Metrics for Hyperbolic tangent

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 9 computations (40% saved)

sample4.1s (52%)

Memory

-126.7MiB live, 6 580.5MiB allocated

Samples

1.4s	2 932×	2	valid
934.0ms	4 782×	1	valid
631.0ms	7 918×	0	exit
38.0ms	542×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.5s

ival-exp: 1.6s (62.3% of total)

ival-div: 335.0ms (13.4% of total)

adjust: 185.0ms (7.4% of total)

ival-add: 154.0ms (6.1% of total)

ival-sub: 134.0ms (5.3% of total)

ival-neg: 116.0ms (4.6% of total)

ival-true: 12.0ms (0.5% of total)

ival-assert: 7.0ms (0.3% of total)

Bogosity

explain274.0ms (3.5%)

Memory

-23.4MiB live, 507.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
247	1	(-0.0025889279716698028)	-	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
3	0	-	-	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0	0	-	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	0	-	-	`(exp.f64 x)`
0	3	(-118.95857724026855)	-	`(exp.f64 (neg.f64 x))`
0	0	-	-	`(neg.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	cancellation	248	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`	o/o	3	0
↳	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	3
↳	`(exp.f64 (neg.f64 x))`	overflow	3
↳	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`	overflow	3
↳	`(exp.f64 (neg.f64 x))`	overflow	3
`exp.f64`	`(exp.f64 (neg.f64 x))`	sensitivity	3	0

Confusion

	Predicted +	Predicted -
+	250	0
-	4	2

Precision

0.984251968503937

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	250	0	0
-	4	0	2

Precision?

0.984251968503937

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

89.0ms	204×	2	valid
48.0ms	264×	1	valid
3.0ms	44×	0	valid

Compiler

Compiled 84 to 25 computations (70.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 116.0ms

ival-exp: 84.0ms (72.6% of total)

adjust: 11.0ms (9.5% of total)

ival-div: 7.0ms (6% of total)

ival-add: 5.0ms (4.3% of total)

ival-sub: 5.0ms (4.3% of total)

ival-neg: 2.0ms (1.7% of total)

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

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

preprocess106.0ms (1.3%)

Memory

7.4MiB live, 86.2MiB allocated

Algorithm

1×	egg-herbie

Rules

528×	`lower-fma.f64`
528×	`lower-fma.f32`
336×	`lower-*.f64`
336×	`lower-*.f32`
320×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	32	27
2	80	26
3	199	26
4	468	26
5	1130	26
6	1547	26
7	1585	26
8	1604	26
9	1623	26
10	1657	26
11	1669	26
0	7	13
0	13	13
1	25	13
2	42	13
3	67	13
4	122	13
5	276	13
6	462	13
7	682	13
8	905	13
9	1058	13
10	1186	13
11	1233	13
0	1233	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 #s(literal -1 binary64) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal -1 binary64))))

Symmetry

(negabs x)

Compiler

Compiled 14 to 7 computations (50% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	11.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 14 to 7 computations (50% saved)

simplify38.0ms (0.5%)

Memory

-1.4MiB live, 37.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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	11648	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Rules

528×	`lower-fma.f64`
528×	`lower-fma.f32`
336×	`lower-*.f64`
336×	`lower-*.f32`
224×	`lower-/.f32`

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	276	33
6	462	33
7	682	33
8	905	33
9	1058	33
10	1186	33
11	1233	33
0	1233	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 #s(literal -1 binary64) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal -1 binary64))))
(-.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))

localize166.0ms (2.1%)

Memory

-4.6MiB live, 153.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 x)
accuracy	0.01171875	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy	0.7461020031524757	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy	55.84132746069507	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Samples

91.0ms	102×	2	valid
63.0ms	132×	1	valid
2.0ms	22×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 142.0ms

ival-exp: 111.0ms (78% of total)

ival-sub: 18.0ms (12.6% of total)

adjust: 6.0ms (4.2% of total)

