Metrics for Hyperbolic tangent

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 15 to 9 computations (40% saved)

sample4.3s (61.1%)

Memory

40.7MiB live, 4 470.8MiB allocated; 847ms collecting garbage

Samples

1.7s	3 177×	2	valid
1.1s	4 700×	1	valid
634.0ms	7 803×	0	exit
24.0ms	379×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

ival-exp: 1.8s (62.8% of total)

adjust: 407.0ms (14.2% of total)

ival-div: 205.0ms (7.1% of total)

ival-sub: 167.0ms (5.8% of total)

ival-neg: 148.0ms (5.2% of total)

ival-add: 123.0ms (4.3% of total)

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

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

Bogosity

explain260.0ms (3.7%)

Memory

-24.9MiB live, 266.8MiB allocated; 28ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
253	0	-	-	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
1	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	(-211.38649565760585)	-	`(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	253	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	1	0
↳	`(exp.f64 x)`	overflow	1
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	1
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	1
↳	`(exp.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

106.0ms	218×	2	valid
79.0ms	280×	1	valid
1.0ms	14×	0	valid

Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-exp: 76.0ms (49.1% of total)

adjust: 41.0ms (26.5% of total)

ival-sub: 22.0ms (14.2% of total)

ival-div: 7.0ms (4.5% of total)

ival-add: 5.0ms (3.2% of total)

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

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

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

preprocess187.0ms (2.7%)

Memory

15.0MiB live, 164.2MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	34	27
2	87	27
3	366	27
4	3937	18
0	7	13
0	13	13
1	26	13
2	66	13
3	263	13
4	1667	9
0	8992	9

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 13 to 7 computations (46.2% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.8%	(/.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)

simplify108.0ms (1.6%)

Memory

1.8MiB live, 138.6MiB allocated; 10ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	13	33
1	26	33
2	66	33
3	263	33
4	1667	25
0	8992	25

Stop Event

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

Calls

Call 1

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

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

localize118.0ms (1.7%)

Memory

7.5MiB live, 111.8MiB allocated; 15ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.0078125	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	0.2578152510508252	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	58.143923322196095	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

62.0ms	140×	1	valid
45.0ms	109×	2	valid
0.0ms	7×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 96.0ms

ival-exp: 44.0ms (45.9% of total)

ival-div: 34.0ms (35.5% of total)

adjust: 11.0ms (11.5% of total)

ival-add: 3.0ms (3.1% 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)

series3.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Counts

4 → 23

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify171.0ms (2.5%)

Memory

-6.4MiB live, 135.7MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	210
1	292	210
2	1009	200
3	4230	200
0	8034	179

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 22

Calls

Call 1

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

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

rewrite279.0ms (4%)

Memory

-4.0MiB live, 221.9MiB allocated; 50ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
0	13	12
1	50	12
2	395	12
0	6938	12

Stop Event

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

Counts

4 → 634

Calls

Call 1

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

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

eval104.0ms (1.5%)

Memory: 24.4MiB live, 114.3MiB allocated; 12ms collecting garbage
Compiler: Compiled 20 870 to 2 037 computations (90.2% saved)

prune36.0ms (0.5%)

Memory

-18.3MiB live, 33.0MiB allocated; 21ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	708	2	710
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	709	2	711

Accuracy

100.0%

Counts

711 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tanh.f64 x)
▶	99.0%	#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))

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify115.0ms (1.7%)

Memory

20.5MiB live, 68.0MiB allocated; 3ms collecting garbage

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	47	24
2	126	24
3	440	24
4	2240	24
0	8715	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

localize159.0ms (2.3%)

Memory

-4.5MiB live, 84.3MiB allocated; 8ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(tanh.f64 x)
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.0078125	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	0.6559392606878212	#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

79.0ms	109×	2	valid
69.0ms	140×	1	valid
1.0ms	7×	0	valid

Compiler

Compiled 31 to 15 computations (51.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-exp: 62.0ms (45.7% of total)

adjust: 52.0ms (38.3% of total)

ival-div: 4.0ms (2.9% of total)

const: 4.0ms (2.9% of total)

ival-add: 4.0ms (2.9% of total)

ival-sub: 3.0ms (2.2% of total)

ival-pow: 3.0ms (2.2% of total)

