Metrics for Hyperbolic tangent

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 9 computations (40% saved)

sample4.4s (53.7%)

Memory

35.3MiB live, 4 193.9MiB allocated

Samples

1.6s	2 865×	2	valid
1.1s	4 831×	1	valid
728.0ms	8 043×	0	exit
72.0ms	560×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.7s

ival-exp: 1.7s (63.5% of total)

adjust: 251.0ms (9.5% of total)

ival-div: 245.0ms (9.2% of total)

ival-sub: 221.0ms (8.3% of total)

ival-add: 148.0ms (5.6% of total)

ival-neg: 87.0ms (3.3% of total)

ival-true: 12.0ms (0.5% of total)

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

Bogosity

explain311.0ms (3.8%)

Memory

-15.3MiB live, 344.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
243	-	1	(-0.006142050636774682)	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
9	-	0	-	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0	-	0	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	-	0	-	`(exp.f64 x)`
0	-	0	-	`(exp.f64 (neg.f64 x))`
0	-	0	-	`(neg.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	cancellation	242	2
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	9	0
↳	`(exp.f64 x)`	overflow	3
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	9
↳	`(exp.f64 (neg.f64 x))`	overflow	6
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	9
↳	`(exp.f64 x)`	overflow	3
↳	`(exp.f64 (neg.f64 x))`	overflow	6

Confusion

	Predicted +	Predicted -
+	251	1
-	0	4

Precision

1.0

Recall

0.996031746031746

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	251	1	0
-	0	2	2

Precision?

0.9921259842519685

Recall?

1.0

Freqs

test

number	freq
0	5
1	251

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

93.0ms	162×	2	valid
65.0ms	310×	1	valid
29.0ms	40×	0	valid

Compiler

Compiled 116 to 32 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 159.0ms

ival-exp: 127.0ms (79.9% of total)

adjust: 11.0ms (6.9% of total)

ival-div: 7.0ms (4.4% of total)

ival-add: 5.0ms (3.1% of total)

ival-sub: 5.0ms (3.1% of total)

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

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

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

preprocess85.0ms (1%)

Memory

27.1MiB live, 72.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	32	27
2	80	26
3	201	26
4	473	26
5	1139	26
6	1555	26
7	1593	26
8	1612	26
9	1631	26
10	1665	26
11	1679	26
0	7	13
0	13	13
1	25	13
2	42	13
3	67	13
4	122	13
5	277	13
6	467	13
7	712	13
8	956	13
9	1123	13
10	1251	13
11	1298	13
0	1298	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

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 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))

Symmetry

(negabs x)

Compiler

Compiled 13 to 7 computations (46.2% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.7%	(/.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)

simplify69.0ms (0.8%)

Memory

-15.5MiB live, 22.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	13	33
1	25	33
2	42	33
3	67	33
4	122	33
5	277	33
6	467	33
7	712	33
8	956	33
9	1123	33
10	1251	33
11	1298	33
0	1298	33

Stop Event

1×	iter limit
1×	saturated
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 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.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)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))

localize85.0ms (1%)

Memory

15.0MiB live, 53.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 (neg.f64 x))
accuracy	0.0	(exp.f64 x)
accuracy	2.1875247594574265	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	56.172674898239315	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

45.0ms	81×	2	valid
30.0ms	155×	1	valid
1.0ms	20×	0	valid

Compiler

Compiled 68 to 16 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-exp: 36.0ms (55% of total)

adjust: 20.0ms (30.5% of total)

ival-div: 3.0ms (4.6% of total)

ival-add: 3.0ms (4.6% of total)

ival-sub: 3.0ms (4.6% of total)

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

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

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

series3.0ms (0%)

Memory

3.4MiB live, 3.4MiB allocated

Counts

4 → 22

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)
(exp.f64 (neg.f64 x))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(* 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
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(- (exp x) (exp (neg x)))
(exp x)
(exp (neg x))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(- (exp x) (exp (* -1 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)))
1.0ms	x	@	inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (- (exp x) (exp (neg x))) (exp x) (exp (neg 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)))

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)))

1.0ms

inf

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

1.0ms

-inf

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

simplify210.0ms (2.5%)

