Metrics for Hyperbolic tangent

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 9 computations (40% saved)

sample5.2s (49.8%)

Memory

40.0MiB live, 4 113.2MiB allocated

Samples

1.9s	2 932×	2	valid
1.4s	4 786×	1	valid
1.1s	8 035×	0	exit
51.0ms	538×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.4s

ival-exp: 1.9s (57.1% of total)

ival-add: 557.0ms (16.4% of total)

ival-sub: 325.0ms (9.6% of total)

ival-div: 238.0ms (7% of total)

adjust: 234.0ms (6.9% of total)

ival-neg: 85.0ms (2.5% of total)

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

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

Bogosity

explain212.0ms (2%)

Memory

2.3MiB live, 322.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
246	-	-	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
6	-	-	`(/.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	246	1
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	6	0
↳	`(exp.f64 x)`	overflow	5
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	6
↳	`(exp.f64 (neg.f64 x))`	overflow	1
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	6
↳	`(exp.f64 x)`	overflow	5
↳	`(exp.f64 (neg.f64 x))`	overflow	1

Confusion

	Predicted +	Predicted -
+	252	0
-	0	4

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	252	0	0
-	0	1	3

Precision?

0.9960474308300395

Recall?

1.0

Freqs

test

number	freq
0	4
1	252

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

76.0ms	186×	2	valid
57.0ms	288×	1	valid
3.0ms	38×	0	valid

Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 114.0ms

ival-exp: 78.0ms (68.2% of total)

adjust: 11.0ms (9.6% of total)

ival-div: 9.0ms (7.9% of total)

ival-sub: 8.0ms (7% of total)

ival-add: 6.0ms (5.2% of total)

ival-neg: 3.0ms (2.6% of total)

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

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

preprocess93.0ms (0.9%)

Memory

-2.2MiB live, 71.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 13 to 7 computations (46.2% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.8%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 13 to 7 computations (46.2% saved)

simplify34.0ms (0.3%)

Memory

11.7MiB live, 50.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize80.0ms (0.8%)

Memory

10.4MiB live, 95.2MiB 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	1.460954006304951	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	56.88735189515063	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

37.0ms	93×	2	valid
27.0ms	144×	1	valid
5.0ms	19×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-exp: 39.0ms (66.1% of total)

ival-add: 7.0ms (11.9% of total)

adjust: 6.0ms (10.2% of total)

ival-div: 4.0ms (6.8% of total)

ival-sub: 3.0ms (5.1% of total)

ival-neg: 1.0ms (1.7% of total)

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

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

series3.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

5 → 28

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(* 2 x)
(* x (+ 2 (* 1/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
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)))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(- (exp x) (exp (neg x)))
(exp x)
(exp (neg x))
(+ (exp x) (exp (neg x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(- (exp x) (exp (* -1 x)))
(exp (* -1 x))
(+ (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) (exp (neg x))))
1.0ms	x	@	inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (- (exp x) (exp (neg x))) (exp x) (exp (neg x)) (+ (exp x) (exp (neg x))))
1.0ms	x	@	-inf	((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (- (exp x) (exp (neg x))) (exp x) (exp (neg x)) (+ (exp x) (exp (neg x))))

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify145.0ms (1.4%)

Memory

6.9MiB live, 121.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	242
1	259	241
2	604	231
3	1672	231
4	2637	231
5	4162	231
6	4866	231
7	6482	231
0	8180	203

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 27

Calls

Call 1

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

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

rewrite152.0ms (1.5%)

Memory

-23.6MiB live, 202.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
0	13	15
1	55	15
2	424	15
3	7120	15
0	8102	15

Stop Event

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

Counts

5 → 644

Calls

Call 1

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

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

eval109.0ms (1%)

Memory: -17.5MiB live, 173.9MiB allocated
Compiler: Compiled 16 689 to 1 766 computations (89.4% saved)

prune10.0ms (0.1%)

Memory

-2.3MiB live, 36.1MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	694	2	696
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	695	2	697

Accuracy

100.0%

Counts

697 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tanh.f64 x)
▶	96.3%	#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)

simplify132.0ms (1.3%)

Memory

12.8MiB live, 133.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
0	17	24
1	46	24
2	88	24
3	135	24
4	215	24
5	414	24
6	744	24
7	1321	24
8	3234	24
9	6982	24
0	8159	24

Stop Event

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

Calls

Call 1

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

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

localize186.0ms (1.8%)

