Metrics for Hyperbolic tangent

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

1.2MiB live, 1.2MiB 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)

sample4.3s (50.2%)

Memory

-158.3MiB live, 3 916.9MiB allocated; 1.8s collecting garbage

Samples

1.9s	3 135×	2	valid
1.0s	4 734×	1	valid
550.0ms	7 796×	0	exit
27.0ms	387×	0	valid

Precisions

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

ival-exp: 2.0s (67.5% of total)

adjust: 370.0ms (12.4% of total)

ival-div: 206.0ms (6.9% of total)

ival-sub: 179.0ms (6% of total)

ival-add: 130.0ms (4.3% of total)

ival-neg: 69.0ms (2.3% of total)

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

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

Bogosity

explain240.0ms (2.8%)

Memory

43.5MiB live, 379.2MiB allocated; 37ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
247	0	-	1	(-0.005937816531907431)	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
2	0	-	0	-	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0	0	-	0	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	0	-	0	-	`(exp.f64 x)`
0	1	(-482.7325389690471)	0	-	`(exp.f64 (neg.f64 x))`
0	0	-	0	-	`(neg.f64 x)`
0	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	246	3
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	2	0
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	2
↳	`(exp.f64 (neg.f64 x))`	overflow	2
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	2
↳	`(exp.f64 (neg.f64 x))`	overflow	2
`exp.f64`	`(exp.f64 (neg.f64 x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	248	1
-	1	6

Precision

0.9959839357429718

Recall

0.9959839357429718

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	248	1	0
-	1	2	4

Precision?

0.9880952380952381

Recall?

1.0

Freqs

test

number	freq
0	7
1	249

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

104.0ms	200×	2	valid
59.0ms	288×	1	valid
2.0ms	24×	0	valid

Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-exp: 102.0ms (71.4% of total)

adjust: 20.0ms (14% of total)

ival-div: 7.0ms (4.9% of total)

ival-sub: 6.0ms (4.2% of total)

ival-add: 5.0ms (3.5% of total)

ival-neg: 2.0ms (1.4% of total)

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

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

preprocess134.0ms (1.6%)

Memory

-2.0MiB live, 188.1MiB allocated; 32ms 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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	10.0%	(/.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)

simplify119.0ms (1.4%)

Memory

-2.6MiB live, 88.5MiB allocated; 10ms 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))

localize139.0ms (1.6%)

Memory

-24.5MiB live, 80.5MiB allocated; 10ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	0.5156305021016504	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	57.08457828183228	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

88.0ms	144×	1	valid
41.0ms	100×	2	valid
1.0ms	12×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 101.0ms

ival-exp: 56.0ms (55.4% of total)

adjust: 35.0ms (34.6% of total)

ival-div: 4.0ms (4% of total)

ival-add: 3.0ms (3% of total)

ival-sub: 3.0ms (3% of total)

ival-neg: 1.0ms (1% of total)

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

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

series3.0ms (0%)

Memory

1.4MiB live, 1.4MiB 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))

simplify203.0ms (2.4%)

Memory

1.8MiB live, 130.5MiB allocated; 21ms 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)))

rewrite306.0ms (3.6%)

Memory

21.0MiB live, 218.8MiB allocated; 17ms 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))

eval144.0ms (1.7%)

Memory: -11.9MiB live, 133.3MiB allocated; 16ms collecting garbage
Compiler: Compiled 19 340 to 1 974 computations (89.8% saved)

prune44.0ms (0.5%)

Memory

-20.8MiB live, 26.6MiB allocated; 2ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	698	3	701
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	699	3	702

Accuracy

100.0%

Counts

702 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (sinh.f64 x))
▶	100.0%	(tanh.f64 x)
▶	97.2%	#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))

Status

Accuracy

Program

▶

98.8%

(*.f64 (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (sinh.f64 x))

▶

100.0%

(tanh.f64 x)

▶

97.2%

#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 34 to 22 computations (35.3% saved)

simplify123.0ms (1.4%)

Memory

9.5MiB live, 61.8MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sinh.f64 x)
cost-diff	0	(*.f64 (sinh.f64 x) #s(literal 2 binary64))
cost-diff	0	(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (sinh.f64 x))
cost-diff	4	(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (sinh.f64 (.f64 #s(literal 2 binary64) x)))
cost-diff	0	(tanh.f64 x)
cost-diff	0	(pow.f64 x #s(literal 3 binary64))
cost-diff	0	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	71
0	30	60
1	71	60
2	193	60
3	705	60
4	4464	52
0	9338	52

Stop Event

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

Calls

Call 1

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

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

localize137.0ms (1.6%)