Memory

-17.7MiB live, 132.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	192
1	220	191
2	490	185
3	1293	185
4	2173	185
5	3652	185
6	4341	185
7	5814	185
8	7937	185
0	8237	163

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 21

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

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

rewrite303.0ms (3.7%)

Memory

-12.4MiB live, 162.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
0	13	11
1	55	11
2	424	11
3	7120	11
0	8102	11

Stop Event

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

Counts

4 → 499

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)
(exp.f64 (neg.f64 x))

Outputs
(tanh.f64 x)
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (tanh.f64 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)))) (-.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (tanh.f64 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 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))) (pow.f64 (exp.f64 x) #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (sinh.f64 x))) (sinh.f64 x))
(.f64 (/.f64 (.f64 (sinh.f64 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 (sinh.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 #s(literal -2 binary64) (sinh.f64 x)) (.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 1/2 binary64) (cosh.f64 x)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.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 #s(literal 1/2 binary64) (cosh.f64 x)) #s(literal 2 binary64)) (sinh.f64 x))
(*.f64 (pow.f64 (pow.f64 (tanh.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (tanh.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (neg.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))))) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(.f64 (/.f64 (.f64 #s(literal -2 binary64) (sinh.f64 x)) (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x)))) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 3 binary64) x))))) (pow.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (.f64 (cosh.f64 x) #s(literal 2 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 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 3 binary64) x))))) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 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 (cosh.f64 x) #s(literal 2 binary64))))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))))
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(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (expm1.f64 (.f64 #s(literal -2 binary64) x)) (.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (expm1.f64 (.f64 #s(literal -2 binary64) x))))
(fma.f64 (/.f64 (exp.f64 x) (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (exp.f64 x) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(fma.f64 (/.f64 (exp.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (/.f64 (exp.f64 x) (pow.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) #s(literal -1 binary64))) (neg.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(fma.f64 (.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 (exp.f64 x) (cosh.f64 x)) (neg.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(fma.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) (exp.f64 (neg.f64 x)) (exp.f64 x))
(fma.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1 binary64) (exp.f64 x))
(fma.f64 (expm1.f64 (.f64 #s(literal -2 binary64) x)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x))))))
(fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 x) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (.f64 (expm1.f64 (.f64 #s(literal -2 binary64) x)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x))))))
(fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(fma.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)) (exp.f64 x))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(fma.f64 (exp.f64 (neg.f64 x)) #s(literal -1 binary64) (exp.f64 x))
(fma.f64 (exp.f64 x) (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (exp.f64 x)) (neg.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1 binary64)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(-.f64 (+.f64 (exp.f64 x) #s(literal 0 binary64)) (exp.f64 (neg.f64 x)))
(-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x))) (.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (.f64 (expm1.f64 (.f64 #s(literal -2 binary64) x)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x))))) (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 3 binary64) x))))))
(+.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x))))) (.f64 (expm1.f64 (.f64 #s(literal -2 binary64) x)) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 3 binary64) x))))))
(+.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (expm1.f64 (.f64 #s(literal -2 binary64) x))) (.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 3 binary64) x)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (expm1.f64 (*.f64 #s(literal -2 binary64) x))))
(+.f64 (neg.f64 (neg.f64 (exp.f64 x))) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1 binary64)) (exp.f64 x))
(+.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x))) (neg.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))))
(+.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (neg.f64 (exp.f64 x)) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(/.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 x #s(literal 2 binary64))))
(*.f64 (pow.f64 (exp.f64 x) #s(literal -1/2 binary64)) (pow.f64 (exp.f64 x) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(*.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(*.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) x)
(pow.f64 (exp.f64 x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 x))))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(neg.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) x))
(exp.f64 (neg.f64 x))

eval204.0ms (2.5%)

Memory: 13.5MiB live, 94.0MiB allocated
Compiler: Compiled 12 676 to 1 365 computations (89.2% saved)

prune23.0ms (0.3%)

Memory

-11.9MiB live, 26.1MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	543	3	546
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	544	3	547

Accuracy

100.0%

Counts

547 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.5%	(/.f64 (sinh.f64 x) (cosh.f64 x))
▶	100.0%	(tanh.f64 x)
▶	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify233.0ms (2.8%)