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

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

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

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

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

series4.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())
#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())
#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())
#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())
#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (patch (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* 1/3 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) (exp (neg x))) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) (exp (neg x))) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) (exp (neg x))) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) (exp (neg x))) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) (exp (* -1 x))) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) (exp (* -1 x))) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) (exp (* -1 x))) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) (exp (* -1 x))) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (neg x)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (neg x)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (neg x)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (neg x)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))) (taylor 0 x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))) (taylor 0 x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp x) (exp (neg x))) (taylor inf x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp x) (exp (neg x))) (taylor inf x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp x) (exp (neg x))) (taylor inf x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp x) (exp (neg x))) (taylor inf x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp x) (exp (* -1 x))) (taylor -inf x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp x) (exp (* -1 x))) (taylor -inf x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp x) (exp (* -1 x))) (taylor -inf x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp x) (exp (* -1 x))) (taylor -inf x) (#s(alt (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (patch (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #<representation binary64>) () ())) ())

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
1.0ms	x	@	inf	(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
1.0ms	x	@	0	(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
0.0ms	x	@	0	(- (exp x) (exp (neg x)))
0.0ms	x	@	0	(+ (exp x) (exp (neg x)))

simplify296.0ms (3.8%)

Memory

3.0MiB live, 191.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 890×	`lower-fma.f64`
12 890×	`lower-fma.f32`
4 156×	`lower-*.f64`
4 156×	`lower-*.f32`
2 544×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	425
1	259	424
2	604	414
3	1659	414
4	2630	414
5	4160	414
6	4872	414
7	6500	414
0	8123	386

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

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))))
(/ (- (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 (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 x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* 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))))))))
(- (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 x) (exp (* -1 x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
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 (* -1 x)))
(+ (exp x) (exp (* -1 x)))
(+ (exp x) (exp (* -1 x)))
(+ (exp x) (exp (* -1 x)))

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

rewrite405.0ms (5.1%)

Memory

6.4MiB live, 250.1MiB allocated

Rules

3 904×	`lower-*.f64`
3 904×	`lower-*.f32`
3 826×	`lower-/.f32`
3 824×	`lower-/.f64`
2 870×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
0	13	15
1	55	15
2	424	15
3	7080	15
0	8062	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 x x)) #s(literal 1 binary64)) (tanh.f64 x)) (.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) #s(literal 1 binary64)))) (-.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal 1 binary64)) (tanh.f64 x)) (+.f64 (pow.f64 (-.f64 (exp.f64 (.f64 #s(literal -2 binary64) x)) #s(literal -1 binary64)) #s(literal 3 binary64)) (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))))) (+.f64 (-.f64 (pow.f64 (-.f64 (exp.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal -1 binary64)) #s(literal 2 binary64)) (fma.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64))) (exp.f64 (fma.f64 #s(literal 2 binary64) x (+.f64 x x)))))
(.f64 (/.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) #s(literal 1/2 binary64))) (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 x 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 x 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 x x))) (.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 3 binary64) x))))) (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x 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 (/.f64 #s(literal 1 binary64) (tanh.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 x)) #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 x 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 x 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 x x))) (.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x 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 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal -1 binary64)) (*.f64 (cosh.f64 x) #s(literal 2 binary64))))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (*.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x)))) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal -1 binary64)))))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal 3 binary64) x)))) (cosh.f64 x)) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (cosh.f64 x)) (/.f64 (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 3 binary64) x))) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (+.f64 x x))) (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 3 binary64) x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 #s(literal 3 binary64) x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (cosh.f64 (+.f64 x x)) #s(literal 1 binary64))) (.f64 (cosh.f64 x) #s(literal 2 binary64))))
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(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

eval356.0ms (4.5%)

Memory: -23.3MiB live, 220.4MiB allocated
Compiler: Compiled 17 692 to 1 738 computations (90.2% saved)

prune99.0ms (1.3%)

Memory

20.3MiB live, 301.9MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	744	3	747
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	745	3	748

Accuracy

100.0%

Counts

748 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tanh.f64 x)
▶	97.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
▶	96.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x))