Memory

5.3MiB live, 50.2MiB allocated; 4ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sinh.f64 x)
accuracy	0.01171875	(sinh.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0.4960992521016504	(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (sinh.f64 x))
accuracy	0.735759968637392	(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (sinh.f64 (.f64 #s(literal 2 binary64) x)))
accuracy	0.01953125	(tanh.f64 x)
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.0078125	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	1.778033597657906	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Samples

78.0ms	100×	2	valid
44.0ms	144×	1	valid
2.0ms	12×	0	valid

Compiler

Compiled 67 to 22 computations (67.2% saved)

Precisions

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

adjust: 40.0ms (37.1% of total)

ival-exp: 38.0ms (35.2% of total)

ival-mult: 6.0ms (5.6% of total)

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

const: 4.0ms (3.7% of total)

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

ival-sub: 3.0ms (2.8% of total)

ival-pow: 3.0ms (2.8% of total)

ival-sinh: 3.0ms (2.8% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

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

Counts

9 → 30

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 3)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(* 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))))))))
(* 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))))))))
(* x (+ 2 (* 4/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (pow x 2))))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(- (exp x) (/ 1 (exp x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
7.0ms	x	@	inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (* (sinh x) 2) (sinh x) (sinh (* 2 x)))
6.0ms	x	@	-inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (* (sinh x) 2) (sinh x) (sinh (* 2 x)))
2.0ms	x	@	0	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (* (sinh x) 2) (sinh x) (sinh (* 2 x)))

Time

Variable

Point

Expression

7.0ms

inf

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

6.0ms

-inf

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

2.0ms

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

simplify161.0ms (1.9%)

Memory

-10.9MiB live, 78.3MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	358
1	442	343
2	1387	343
3	4779	343
0	8445	310

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))))
(pow x 3)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(* 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))))))))
(* 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))))))))
(* x (+ 2 (* 4/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (pow x 2))))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(- (exp x) (/ 1 (exp x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64))) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -61/720 binary64) (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(* 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)
(* 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)
(* x (+ 2 (* 4/3 (pow x 2))))
(.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 4/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) #s(literal 0 binary64)) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) #s(literal 0 binary64)) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) #s(literal 0 binary64)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))) #s(literal 2 binary64))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) #s(literal 0 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64))))
(- (exp x) (/ 1 (exp x)))
(fma.f64 #s(literal 2 binary64) (sinh.f64 x) #s(literal 0 binary64))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(*.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(* 1/2 (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(*.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 1/2 binary64))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) #s(literal 0 binary64)) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(.f64 (neg.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (pow.f64 x #s(literal 3 binary64)))

rewrite119.0ms (1.4%)

Memory

-29.3MiB live, 59.1MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	62
0	30	51
1	117	49
0	799	49

Stop Event

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

Counts

9 → 128

Calls

Call 1

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

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))) (-.f64 x (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 x x))) (neg.f64 (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))
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eval29.0ms (0.3%)

Memory: -8.5MiB live, 37.2MiB allocated; 4ms collecting garbage
Compiler: Compiled 3 423 to 582 computations (83% saved)

prune4.0ms (0%)

Memory

13.5MiB live, 13.5MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	0	0	0
Picked	2	1	3
Done	0	0	0
Total	168	3	171

Accuracy

100.0%

Counts

171 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

98.0%

(*.f64 (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh (* 2 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (*.f64 x x) #s(literal 4/15 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))

✓

100.0%

(tanh.f64 x)

▶

97.2%

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

Compiler

Compiled 55 to 32 computations (41.8% saved)

simplify180.0ms (2.1%)

Memory

-7.1MiB live, 137.2MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sinh.f64 x)
cost-diff	0	(*.f64 (sinh.f64 x) #s(literal 2 binary64))
cost-diff	0	(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
cost-diff	0	(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
cost-diff	0	(*.f64 x #s(literal -1/3 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x))
cost-diff	2	(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	185
0	42	185
1	92	185
2	297	183
3	1288	181
4	6671	181
0	8200	179

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 x x) (.f64 x #s(literal -1/3 binary64)) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)
(*.f64 x x)
x
(*.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
(*.f64 (sinh.f64 x) #s(literal 2 binary64))
(sinh.f64 x)
x
#s(literal 2 binary64)
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 2 binary64))
(fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64))
(fma.f64 #s(literal 8/315 binary64) (*.f64 x x) #s(literal 4/15 binary64))
#s(literal 8/315 binary64)
(*.f64 x x)
#s(literal 4/15 binary64)
#s(literal 4/3 binary64)