Memory

2.3MiB live, 79.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(cosh.f64 x)
cost-diff	0	(sinh.f64 x)
cost-diff	7104	(/.f64 (sinh.f64 x) (cosh.f64 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: 0 (0.0ms)

Iter	Nodes	Cost
0	16	45
0	23	31
1	54	31
2	103	31
3	168	31
4	326	31
5	751	31
6	2226	31
7	4775	31
0	8281	31

Stop Event

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

Calls

Call 1

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

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

localize208.0ms (2.5%)

Memory

0.5MiB live, 122.6MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(cosh.f64 x)
accuracy	0.0078125	(sinh.f64 x)
accuracy	2.1875247594574265	(/.f64 (sinh.f64 x) (cosh.f64 x))
accuracy	0.0078125	(tanh.f64 x)
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.01171875	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	2.8428978868214614	#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

103.0ms	81×	2	valid
90.0ms	155×	1	valid
3.0ms	20×	0	valid

Compiler

Compiled 86 to 34 computations (60.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 181.0ms

ival-exp: 67.0ms (36.9% of total)

ival-mult: 43.0ms (23.7% of total)

ival-pow: 39.0ms (21.5% of total)

adjust: 11.0ms (6.1% of total)

ival-div: 5.0ms (2.8% of total)

const: 4.0ms (2.2% of total)

ival-add: 4.0ms (2.2% of total)

ival-sub: 3.0ms (1.7% of total)

ival-cosh: 2.0ms (1.1% of total)

ival-tanh: 1.0ms (0.6% of total)

ival-sinh: 1.0ms (0.6% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

17.4MiB live, 17.4MiB allocated

Counts

7 → 20

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	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) (cosh x)) (sinh x) (cosh x))
4.0ms	x	@	inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (sinh x) (cosh x)) (sinh x) (cosh x))
2.0ms	x	@	0	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (sinh x) (cosh x)) (sinh x) (cosh x))

Time

Variable

Point

Expression

5.0ms

-inf

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

4.0ms

inf

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

2.0ms

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

simplify138.0ms (1.7%)

Memory

4.1MiB live, 87.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	212
1	234	196
2	589	196
3	1670	196
4	3235	196
5	6169	196
0	8102	176

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

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

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

rewrite268.0ms (3.2%)

Memory

-46.9MiB live, 164.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
0	23	26
1	103	26
2	713	26
0	8981	26

