Metrics for Hyperbolic tangent

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

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

Compiler

Compiled 15 to 9 computations (40% saved)

sample4.7s (51%)

Memory

-63.1MiB live, 4 529.4MiB allocated; 1.9s collecting garbage

Samples

1.8s	3 210×	2	valid
1.0s	4 674×	1	valid
515.0ms	7 653×	0	exit
23.0ms	372×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.8s

ival-exp: 1.6s (58% of total)

adjust: 489.0ms (17.7% of total)

ival-div: 269.0ms (9.7% of total)

ival-sub: 172.0ms (6.2% of total)

ival-add: 122.0ms (4.4% of total)

ival-neg: 90.0ms (3.3% of total)

ival-true: 11.0ms (0.4% of total)

ival-assert: 6.0ms (0.2% of total)

Bogosity

explain285.0ms (3.1%)

Memory

-43.6MiB live, 293.4MiB allocated; 46ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
249	-	1	(0.007427964569686424)	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
4	-	0	-	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0	-	0	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	-	0	-	`(exp.f64 x)`
0	-	0	-	`(exp.f64 (neg.f64 x))`
0	-	0	-	`(neg.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	cancellation	248	1
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	4	0
↳	`(exp.f64 x)`	overflow	4
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	4
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	4
↳	`(exp.f64 x)`	overflow	4

Confusion

	Predicted +	Predicted -
+	252	1
-	0	3

Precision

1.0

Recall

0.9960474308300395

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	252	1	0
-	0	0	3

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	4
1	252

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

96.0ms	218×	2	valid
51.0ms	276×	1	valid
1.0ms	18×	0	valid

Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

ival-exp: 84.0ms (66.6% of total)

adjust: 21.0ms (16.6% of total)

ival-div: 7.0ms (5.5% of total)

ival-sub: 6.0ms (4.8% of total)

ival-add: 5.0ms (4% of total)

ival-neg: 2.0ms (1.6% of total)

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

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

preprocess129.0ms (1.4%)

Memory

15.5MiB live, 163.8MiB allocated; 25ms collecting garbage

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: 0.2MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

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)

simplify91.0ms (1%)

Memory

29.1MiB live, 164.9MiB allocated; 11ms collecting garbage

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))

localize108.0ms (1.2%)

Memory

-40.2MiB live, 147.5MiB allocated; 27ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.01171875	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	0.9765735042033008	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	57.059727100427565	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

58.0ms	109×	2	valid
34.0ms	138×	1	valid
1.0ms	9×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-exp: 43.0ms (59.1% of total)

adjust: 19.0ms (26.1% of total)

ival-div: 4.0ms (5.5% of total)

ival-sub: 3.0ms (4.1% of total)

ival-add: 2.0ms (2.8% of total)

ival-neg: 1.0ms (1.4% of total)

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

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

series3.0ms (0%)

Memory

9.8MiB live, 9.8MiB allocated; 0ms collecting garbage

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))

simplify151.0ms (1.6%)

Memory

27.4MiB live, 224.0MiB allocated; 12ms collecting garbage

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)))

rewrite339.0ms (3.7%)

Memory

-48.2MiB live, 246.0MiB allocated; 32ms collecting garbage

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)))
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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))

eval106.0ms (1.2%)

Memory: 51.7MiB live, 139.6MiB allocated; 9ms collecting garbage
Compiler: Compiled 19 340 to 1 974 computations (89.8% saved)

prune18.0ms (0.2%)

Memory

-28.3MiB live, 28.1MiB allocated; 7ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	696	5	701
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	697	5	702

Accuracy

100.0%

Counts

702 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
▶	98.4%	(/.f64 (sinh.f64 x) (cosh.f64 x))
▶	98.4%	(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
▶	100.0%	(tanh.f64 x)
▶	97.3%	#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 98 to 70 computations (28.6% saved)

simplify133.0ms (1.5%)

Memory

11.2MiB live, 100.3MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) x)
cost-diff	0	(expm1.f64 (*.f64 #s(literal 2 binary64) x))
cost-diff	9	(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
cost-diff	0	(exp.f64 (neg.f64 x))
cost-diff	0	(exp.f64 x)
cost-diff	1	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
cost-diff	8	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
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	(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))
cost-diff	0	(tanh.f64 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	106
0	49	74
1	101	74
2	257	74
3	1065	74
0	8385	73