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 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 x x) (.f64 x #s(literal -1/3 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(*.f64 x x)
x
(*.f64 x #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(.f64 (/.f64 (sinh.f64 x) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 x)))
(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
(/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
(*.f64 (sinh.f64 x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (sinh.f64 x))
(sinh.f64 x)
x
#s(literal 2 binary64)
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 2 binary64))
(fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64))
(fma.f64 #s(literal 8/315 binary64) (*.f64 x x) #s(literal 4/15 binary64))
#s(literal 8/315 binary64)
(*.f64 x x)
#s(literal 4/15 binary64)
#s(literal 4/3 binary64)

localize205.0ms (2.4%)

Memory

21.6MiB live, 257.3MiB allocated; 19ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
accuracy	0.4960992521016504	(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
accuracy	0.735759968637392	(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
accuracy	1.2871939518413185	#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)
accuracy	0.296875	(*.f64 x #s(literal -1/3 binary64))
accuracy	1.778033597657906	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x))

Samples

106.0ms	100×	2	valid
77.0ms	144×	1	valid
3.0ms	12×	0	valid

Compiler

Compiled 131 to 31 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-exp: 40.0ms (30.8% of total)

adjust: 32.0ms (24.7% of total)

ival-mult: 18.0ms (13.9% of total)

const: 17.0ms (13.1% of total)

ival-add: 10.0ms (7.7% of total)

ival-div: 5.0ms (3.9% of total)

ival-sub: 3.0ms (2.3% of total)

ival-sinh: 3.0ms (2.3% 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)

series14.0ms (0.2%)

Memory

-22.0MiB live, 24.4MiB allocated; 4ms collecting garbage

Counts

10 → 36

Calls

Call 1

Inputs
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x))
(*.f64 x x)
(*.f64 x #s(literal -1/3 binary64))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
(*.f64 (sinh.f64 x) #s(literal 2 binary64))
(sinh.f64 x)
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 2)
(* -1/3 x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(* 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))))))))
(* 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))))))))
(* x (+ 2 (* 4/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (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))))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(- (exp x) (/ 1 (exp x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(* 8/315 (pow x 7))
(* (pow x 7) (+ 8/315 (* 4/15 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 8/315 (+ (* 4/15 (/ 1 (pow x 2))) (/ 4/3 (pow x 4)))))
(* (pow x 7) (+ 8/315 (+ (* 4/15 (/ 1 (pow x 2))) (+ (* 2 (/ 1 (pow x 6))) (/ 4/3 (pow x 4))))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 4/15 (* 4/3 (/ 1 (pow x 2)))) (pow x 2))) 8/315)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 8/315 (* 4/15 (/ 1 (pow x 2)))))))

Calls

3 calls:

Time

Variable

Point

Expression

9.0ms

inf

((+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (sinh x) 2) (sinh x) (sinh (* 2 x)) (* (+ (* (+ (* (+ (* 8/315 (* x x)) 4/15) (* x x)) 4/3) (* x x)) 2) x))

3.0ms

-inf

((+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (sinh x) 2) (sinh x) (sinh (* 2 x)) (* (+ (* (+ (* (+ (* 8/315 (* x x)) 4/15) (* x x)) 4/3) (* x x)) 2) x))

1.0ms

((+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (sinh x) 2) (sinh x) (sinh (* 2 x)) (* (+ (* (+ (* (+ (* 8/315 (* x x)) 4/15) (* x x)) 4/3) (* x x)) 2) x))

simplify144.0ms (1.7%)

Memory

27.7MiB live, 216.6MiB allocated; 14ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	448
1	548	433
2	1713	431
3	6040	431
0	8517	405