Stop Event

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

Counts

7 → 834

Calls

Call 1

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

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
(.f64 (fma.f64 x x (.f64 #s(literal -1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 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 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))))
(.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (neg.f64 x) x)) (pow.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))) (.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) (pow.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal -1 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal -1 binary64))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))
(/.f64 (.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))) (.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))) (+.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (fma.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))))
(/.f64 (neg.f64 (fma.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 (neg.f64 x) x)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 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)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (.f64 (fma.f64 #s(literal -1/19683 binary64) (pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal -1/27 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64))))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) (.f64 x x))) (*.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))
(/.f64 (fma.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 (neg.f64 x) x))) (neg.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 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 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x (.f64 #s(literal -1/9 binary64) (pow.f64 x #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (neg.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(neg.f64 (/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))))
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)) x)
(fma.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
(fma.f64 (.f64 #s(literal -1/3 binary64) x) (.f64 x x) x)
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/3 binary64))) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/3 binary64)) x)
(fma.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) 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 x (.f64 (.f64 x x) #s(literal -1/3 binary64)) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (.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 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))
(+.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(+.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)
(+.f64 x (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
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(.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 4 binary64) (cosh.f64 x))))
(*.f64 #s(literal -1 binary64) (neg.f64 (sinh.f64 x)))
(.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal -3 binary64))) (.f64 (pow.f64 (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (sinh.f64 x)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (sinh.f64 x))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 (sinh.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (sinh.f64 x) #s(literal 1/2 binary64)))
(*.f64 (cosh.f64 x) (tanh.f64 x))
(*.f64 (sinh.f64 x) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (sinh.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (exp.f64 x) #s(literal 1/2 binary64)) (.f64 (exp.f64 x) #s(literal 1/2 binary64))) (.f64 (.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64)) (.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64)))) (fma.f64 (exp.f64 x) #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (exp.f64 x) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (exp.f64 x) #s(literal 1/2 binary64)) (.f64 (exp.f64 x) #s(literal 1/2 binary64)) (fma.f64 (.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64)) (.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64)) (.f64 (.f64 (exp.f64 x) #s(literal 1/2 binary64)) (*.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (exp.f64 (neg.f64 x)))) #s(literal 4 binary64))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))) (neg.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal -3 binary64)))) (neg.f64 (fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (*.f64 #s(literal 4 binary64) (cosh.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sinh.f64 x) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal -3 binary64))) (fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 2 binary64) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) (sinh.f64 x)) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 2 binary64) #s(literal 2 binary64)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal -3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sinh.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sinh.f64 x) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))
(sinh.f64 x)
(neg.f64 (neg.f64 (sinh.f64 x)))
(fma.f64 (exp.f64 x) #s(literal 1/2 binary64) (neg.f64 (*.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (cosh.f64 x))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (.f64 #s(literal 4 binary64) (cosh.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x))) #s(literal 2 binary64)) (/.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x))) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))) #s(literal 2 binary64)))
(-.f64 (.f64 (exp.f64 x) #s(literal 1/2 binary64)) (.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sinh.f64 x)))
(+.f64 (.f64 (exp.f64 x) #s(literal 1/2 binary64)) (neg.f64 (.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64))))
(.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (cosh.f64 x)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x)))))
(.f64 (/.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal -3 binary64)))) (.f64 (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (sinh.f64 x))) #s(literal 1/2 binary64)))
(.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 4 binary64) (sinh.f64 x))))
(*.f64 #s(literal -1 binary64) (neg.f64 (cosh.f64 x)))
(.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))))))
(.f64 (.f64 #s(literal -2 binary64) (cosh.f64 x)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (cosh.f64 x))
(.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 1/2 binary64)))
(.f64 (cosh.f64 x) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) (*.f64 #s(literal 2 binary64) (sinh.f64 x))))
(*.f64 (cosh.f64 x) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (cosh.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (neg.f64 (.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x))))))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))) (neg.f64 (*.f64 #s(literal 4 binary64) (sinh.f64 x))))
(/.f64 (.f64 (.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (*.f64 #s(literal 4 binary64) (sinh.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cosh.f64 x)))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x)))))
(/.f64 (neg.f64 (cosh.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 4 binary64) (sinh.f64 x)) (.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (.f64 #s(literal -2 binary64) x)))) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (cosh.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (cosh.f64 x) #s(literal -1 binary64)))
(/.f64 (cosh.f64 x) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
(neg.f64 (neg.f64 (cosh.f64 x)))
(cosh.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (sinh.f64 x))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (.f64 #s(literal 4 binary64) (sinh.f64 x))))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (cosh.f64 x)))

eval97.0ms (1.2%)

Memory: 24.2MiB live, 98.0MiB allocated
Compiler: Compiled 12 034 to 1 363 computations (88.7% saved)

prune30.0ms (0.4%)

Memory

-16.4MiB live, 28.0MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	501	4	505
Fresh	0	0	0
Picked	2	1	3
Done	0	0	0
Total	503	5	508

Accuracy

100.0%

Counts

508 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.2%	(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
✓	100.0%	(tanh.f64 x)
▶	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
▶	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
▶	95.6%	#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 90 to 51 computations (43.3% saved)

simplify178.0ms (2.2%)

Memory

20.2MiB live, 132.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(sinh.f64 x)
cost-diff	0	(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
cost-diff	-5824	(.f64 (.f64 x x) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
cost-diff	-5824	(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
cost-diff	0	(*.f64 #s(literal -1/3 binary64) x)
cost-diff	0	(.f64 (.f64 #s(literal -1/3 binary64) x) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
cost-diff	-5824	(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) 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))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	202
0	49	202
1	91	188
2	141	188
3	290	188
4	626	188
5	1179	188
6	1786	188
7	2622	188
8	4013	188
9	6036	188
0	8387	188