Memory

1.0MiB live, 154.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(tanh.f64 x)
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.015625	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy	2.3549510896196746	#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

107.0ms	93×	2	valid
52.0ms	144×	1	valid
2.0ms	19×	0	valid

Compiler

Compiled 31 to 15 computations (51.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-exp: 41.0ms (55.2% of total)

adjust: 11.0ms (14.8% of total)

ival-div: 4.0ms (5.4% of total)

ival-add: 4.0ms (5.4% of total)

const: 4.0ms (5.4% of total)

ival-sub: 3.0ms (4% of total)

ival-pow: 3.0ms (4% of total)

ival-mult: 2.0ms (2.7% of total)

ival-tanh: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% 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

12.0MiB live, 12.0MiB allocated

Counts

4 → 11

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

3.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify111.0ms (1.1%)

Memory

-0.5MiB live, 124.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 10

Calls

Call 1

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

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

rewrite239.0ms (2.3%)

Memory

-26.7MiB live, 210.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 473

Calls

Call 1

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

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

eval78.0ms (0.8%)

Memory: 0.0MiB live, 86.6MiB allocated
Compiler: Compiled 13 094 to 1 224 computations (90.7% saved)

prune7.0ms (0.1%)

Memory

22.2MiB live, 22.2MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Accuracy

100.0%

Counts

483 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(tanh.f64 x)

▶

96.3%

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

▶

96.3%

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

Compiler

Compiled 46 to 27 computations (41.3% saved)

simplify226.0ms (2.2%)

Memory

-9.3MiB live, 145.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize159.0ms (1.5%)

Memory

-4.3MiB live, 122.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.01953125	(fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x)
accuracy	0.34765625	(*.f64 x #s(literal -1/3 binary64))
accuracy	2.3549510896196746	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)) x))
accuracy	0.0078125	(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
accuracy	0.01171875	(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
accuracy	0.34765625	(*.f64 #s(literal -1/3 binary64) x)
accuracy	2.3549510896196746	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))

Samples

105.0ms	93×	2	valid
39.0ms	144×	1	valid
3.0ms	19×	0	valid

Compiler

Compiled 67 to 19 computations (71.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 131.0ms

ival-exp: 73.0ms (55.6% of total)

ival-div: 26.0ms (19.8% of total)

adjust: 10.0ms (7.6% of total)

ival-mult: 9.0ms (6.9% of total)

ival-add: 5.0ms (3.8% of total)

const: 4.0ms (3% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

8 → 15

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify109.0ms (1.1%)

Memory

-7.1MiB live, 64.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 14

Calls

Call 1

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

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

rewrite591.0ms (5.7%)

Memory

16.5MiB live, 210.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

8 → 231

Calls

Call 1

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

Outputs
(.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x) (pow.f64 (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) #s(literal -1 binary64)))
(.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))))
(.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (neg.f64 x) x)) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) #s(literal -1 binary64))))
(.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) #s(literal -1 binary64)) x))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)) x)
(*.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(.f64 x (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)) #s(literal -1 binary64))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x)))
(/.f64 (.f64 x (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)))
(/.f64 (.f64 x (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))) (.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))) (+.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (fma.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x)) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/729 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/729 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 3 binary64)) #s(literal -1/19683 binary64) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/729 binary64) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) (.f64 x x))) (*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x) (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x))))
(/.f64 (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)))
(/.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/3 binary64) (*.f64 x x)))))
(/.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/3 binary64)) x))))
(/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) (.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x #s(literal -1/3 binary64)) x #s(literal -1 binary64)) (.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/3 binary64)) x))) (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))) (-.f64 (.f64 x x) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))))
(fma.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
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eval58.0ms (0.6%)

Memory: -12.4MiB live, 38.3MiB allocated
Compiler: Compiled 5 199 to 603 computations (88.4% saved)

prune3.0ms (0%)

Memory

10.0MiB live, 10.0MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	154	4	158

Accuracy

100.0%

Counts

158 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tanh.f64 x)
▶	96.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)))))
✓	96.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
▶	96.4%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 73 to 45 computations (38.4% saved)

simplify286.0ms (2.8%)

Memory

7.2MiB live, 164.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	101
0	26	98
1	48	94
2	76	94
3	125	92
4	224	92
5	386	92
6	622	92
7	924	92
8	1380	92
9	2574	92
10	5217	92
11	6768	92
0	8142	90