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 35

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 2)
(* -1/3 x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(* 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))))))))
(* 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))))))))
(* x (+ 2 (* 4/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (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))))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(- (exp x) (/ 1 (exp x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(* 8/315 (pow x 7))
(* (pow x 7) (+ 8/315 (* 4/15 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 8/315 (+ (* 4/15 (/ 1 (pow x 2))) (/ 4/3 (pow x 4)))))
(* (pow x 7) (+ 8/315 (+ (* 4/15 (/ 1 (pow x 2))) (+ (* 2 (/ 1 (pow x 6))) (/ 4/3 (pow x 4))))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 4/15 (* 4/3 (/ 1 (pow x 2)))) (pow x 2))) 8/315)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 8/315 (* 4/15 (/ 1 (pow x 2)))))))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64))) x)
(pow x 2)
(*.f64 x x)
(* -1/3 x)
(*.f64 #s(literal -1/3 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) (- (* 5/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -61/720 binary64) (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(* 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)
(* x (+ 1 (* 1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (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)) x)
(* x (+ 2 (* 4/3 (pow x 2))))
(.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 4/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (exp x) (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)))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(/.f64 (pow.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64))))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(*.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))) #s(literal 2 binary64))
(- (exp x) (/ 1 (exp x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(* 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 (* 2 x)) (/ 1 (exp (* 2 x)))))
(*.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 1/2 binary64))
(* 8/315 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 8/315 binary64))
(* (pow x 7) (+ 8/315 (* 4/15 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 4/15 binary64) (.f64 x x)) #s(literal 8/315 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 8/315 (+ (* 4/15 (/ 1 (pow x 2))) (/ 4/3 (pow x 4)))))
(.f64 (-.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal -4/15 binary64) (.f64 x x)) #s(literal 8/315 binary64))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 8/315 (+ (* 4/15 (/ 1 (pow x 2))) (+ (* 2 (/ 1 (pow x 6))) (/ 4/3 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (/.f64 #s(literal -4/15 binary64) (.f64 x x)) #s(literal 8/315 binary64))) (pow.f64 x #s(literal 7 binary64)))
(* -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)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 4/15 (* 4/3 (/ 1 (pow x 2)))) (pow x 2))) 8/315)))
(.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -4/15 binary64) (/.f64 #s(literal 4/3 binary64) (.f64 x x))) x) x) #s(literal 8/315 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 8/315 (* 4/15 (/ 1 (pow x 2)))))))
(.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (-.f64 (/.f64 (-.f64 #s(literal -4/3 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 4/15 binary64) (*.f64 x x)) #s(literal 8/315 binary64))))

rewrite239.0ms (2.8%)

Memory

-26.4MiB live, 301.6MiB allocated; 82ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	142
0	42	131
1	177	129
2	1277	128
0	8381	126

Stop Event

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

Counts

10 → 299

Calls

Call 1

Inputs
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x))
(*.f64 x x)
(*.f64 x #s(literal -1/3 binary64))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
(*.f64 (sinh.f64 x) #s(literal 2 binary64))
(sinh.f64 x)
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)

Outputs
(/.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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 #s(literal -1/3 binary64) x)) (.f64 x x)) (.f64 (neg.f64 (.f64 #s(literal -1/3 binary64) x)) (.f64 x x)))) (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 #s(literal -1/3 binary64) x)) (.f64 (neg.f64 (.f64 x x)) (.f64 #s(literal -1/3 binary64) x)))) (+.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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal -1/3 binary64) x)) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (.f64 (neg.f64 (.f64 #s(literal -1/3 binary64) x)) (.f64 x x)) (.f64 (neg.f64 (.f64 #s(literal -1/3 binary64) x)) (.f64 x x)) (.f64 x (.f64 (neg.f64 (.f64 #s(literal -1/3 binary64) x)) (*.f64 x x))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 #s(literal -1/3 binary64) x)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 #s(literal -1/3 binary64) x)) (.f64 (neg.f64 (.f64 x x)) (.f64 #s(literal -1/3 binary64) x)) (.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 #s(literal -1/3 binary64) x))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 x) (.f64 (.f64 #s(literal -1/3 binary64) x) x)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (.f64 (neg.f64 x) (.f64 (*.f64 #s(literal -1/3 binary64) x) x))))))
(/.f64 (+.f64 (pow.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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))) #s(literal 3 binary64)) (pow.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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))) #s(literal 3 binary64))) (fma.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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))) (-.f64 (.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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (neg.f64 x))))) (neg.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (+.f64 x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))))))
(/.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 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x) (.f64 x x))) (.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)))
(/.f64 (fma.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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (+.f64 x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (+.f64 x (.f64 #s(literal 1/3 binary64) (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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))))
(/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (neg.f64 x)))) (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (.f64 #s(literal -1/3 binary64) x))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (+.f64 x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))))
(/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (neg.f64 x))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (.f64 #s(literal -1/3 binary64) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (+.f64 x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (*.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (.f64 (neg.f64 (neg.f64 (.f64 #s(literal -1/3 binary64) x))) (*.f64 x x)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (*.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (.f64 (neg.f64 (neg.f64 (.f64 #s(literal -1/3 binary64) x))) (*.f64 x x)))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 #s(literal -1/3 binary64) x))) (*.f64 x x)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (neg.f64 x)) (neg.f64 x) x)
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) (.f64 #s(literal -1/3 binary64) x)) x)
(fma.f64 (.f64 #s(literal -1/3 binary64) x) (.f64 x x) x)
(fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 (.f64 x x) (.f64 #s(literal -1/3 binary64) x) x)
(fma.f64 x (.f64 #s(literal -1/3 binary64) (.f64 x x)) x)
(fma.f64 x (.f64 (.f64 #s(literal -1/3 binary64) x) x) x)
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(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 8 binary64)) x)) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) (.f64 #s(literal 2 binary64) x)))))
(/.f64 (neg.f64 (.f64 x (-.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 4 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 8 binary64)))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) (.f64 #s(literal 2 binary64) x)))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 4 binary64)) x) (-.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x) #s(literal 2 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 8 binary64)) x) (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) (.f64 #s(literal 2 binary64) x))))
(/.f64 (.f64 x (-.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 4 binary64))) (-.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x) #s(literal 2 binary64)))
(/.f64 (.f64 x (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 8 binary64))) (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) (.f64 #s(literal 2 binary64) x))))
(fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x) x (*.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 2 binary64) x (.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) x) x) x))
(fma.f64 #s(literal 2 binary64) x (.f64 x (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) x) x)))
(fma.f64 x (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 2 binary64) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) x) x) x))
(fma.f64 x #s(literal 2 binary64) (.f64 x (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) x) x)))
(-.f64 (.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x) x) (.f64 #s(literal -2 binary64) x))
(-.f64 (.f64 x (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x)) (.f64 #s(literal -2 binary64) x))
(-.f64 (.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x)) x))
(-.f64 (.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 x) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x)))
(+.f64 (.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x) x) (.f64 #s(literal 2 binary64) x))
(+.f64 (.f64 x (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x)) (.f64 #s(literal 2 binary64) x))
(+.f64 (.f64 #s(literal 2 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x) x))
(+.f64 (.f64 #s(literal 2 binary64) x) (.f64 x (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x) x)))

