Metrics for Hyperbolic tangent

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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)

sample3.9s (50.1%)

Memory

60.3MiB live, 3 980.8MiB allocated; 777ms collecting garbage

Samples

1.5s	3 124×	2	valid
966.0ms	4 747×	1	valid
672.0ms	7 631×	0	exit
24.0ms	385×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.6s

ival-exp: 1.6s (60.8% of total)

adjust: 355.0ms (13.5% of total)

ival-div: 222.0ms (8.5% of total)

ival-add: 185.0ms (7% of total)

ival-sub: 166.0ms (6.3% of total)

ival-neg: 84.0ms (3.2% of total)

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

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

Bogosity

explain289.0ms (3.7%)

Memory

-25.8MiB live, 312.9MiB allocated; 38ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
244	-	-	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
7	-	-	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0	-	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	-	-	`(exp.f64 x)`
0	-	-	`(exp.f64 (neg.f64 x))`
0	-	-	`(neg.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	cancellation	244	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	7	0
↳	`(exp.f64 x)`	overflow	4
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	7
↳	`(exp.f64 (neg.f64 x))`	overflow	3
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	7
↳	`(exp.f64 x)`	overflow	4
↳	`(exp.f64 (neg.f64 x))`	overflow	3

Confusion

	Predicted +	Predicted -
+	251	0
-	0	5

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	251	0	0
-	0	0	5

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	5
1	251

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

145.0ms	328×	1	valid
64.0ms	158×	2	valid
2.0ms	26×	0	valid

Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 190.0ms

ival-exp: 64.0ms (33.8% of total)

adjust: 61.0ms (32.2% of total)

ival-sub: 42.0ms (22.2% of total)

ival-div: 14.0ms (7.4% of total)

ival-add: 5.0ms (2.6% of total)

ival-neg: 3.0ms (1.6% of total)

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

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

preprocess132.0ms (1.7%)

Memory

20.7MiB live, 164.5MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 13 to 7 computations (46.2% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.2%	(/.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)

simplify89.0ms (1.2%)

Memory

-10.5MiB live, 124.5MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize145.0ms (1.9%)

Memory

-43.1MiB live, 133.2MiB allocated; 73ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.015625	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	1.7187692573557762	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	56.34807746507474	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

62.0ms	79×	2	valid
52.0ms	164×	1	valid
1.0ms	13×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-exp: 65.0ms (77.2% of total)

adjust: 10.0ms (11.9% of total)

ival-div: 3.0ms (3.6% of total)

ival-add: 3.0ms (3.6% of total)

ival-sub: 3.0ms (3.6% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

series3.0ms (0%)

Memory

5.7MiB live, 5.7MiB 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))

simplify193.0ms (2.5%)

Memory

19.1MiB live, 159.9MiB allocated; 29ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 22

Calls

Call 1

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

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

rewrite288.0ms (3.7%)

Memory

2.5MiB live, 194.4MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 636

Calls

Call 1

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

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

eval115.0ms (1.5%)

Memory: -11.0MiB live, 135.0MiB allocated; 16ms collecting garbage
Compiler: Compiled 19 340 to 1 974 computations (89.8% saved)

prune19.0ms (0.2%)

Memory

-16.3MiB live, 30.9MiB allocated; 2ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Accuracy

100.0%

Counts

702 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.2%	(/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	100.0%	(tanh.f64 x)
▶	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Status

Accuracy

Program

▶

97.2%

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

▶

100.0%

(tanh.f64 x)

▶

95.6%

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

Compiler

Compiled 33 to 23 computations (30.3% saved)

simplify130.0ms (1.7%)

Memory

19.9MiB live, 112.4MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sinh.f64 x)
cost-diff	0	(*.f64 (sinh.f64 x) #s(literal 2 binary64))
cost-diff	2	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
cost-diff	7	(/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
cost-diff	0	(tanh.f64 x)
cost-diff	0	(pow.f64 x #s(literal 3 binary64))
cost-diff	0	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	67
0	34	47
1	67	47
2	156	47
3	515	47
4	2735	45
0	8990	45

Stop Event

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

Calls

Call 1

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

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

localize173.0ms (2.2%)

Memory

-17.9MiB live, 88.7MiB allocated; 13ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(sinh.f64 x)
accuracy	0.015625	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	1.7187692573557762	(/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	0.01953125	(tanh.f64 x)
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.038309980164287515	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	2.8313068589030945	#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

113.0ms	164×	1	valid
44.0ms	79×	2	valid
2.0ms	13×	0	valid

Compiler

Compiled 63 to 19 computations (69.8% saved)

Precisions

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

ival-sub: 37.0ms (28.8% of total)

adjust: 34.0ms (26.5% of total)

ival-exp: 33.0ms (25.7% of total)

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

const: 4.0ms (3.1% of total)

ival-add: 4.0ms (3.1% of total)

