Metrics for Hyperbolic tangent

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 9 computations (40% saved)

sample4.7s (55.1%)

Memory

-87.9MiB live, 4 489.8MiB allocated

Samples

1.7s	4 756×	1	valid
1.5s	2 962×	2	valid
708.0ms	7 859×	0	exit
50.0ms	538×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.3s

ival-exp: 1.7s (51% of total)

ival-neg: 651.0ms (19.8% of total)

ival-add: 268.0ms (8.2% of total)

ival-sub: 253.0ms (7.7% of total)

ival-div: 212.0ms (6.5% of total)

adjust: 206.0ms (6.3% of total)

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

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

Bogosity

explain250.0ms (3%)

Memory

-0.5MiB live, 202.6MiB 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)))`
3	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	(588.2446784514966)	-	`(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	3	0
↳	`(exp.f64 x)`	overflow	1
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	3
↳	`(exp.f64 (neg.f64 x))`	overflow	2
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	3
↳	`(exp.f64 x)`	overflow	1
↳	`(exp.f64 (neg.f64 x))`	overflow	2
`exp.f64`	`(exp.f64 (neg.f64 x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	253	0
-	1	2

Precision

0.9960629921259843

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	253	0	0
-	1	0	2

Precision?

0.9960629921259843

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

93.0ms	174×	2	valid
57.0ms	306×	1	valid
2.0ms	32×	0	valid

Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 128.0ms

ival-exp: 96.0ms (75.1% of total)

adjust: 11.0ms (8.6% of total)

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

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

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

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

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

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

preprocess128.0ms (1.5%)

Memory

-0.1MiB live, 138.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	34	27
2	87	27
3	351	27
4	3679	19
0	7	13
0	13	13
1	26	13
2	66	13
3	258	13
4	1659	9
0	8837	9

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 13 to 7 computations (46.2% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
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
▶	9.0%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 13 to 7 computations (46.2% saved)

simplify102.0ms (1.2%)

Memory

8.8MiB live, 156.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	13	33
1	26	33
2	66	33
3	258	33
4	1659	25
0	8837	25

Stop Event

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

Calls

Call 1

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

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

localize74.0ms (0.9%)

Memory

11.5MiB live, 103.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	0.7343832531524757	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	57.51275224777552	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

38.0ms	87×	2	valid
27.0ms	153×	1	valid
1.0ms	16×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-exp: 40.0ms (72.5% of total)

adjust: 5.0ms (9.1% of total)

ival-div: 3.0ms (5.4% of total)

ival-sub: 3.0ms (5.4% of total)

ival-add: 2.0ms (3.6% of total)

ival-neg: 1.0ms (1.8% of total)

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

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

series21.0ms (0.2%)

Memory

-42.1MiB live, 10.5MiB allocated

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
11.0ms	x	@	0	((- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (exp x))
9.0ms	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

11.0ms

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

9.0ms

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))

simplify150.0ms (1.8%)

Memory

40.3MiB live, 171.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	210
1	292	210
2	958	200
3	3882	200
0	8155	179

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 22

Calls

Call 1

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

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

rewrite282.0ms (3.3%)

Memory

-4.6MiB live, 188.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
0	13	12
1	50	12
2	395	12
3	6196	12
0	9201	12

Stop Event

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

Counts

4 → 636

Calls

Call 1

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

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

eval174.0ms (2.1%)

Memory: -3.7MiB live, 140.1MiB allocated
Compiler: Compiled 19 340 to 1 974 computations (89.8% saved)

prune32.0ms (0.4%)

Memory

3.0MiB live, 47.8MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	699	2	701
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	700	2	702

Accuracy

100.0%

Counts

702 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tanh.f64 x)
▶	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify108.0ms (1.3%)

Memory

11.5MiB live, 111.2MiB 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	47	24
2	126	24
3	428	24
4	2098	24
0	9006	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

localize138.0ms (1.6%)

Memory

-34.2MiB live, 112.3MiB 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	0.0078125	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	1.5276643972742614	#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

56.0ms	153×	1	valid
55.0ms	87×	2	valid
2.0ms	16×	0	valid

Compiler

Compiled 31 to 15 computations (51.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-exp: 36.0ms (35.9% of total)

ival-tanh: 20.0ms (19.9% of total)

const: 19.0ms (18.9% of total)

adjust: 9.0ms (9% of total)