eval57.0ms (0.7%)

Memory: 29.2MiB live, 121.0MiB allocated; 6ms collecting garbage
Compiler: Compiled 18 183 to 1 879 computations (89.7% saved)

prune12.0ms (0.1%)

Memory

-23.7MiB live, 28.6MiB allocated; 8ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	414	2	416
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	415	4	419

Accuracy

100.0%

Counts

419 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.0%	(.f64 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
✓	100.0%	(tanh.f64 x)
✓	97.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x))
▶	96.5%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))))

Compiler

Compiled 102 to 57 computations (44.1% saved)

simplify189.0ms (2.2%)

Memory

43.7MiB live, 223.3MiB allocated; 47ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(.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)
cost-diff	0	#s(approx (* (sinh 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))
cost-diff	0	(/.f64 #s(approx (* (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
cost-diff	0	(.f64 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))))
cost-diff	2	(neg.f64 (neg.f64 (*.f64 x x)))
cost-diff	2	(.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))
cost-diff	4	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	328
0	65	314
1	139	314
2	553	308
3	2929	306
0	8297	304

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 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))
(sqrt.f64 x)
x
(.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))
(neg.f64 (neg.f64 (*.f64 x x)))
(neg.f64 (*.f64 x x))
(*.f64 x x)
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
(.f64 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(/.f64 #s(approx (* (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
#s(approx (* (sinh 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))
(.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)
(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))
(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))
(fma.f64 #s(literal 1/2520 binary64) (*.f64 x x) #s(literal 1/60 binary64))
#s(literal 1/2520 binary64)
(*.f64 x x)
x
#s(literal 1/60 binary64)
#s(literal 1/3 binary64)
#s(literal 2 binary64)
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 2 binary64))
(fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64))
(fma.f64 #s(literal 8/315 binary64) (*.f64 x x) #s(literal 4/15 binary64))
#s(literal 8/315 binary64)
#s(literal 4/15 binary64)
#s(literal 4/3 binary64)
(sinh.f64 x)

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #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 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(sqrt.f64 x)
x
(.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(neg.f64 (neg.f64 (*.f64 x x)))
(*.f64 x x)
(neg.f64 (*.f64 x x))
(*.f64 (neg.f64 x) x)
(*.f64 x x)
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
(.f64 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(.f64 (/.f64 (sinh.f64 x) #s(approx (sinh ( 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) #s(approx (* (sinh 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)))
(/.f64 #s(approx (* (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
#s(approx (* (sinh 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))
(.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)
(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))
(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))
(fma.f64 #s(literal 1/2520 binary64) (*.f64 x x) #s(literal 1/60 binary64))
#s(literal 1/2520 binary64)
(*.f64 x x)
x
#s(literal 1/60 binary64)
#s(literal 1/3 binary64)
#s(literal 2 binary64)
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 2 binary64))
(fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64))
(fma.f64 #s(literal 8/315 binary64) (*.f64 x x) #s(literal 4/15 binary64))
#s(literal 8/315 binary64)
#s(literal 4/15 binary64)
#s(literal 4/3 binary64)
(sinh.f64 x)

localize322.0ms (3.8%)