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)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
(.f64 (.f64 #s(literal -1/3 binary64) x) x)
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
x
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(.f64 (.f64 x x) x)
(*.f64 x x)
x
#s(literal -1/3 binary64)
(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sinh.f64 x)
x
#s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/720 binary64)
(*.f64 x x)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(literal 1 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)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.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)
(.f64 (.f64 #s(literal -1/3 binary64) x) x)
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
x
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(.f64 (.f64 x x) x)
(pow.f64 x #s(literal 3 binary64))
(*.f64 x x)
x
#s(literal -1/3 binary64)
(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sinh.f64 x)
x
#s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/720 binary64)
(*.f64 x x)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

localize298.0ms (3.6%)

Memory

11.8MiB live, 292.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
accuracy	0.01953125	(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	2.1875247594574265	(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
accuracy	2.398580227706275	#s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	0.01171875	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
accuracy	0.1171875	(.f64 (.f64 x x) x)
accuracy	2.8428978868214614	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
accuracy	0.00390625	(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
accuracy	0.125	(.f64 (.f64 #s(literal -1/3 binary64) x) x)
accuracy	0.3046875	(*.f64 #s(literal -1/3 binary64) x)
accuracy	2.8428978868214614	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
accuracy	0.0	(*.f64 x x)
accuracy	0.01953125	(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)
accuracy	0.3046875	(*.f64 x #s(literal -1/3 binary64))
accuracy	2.8428978868214614	#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

141.0ms	81×	2	valid
130.0ms	155×	1	valid
5.0ms	20×	0	valid

Compiler

Compiled 354 to 64 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 208.0ms

ival-exp: 78.0ms (37.6% of total)

ival-mult: 56.0ms (27% of total)

const: 28.0ms (13.5% of total)

adjust: 19.0ms (9.1% of total)

ival-add: 12.0ms (5.8% of total)

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

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

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

ival-sinh: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

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

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

exact: 0.0ms (0% of total)

series37.0ms (0.5%)

Memory

-25.3MiB live, 12.9MiB allocated

Counts

16 → 31

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))
(*.f64 x x)
(*.f64 x #s(literal -1/3 binary64))
(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) x) x) x x))
(.f64 (.f64 #s(literal -1/3 binary64) x) x)
(*.f64 #s(literal -1/3 binary64) x)
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(.f64 (.f64 x x) x)
(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sinh.f64 x)
#s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 2)
(* -1/3 x)
(* -1/3 (pow x 2))
(pow x 3)
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
1/24
(+ 1/24 (* 1/720 (pow x 2)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/720 (pow x 6))
(* (pow x 6) (+ 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/720 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/720 (+ (/ 1/2 (pow x 4)) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/720 (pow x 2))
(* (pow x 2) (+ 1/720 (* 1/24 (/ 1 (pow x 2)))))
(/ (- (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

32.0ms

inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (* -1/3 x) x) (* -1/3 x) (+ (* (* (* -1/3 x) x) x) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* (* x x) x) -1/3) x) (* (* x x) x) (/ (sinh x) (cosh x)) (sinh x) (cosh x) (+ (* (+ (* (+ (* 1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (+ (* 1/720 (* x x)) 1/24))

3.0ms

-inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (* -1/3 x) x) (* -1/3 x) (+ (* (* (* -1/3 x) x) x) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* (* x x) x) -1/3) x) (* (* x x) x) (/ (sinh x) (cosh x)) (sinh x) (cosh x) (+ (* (+ (* (+ (* 1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (+ (* 1/720 (* x x)) 1/24))

2.0ms

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (* -1/3 x) x) (* -1/3 x) (+ (* (* (* -1/3 x) x) x) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* (* x x) x) -1/3) x) (* (* x x) x) (/ (sinh x) (cosh x)) (sinh x) (cosh x) (+ (* (+ (* (+ (* 1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (+ (* 1/720 (* x x)) 1/24))

simplify123.0ms (1.5%)

Memory

14.7MiB live, 102.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	299
1	292	283
2	726	279
3	1996	279
4	5442	279
0	8404	253

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 30

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

rewrite265.0ms (3.2%)

Memory

-6.6MiB live, 187.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	174
0	49	127
1	203	127
2	1213	127
0	8335	127