Status

Accuracy

Program

▶

100.0%

(tanh.f64 x)

▶

97.2%

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

▶

96.6%

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

Compiler

Compiled 28 to 16 computations (42.9% saved)

simplify177.0ms (2.2%)

Memory

-22.6MiB live, 263.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(tanh.f64 x)
cost-diff	0	(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x))

Rules

12 046×	`lower-fma.f32`
12 040×	`lower-fma.f64`
3 400×	`lower-*.f32`
3 394×	`lower-*.f64`
2 388×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	109
0	29	87
1	67	87
2	128	87
3	227	83
4	458	83
5	699	83
6	1095	83
7	1768	83
8	4009	83
9	7990	83
0	8004	79

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

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

localize142.0ms (1.8%)

Memory

3.3MiB live, 360.5MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(tanh.f64 x)
accuracy	0.01171875	(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
accuracy	0.01171875	(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
accuracy	0.01171875	(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
accuracy	1.787425154521566	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
accuracy	0.015625	(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
accuracy	2.1556312679819576	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x))

Samples

67.0ms	102×	2	valid
48.0ms	132×	1	valid
4.0ms	22×	0	valid

Compiler

Compiled 95 to 22 computations (76.8% saved)

Precisions

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

ival-exp: 41.0ms (41.9% of total)

adjust: 15.0ms (15.3% of total)

ival-mult: 14.0ms (14.3% of total)

ival-add: 10.0ms (10.2% of total)

const: 10.0ms (10.2% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

-11.4MiB live, 27.6MiB allocated

Counts

9 → 108

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())
#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 3)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/3 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/3 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/3 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 2/15 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/15 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3)))) (taylor 0 x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (taylor inf x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (taylor inf x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (taylor inf x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (taylor inf x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (taylor -inf x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (taylor -inf x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (taylor -inf x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (taylor -inf x) (#s(alt (tanh.f64 x) (patch (tanh.f64 x) #<representation binary64>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(tanh x)
1.0ms	x	@	inf	(* (+ (* (* x x) -1/3) 1) x)
1.0ms	x	@	inf	(tanh x)
0.0ms	x	@	0	(* (+ (* (* x x) -1/3) 1) x)
0.0ms	x	@	inf	(* (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) x)

simplify132.0ms (1.7%)

Memory

1.5MiB live, 244.0MiB allocated

Algorithm

1×	egg-herbie

Rules

8 770×	`lower-fma.f64`
8 770×	`lower-fma.f32`
3 082×	`lower-*.f64`
3 082×	`lower-*.f32`
1 558×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	984
1	180	942
2	437	942
3	1286	942
4	4017	942
5	7790	942
0	8118	877

