Metrics for Hyperbolic tangent

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample5.0s (51.8%)

Memory

55.7MiB live, 4 278.8MiB allocated

Samples

1.6s	2 892×	2	valid
1.4s	4 807×	1	valid
1.0s	8 018×	0	exit
37.0ms	557×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.1s

ival-exp: 1.9s (60.7% of total)

adjust: 556.0ms (17.8% of total)

ival-div: 267.0ms (8.6% of total)

ival-sub: 167.0ms (5.4% of total)

ival-add: 140.0ms (4.5% of total)

ival-neg: 76.0ms (2.4% of total)

ival-true: 13.0ms (0.4% of total)

ival-assert: 8.0ms (0.3% of total)

Bogosity

explain510.0ms (5.2%)

Memory

-3.3MiB live, 208.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
250	0	-	-	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
4	0	-	-	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0	0	-	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	0	-	-	`(exp.f64 x)`
0	1	(446.76280088781346)	-	`(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	250	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	4	0
↳	`(exp.f64 x)`	overflow	3
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	4
↳	`(exp.f64 (neg.f64 x))`	overflow	1
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	4
↳	`(exp.f64 x)`	overflow	3
↳	`(exp.f64 (neg.f64 x))`	overflow	1
`exp.f64`	`(exp.f64 (neg.f64 x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	254	0
-	1	1

Precision

0.996078431372549

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	0	0
-	1	0	1

Precision?

0.996078431372549

Recall?

1.0

Freqs

test

number	freq
0	1
1	255

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

216.0ms	184×	2	valid
143.0ms	306×	1	valid
1.0ms	22×	0	valid

Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 249.0ms

ival-exp: 215.0ms (86.5% of total)

adjust: 12.0ms (4.8% of total)

ival-div: 7.0ms (2.8% of total)

ival-add: 6.0ms (2.4% of total)

ival-sub: 6.0ms (2.4% of total)

ival-neg: 2.0ms (0.8% of total)

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

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

preprocess181.0ms (1.9%)

Memory

-7.8MiB live, 69.9MiB 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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.8%	(/.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)

simplify35.0ms (0.4%)

Memory

33.7MiB live, 33.7MiB 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))

localize91.0ms (0.9%)

Memory

-22.0MiB live, 94.3MiB 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	0.9687610042033008	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	58.016010622864734	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

50.0ms	92×	2	valid
32.0ms	153×	1	valid
1.0ms	11×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-exp: 36.0ms (67% of total)

adjust: 6.0ms (11.2% of total)

ival-div: 5.0ms (9.3% of total)

ival-add: 3.0ms (5.6% of total)

ival-sub: 3.0ms (5.6% of total)

ival-neg: 1.0ms (1.9% of total)

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

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

series3.0ms (0%)

Memory

4.5MiB live, 4.5MiB 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)))

simplify265.0ms (2.7%)

Memory

15.6MiB live, 171.7MiB 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))

rewrite219.0ms (2.3%)

Memory

-42.9MiB live, 148.7MiB 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))

eval98.0ms (1%)

Memory: 24.1MiB live, 100.2MiB allocated
Compiler: Compiled 12 676 to 1 365 computations (89.2% saved)

prune37.0ms (0.4%)

Memory

-13.0MiB live, 29.9MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	544	2	546
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	545	2	547

Accuracy

100.0%

Counts

547 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tanh.f64 x)
▶	97.8%	#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 22 to 14 computations (36.4% saved)

simplify151.0ms (1.6%)

Memory

13.2MiB live, 91.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
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	13	35
0	17	24
1	46	24
2	88	24
3	135	24
4	215	24
5	414	24
6	744	24
7	1321	24
8	3234	24
9	6982	24
0	8159	24

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

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

localize170.0ms (1.8%)

Memory

-13.7MiB live, 102.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(tanh.f64 x)
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.00390625	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	1.4150033295381532	#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

80.0ms	92×	2	valid
65.0ms	153×	1	valid
1.0ms	11×	0	valid

Compiler

Compiled 31 to 15 computations (51.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 133.0ms

ival-exp: 65.0ms (48.8% of total)

adjust: 46.0ms (34.5% of total)

ival-div: 4.0ms (3% of total)

const: 4.0ms (3% of total)

ival-add: 4.0ms (3% of total)

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

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

ival-mult: 2.0ms (1.5% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

4 → 11

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)

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x))
2.0ms	x	@	-inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x))
1.0ms	x	@	0	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x))