Stop Event

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

Calls

Call 1

Inputs
(tanh.f64 x)
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 (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)
(/.f64 (sinh.f64 x) (cosh.f64 x))
(sinh.f64 x)
x
(cosh.f64 x)
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(*.f64 (cosh.f64 x) #s(literal 2 binary64))
(cosh.f64 x)
#s(literal 2 binary64)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
#s(literal 1 binary64)

Outputs
(tanh.f64 x)
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))
#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)
(/.f64 (sinh.f64 x) (cosh.f64 x))
(tanh.f64 x)
(sinh.f64 x)
x
(cosh.f64 x)
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(tanh.f64 x)
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(fma.f64 #s(literal 2 binary64) (sinh.f64 x) #s(literal 0 binary64))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(*.f64 (cosh.f64 x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
(cosh.f64 x)
#s(literal 2 binary64)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
(tanh.f64 x)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
#s(literal 1 binary64)

localize233.0ms (2.5%)

Memory

-23.0MiB live, 169.1MiB allocated; 17ms collecting garbage

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.0	(expm1.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0.0	(exp.f64 x)
accuracy	0.01953125	(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))
accuracy	0.9765735042033008	(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(cosh.f64 x)
accuracy	0.9765735042033008	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
accuracy	57.059727100427565	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	0.00390625	(cosh.f64 x)
accuracy	0.01171875	(sinh.f64 x)
accuracy	0.9765735042033008	(/.f64 (sinh.f64 x) (cosh.f64 x))
accuracy	0.00390625	(pow.f64 x #s(literal 3 binary64))
accuracy	0.01171875	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	1.7112756087119827	#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))
accuracy	0.025722509768442016	(tanh.f64 x)

Samples

118.0ms	109×	2	valid
65.0ms	138×	1	valid
2.0ms	9×	0	valid

Compiler

Compiled 108 to 27 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 124.0ms

ival-exp: 53.0ms (42.8% of total)

adjust: 26.0ms (21% of total)

ival-div: 11.0ms (8.9% of total)

ival-mult: 8.0ms (6.5% of total)

ival-add: 6.0ms (4.8% of total)

const: 4.0ms (3.2% of total)

ival-cosh: 3.0ms (2.4% of total)

ival-sub: 3.0ms (2.4% of total)

ival-pow: 3.0ms (2.4% of total)

ival-tanh: 2.0ms (1.6% of total)

ival-sinh: 2.0ms (1.6% of total)

ival-expm1: 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)

series16.0ms (0.2%)

Memory

24.9MiB live, 24.9MiB allocated; 0ms collecting garbage

Counts

15 → 47

Calls

Call 1

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

Calls

3 calls:

Time	Variable		Point	Expression
7.0ms	x	@	inf	((tanh x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (/ (sinh x) (cosh x)) (sinh x) (cosh x) (/ (- (exp x) (exp (neg x))) (* (cosh x) 2)) (- (exp x) (exp (neg x))) (exp x) (exp (neg x)) (/ (- (exp (* 2 x)) 1) (+ (* (exp x) (exp x)) 1)) (- (exp (* 2 x)) 1) (* 2 x) (+ (* (exp x) (exp x)) 1))
6.0ms	x	@	-inf	((tanh x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (/ (sinh x) (cosh x)) (sinh x) (cosh x) (/ (- (exp x) (exp (neg x))) (* (cosh x) 2)) (- (exp x) (exp (neg x))) (exp x) (exp (neg x)) (/ (- (exp (* 2 x)) 1) (+ (* (exp x) (exp x)) 1)) (- (exp (* 2 x)) 1) (* 2 x) (+ (* (exp x) (exp x)) 1))
3.0ms	x	@	0	((tanh x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (/ (sinh x) (cosh x)) (sinh x) (cosh x) (/ (- (exp x) (exp (neg x))) (* (cosh x) 2)) (- (exp x) (exp (neg x))) (exp x) (exp (neg x)) (/ (- (exp (* 2 x)) 1) (+ (* (exp x) (exp x)) 1)) (- (exp (* 2 x)) 1) (* 2 x) (+ (* (exp x) (exp x)) 1))

Time

Variable

Point

Expression

7.0ms

inf

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

6.0ms

-inf

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

3.0ms

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

simplify203.0ms (2.2%)

Memory

-11.9MiB live, 135.9MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	448
1	542	435
2	1747	435
3	5047	369
0	8473	325

Stop Event

1×	iter limit
1×	node limit

Counts

47 → 46

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

rewrite230.0ms (2.5%)

Memory

18.4MiB live, 210.2MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	86
0	49	52
1	176	52
2	1070	52
0	8395	52