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

ival-tanh: 1.0ms (0.7% 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)

series6.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

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
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))
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

2.0ms

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))

simplify204.0ms (2.9%)

Memory

6.7MiB live, 108.7MiB allocated; 52ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	116
1	135	110
2	343	110
3	1322	110
4	5936	110
0	8205	104

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

rewrite59.0ms (0.8%)

Memory

2.8MiB live, 49.4MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
0	17	20
1	85	20
0	643	20

Stop Event

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

Counts

4 → 55

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 (.f64 x x) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))) (-.f64 x (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 x x))) (neg.f64 (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 x x)) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))
(/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))))
(/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 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)
(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
(fma.f64 (.f64 #s(literal -1/3 binary64) x) (.f64 x x) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/3 binary64)) x)
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)
(fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/3 binary64)) x)
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))
(-.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))
(-.f64 x (*.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/3 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)
(+.f64 x (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 x #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))))
(tanh.f64 x)
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64)))) (.f64 (sinh.f64 x) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 (neg.f64 x) #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (tanh.f64 x))
(.f64 #s(literal 2 binary64) (/.f64 (sinh.f64 x) (.f64 (cosh.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) (/.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x))) (.f64 (/.f64 (exp.f64 (neg.f64 x)) (.f64 (cosh.f64 x) #s(literal 2 binary64))) (/.f64 (exp.f64 (neg.f64 x)) (.f64 (cosh.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) (/.f64 (exp.f64 (neg.f64 x)) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 x)) (.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) (/.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) (fma.f64 (/.f64 (exp.f64 (neg.f64 x)) (.f64 (cosh.f64 x) #s(literal 2 binary64))) (/.f64 (exp.f64 (neg.f64 x)) (.f64 (cosh.f64 x) #s(literal 2 binary64))) (.f64 (/.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) (/.f64 (exp.f64 (neg.f64 x)) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (.f64 #s(literal -2 binary64) (sinh.f64 x))) (neg.f64 (.f64 #s(literal -2 binary64) (cosh.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -2 binary64)) x))) (neg.f64 (+.f64 (pow.f64 (exp.f64 #s(literal -2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (exp.f64 x) (.f64 (cosh.f64 x) #s(literal 2 binary64))) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (cosh.f64 x) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64))) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (cosh.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 3 binary64))) (.f64 (fma.f64 (exp.f64 (neg.f64 x)) (.f64 (cosh.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (*.f64 (cosh.f64 x) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal -2 binary64) (sinh.f64 x)) (.f64 #s(literal -2 binary64) (cosh.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -2 binary64)) x)) (+.f64 (pow.f64 (exp.f64 #s(literal -2 binary64)) x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (sinh.f64 x) (cosh.f64 x))
(/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (cosh.f64 x) #s(literal 2 binary64)))
(neg.f64 (/.f64 (.f64 #s(literal -2 binary64) (sinh.f64 x)) (.f64 (cosh.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 #s(literal -2 binary64) (cosh.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (exp.f64 #s(literal -2 binary64)) x) #s(literal 1 binary64))) (/.f64 (pow.f64 (exp.f64 #s(literal -2 binary64)) x) (+.f64 (pow.f64 (exp.f64 #s(literal -2 binary64)) x) #s(literal 1 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 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) (/.f64 (exp.f64 (neg.f64 x)) (*.f64 (cosh.f64 x) #s(literal 2 binary64))))

eval24.0ms (0.3%)

Memory: -30.2MiB live, 14.7MiB allocated; 3ms collecting garbage
Compiler: Compiled 1 515 to 243 computations (84% saved)

prune3.0ms (0%)

Memory

7.7MiB live, 7.7MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	64	2	66

Accuracy

100.0%

Counts

66 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tanh.f64 x)
▶	99.0%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))

Compiler

Compiled 24 to 14 computations (41.7% saved)

simplify130.0ms (1.9%)

Memory

3.1MiB live, 189.9MiB allocated; 30ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	40
0	16	40
1	37	34
2	120	34
3	455	34
4	2074	30
0	8822	30

Stop Event

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

Calls

Call 1

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

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

localize112.0ms (1.6%)

Memory

0.7MiB live, 195.6MiB allocated; 12ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
accuracy	0.0859375	(.f64 (.f64 x x) x)
accuracy	0.6559392606878212	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))