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 103

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))))
(/ (- (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 (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 x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* -1/3 (pow x 2))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* -1/3 (pow x 3))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/3 (pow x 2)))
(+ 1 (* -1/3 (pow x 2)))
(+ 1 (* -1/3 (pow x 2)))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(/ (- (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 (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 x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
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) (- (* 2/15 (pow x 2)) 1/3))))
(* 2/15 (pow x 5))
(* (pow x 5) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* 2/15 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) 2/15)))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4))))))
1
(+ 1 (* -1/3 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))
(+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))
(* 2/15 (pow x 4))
(* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* 2/15 (pow x 4))
(* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
-1/3
(- (* 2/15 (pow x 2)) 1/3)
(- (* 2/15 (pow x 2)) 1/3)
(- (* 2/15 (pow x 2)) 1/3)
(* 2/15 (pow x 2))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* 2/15 (pow x 2))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 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)))
(/ (- (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))) (+ (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))) (+ (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 (* -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))) (+ (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))) (+ (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))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* -1/3 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* -1/3 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(fma.f64 (.f64 (.f64 x 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 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(+ 1 (* -1/3 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* -1/3 (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))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* -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))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 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)))
(/ (- (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))) (+ (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))) (+ (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 (* -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))) (+ (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))) (+ (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))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* 2/15 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64))
(* (pow x 5) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 2/15 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal -1/3 binary64) (.f64 x x)) (-.f64 #s(literal -2/15 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal -1/3 binary64) (.f64 x x)) (-.f64 #s(literal -2/15 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) (pow.f64 x #s(literal 5 binary64)))
(* 2/15 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) 2/15)))
(.f64 (-.f64 #s(literal 2/15 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4))))))
(.f64 (-.f64 (/.f64 #s(literal -1/3 binary64) (.f64 x x)) (-.f64 #s(literal -2/15 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4))))))
(.f64 (-.f64 (/.f64 #s(literal -1/3 binary64) (.f64 x x)) (-.f64 #s(literal -2/15 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) (pow.f64 x #s(literal 5 binary64)))
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 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(* 2/15 (pow x 4))
(.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 2/15 binary64))
(* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x) x)
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(* 2/15 (pow x 4))
(.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 2/15 binary64))
(* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x) x)
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
-1/3
#s(literal -1/3 binary64)
(- (* 2/15 (pow x 2)) 1/3)
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(- (* 2/15 (pow x 2)) 1/3)
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(- (* 2/15 (pow x 2)) 1/3)
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(* 2/15 (pow x 2))
(.f64 #s(literal 2/15 binary64) (.f64 x x))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(* 2/15 (pow x 2))
(.f64 #s(literal 2/15 binary64) (.f64 x x))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 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) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))

rewrite142.0ms (1.8%)

Memory

13.2MiB live, 292.3MiB allocated

Rules

4 354×	`lower-/.f64`
4 354×	`lower-/.f32`
4 350×	`lower-*.f32`
4 344×	`lower-*.f64`
4 148×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	98
0	29	76
1	132	76
2	966	76
0	8641	76

Stop Event

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

Counts

9 → 447

Calls

Call 1

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

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

eval75.0ms (1%)

Memory: -6.8MiB live, 184.9MiB allocated
Compiler: Compiled 15 800 to 1 452 computations (90.8% saved)

prune84.0ms (1.1%)

Memory

26.0MiB live, 190.5MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	586	2	588
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	587	4	591

Accuracy

100.0%

Counts

591 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tanh.f64 x)
▶	96.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
✓	97.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
▶	96.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 34 to 18 computations (47.1% saved)

simplify183.0ms (2.3%)

Memory

-14.2MiB live, 217.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) x)
cost-diff	0	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
cost-diff	0	#s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -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 (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x))

Rules

20 974×	`lower-fma.f32`
20 972×	`lower-fma.f64`
2 992×	`lower-+.f64`
2 992×	`lower-+.f32`
2 542×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	105
0	27	105
1	53	99
2	91	99
3	155	99
4	235	99
5	399	99
6	645	99
7	1008	99
8	1482	99
9	3483	99
10	6387	99
0	8216	93

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 (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (+ (* 2/15 (* x x)) -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)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(.f64 (.f64 x x) x)
(*.f64 x x)
x
#s(literal -1/3 binary64)

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

localize128.0ms (1.6%)

Memory

22.4MiB live, 266.4MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
accuracy	0.09765625	(.f64 (.f64 x x) x)
accuracy	2.1556312679819576	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
accuracy	0.01171875	(.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)
accuracy	1.787425154521566	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x))
accuracy	2.474450130168856	#s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64))

Samples

59.0ms	102×	2	valid
47.0ms	132×	1	valid
3.0ms	22×	0	valid

Compiler

Compiled 77 to 21 computations (72.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-exp: 42.0ms (44.6% of total)

ival-mult: 14.0ms (14.9% of total)

adjust: 12.0ms (12.7% of total)

ival-add: 9.0ms (9.6% of total)

const: 9.0ms (9.6% of total)

ival-div: 4.0ms (4.2% of total)