Stop Event

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

Counts

15 → 1 105

Calls

Call 1

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

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

eval182.0ms (2%)

Memory: -28.7MiB live, 201.8MiB allocated; 26ms collecting garbage
Compiler: Compiled 26 537 to 3 138 computations (88.2% saved)

prune35.0ms (0.4%)

Memory

7.3MiB live, 54.4MiB allocated; 2ms collecting garbage

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	933	3	936
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	936	5	941

Accuracy

100.0%

Counts

941 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(/.f64 (sinh.f64 x) (cosh.f64 x))
▶	98.4%	(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
✓	100.0%	(tanh.f64 x)
▶	97.3%	#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))
▶	97.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x))

Compiler

Compiled 62 to 37 computations (40.3% saved)

simplify120.0ms (1.3%)

Memory

29.2MiB live, 174.7MiB allocated; 16ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))
cost-diff	0	(+.f64 x x)
cost-diff	0	(expm1.f64 (+.f64 x x))
cost-diff	9	(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
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 x x)
cost-diff	0	(.f64 #s(literal -1/3 binary64) (.f64 x x))
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x))
cost-diff	2	(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	108
0	36	108
1	82	89
2	243	67
3	827	67
4	3764	67
0	9473	67

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 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x))
(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
(.f64 #s(literal -1/3 binary64) (.f64 x x))
#s(literal -1/3 binary64)
(*.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 (.f64 x x) x)
(*.f64 x x)
x
#s(literal -1/3 binary64)
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
x
(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
#s(literal 1 binary64)

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

localize202.0ms (2.2%)

Memory

-27.2MiB live, 282.6MiB allocated; 78ms collecting garbage

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(expm1.f64 (+.f64 x x))
accuracy	0.0	(exp.f64 x)
accuracy	0.01953125	(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))
accuracy	0.9765735042033008	(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	0.01171875	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
accuracy	0.06640625	(.f64 (.f64 x x) x)
accuracy	1.7112756087119827	#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	0.0	(*.f64 x x)
accuracy	0.015625	(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
accuracy	0.203125	(.f64 #s(literal -1/3 binary64) (.f64 x x))
accuracy	1.7112756087119827	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x))

Samples

92.0ms	138×	1	valid
79.0ms	109×	2	valid
2.0ms	9×	0	valid

Compiler

Compiled 100 to 23 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-exp: 51.0ms (33.8% of total)

const: 39.0ms (25.9% of total)

adjust: 24.0ms (15.9% of total)

ival-add: 13.0ms (8.6% of total)

ival-mult: 10.0ms (6.6% of total)

ival-div: 7.0ms (4.6% of total)

ival-sub: 3.0ms (2% of total)

ival-expm1: 2.0ms (1.3% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Counts

12 → 30

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify207.0ms (2.3%)

Memory

-26.6MiB live, 209.6MiB allocated; 27ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	247
1	299	241
2	913	241
3	3482	197
0	8625	172

Stop Event

1×	iter limit
1×	node limit

Counts

30 → 29

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))))
(* -1/3 (pow x 2))
(pow x 2)
(pow x 3)
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
2
(+ 2 (* 2 x))
(+ 2 (* x (+ 2 (* 2 x))))
(+ 2 (* x (+ 2 (* x (+ 2 (* 4/3 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/ (- (exp (* 2 x)) 1) (+ 1 (pow (exp x) 2)))
(- (exp (* 2 x)) 1)
(+ 1 (pow (exp x) 2))
(exp x)
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/ (- (exp (neg (* -2 x))) 1) (+ 1 (pow (exp x) 2)))
(- (exp (neg (* -2 x))) 1)

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

rewrite179.0ms (2%)

Memory

6.5MiB live, 201.1MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	99
0	36	60
1	157	60
2	1122	52
0	11278	52

Stop Event

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

Counts

12 → 1 161

Calls

Call 1

Inputs
(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x))
(.f64 #s(literal -1/3 binary64) (.f64 x x))
(*.f64 x 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 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)

