)))) (.f64 x x))
(fma.f64 (.f64 x x) (pow.f64 (.f64 #s(literal -1/3 binary64) (.f64 (neg.f64 x) x)) #s(literal 2 binary64)) (.f64 x x))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 x x))
(fma.f64 (neg.f64 x) (.f64 x (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/9 binary64) (*.f64 x x))))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))
(fma.f64 (neg.f64 x) x (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))
(fma.f64 x (fabs.f64 (.f64 x (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))))) (*.f64 x x))
(fma.f64 x (fabs.f64 (.f64 (neg.f64 x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))))) (*.f64 x x))
(fma.f64 x (.f64 (neg.f64 x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 x x))
(fma.f64 x (neg.f64 x) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))
(fma.f64 x x (.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/9 binary64) (*.f64 x x))))
(fma.f64 x x (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x))) (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64)) (+.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64) (*.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (.f64 x x) (.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/9 binary64) (.f64 x x))))
(-.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64)) (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64))))) (/.f64 (.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1/729 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/81 binary64)) (*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/9 binary64))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x))) (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 2 binary64)))
(+.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 x x))
(+.f64 (.f64 (neg.f64 x) x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))
(+.f64 (.f64 x x) (.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/9 binary64) (.f64 x x))))
(+.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(*.f64 #s(literal -1/3 binary64) x)
(*.f64 x #s(literal -1/3 binary64))

eval125.0ms (1.4%)

Memory: -37.3MiB live, 107.3MiB allocated
Compiler: Compiled 34 192 to 2 590 computations (92.4% saved)

prune35.0ms (0.4%)

Memory

-6.5MiB live, 40.3MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	701	1	702
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	702	7	709

Accuracy

100.0%

Counts

709 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.0%	(/.f64 (sinh.f64 x) (cosh.f64 x))
✓	98.0%	(*.f64 (sinh.f64 x) (/.f64 #s(literal 1 binary64) (cosh.f64 x)))
✓	100.0%	(tanh.f64 x)
✓	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
	53.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 #s(approx (- (* x x) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3)))) (.f64 x x)) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))))
✓	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
✓	97.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 354 to 138 computations (61% saved)

regimes6.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

11 → 1

Calls

Call 1

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

Outputs
(tanh.f64 x)

Calls

2 calls:

3.0ms	x
2.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes4.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 #s(approx (- (* x x) (* (* (neg (* x x)) (* x -1/3)) (* (neg (* x x)) (* x -1/3)))) (.f64 x x)) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 x #s(literal -1/3 binary64))))))

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))

Calls

2 calls:

2.0ms	x
1.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Accuracy	Segments	Branch
97.6%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
97.6%	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes2.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))

Calls

2 calls:

1.0ms	x
1.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Accuracy	Segments	Branch
97.6%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
97.6%	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes2.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

Calls

2 calls:

1.0ms	x
1.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Accuracy	Segments	Branch
97.3%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
97.3%	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify69.0ms (0.8%)

Memory

-15.8MiB live, 29.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	71
1	43	71
2	93	71
3	326	71
4	1760	59

Stop Event

1×	node limit

Calls

Call 1

Inputs
(tanh.f64 x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

Outputs
(tanh.f64 x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

soundness728.0ms (8%)

Memory

12.4MiB live, 384.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
0	13	12
1	50	12
2	395	12
3	6196	12
0	9201	12
0	101	293
1	326	281
2	971	281
3	3966	281
0	8031	260
0	20	59
0	30	38
1	113	36
2	762	36
0	8547	36
0	79	210
1	292	210
2	958	200
3	3882	200
0	8155	179

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 181 to 95 computations (47.5% saved)

preprocess124.0ms (1.4%)

Memory: -16.3MiB live, 91.1MiB allocated
Remove: (negabs x)
Compiler: Compiled 172 to 70 computations (59.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze1.0ms (0%)

sample4.4s (48%)

explain265.0ms (2.9%)

preprocess160.0ms (1.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify109.0ms (1.2%)

localize85.0ms (0.9%)

series3.0ms (0%)

simplify181.0ms (2%)

rewrite250.0ms (2.7%)

eval144.0ms (1.6%)

prune24.0ms (0.3%)

simplify126.0ms (1.4%)

localize146.0ms (1.6%)

series12.0ms (0.1%)

simplify166.0ms (1.8%)

rewrite226.0ms (2.5%)

eval191.0ms (2.1%)

prune24.0ms (0.3%)

simplify121.0ms (1.3%)

localize162.0ms (1.8%)

series8.0ms (0.1%)

simplify215.0ms (2.4%)

rewrite175.0ms (1.9%)

eval91.0ms (1%)

prune7.0ms (0.1%)

simplify130.0ms (1.4%)

localize187.0ms (2.1%)

series8.0ms (0.1%)

simplify167.0ms (1.8%)

rewrite259.0ms (2.8%)

eval125.0ms (1.4%)

prune35.0ms (0.4%)

regimes6.0ms (0.1%)

regimes4.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

simplify69.0ms (0.8%)

soundness728.0ms (8%)

preprocess124.0ms (1.4%)

end0.0ms (0%)

Profiling