Stop Event

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

Counts

16 → 343

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))
(*.f64 x x)
(*.f64 x #s(literal -1/3 binary64))
(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) x) x) x x))
(.f64 (.f64 #s(literal -1/3 binary64) x) x)
(*.f64 #s(literal -1/3 binary64) x)
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(.f64 (.f64 x x) x)
(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sinh.f64 x)
#s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))

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))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal -1/3 binary64) x)
(*.f64 x #s(literal -1/3 binary64))
(.f64 (fma.f64 x x (.f64 #s(literal -1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 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)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))))
(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
(.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (neg.f64 x) x)) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(.f64 x (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)) #s(literal -1 binary64))
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(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x))) (/.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))))
(-.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal -1 binary64))) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (.f64 x x)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal 1/17280 binary64)))))))
(.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (pow.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64))))))
(.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (pow.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal 1/17280 binary64)))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))))) (+.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (fma.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/17280 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (neg.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/17280 binary64))))))
(/.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/17280 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (.f64 x x))) (-.f64 #s(literal 1/576 binary64) (*.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))) (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 (*.f64 #s(literal 1/720 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal 1/720 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))))
(+.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)))))
(+.f64 (.f64 #s(literal 1/720 binary64) (.f64 x x)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (.f64 x x)))

eval72.0ms (0.9%)

Memory: 3.3MiB live, 89.2MiB allocated
Compiler: Compiled 9 777 to 1 150 computations (88.2% saved)

prune14.0ms (0.2%)

Memory

-2.7MiB live, 36.1MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	294	5	299

Accuracy

100.0%

Counts

299 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	96.2%	(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
✓	100.0%	(tanh.f64 x)
✓	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
✓	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
✓	95.6%	#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 218 to 94 computations (56.9% saved)

regimes5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

8 → 1

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))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(tanh.f64 x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(/.f64 (sinh.f64 x) #s(approx (cosh x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (sinh.f64 x) (cosh.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	`x`
100.0%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes11.0ms (0.1%)

Memory

-31.9MiB live, 7.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

3 → 1

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))

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

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

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:

9.0ms	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
95.6%	1	`x`
95.6%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify61.0ms (0.7%)

Memory

27.7MiB live, 66.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	25	24
2	42	24
3	70	24
4	146	24
5	394	24
6	1667	24
7	5197	24

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))

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))

soundness461.0ms (5.6%)

Memory

-12.0MiB live, 345.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
0	23	26
1	103	26
2	713	26
0	8981	26
0	7	24
0	13	11
1	55	11
2	424	11
3	7120	11
0	8102	11
0	77	192
1	220	191
2	490	185
3	1293	185
4	2173	185
5	3652	185
6	4341	185
7	5814	185
8	7937	185
0	8237	163

Stop Event

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

Compiler

Compiled 65 to 38 computations (41.5% saved)

preprocess22.0ms (0.3%)

Memory: -3.1MiB live, 34.7MiB allocated
Remove: (negabs x)
Compiler: Compiled 78 to 44 computations (43.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample4.4s (53.7%)

explain311.0ms (3.8%)

preprocess85.0ms (1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify69.0ms (0.8%)

localize85.0ms (1%)

series3.0ms (0%)

simplify210.0ms (2.5%)

rewrite303.0ms (3.7%)

eval204.0ms (2.5%)

prune23.0ms (0.3%)

simplify233.0ms (2.8%)

localize208.0ms (2.5%)

series10.0ms (0.1%)

simplify138.0ms (1.7%)

rewrite268.0ms (3.2%)

eval97.0ms (1.2%)

prune30.0ms (0.4%)

simplify178.0ms (2.2%)

localize298.0ms (3.6%)

series37.0ms (0.5%)

simplify123.0ms (1.5%)

rewrite265.0ms (3.2%)

eval72.0ms (0.9%)

prune14.0ms (0.2%)

regimes5.0ms (0.1%)

regimes11.0ms (0.1%)

simplify61.0ms (0.7%)

soundness461.0ms (5.6%)

preprocess22.0ms (0.3%)

end0.0ms (0%)

Profiling