Time

Variable

Point

Expression

3.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify183.0ms (1.9%)

Memory

-17.1MiB live, 143.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	111
1	122	101
2	269	101
3	792	101
4	2068	101
5	4649	101
0	8228	93

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 10

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)
(/ (- (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))))
(/ (- (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 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #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 5 binary64)) (fma.f64 #s(literal -17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1/3 (pow x 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)))
(/ (- (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)

rewrite227.0ms (2.3%)

Memory

21.4MiB live, 144.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
0	17	20
1	90	20
2	643	20
0	8962	20

Stop Event

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

Counts

4 → 473

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)

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

eval66.0ms (0.7%)

Memory: 8.5MiB live, 83.2MiB allocated
Compiler: Compiled 13 094 to 1 224 computations (90.7% saved)

prune35.0ms (0.4%)

Memory

-16.2MiB live, 20.9MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	479	2	481
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	480	3	483

Accuracy

100.0%

Counts

483 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(tanh.f64 x)

▶

97.8%

#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))

▶

97.8%

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

Compiler

Compiled 46 to 27 computations (41.3% saved)

simplify203.0ms (2.1%)

Memory

18.6MiB live, 135.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	80
0	25	80
1	49	80
2	77	76
3	104	76
4	186	76
5	352	76
6	579	76
7	880	76
8	1309	76
9	2402	76
10	4827	76
11	6307	76
0	8062	72

Stop Event

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

Calls

Call 1

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

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

localize238.0ms (2.4%)

Memory

4.0MiB live, 160.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)
accuracy	0.30859375	(*.f64 x #s(literal -1/3 binary64))
accuracy	1.4150033295381532	#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))
accuracy	0.00390625	(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
accuracy	0.0078125	(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
accuracy	0.30859375	(*.f64 #s(literal -1/3 binary64) x)
accuracy	1.4150033295381532	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))

Samples

137.0ms	153×	1	valid
88.0ms	92×	2	valid
2.0ms	11×	0	valid

Compiler

Compiled 67 to 19 computations (71.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 145.0ms

ival-exp: 84.0ms (57.8% of total)

ival-add: 30.0ms (20.6% of total)

adjust: 10.0ms (6.9% of total)

ival-mult: 9.0ms (6.2% of total)

ival-div: 4.0ms (2.8% of total)

const: 4.0ms (2.8% of total)

ival-sub: 3.0ms (2.1% of total)

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

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

-25.6MiB live, 11.7MiB allocated

Counts

8 → 15

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

7.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify105.0ms (1.1%)

Memory

32.6MiB live, 152.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	121
1	117	111
2	264	111
3	774	111
4	2527	111
5	5795	111
0	8090	101

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 14

Calls

Call 1

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

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

rewrite196.0ms (2%)

Memory

-24.6MiB live, 179.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	75
0	25	53
1	103	53
2	746	49
0	8594	45

Stop Event

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

Counts

8 → 231

Calls

Call 1

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

Outputs
(.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x) (pow.f64 (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) #s(literal -1 binary64)))
(.f64 (-.f64 (.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)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))))
(.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (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 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) #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 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(.f64 (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)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) #s(literal -1 binary64)) x))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 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 (.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)) x)
(*.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 x #s(literal -1/3 binary64)) 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))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x)))
(/.f64 (.f64 x (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)))
(/.f64 (.f64 x (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x)))))
(/.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 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 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)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))) (.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))) (+.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 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 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (fma.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x)) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 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 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 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 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/729 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 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 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/729 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 3 binary64)) #s(literal -1/19683 binary64) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/729 binary64) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) (.f64 x x))) (*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x) (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x))))
(/.f64 (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)))
(/.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/3 binary64) (*.f64 x x)))))
(/.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x))))
(/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 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))) (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)))) (neg.f64 (fma.f64 x x (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))) (-.f64 (.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 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) (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) (/.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)))
(/.f64 #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 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64))))
(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 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 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 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))))
(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)
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eval47.0ms (0.5%)

Memory: -7.1MiB live, 40.4MiB allocated
Compiler: Compiled 5 199 to 603 computations (88.4% saved)

prune3.0ms (0%)

Memory

8.9MiB live, 8.9MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	155	3	158

Accuracy

100.0%

Counts

158 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(tanh.f64 x)

✓

97.8%

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

▶

97.9%

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

Compiler

Compiled 49 to 31 computations (36.7% saved)

simplify160.0ms (1.6%)