Memory

7.1MiB live, 284.2MiB allocated; 105ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.4960992521016504	(.f64 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
accuracy	0.735759968637392	(/.f64 #s(approx (* (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
accuracy	1.2252105970861757	#s(approx (* (sinh 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))
accuracy	1.2871939518413185	#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))
accuracy	0.1171875	(.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))
accuracy	0.296875	(*.f64 #s(literal -1/3 binary64) x)
accuracy	0.484375	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))
accuracy	1.778033597657906	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))))

Samples

162.0ms	144×	1	valid
123.0ms	100×	2	valid
4.0ms	12×	0	valid

Compiler

Compiled 220 to 45 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 207.0ms

adjust: 64.0ms (30.9% of total)

ival-exp: 39.0ms (18.8% of total)

ival-mult: 37.0ms (17.9% of total)

const: 29.0ms (14% of total)

ival-add: 17.0ms (8.2% of total)

ival-neg: 6.0ms (2.9% of total)

ival-div: 5.0ms (2.4% of total)

ival-sub: 3.0ms (1.4% of total)

ival-sqrt: 3.0ms (1.4% of total)

ival-sinh: 3.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory

-21.3MiB live, 21.2MiB allocated; 7ms collecting garbage

Counts

10 → 32

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))
(.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))
(neg.f64 (neg.f64 (*.f64 x x)))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))))
(.f64 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(/.f64 #s(approx (* (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
#s(approx (* (sinh 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))
(.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)
(*.f64 #s(literal -1/3 binary64) x)
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* -1/3 (pow x 3))
(pow x 2)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(* 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))))))))
(* -1/3 x)
(* x (+ 2 (* 4/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (pow x 2))))))))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(- (exp x) (/ 1 (exp x)))
(* 1/2520 (pow x 7))
(* (pow x 7) (+ 1/2520 (* 1/60 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 1/2520 (+ (/ 1/3 (pow x 4)) (* 1/60 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 1/2520 (+ (/ 1/3 (pow x 4)) (+ (* 1/60 (/ 1 (pow x 2))) (* 2 (/ 1 (pow x 6)))))))
(* 1/2 (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(* -1 (* (pow x 3) (+ 1/3 (/ (pow (sqrt -1) 2) (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/60 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 1/2520)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/3 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2520 (* 1/60 (/ 1 (pow x 2)))))))

Calls

3 calls:

Time

Variable

Point

Expression

8.0ms

-inf

((+ (* (sqrt x) (sqrt x)) (* (neg (neg (* x x))) (* -1/3 x))) (* (neg (neg (* x x))) (* -1/3 x)) (neg (neg (* x x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (sinh x) 2) (* (+ (* (+ (* (+ (* 1/2520 (* x x)) 1/60) (* x x)) 1/3) (* x x)) 2) x) (* -1/3 x) (sinh (* 2 x)))

4.0ms

inf

((+ (* (sqrt x) (sqrt x)) (* (neg (neg (* x x))) (* -1/3 x))) (* (neg (neg (* x x))) (* -1/3 x)) (neg (neg (* x x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (sinh x) 2) (* (+ (* (+ (* (+ (* 1/2520 (* x x)) 1/60) (* x x)) 1/3) (* x x)) 2) x) (* -1/3 x) (sinh (* 2 x)))

2.0ms

((+ (* (sqrt x) (sqrt x)) (* (neg (neg (* x x))) (* -1/3 x))) (* (neg (neg (* x x))) (* -1/3 x)) (neg (neg (* x x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (/ (* (sinh x) 2) (sinh (* 2 x))) (sinh x)) (/ (* (sinh x) 2) (sinh (* 2 x))) (* (sinh x) 2) (* (+ (* (+ (* (+ (* 1/2520 (* x x)) 1/60) (* x x)) 1/3) (* x x)) 2) x) (* -1/3 x) (sinh (* 2 x)))

simplify131.0ms (1.5%)

Memory

31.8MiB live, 175.0MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	398
1	482	386
2	1502	383
3	6194	383
0	8606	363