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Counts

9 → 33

Calls

Call 1

Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(pow.f64 x #s(literal 3 binary64))
(tanh.f64 x)
(/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(*.f64 (sinh.f64 x) #s(literal 2 binary64))
(sinh.f64 x)
(exp.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)
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)))))))
(* 2 x)
(* x (+ 2 (* 1/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
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))))
(* -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) (/ 1 (exp x))) (+ (exp x) (exp (neg x))))
(+ (exp x) (exp (neg x)))
(- (exp x) (/ 1 (exp x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(exp x)
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (exp (* -1 x))))
(+ (exp x) (exp (* -1 x)))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (* (sinh x) 2) (+ (exp x) (exp (neg x)))) (+ (exp x) (exp (neg x))) (* (sinh x) 2) (sinh x) (exp x))
4.0ms	x	@	inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (* (sinh x) 2) (+ (exp x) (exp (neg x)))) (+ (exp x) (exp (neg x))) (* (sinh x) 2) (sinh x) (exp x))
2.0ms	x	@	0	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (* (sinh x) 2) (+ (exp x) (exp (neg x)))) (+ (exp x) (exp (neg x))) (* (sinh x) 2) (sinh x) (exp x))

Time

Variable

Point

Expression

5.0ms

-inf

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

4.0ms

inf

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

2.0ms

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

simplify165.0ms (2.1%)

Memory

27.0MiB live, 72.3MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	327
1	398	315
2	1309	311
3	4321	311
0	8128	284

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 32

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)
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)))))))
(* 2 x)
(* x (+ 2 (* 1/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
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))))
(* -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) (/ 1 (exp x))) (+ (exp x) (exp (neg x))))
(+ (exp x) (exp (neg x)))
(- (exp x) (/ 1 (exp x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(exp x)
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (/ 1 (exp x))) (+ (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)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
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 #s(literal 1/12 binary64) (pow.f64 x #s(literal 3 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 (fma.f64 #s(literal 1/360 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 2 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 1/3 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/60 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2520 binary64) (.f64 x x) #s(literal 1/60 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 1 (* 1/6 (pow x 2))))
(fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
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))) (+ (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) (/ 1 (exp x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(+ (exp x) (exp (neg x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(- (exp x) (/ 1 (exp x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #s(literal 1/2 binary64))
(exp 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))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(+ (exp x) (exp (* -1 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))

rewrite242.0ms (3.1%)

Memory

-0.1MiB live, 183.9MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	56
0	34	34
1	107	34
2	689	34
0	8611	34

Stop Event

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

Counts

9 → 896

Calls

Call 1

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

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

eval198.0ms (2.6%)

Memory: -33.9MiB live, 157.3MiB allocated; 21ms collecting garbage
Compiler: Compiled 20 355 to 2 301 computations (88.7% saved)

prune11.0ms (0.1%)

Memory

38.9MiB live, 38.9MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	706	2	708
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	707	4	711

Accuracy

100.0%

Counts

711 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.2%	(/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	100.0%	(tanh.f64 x)
▶	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
▶	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))

Compiler

Compiled 57 to 35 computations (38.6% saved)

simplify116.0ms (1.5%)

Memory

-45.8MiB live, 149.5MiB allocated; 12ms collecting garbage

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)

localize141.0ms (1.8%)

Memory

2.4MiB live, 192.3MiB allocated; 22ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.038309980164287515	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
accuracy	0.09765625	(.f64 (.f64 x x) x)
accuracy	2.8313068589030945	#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	0.021325904760301946	(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x)
accuracy	0.11328125	(.f64 (.f64 #s(literal -1/3 binary64) x) x)
accuracy	0.37109375	(*.f64 #s(literal -1/3 binary64) x)
accuracy	2.8313068589030945	#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	164×	1	valid
42.0ms	79×	2	valid
2.0ms	13×	0	valid

Compiler

Compiled 66 to 18 computations (72.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-exp: 56.0ms (50.3% of total)

adjust: 31.0ms (27.8% of total)

ival-mult: 9.0ms (8.1% of total)

ival-add: 5.0ms (4.5% 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)

series5.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated; 0ms collecting garbage

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

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))

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))

simplify104.0ms (1.4%)

Memory

22.0MiB live, 167.3MiB allocated; 11ms collecting garbage

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)))

rewrite178.0ms (2.3%)

Memory

6.1MiB live, 266.2MiB allocated; 53ms collecting garbage

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

eval16.0ms (0.2%)

Memory: 29.1MiB live, 29.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 4 334 to 494 computations (88.6% saved)

prune29.0ms (0.4%)

Memory

-44.5MiB live, 20.2MiB allocated; 22ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	140	6	146

Accuracy

100.0%

Counts

146 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.2%	(/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	100.0%	(tanh.f64 x)
✓	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
✓	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
▶	94.8%	#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))))
▶	95.6%	#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 108 to 64 computations (40.7% saved)

simplify118.0ms (1.5%)

Memory

44.5MiB live, 172.4MiB allocated; 26ms collecting garbage

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)

localize179.0ms (2.3%)