Outputs
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x))) (.f64 (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)))) (+.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)) (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)))) (+.f64 x (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64))) x) (.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64))) x))) (+.f64 x (.f64 (neg.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64))) 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 x) (.f64 (.f64 x x) #s(literal -1/3 binary64))) (.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal -1/3 binary64))))) (+.f64 x (.f64 (neg.f64 x) (.f64 (*.f64 x x) #s(literal -1/3 binary64)))))
(/.f64 (-.f64 (.f64 x x) (.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 (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))) (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))))) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))))) (-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)) (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)) (.f64 x (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64))) x) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64))) x) (.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64))) x) (.f64 x (.f64 (neg.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64))) x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 x #s(literal -1/3 binary64))) #s(literal 3 binary64))) (fma.f64 x x (fma.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 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal -1/3 binary64))) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal -1/3 binary64))) (.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal -1/3 binary64))) (.f64 x (.f64 (neg.f64 x) (.f64 (*.f64 x x) #s(literal -1/3 binary64)))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64))) (fma.f64 x x (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 (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))))
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(/.f64 (.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64)))) (exp.f64 (neg.f64 x))))
(/.f64 (.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64)))) (.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64)))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (neg.f64 (tanh.f64 x)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (tanh.f64 x))) #s(literal 4 binary64))
(/.f64 (fma.f64 (tanh.f64 x) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64)))) #s(literal 4 binary64))
(/.f64 (-.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) (neg.f64 (tanh.f64 x))) #s(literal 2 binary64))
(/.f64 (fabs.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64)))) (fabs.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64))))))
(/.f64 (pow.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64)))) #s(literal 3 binary64)))
(/.f64 (exp.f64 (/.f64 (.f64 x x) #s(literal 0 binary64))) (exp.f64 (/.f64 (.f64 x x) #s(literal 0 binary64))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 (cosh.f64 x)) (sinh.f64 (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(neg.f64 (exp.f64 x))
(fma.f64 (cosh.f64 x) (exp.f64 x) (*.f64 (sinh.f64 x) (exp.f64 x)))
(fma.f64 #s(literal 2 binary64) (*.f64 (sinh.f64 x) (cosh.f64 x)) (cosh.f64 x))
(fma.f64 (exp.f64 x) (cosh.f64 x) (*.f64 (exp.f64 x) (sinh.f64 x)))
(sqrt.f64 (exp.f64 x))
(-.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))))
(-.f64 (cosh.f64 x) (sinh.f64 (neg.f64 x)))
(fabs.f64 (exp.f64 x))
(exp.f64 (fma.f64 x #s(literal 3 binary64) (*.f64 x #s(literal 3 binary64))))
(exp.f64 (fma.f64 x #s(literal 3 binary64) x))
(exp.f64 (+.f64 x (*.f64 x #s(literal 3 binary64))))
(exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)))
(exp.f64 (*.f64 x #s(literal 6 binary64)))
(exp.f64 (*.f64 x #s(literal 4 binary64)))
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(exp.f64 (*.f64 x #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) x))
(exp.f64 (/.f64 x #s(literal 2 binary64)))
(exp.f64 (*.f64 x #s(literal 3 binary64)))
(exp.f64 x)
(+.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64))))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (tanh.f64 x) #s(literal 4 binary64))))))
(+.f64 (cosh.f64 (.f64 x #s(literal 3 binary64))) (sinh.f64 (.f64 x #s(literal 3 binary64))))
(+.f64 (.f64 (cosh.f64 x) (exp.f64 x)) (.f64 (sinh.f64 x) (exp.f64 x)))
(+.f64 (.f64 (exp.f64 x) (cosh.f64 x)) (.f64 (exp.f64 x) (sinh.f64 x)))
(+.f64 (neg.f64 (cosh.f64 x)) (sinh.f64 (neg.f64 x)))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(+.f64 (sinh.f64 x) (cosh.f64 x))

eval253.0ms (2.8%)

Memory: 0.5MiB live, 267.9MiB allocated; 52ms collecting garbage
Compiler: Compiled 23 199 to 2 957 computations (87.3% saved)

prune83.0ms (0.9%)

Memory

15.5MiB live, 73.4MiB allocated; 27ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	991	1	992
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	991	6	997

Accuracy

100.0%

Counts

997 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(/.f64 (sinh.f64 x) (cosh.f64 x))
✓	98.4%	(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
✓	100.0%	(tanh.f64 x)
✓	97.3%	#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))
✓	97.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x))
▶	97.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (-.f64 x (.f64 (neg.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64))) x)))

Compiler

Compiled 86 to 51 computations (40.7% saved)

simplify129.0ms (1.4%)

Memory

-3.7MiB live, 88.1MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
0	19	54
1	50	54
2	156	48
3	507	48
4	2092	44
0	9292	42

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

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

localize135.0ms (1.5%)