Stop Event

1×	iter limit
1×	node limit

Counts

32 → 31

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* -1/3 (pow x 3))
(pow x 2)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(* 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))))))))
(* -1/3 x)
(* x (+ 2 (* 4/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (pow x 2))))))))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(- (exp x) (/ 1 (exp x)))
(* 1/2520 (pow x 7))
(* (pow x 7) (+ 1/2520 (* 1/60 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 1/2520 (+ (/ 1/3 (pow x 4)) (* 1/60 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 1/2520 (+ (/ 1/3 (pow x 4)) (+ (* 1/60 (/ 1 (pow x 2))) (* 2 (/ 1 (pow x 6)))))))
(* 1/2 (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(* -1 (* (pow x 3) (+ 1/3 (/ (pow (sqrt -1) 2) (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/60 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 1/2520)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/3 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2520 (* 1/60 (/ 1 (pow x 2)))))))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(pow x 2)
(*.f64 x x)
(* 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
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 5/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/24 (* -61/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -61/720 binary64) (-.f64 (.f64 #s(literal 5/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(* 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)
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(* x (+ 2 (* 4/3 (pow x 2))))
(.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 4/3 (* 4/15 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 4/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 4/15 (* 8/315 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(* (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)))
(/ (pow (- (exp x) (/ 1 (exp x))) 2) (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(/.f64 (pow.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64))))
(* 2 (/ (- (exp x) (/ 1 (exp x))) (- (exp (* 2 x)) (/ 1 (exp (* 2 x))))))
(*.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))) #s(literal 2 binary64))
(- (exp x) (/ 1 (exp x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(* 1/2520 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/2520 binary64))
(* (pow x 7) (+ 1/2520 (* 1/60 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/60 binary64) (.f64 x x)) #s(literal 1/2520 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 1/2520 (+ (/ 1/3 (pow x 4)) (* 1/60 (/ 1 (pow x 2))))))
(.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal -1/60 binary64) (.f64 x x)) #s(literal 1/2520 binary64))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 1/2520 (+ (/ 1/3 (pow x 4)) (+ (* 1/60 (/ 1 (pow x 2))) (* 2 (/ 1 (pow x 6)))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal -1/60 binary64) (.f64 x x)) #s(literal 1/2520 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 7 binary64)))
(* 1/2 (- (exp (* 2 x)) (/ 1 (exp (* 2 x)))))
(*.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 1/2 binary64))
(* -1 (* (pow x 3) (+ 1/3 (/ (pow (sqrt -1) 2) (pow x 2)))))
(.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 (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/60 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 1/2520)))
(.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -1/60 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) x) x) #s(literal 1/2520 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/3 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2520 (* 1/60 (/ 1 (pow x 2)))))))
(.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (-.f64 (/.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/60 binary64) (*.f64 x x)) #s(literal 1/2520 binary64))))

rewrite129.0ms (1.5%)

Memory

2.7MiB live, 101.5MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	220
0	65	195
1	263	189
0	1962	187

Stop Event

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

Counts

10 → 118

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)))
(.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))
(neg.f64 (neg.f64 (*.f64 x x)))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))))
(.f64 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(/.f64 #s(approx (* (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)))
#s(approx (* (sinh 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))
(.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)
(*.f64 #s(literal -1/3 binary64) x)
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))

Outputs
(.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)) (.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 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64))) (fma.f64 x x (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)) (.f64 x (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))))
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(/.f64 (.f64 x (+.f64 #s(literal 8 binary64) (pow.f64 (.f64 (.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)) x) x) #s(literal 3 binary64)))) (+.f64 (-.f64 #s(literal 4 binary64) (.f64 (.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)) x) (.f64 #s(literal 2 binary64) x))) (pow.f64 (.f64 (.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)) x) x) #s(literal 2 binary64))))
(fma.f64 (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)) (.f64 (.f64 (.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)) x) x) x))
(fma.f64 (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)) (.f64 x (.f64 (.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)) x) x)))
(fma.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (.f64 (.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)) x) x) x))
(fma.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x) (.f64 x (.f64 (.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)) x) x)))
(fma.f64 (neg.f64 (sqrt.f64 x)) (.f64 (neg.f64 (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (.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)) x) x) x))
(fma.f64 (neg.f64 (sqrt.f64 x)) (.f64 (neg.f64 (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 x (.f64 (.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)) x) x)))
(fma.f64 (neg.f64 (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (.f64 (.f64 (.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)) x) x) x))
(fma.f64 (neg.f64 (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (.f64 x (.f64 (.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)) x) x)))
(fma.f64 (.f64 (.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)) x) x) x (*.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 2 binary64) x (.f64 (.f64 (.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)) x) x) x))
(fma.f64 #s(literal 2 binary64) x (.f64 x (.f64 (.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)) x) x)))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (.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)) x) x) x))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (.f64 x (.f64 (.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)) x) x)))
(fma.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (.f64 (.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)) x) x) x))
(fma.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 x (.f64 (.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)) x) x)))
(fma.f64 x (.f64 (.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)) x) x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 2 binary64) (.f64 (.f64 (.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)) x) x) x))
(fma.f64 x #s(literal 2 binary64) (.f64 x (.f64 (.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)) x) x)))
(+.f64 (.f64 (.f64 (.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)) x) x) x) (.f64 #s(literal 2 binary64) x))
(+.f64 (.f64 x (.f64 (.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)) x) x)) (.f64 #s(literal 2 binary64) x))
(+.f64 (.f64 #s(literal 2 binary64) x) (.f64 (.f64 (.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)) x) x) x))
(+.f64 (.f64 #s(literal 2 binary64) x) (.f64 x (.f64 (.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)) x) x)))
(.f64 (.f64 #s(literal -1/3 binary64) (neg.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(.f64 (.f64 #s(literal -1/3 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (neg.f64 (sqrt.f64 x)) (.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/3 binary64)))
(*.f64 #s(literal -1/3 binary64) x)
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal -1/3 binary64)))
(*.f64 x #s(literal -1/3 binary64))
#s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))