Memory

7.4MiB live, 119.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

cost-diff

#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))

cost-diff

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

cost-diff

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	47
0	16	47
1	34	47
2	50	47
3	75	47
4	130	47
5	287	47
6	509	47
7	769	47
8	1056	47
9	1558	47
10	3102	47
11	4730	47
12	6517	47
0	8102	44

Stop Event

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

Calls

Call 1

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

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

localize118.0ms (1.2%)

Memory

2.0MiB live, 158.8MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

accuracy

0.0078125

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

accuracy

1.4150033295381532

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

accuracy

1.5120208100726553

#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))

Samples

50.0ms	92×	2	valid
40.0ms	153×	1	valid
19.0ms	11×	0	valid

Compiler

Compiled 33 to 15 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

ival-exp: 43.0ms (44.1% of total)

const: 26.0ms (26.7% of total)

adjust: 11.0ms (11.3% of total)

ival-mult: 5.0ms (5.1% of total)

ival-div: 4.0ms (4.1% of total)

ival-add: 4.0ms (4.1% of total)

ival-sub: 3.0ms (3.1% of total)

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

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

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

3 → 13

Calls

Call 1

Inputs

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

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

#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))

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

1.0ms

-inf

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

1.0ms

inf

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

0.0ms

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

simplify110.0ms (1.1%)

Memory

-4.0MiB live, 156.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	115
1	115	105
2	266	105
3	791	105
4	2535	105
5	5798	105
0	8097	95

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 12

Calls

Call 1

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

rewrite172.0ms (1.8%)

Memory

-0.4MiB live, 207.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	45
0	16	34
1	76	34
2	567	34
0	8486	31

Stop Event

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

Counts

3 → 4

Calls

Call 1

Inputs

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

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

#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))

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

eval2.0ms (0%)

Memory: 4.0MiB live, 4.0MiB allocated
Compiler: Compiled 320 to 54 computations (83.1% saved)

prune5.0ms (0.1%)

Memory

-29.6MiB live, 7.0MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	12	0	12
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	12	3	15

Accuracy

100.0%

Counts

15 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(tanh.f64 x)

✓

97.8%

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

✓

97.9%

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

Compiler

Compiled 153 to 67 computations (56.2% saved)

regimes5.0ms (0%)

Memory

17.3MiB live, 17.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
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)

regimes3.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Accuracy

Total -0.1b remaining (-10.4%)

Threshold costs -0.1b (-10.4%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	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 (0.6%)

Memory

11.0MiB live, 85.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	33	27
2	49	27
3	77	27
4	153	27
5	400	27
6	1237	27
7	2870	27

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness952.0ms (9.8%)

Memory

-36.3MiB live, 450.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
0	17	20
1	90	20
2	643	20
0	8962	20
0	46	121
1	117	111
2	264	111
3	774	111
4	2527	111
5	5795	111
0	8090	101
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
0	7	24
0	13	11
1	55	11
2	424	11
3	7120	11
0	8102	11

Stop Event

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

Compiler

Compiled 85 to 52 computations (38.8% saved)

preprocess19.0ms (0.2%)

Memory: 32.1MiB live, 32.1MiB allocated
Remove: (negabs x)
Compiler: Compiled 84 to 52 computations (38.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample5.0s (51.8%)

explain510.0ms (5.2%)

preprocess181.0ms (1.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify35.0ms (0.4%)

localize91.0ms (0.9%)

series3.0ms (0%)

simplify265.0ms (2.7%)

rewrite219.0ms (2.3%)

eval98.0ms (1%)

prune37.0ms (0.4%)

simplify151.0ms (1.6%)

localize170.0ms (1.8%)

series6.0ms (0.1%)

simplify183.0ms (1.9%)

rewrite227.0ms (2.3%)

eval66.0ms (0.7%)

prune35.0ms (0.4%)

simplify203.0ms (2.1%)

localize238.0ms (2.4%)

series10.0ms (0.1%)

simplify105.0ms (1.1%)

rewrite196.0ms (2%)

eval47.0ms (0.5%)

prune3.0ms (0%)

simplify160.0ms (1.6%)

localize118.0ms (1.2%)

series2.0ms (0%)

simplify110.0ms (1.1%)

rewrite172.0ms (1.8%)

eval2.0ms (0%)

prune5.0ms (0.1%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify61.0ms (0.6%)

soundness952.0ms (9.8%)

preprocess19.0ms (0.2%)

end0.0ms (0%)

Profiling