Memory

-1.9MiB live, 143.0MiB allocated; 61ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.125	(.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))
accuracy	0.37109375	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0.520499716849389	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x)))
accuracy	2.8313068589030945	#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	0.01953125	(+.f64 x (.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x)))
accuracy	0.125	(.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))
accuracy	0.37109375	(*.f64 #s(literal 1/3 binary64) x)
accuracy	2.8313068589030945	#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

86.0ms	79×	2	valid
79.0ms	164×	1	valid
2.0ms	13×	0	valid

Compiler

Compiled 94 to 18 computations (80.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 148.0ms

ival-exp: 60.0ms (40.6% of total)

ival-add: 47.0ms (31.8% of total)

adjust: 17.0ms (11.5% of total)

ival-mult: 7.0ms (4.7% of total)

ival-div: 4.0ms (2.7% of total)

const: 4.0ms (2.7% of total)

ival-sub: 3.0ms (2% of total)

ival-sqrt: 3.0ms (2% of total)

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

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

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

series10.0ms (0.1%)

Memory

-37.8MiB live, 7.7MiB allocated; 9ms collecting garbage

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

6.0ms

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))

2.0ms

-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))

simplify122.0ms (1.6%)

Memory

12.5MiB live, 106.1MiB allocated; 18ms collecting garbage

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)

rewrite52.0ms (0.7%)

Memory

-0.1MiB live, 44.4MiB allocated; 5ms collecting garbage

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))

eval11.0ms (0.1%)

Memory: 21.5MiB live, 21.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 822 to 332 computations (88.2% saved)

prune8.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	2	0	2
Done	0	4	4
Total	99	10	109

Accuracy

100.0%

Counts

109 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.2%	(/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	100.0%	(tanh.f64 x)
✓	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) (sqrt.f64 x)) (sqrt.f64 x) x))
✓	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) x x))
	94.8%	#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)))
	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 (.f64 (*.f64 x x) #s(literal -1/3 binary64)) x)))
	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 (.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) (sqrt.f64 x)) (sqrt.f64 x))))
	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 (.f64 (.f64 #s(literal -1/3 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (.f64 x x))))
	95.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 #s(literal 1/3 binary64) (.f64 (neg.f64 x) (*.f64 x x)))))

Compiler

Compiled 504 to 182 computations (63.9% saved)

regimes10.0ms (0.1%)

Memory

-32.3MiB live, 12.8MiB allocated; 4ms collecting garbage

Counts

14 → 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 (*.f64 x x) #s(literal -1/3 binary64)) x)))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 #s(literal 1/3 binary64) (.f64 (neg.f64 x) (*.f64 x 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 (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) (sqrt.f64 x)) (sqrt.f64 x) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 (.f64 (.f64 #s(literal -1/3 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (.f64 x x))))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+.f64 x (.f64 (.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) (sqrt.f64 x)) (sqrt.f64 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 (sinh.f64 x) #s(literal 2 binary64)) (+.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))))

Outputs
(tanh.f64 x)

Calls

2 calls:

6.0ms	x
3.0ms	(/.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)

regimes6.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Accuracy

Total -0.5b remaining (-17.1%)

Threshold costs -0.5b (-17.1%)

Counts

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

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify52.0ms (0.7%)

Memory

-2.1MiB live, 50.6MiB allocated; 7ms collecting garbage

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))

derivations395.0ms (5.1%)

Memory

-3.0MiB live, 314.3MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	56
0	34	34
1	107	34
2	689	34
0	8611	34
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 24 to 13 computations (45.8% saved)

preprocess103.0ms (1.3%)

Memory: -20.7MiB live, 96.7MiB allocated; 89ms 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%)

sample3.9s (50.1%)

explain289.0ms (3.7%)

preprocess132.0ms (1.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify89.0ms (1.2%)

localize145.0ms (1.9%)

series3.0ms (0%)

simplify193.0ms (2.5%)

rewrite288.0ms (3.7%)

eval115.0ms (1.5%)

prune19.0ms (0.2%)

simplify130.0ms (1.7%)

localize173.0ms (2.2%)

series11.0ms (0.1%)

simplify165.0ms (2.1%)

rewrite242.0ms (3.1%)

eval198.0ms (2.6%)

prune11.0ms (0.1%)

simplify116.0ms (1.5%)

localize141.0ms (1.8%)

series5.0ms (0.1%)

simplify104.0ms (1.4%)

rewrite178.0ms (2.3%)

eval16.0ms (0.2%)

prune29.0ms (0.4%)

simplify118.0ms (1.5%)

localize179.0ms (2.3%)

series10.0ms (0.1%)

simplify122.0ms (1.6%)

rewrite52.0ms (0.7%)

eval11.0ms (0.1%)

prune8.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

simplify52.0ms (0.7%)

derivations395.0ms (5.1%)

preprocess103.0ms (1.3%)

end0.0ms (0%)

Profiling