eval19.0ms (0.2%)

Memory: -10.4MiB live, 36.0MiB allocated; 2ms collecting garbage
Compiler: Compiled 5 932 to 637 computations (89.3% saved)

prune9.0ms (0.1%)

Memory

-29.9MiB live, 17.2MiB allocated; 2ms collecting garbage

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	143	7	150

Accuracy

100.0%

Counts

150 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.0%	(.f64 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
✓	100.0%	(tanh.f64 x)
	97.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) (sqrt.f64 x)) (sqrt.f64 x) x))
✓	97.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x))
	96.5%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (.f64 #s(literal -1/3 binary64) x))))
	96.5%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (.f64 (.f64 #s(literal -1/3 binary64) (sqrt.f64 x)) (sqrt.f64 x)))))
	97.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x))

Compiler

Compiled 472 to 180 computations (61.9% saved)

regimes6.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) (sqrt.f64 x)) (sqrt.f64 x) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (*.f64 #s(literal -1/3 binary64) x))))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (.f64 #s(literal -1/3 binary64) x))))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (.f64 (.f64 #s(literal -1/3 binary64) (sqrt.f64 x)) (sqrt.f64 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 (/.f64 #s(approx ( (sinh 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)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(approx (sinh (* 2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 8/315 binary64) (.f64 x x) #s(literal 4/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x))) (sinh.f64 x))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (sinh.f64 x))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(tanh.f64 x)

Calls

2 calls:

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

Results

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes4.0ms (0%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	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
97.2%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
97.2%	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes2.0ms (0%)

Memory

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

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
97.2%	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify58.0ms (0.7%)

Memory

-9.5MiB live, 36.9MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	46
1	31	46
2	69	46
3	261	46
4	1657	38

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

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

Outputs

(tanh.f64 x)

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

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

derivations584.0ms (6.8%)

Memory

-15.2MiB live, 324.0MiB allocated; 62ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	142
0	42	131
1	177	129
2	1277	128
0	8381	126
0	40	220
0	65	195
1	263	189
0	1962	187
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
0	20	62
0	30	51
1	117	49
0	799	49

Stop Event

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

Compiler

Compiled 46 to 17 computations (63% saved)

preprocess22.0ms (0.3%)

Memory: 36.3MiB live, 36.3MiB allocated; 0ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 122 to 52 computations (57.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample4.3s (50.2%)

explain240.0ms (2.8%)

preprocess134.0ms (1.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify119.0ms (1.4%)

localize139.0ms (1.6%)

series3.0ms (0%)

simplify203.0ms (2.4%)

rewrite306.0ms (3.6%)

eval144.0ms (1.7%)

prune44.0ms (0.5%)

simplify123.0ms (1.4%)

localize137.0ms (1.6%)

series15.0ms (0.2%)

simplify161.0ms (1.9%)

rewrite119.0ms (1.4%)

eval29.0ms (0.3%)

prune4.0ms (0%)

simplify180.0ms (2.1%)

localize205.0ms (2.4%)

series14.0ms (0.2%)

simplify144.0ms (1.7%)

rewrite239.0ms (2.8%)

eval57.0ms (0.7%)

prune12.0ms (0.1%)

simplify189.0ms (2.2%)

localize322.0ms (3.8%)

series14.0ms (0.2%)

simplify131.0ms (1.5%)

rewrite129.0ms (1.5%)

eval19.0ms (0.2%)

prune9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0%)

regimes2.0ms (0%)

simplify58.0ms (0.7%)

derivations584.0ms (6.8%)

preprocess22.0ms (0.3%)

end0.0ms (0%)

Profiling