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

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

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

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

ival-mult: 2.0ms (2% 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)

series6.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB 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
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))

simplify148.0ms (1.7%)

Memory

-1.2MiB live, 91.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	116
1	135	110
2	333	110
3	1237	110
4	3826	110
0	8053	106

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)) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64))) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(/ (- (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 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))

rewrite300.0ms (3.5%)

Memory

9.5MiB live, 155.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
0	17	20
1	85	20
2	640	20
0	8598	20

Stop Event

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

Counts

4 → 328

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)) (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 (neg.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 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))) (.f64 (/.f64 (.f64 x x) (-.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 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 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 (-.f64 (.f64 (/.f64 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (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 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (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 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (fma.f64 (/.f64 (.f64 x x) (-.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 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 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 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (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 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (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 (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 (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) 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 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (.f64 (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x) (.f64 x x))) (.f64 (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))
(/.f64 (fma.f64 (.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 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)) (fma.f64 x x (.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 3 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))))) (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 (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))) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (-.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) 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)))))
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eval43.0ms (0.5%)

Memory: -3.8MiB live, 85.8MiB allocated
Compiler: Compiled 10 648 to 1 031 computations (90.3% saved)

prune6.0ms (0.1%)

Memory

22.4MiB live, 22.4MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	336	3	339

Accuracy

100.0%

Counts

339 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(tanh.f64 x)

▶

97.6%

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

▶

97.6%

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

Compiler

Compiled 46 to 26 computations (43.5% saved)

simplify103.0ms (1.2%)

Memory

2.9MiB live, 151.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 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)
cost-diff	0	(*.f64 #s(literal -1/3 binary64) x)
cost-diff	0	(.f64 (.f64 #s(literal -1/3 binary64) x) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
cost-diff	2	(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	80
0	24	80
1	53	70
2	147	70
3	505	70
4	2076	62
0	8965	62

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

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

localize147.0ms (1.7%)

Memory

1.9MiB live, 192.4MiB allocated

Localize:

Found 8 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	0.0625	(.f64 (.f64 x x) x)
accuracy	1.5276643972742614	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
accuracy	0.0	(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
accuracy	0.09765625	(.f64 (.f64 #s(literal -1/3 binary64) x) x)
accuracy	0.30078125	(*.f64 #s(literal -1/3 binary64) x)
accuracy	1.5276643972742614	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))

Samples

84.0ms	153×	1	valid
49.0ms	87×	2	valid
2.0ms	16×	0	valid

Compiler

Compiled 66 to 18 computations (72.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-exp: 39.0ms (35.5% of total)

ival-mult: 35.0ms (31.9% of total)

ival-add: 15.0ms (13.7% of total)

adjust: 10.0ms (9.1% of total)

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

const: 4.0ms (3.6% of total)

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

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

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

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

series44.0ms (0.5%)

Memory

-35.6MiB live, 11.1MiB allocated

Counts

8 → 13

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

41.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify116.0ms (1.4%)

Memory

31.8MiB live, 174.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	114
1	128	108
2	322	108
3	1206	108
4	3783	108
0	8111	104

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

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

rewrite287.0ms (3.4%)

Memory

-26.5MiB live, 220.7MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	76
0	24	52
1	99	44
2	802	44
0	8518	44

Stop Event

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

Counts

8 → 220

Calls

Call 1

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

eval67.0ms (0.8%)

Memory: 20.7MiB live, 76.8MiB allocated
Compiler: Compiled 4 334 to 494 computations (88.6% saved)

prune27.0ms (0.3%)

Memory

-24.7MiB live, 17.8MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	140	5	145

Accuracy

100.0%

Counts

145 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tanh.f64 x)
✓	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
✓	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
▶	96.8%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))))
▶	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))))

Compiler

Compiled 97 to 55 computations (43.3% saved)

simplify115.0ms (1.4%)

Memory

0.3MiB live, 92.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	116
0	25	102
1	60	102
2	213	90
3	806	90
4	2707	82
0	9152	78

Stop Event

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

Calls

Call 1

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

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

localize139.0ms (1.6%)