Stop Event

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

Calls

Call 1

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

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

localize122.0ms (1.2%)

Memory

-3.8MiB live, 72.5MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)))
accuracy	0.015625	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64))))
accuracy	0.34765625	(*.f64 x #s(literal -1/3 binary64))
accuracy	2.3549510896196746	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)))))
accuracy	0.01171875	(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
accuracy	2.3549510896196746	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
accuracy	2.61180815407384	#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))

Samples

60.0ms	93×	2	valid
48.0ms	144×	1	valid
3.0ms	19×	0	valid

Compiler

Compiled 79 to 20 computations (74.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

ival-exp: 50.0ms (52.8% of total)

const: 12.0ms (12.7% of total)

adjust: 10.0ms (10.6% of total)

ival-div: 7.0ms (7.4% of total)

ival-mult: 7.0ms (7.4% of total)

ival-add: 5.0ms (5.3% of total)

ival-sub: 3.0ms (3.2% of total)

ival-neg: 1.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

8 → 21

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/3 (pow x 2)))
(+ 1 (* 1/3 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/3 (* 1/9 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/9 (* 1/27 (pow x 2)))))))
(* -1/3 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))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(/ -3 (pow x 2))
(* -1 (/ (+ 3 (* 9 (/ 1 (pow x 2)))) (pow x 2)))
(/ (- (* -1 (/ (+ 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))) 3) (pow x 2))
(/ (- (* -1 (/ (+ 27 (* 81 (/ 1 (pow x 2)))) (pow x 4))) (+ 3 (* 9 (/ 1 (pow x 2))))) (pow x 2))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify182.0ms (1.8%)

Memory

-19.3MiB live, 98.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	216
1	216	206
2	553	203
3	1618	203
4	5410	203
0	8556	187

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 20

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/3 (pow x 2)))
(+ 1 (* 1/3 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/3 (* 1/9 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/9 (* 1/27 (pow x 2)))))))
(* -1/3 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))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(/ -3 (pow x 2))
(* -1 (/ (+ 3 (* 9 (/ 1 (pow x 2)))) (pow x 2)))
(/ (- (* -1 (/ (+ 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))) 3) (pow x 2))
(/ (- (* -1 (/ (+ 27 (* 81 (/ 1 (pow x 2)))) (pow x 4))) (+ 3 (* 9 (/ 1 (pow x 2))))) (pow x 2))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal -1/3 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/3 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(+ 1 (* 1/3 (pow x 2)))
(fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/3 (* 1/9 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/9 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/9 (* 1/27 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/27 binary64) (.f64 x x) #s(literal 1/9 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* -1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(/ -3 (pow x 2))
(/.f64 #s(literal -3 binary64) (*.f64 x x))
(* -1 (/ (+ 3 (* 9 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 9 binary64) (*.f64 x x))) x) x)
(/ (- (* -1 (/ (+ 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))) 3) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal 27 binary64) (*.f64 x x)) #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64)))) x)
(/ (- (* -1 (/ (+ 27 (* 81 (/ 1 (pow x 2)))) (pow x 4))) (+ 3 (* 9 (/ 1 (pow x 2))))) (pow x 2))
(/.f64 (-.f64 (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 9 binary64) (.f64 x x))) (/.f64 (+.f64 (/.f64 #s(literal 81 binary64) (.f64 x x)) #s(literal 27 binary64)) (pow.f64 x #s(literal 4 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)))
(* -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)

rewrite236.0ms (2.3%)

Memory

10.0MiB live, 170.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	96
0	26	71
1	116	67
2	706	65
0	8700	63