Memory

21.0MiB live, 114.2MiB allocated; 15ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(neg.f64 (.f64 (.f64 x x) #s(literal -1/3 binary64)))
accuracy	0.0625	(.f64 (neg.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64))) x)
accuracy	0.203125	(.f64 (.f64 x x) #s(literal -1/3 binary64))
accuracy	1.7112756087119827	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (-.f64 x (.f64 (neg.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64))) x)))

Samples

77.0ms	109×	2	valid
46.0ms	138×	1	valid
1.0ms	9×	0	valid

Compiler

Compiled 49 to 15 computations (69.4% saved)

Precisions

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

ival-exp: 58.0ms (52.1% of total)

const: 16.0ms (14.4% of total)

adjust: 15.0ms (13.5% of total)

ival-div: 9.0ms (8.1% of total)

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

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

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

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

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

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

series17.0ms (0.2%)

Memory

-30.6MiB live, 15.2MiB allocated; 5ms collecting garbage

Counts

5 → 12

Calls

Call 1

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

Outputs
(* 1/3 (pow x 3))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* 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))))
(* -1/3 (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 (* (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

14.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify128.0ms (1.4%)

Memory

30.5MiB live, 119.5MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	115
1	129	109
2	334	109
3	1264	109
4	3860	109
0	8090	105

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 11

Calls

Call 1

Inputs
(* 1/3 (pow x 3))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* 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))))
(* -1/3 (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 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))

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

rewrite186.0ms (2%)

Memory

11.1MiB live, 197.8MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	53
0	19	38
1	86	32
2	645	32
0	8516	30

Stop Event

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

Counts

5 → 110

Calls

Call 1

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

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

eval57.0ms (0.6%)

Memory: -30.2MiB live, 25.7MiB allocated; 9ms collecting garbage
Compiler: Compiled 4 175 to 484 computations (88.4% saved)

prune6.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	120	6	126

Accuracy

100.0%

Counts

126 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(/.f64 (sinh.f64 x) (cosh.f64 x))
✓	98.4%	(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
✓	100.0%	(tanh.f64 x)
✓	97.3%	#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))
✓	97.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x))
	97.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (-.f64 x (.f64 (.f64 (*.f64 x x) #s(literal 1/3 binary64)) x)))

Compiler

Compiled 249 to 100 computations (59.8% saved)

regimes6.0ms (0.1%)

Memory

7.3MiB live, 7.3MiB allocated; 0ms collecting garbage

Counts

11 → 1

Calls

Call 1

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

regimes3.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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
97.3%	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)

simplify42.0ms (0.5%)

Memory

-2.0MiB live, 43.1MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	26	24
2	66	24
3	262	24
4	1669	20

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 #s(literal -1/3 binary64) (.f64 x x)) x x))

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

derivations396.0ms (4.3%)

Memory

11.3MiB live, 304.2MiB allocated; 61ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	86
0	49	52
1	176	52
2	1070	52
0	8395	52
0	79	210
1	292	210
2	958	200
3	3882	200
0	8155	179
0	7	27
0	13	12
1	50	12
2	395	12
3	6196	12
0	9201	12

Stop Event

1×	fuel
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 24 to 13 computations (45.8% saved)

preprocess72.0ms (0.8%)

Memory: -12.6MiB live, 86.9MiB allocated; 14ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 78 to 44 computations (43.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample4.7s (51%)

explain285.0ms (3.1%)

preprocess129.0ms (1.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify91.0ms (1%)

localize108.0ms (1.2%)

series3.0ms (0%)

simplify151.0ms (1.6%)

rewrite339.0ms (3.7%)

eval106.0ms (1.2%)

prune18.0ms (0.2%)

simplify133.0ms (1.5%)

localize233.0ms (2.5%)

series16.0ms (0.2%)

simplify203.0ms (2.2%)

rewrite230.0ms (2.5%)

eval182.0ms (2%)

prune35.0ms (0.4%)

simplify120.0ms (1.3%)

localize202.0ms (2.2%)

series7.0ms (0.1%)

simplify207.0ms (2.3%)

rewrite179.0ms (2%)

eval253.0ms (2.8%)

prune83.0ms (0.9%)

simplify129.0ms (1.4%)

localize135.0ms (1.5%)

series17.0ms (0.2%)

simplify128.0ms (1.4%)

rewrite186.0ms (2%)

eval57.0ms (0.6%)

prune6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes3.0ms (0%)

simplify42.0ms (0.5%)

derivations396.0ms (4.3%)

preprocess72.0ms (0.8%)

end0.0ms (0%)

Profiling