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

ival-neg: 2.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

-27.4MiB live, 11.6MiB allocated

Counts

7 → 84

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2/15 (pow x 5)) (taylor inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2/15 (pow x 5)) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) 2/15))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/3 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/15 (pow x 4)) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/15 (pow x 4)) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (taylor inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 3)) (taylor inf x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) (patch (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* (* (* x x) x) -1/3) x)
0.0ms	x	@	-inf	(* (* x x) x)
0.0ms	x	@	0	(+ (* (* (* x x) x) -1/3) x)
0.0ms	x	@	0	(* (* x x) x)
0.0ms	x	@	0	(+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1)

simplify123.0ms (1.6%)

Memory

25.1MiB live, 188.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8 006×	`lower-fma.f64`
8 006×	`lower-fma.f32`
3 056×	`lower-*.f64`
3 056×	`lower-*.f32`
1 696×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	722
1	167	686
2	412	686
3	1221	686
4	3071	686
5	5845	686
0	8135	645

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 80

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))))
(/ (- (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 (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 x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
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) (- (* 2/15 (pow x 2)) 1/3))))
(* 2/15 (pow x 5))
(* (pow x 5) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* 2/15 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) 2/15)))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4))))))
1
(+ 1 (* -1/3 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))
(+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))
(* 2/15 (pow x 4))
(* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* 2/15 (pow x 4))
(* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(/ (- (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 (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 x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* -1/3 (pow x 2))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* -1/3 (pow x 3))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 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)))
(/ (- (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))) (+ (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))) (+ (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 (* -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))) (+ (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))) (+ (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))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* 2/15 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64))
(* (pow x 5) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 2/15 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -2/15 binary64)) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -2/15 binary64)) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* 2/15 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) 2/15)))
(.f64 (-.f64 #s(literal 2/15 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -2/15 binary64)) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -2/15 binary64)) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
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 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(* 2/15 (pow x 4))
(.f64 (.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) x) x)
(* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x) x)
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(* 2/15 (pow x 4))
(.f64 (.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) x) x)
(* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x) x)
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 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)))
(/ (- (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))) (+ (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))) (+ (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 (* -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))) (+ (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))) (+ (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))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* -1/3 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* -1/3 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite134.0ms (1.7%)

Memory

-36.3MiB live, 242.4MiB allocated

Rules

4 564×	`lower-*.f32`
4 558×	`lower-*.f64`
4 466×	`lower-fma.f32`
4 464×	`lower-fma.f64`
4 350×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	101
0	27	73
1	121	73
2	896	73
0	8545	67

Stop Event

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

Counts

7 → 69

Calls

Call 1

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

Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x)
(.f64 x #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
(.f64 (fma.f64 x x (.f64 #s(literal -1/9 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64)))))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64))))))))
(.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 1/3 binary64) (.f64 (.f64 (.f64 x x) x) x))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64)))))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))) (.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))) (+.f64 (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (fma.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (.f64 (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))))))
(/.f64 (neg.f64 (fma.f64 x x (.f64 #s(literal -1/9 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))))) (neg.f64 (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (neg.f64 x) x)))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x)))) (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64))))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) #s(literal 1/81 binary64) (.f64 (.f64 (neg.f64 x) x) (.f64 x x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x))) #s(literal 1/729 binary64) (.f64 (neg.f64 (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) #s(literal 1/81 binary64) (fma.f64 (.f64 (.f64 x x) x) x (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 #s(literal 1/9 binary64) (.f64 x x))))) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x))) #s(literal 1/729 binary64) (.f64 (neg.f64 (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 (neg.f64 x) x) x)) (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)))))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64)) #s(literal 9 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x))) #s(literal 1/729 binary64) (-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) (.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x))))) (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)) (.f64 x x))) (.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (fma.f64 x x (.f64 #s(literal -1/9 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)))) (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (neg.f64 x) x))) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 x x (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 1/3 binary64) (.f64 (.f64 (*.f64 x x) x) x))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)))))))
(/.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (neg.f64 x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x)) (fma.f64 x x (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 1/3 binary64) (.f64 (.f64 (*.f64 x x) x) x)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x)) (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64))) (fma.f64 x x (.f64 #s(literal -1/9 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 1/3 binary64) (.f64 (.f64 (.f64 x x) x) x)))) (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (*.f64 x x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (neg.f64 x) x))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x))) (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)))))))
(neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (neg.f64 x) x)) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))))
(neg.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal -1/27 binary64) (.f64 (.f64 x x) x)) (neg.f64 (fma.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64))))))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)))
(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
(fma.f64 (.f64 #s(literal -1/3 binary64) x) (.f64 x x) x)
(fma.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x)
(fma.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) x) x)
(fma.f64 (.f64 x x) (.f64 #s(literal -1/3 binary64) x) x)
(fma.f64 x (.f64 x (.f64 #s(literal -1/3 binary64) x)) x)
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/3 binary64)) x)
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64)))) (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(+.f64 (/.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))))
(+.f64 (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)) x)
(+.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 x #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval15.0ms (0.2%)