Samples

64.0ms	109×	2	valid
38.0ms	140×	1	valid
1.0ms	7×	0	valid

Compiler

Compiled 34 to 14 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-exp: 39.0ms (42.8% of total)

adjust: 21.0ms (23% of total)

ival-add: 14.0ms (15.4% of total)

ival-div: 4.0ms (4.4% of total)

const: 4.0ms (4.4% of total)

ival-mult: 4.0ms (4.4% of total)

ival-sub: 3.0ms (3.3% of total)

ival-neg: 2.0ms (2.2% of total)

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

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

series3.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Counts

4 → 11

Calls

Call 1

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

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

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

1.0ms

inf

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

1.0ms

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

simplify165.0ms (2.4%)

Memory

-7.0MiB live, 174.7MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	106
1	126	100
2	334	100
3	1300	100
4	5924	100
0	8191	94

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 10

Calls

Call 1

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

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

rewrite93.0ms (1.3%)

Memory

-2.5MiB live, 68.6MiB allocated; 58ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	38
0	16	21
1	73	21
0	606	21

Stop Event

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

Counts

4 → 46

Calls

Call 1

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

Outputs
(.f64 (.f64 x (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 x (neg.f64 x)) (neg.f64 x))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) x))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) x))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))) (-.f64 x (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 x x))) (neg.f64 (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 x x)) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))
(/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))))
(/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))))
(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
(fma.f64 (.f64 #s(literal -1/3 binary64) x) (.f64 x x) x)
(fma.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (.f64 #s(literal -1/3 binary64) x)) x)
(fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) (.f64 #s(literal -1/3 binary64) x)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(fma.f64 (.f64 x x) (.f64 #s(literal -1/3 binary64) x) x)
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/3 binary64)) x)
(fma.f64 x (.f64 x (.f64 #s(literal -1/3 binary64) x)) x)
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))
(-.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))
(-.f64 x (*.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/3 binary64)))
(-.f64 x (.f64 (neg.f64 (.f64 x x)) (*.f64 #s(literal -1/3 binary64) x)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)
(+.f64 x (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval6.0ms (0.1%)

Memory: 11.1MiB live, 11.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 432 to 221 computations (84.6% saved)

prune8.0ms (0.1%)

Memory

-39.9MiB live, 9.1MiB allocated; 5ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	54	2	56

Accuracy

100.0%

Counts

56 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tanh.f64 x)
✓	99.0%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))

Compiler

Compiled 81 to 37 computations (54.3% saved)

regimes3.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(tanh.f64 x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(/.f64 (-.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
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
100.0%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
100.0%	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes2.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
99.0%	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify35.0ms (0.5%)

Memory

2.9MiB live, 49.4MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations304.0ms (4.4%)

Memory

0.1MiB live, 189.0MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	210
1	292	210
2	1009	200
3	4230	200
0	8034	179
0	7	27
0	13	12
1	50	12
2	395	12
0	6938	12
0	13	31
0	17	20
1	85	20
0	643	20

Stop Event

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

Compiler

Compiled 24 to 13 computations (45.8% saved)

preprocess15.0ms (0.2%)

Memory: 31.4MiB live, 31.4MiB allocated; 0ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 78 to 44 computations (43.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample4.3s (61.1%)

explain260.0ms (3.7%)

preprocess187.0ms (2.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify108.0ms (1.6%)

localize118.0ms (1.7%)

series3.0ms (0%)

simplify171.0ms (2.5%)

rewrite279.0ms (4%)

eval104.0ms (1.5%)

prune36.0ms (0.5%)

simplify115.0ms (1.7%)

localize159.0ms (2.3%)

series6.0ms (0.1%)

simplify204.0ms (2.9%)

rewrite59.0ms (0.8%)

eval24.0ms (0.3%)

prune3.0ms (0%)

simplify130.0ms (1.9%)

localize112.0ms (1.6%)

series3.0ms (0%)

simplify165.0ms (2.4%)

rewrite93.0ms (1.3%)

eval6.0ms (0.1%)

prune8.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify35.0ms (0.5%)

derivations304.0ms (4.4%)

preprocess15.0ms (0.2%)

end0.0ms (0%)

Profiling