Stop Event

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

Counts

8 → 311

Calls

Call 1

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

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
(.f64 (.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x) #s(literal 1 binary64))
(.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
(.f64 x (.f64 #s(literal 1 binary64) #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))))
(.f64 x #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)))
(/.f64 (.f64 (neg.f64 x) #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (.f64 #s(literal 1 binary64) #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x) #s(literal 1 binary64))
(/.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
(*.f64 (pow.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(.f64 (/.f64 x (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 x (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal -1/3 binary64) x) x))) #s(literal -1 binary64)))
(.f64 (/.f64 x (pow.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) #s(literal -1/2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (.f64 (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x))) #s(literal -1 binary64)) x))
(*.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
(*.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(.f64 (neg.f64 x) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)))
(.f64 x (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)))
(pow.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64))
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(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal -1/3 binary64) x) x)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (neg.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x))))
(/.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))))
(/.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x)) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(neg.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/3 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) x)) x #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) x)) #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal -1/3 binary64) x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x))) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal -1/3 binary64) x) x))))
(-.f64 (/.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (.f64 (log1p.f64 (.f64 (*.f64 #s(literal -1/3 binary64) x) x)) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log1p.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log1p.f64 (.f64 (*.f64 #s(literal -1/3 binary64) x) x)) #s(literal 1 binary64)))
(+.f64 (neg.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x))) #s(literal 1 binary64))
(+.f64 (.f64 (.f64 #s(literal 1/3 binary64) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64))
(+.f64 (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 #s(literal 1 binary64) (neg.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/3 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) x))
(+.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) x) #s(literal 1 binary64))
(.f64 (.f64 #s(literal -1/3 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) x)
(*.f64 x #s(literal -1/3 binary64))
(/.f64 (*.f64 (neg.f64 x) #s(literal -1/3 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal -1/3 binary64) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal -1/3 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal -1 binary64)))

eval82.0ms (0.8%)

Memory: 23.5MiB live, 96.4MiB allocated
Compiler: Compiled 10 802 to 1 279 computations (88.2% saved)

prune32.0ms (0.3%)

Memory

-26.5MiB live, 21.6MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	325	1	326
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	326	4	330

Accuracy

100.0%

Counts

330 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tanh.f64 x)
	96.8%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (/.f64 x #s(approx (/ 1 (+ (* (* x -1/3) x) 1)) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)))))
✓	96.3%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
✓	96.4%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 241 to 100 computations (58.5% saved)

regimes5.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes4.0ms (0%)

Memory

6.3MiB live, 6.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
96.8%	1	`x`
96.8%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes3.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Accuracy

Total -0.3b remaining (-11.9%)

Threshold costs -0.3b (-11.9%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
96.4%	1	`x`
96.4%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify348.0ms (3.4%)

Memory

3.5MiB live, 80.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	59
1	44	59
2	60	59
3	88	59
4	164	59
5	411	59
6	1278	59
7	2924	59

Stop Event

1×	node limit

Calls

Call 1

Inputs

(tanh.f64 x)

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

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

Outputs

(tanh.f64 x)

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

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

soundness1.1s (10.6%)

Memory

-20.4MiB live, 542.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
0	13	15
1	55	15
2	424	15
3	7120	15
0	8102	15
0	13	31
0	17	20
1	90	20
2	643	20
0	8962	20
0	17	75
0	25	53
1	103	53
2	746	49
0	8594	45
0	90	242
1	259	241
2	604	231
3	1672	231
4	2637	231
5	4162	231
6	4866	231
7	6482	231
0	8180	203
0	46	121
1	117	111
2	264	111
3	774	111
4	2527	111
5	5795	111
0	8090	101
0	83	216
1	216	206
2	553	203
3	1618	203
4	5410	203
0	8556	187

Stop Event

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

Compiler

Compiled 165 to 93 computations (43.6% saved)

preprocess54.0ms (0.5%)

Memory: 8.1MiB live, 46.5MiB allocated
Remove: (negabs x)
Compiler: Compiled 148 to 72 computations (51.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample5.2s (49.8%)

explain212.0ms (2%)

preprocess93.0ms (0.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify34.0ms (0.3%)

localize80.0ms (0.8%)

series3.0ms (0%)

simplify145.0ms (1.4%)

rewrite152.0ms (1.5%)

eval109.0ms (1%)

prune10.0ms (0.1%)

simplify132.0ms (1.3%)

localize186.0ms (1.8%)

series6.0ms (0.1%)

simplify111.0ms (1.1%)

rewrite239.0ms (2.3%)

eval78.0ms (0.8%)

prune7.0ms (0.1%)

simplify226.0ms (2.2%)

localize159.0ms (1.5%)

series6.0ms (0.1%)

simplify109.0ms (1.1%)

rewrite591.0ms (5.7%)

eval58.0ms (0.6%)

prune3.0ms (0%)

simplify286.0ms (2.8%)

localize122.0ms (1.2%)

series4.0ms (0%)

simplify182.0ms (1.8%)

rewrite236.0ms (2.3%)

eval82.0ms (0.8%)

prune32.0ms (0.3%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify348.0ms (3.4%)

soundness1.1s (10.6%)

preprocess54.0ms (0.5%)

end0.0ms (0%)

Profiling