Memory

1.9MiB live, 103.2MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.109375	(.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))
accuracy	0.30078125	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0.515625	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x)))
accuracy	1.5276643972742614	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))))
accuracy	0.015625	(+.f64 x (.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x)))
accuracy	0.109375	(.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))
accuracy	0.30078125	(*.f64 #s(literal 1/3 binary64) x)
accuracy	1.5276643972742614	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))))

Samples

68.0ms	153×	1	valid
55.0ms	87×	2	valid
2.0ms	16×	0	valid

Compiler

Compiled 94 to 18 computations (80.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 109.0ms

ival-exp: 40.0ms (36.8% of total)

ival-neg: 23.0ms (21.2% of total)

ival-mult: 16.0ms (14.7% of total)

adjust: 10.0ms (9.2% of total)

ival-add: 6.0ms (5.5% of total)

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

const: 4.0ms (3.7% of total)

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

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

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

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

series6.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

7 → 12

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify125.0ms (1.5%)

Memory

8.9MiB live, 97.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	110
1	148	98
2	427	98
3	1699	98
4	6484	98
0	8832	91

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 11

Calls

Call 1

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

Outputs
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64))) (pow.f64 x #s(literal 3 binary64)) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* (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 (* (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)))
(* -1 (* (pow x 3) (+ 1/3 (/ (pow (sqrt -1) 2) (pow x 2)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)

rewrite69.0ms (0.8%)

Memory

-30.8MiB live, 23.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	89
0	25	55
1	100	45
0	766	41

Stop Event

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

Counts

7 → 97

Calls

Call 1

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

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

eval27.0ms (0.3%)

Memory: 23.9MiB live, 23.9MiB allocated
Compiler: Compiled 2 822 to 332 computations (88.2% saved)

prune6.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	0	0
Picked	2	0	2
Done	0	3	3
Total	103	5	108

Accuracy

100.0%

Counts

108 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tanh.f64 x)
✓	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
✓	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
	96.8%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64)) x)))
	97.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 (.f64 x x) (*.f64 #s(literal -1/3 binary64) x))))

Compiler

Compiled 274 to 96 computations (65% saved)

regimes5.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Results

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes15.0ms (0.2%)

Memory

-37.6MiB live, 7.0MiB allocated

Accuracy

Total -0.5b remaining (-32.7%)

Threshold costs -0.5b (-32.7%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

13.0ms	x
2.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Accuracy	Segments	Branch
97.6%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
97.6%	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify35.0ms (0.4%)

Memory

43.1MiB live, 43.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness488.0ms (5.8%)

Memory

0.6MiB live, 330.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
0	17	20
1	85	20
2	640	20
0	8598	20
0	79	210
1	292	210
2	958	200
3	3882	200
0	8155	179
0	7	27
0	13	12
1	50	12
2	395	12
3	6196	12
0	9201	12

Stop Event

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

Compiler

Compiled 65 to 38 computations (41.5% saved)

preprocess23.0ms (0.3%)

Memory: 7.7MiB live, 51.3MiB allocated
Remove: (negabs x)
Compiler: Compiled 78 to 44 computations (43.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample4.7s (55.1%)

explain250.0ms (3%)

preprocess128.0ms (1.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify102.0ms (1.2%)

localize74.0ms (0.9%)

series21.0ms (0.2%)

simplify150.0ms (1.8%)

rewrite282.0ms (3.3%)

eval174.0ms (2.1%)

prune32.0ms (0.4%)

simplify108.0ms (1.3%)

localize138.0ms (1.6%)

series6.0ms (0.1%)

simplify148.0ms (1.7%)

rewrite300.0ms (3.5%)

eval43.0ms (0.5%)

prune6.0ms (0.1%)

simplify103.0ms (1.2%)

localize147.0ms (1.7%)

series44.0ms (0.5%)

simplify116.0ms (1.4%)

rewrite287.0ms (3.4%)

eval67.0ms (0.8%)

prune27.0ms (0.3%)

simplify115.0ms (1.4%)

localize139.0ms (1.6%)

series6.0ms (0.1%)

simplify125.0ms (1.5%)

rewrite69.0ms (0.8%)

eval27.0ms (0.3%)

prune6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes15.0ms (0.2%)

simplify35.0ms (0.4%)

soundness488.0ms (5.8%)

preprocess23.0ms (0.3%)

end0.0ms (0%)

Profiling