Memory: 36.7MiB live, 36.7MiB allocated
Compiler: Compiled 3 130 to 234 computations (92.5% saved)

prune16.0ms (0.2%)

Memory

0.8MiB live, 39.3MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	149	4	153

Accuracy

100.0%

Counts

153 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tanh.f64 x)
✓	96.6%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) x))
✓	97.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
✓	96.2%	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (.f64 #s(approx (+ ( (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 87 to 38 computations (56.3% saved)

regimes5.0ms (0.1%)

Memory

-28.0MiB live, 11.1MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs
(tanh.f64 x)

Calls

2 calls:

3.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	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 16 to 8 computations (50% saved)

regimes4.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 16 to 8 computations (50% saved)

regimes4.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

Calls

2 calls:

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
96.6%	1	`x`
96.6%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 16 to 8 computations (50% saved)

regimes3.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
96.6%	1	`x`
96.6%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 16 to 8 computations (50% saved)

regimes2.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
96.2%	1	`x`
96.2%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 16 to 8 computations (50% saved)

simplify7.0ms (0.1%)

Memory

-27.0MiB live, 17.8MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	104
1	37	104

Stop Event

1×

saturated

Calls

Call 1

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

soundness588.0ms (7.5%)

Memory

-2.4MiB live, 434.2MiB allocated

Rules

12 890×	`lower-fma.f64`
12 890×	`lower-fma.f32`
8 770×	`lower-fma.f64`
8 770×	`lower-fma.f32`
4 156×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
0	13	15
1	55	15
2	424	15
3	7080	15
0	8062	15
0	90	425
1	259	424
2	604	414
3	1659	414
4	2630	414
5	4160	414
6	4872	414
7	6500	414
0	8123	386
0	71	984
1	180	942
2	437	942
3	1286	942
4	4017	942
5	7790	942
0	8118	877

Stop Event

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

Compiler

Compiled 116 to 58 computations (50% saved)

preprocess53.0ms (0.7%)

Memory: 3.9MiB live, 123.0MiB allocated
Remove: (negabs x)
Compiler: Compiled 114 to 46 computations (59.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze1.0ms (0%)

sample4.1s (52%)

explain274.0ms (3.5%)

preprocess106.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify38.0ms (0.5%)

localize166.0ms (2.1%)

series4.0ms (0.1%)

simplify296.0ms (3.8%)

rewrite405.0ms (5.1%)

eval356.0ms (4.5%)

prune99.0ms (1.3%)

simplify177.0ms (2.2%)

localize142.0ms (1.8%)

series12.0ms (0.2%)

simplify132.0ms (1.7%)

rewrite142.0ms (1.8%)

eval75.0ms (1%)

prune84.0ms (1.1%)

simplify183.0ms (2.3%)

localize128.0ms (1.6%)

series6.0ms (0.1%)

simplify123.0ms (1.6%)

rewrite134.0ms (1.7%)

eval15.0ms (0.2%)

prune16.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify7.0ms (0.1%)

soundness588.0ms (7.5%)

preprocess53.0ms (0.7%)

end0.0ms (0%)

Profiling