Metrics for Hyperbolic tangent

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 9 computations (40% saved)

sample4.2s (53%)

Memory

15.0MiB live, 6 619.2MiB allocated

Samples

1.6s	2 932×	2	valid
1.2s	4 782×	1	valid
680.0ms	7 918×	0	exit
33.0ms	542×	0	valid

Precisions

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

ival-exp: 2.0s (67.2% of total)

ival-div: 322.0ms (10.9% of total)

adjust: 223.0ms (7.6% of total)

ival-sub: 138.0ms (4.7% of total)

ival-add: 135.0ms (4.6% of total)

ival-neg: 131.0ms (4.4% of total)

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

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

Bogosity

explain208.0ms (2.6%)

Memory

-6.0MiB live, 437.8MiB 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

82.0ms	204×	2	valid
47.0ms	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: 109.0ms

ival-exp: 75.0ms (68.6% of total)

adjust: 12.0ms (11% of total)

ival-div: 8.0ms (7.3% of total)

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

ival-sub: 5.0ms (4.6% of total)

ival-neg: 2.0ms (1.8% of total)

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

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

preprocess83.0ms (1%)

Memory

24.2MiB live, 102.2MiB 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: 0.7MiB live, 0.7MiB 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)

simplify35.0ms (0.4%)

Memory

-11.1MiB live, 27.9MiB 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))

localize81.0ms (1%)

Memory

-11.0MiB live, 148.0MiB 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

41.0ms	102×	2	valid
28.0ms	132×	1	valid
1.0ms	22×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-exp: 37.0ms (69.7% of total)

adjust: 5.0ms (9.4% of total)

ival-div: 4.0ms (7.5% of total)

ival-add: 3.0ms (5.7% of total)

ival-sub: 3.0ms (5.7% of total)

ival-neg: 1.0ms (1.9% of total)

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

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

series4.0ms (0%)

Memory

10.6MiB live, 10.6MiB 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 (* 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 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 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 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))) (+ (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 (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) (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 (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 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))) (+ (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 (- (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 (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 (* -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 (+ (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

3 calls:

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

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify159.0ms (2%)

Memory

13.5MiB live, 213.1MiB 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	1672	414
4	2645	414
5	4176	414
6	4889	414
7	6516	414
0	8145	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))))
(* 2 x)
(* x (+ 2 (* 1/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
2
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (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 x)
(exp x)
(exp x)
(exp (neg x))
(exp (neg x))
(exp (neg 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))))
(- (exp x) (exp (* -1 x)))
(- (exp x) (exp (* -1 x)))
(- (exp x) (exp (* -1 x)))
(- (exp x) (exp (* -1 x)))
(exp x)
(exp x)
(exp x)
(exp x)
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 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)
(* 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)
1
#s(literal 1 binary64)
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
2
#s(literal 2 binary64)
(+ 2 (pow x 2))
(fma.f64 x x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(fma.f64 (fma.f64 #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))) (+ (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 (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.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.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 (neg x))
(exp.f64 (neg.f64 x))
(+ (exp x) (exp (neg x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+ (exp x) (exp (neg x)))
(+.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))) (+ (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)))
(- (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)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.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))
(+ (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))

rewrite151.0ms (1.9%)

Memory

-16.6MiB live, 267.2MiB 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)))
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eval91.0ms (1.1%)

Memory: 2.2MiB live, 202.5MiB allocated
Compiler: Compiled 17 692 to 1 738 computations (90.2% saved)

prune94.0ms (1.2%)

Memory

3.0MiB live, 243.1MiB 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)

simplify158.0ms (2%)

Memory

5.4MiB live, 202.4MiB 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

localize144.0ms (1.8%)

Memory

3.9MiB live, 286.1MiB 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

76.0ms	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: 108.0ms

ival-exp: 53.0ms (49.3% of total)

ival-mult: 14.0ms (13% of total)

adjust: 12.0ms (11.2% of total)

ival-add: 9.0ms (8.4% of total)

const: 9.0ms (8.4% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory

-11.4MiB live, 27.4MiB 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 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 (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 (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 x (taylor 0 x) (#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 (* 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 (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 (* 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 (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 (* 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 (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 x (taylor 0 x) (#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 (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#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 (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#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 (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))) (taylor 0 x) (#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 1 (taylor 0 x) (#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 (+ 1 (* -1/3 (pow x 2))) (taylor 0 x) (#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 (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))) (taylor 0 x) (#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>) () ())) ())
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#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 (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 (* 2/15 (pow x 5)) (taylor -inf x) (#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 (* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) 2/15))) (taylor -inf x) (#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 (* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4)))))) (taylor -inf x) (#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 (* -1 (* (pow x 5) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/15 (/ 1 (pow x 4)))))) (taylor -inf x) (#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 (* 2/15 (pow x 4)) (taylor -inf x) (#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 (* (pow x 4) (- 2/15 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#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 (* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#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 (* (pow x 4) (- (+ 2/15 (/ 1 (pow x 4))) (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#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 (* 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 (/ (- (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

3 calls:

Time

Variable

Point

Expression

6.0ms

-inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* x x) -1/3) 1) x) (+ (* (* x x) -1/3) 1) (* x x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) (+ (* 2/15 (* x x)) -1/3) (tanh x))

3.0ms

inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* x x) -1/3) 1) x) (+ (* (* x x) -1/3) 1) (* x x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) (+ (* 2/15 (* x x)) -1/3) (tanh x))

2.0ms

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* x x) -1/3) 1) x) (+ (* (* x x) -1/3) 1) (* x x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) (+ (* 2/15 (* x x)) -1/3) (tanh x))

simplify117.0ms (1.5%)

Memory

22.1MiB live, 179.8MiB 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	1292	942
4	3980	942
5	7740	942
0	8068	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))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* -1/3 (pow x 2))))
1
(+ 1 (* -1/3 (pow x 2)))
(+ 1 (* -1/3 (pow x 2)))
(+ 1 (* -1/3 (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))))
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))))
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)))
-1/3
(- (* 2/15 (pow x 2)) 1/3)
(- (* 2/15 (pow x 2)) 1/3)
(- (* 2/15 (pow x 2)) 1/3)
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(/ (- (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))))
(* -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 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)
(/ (- (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))))
(* 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 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 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)))))
(/ (- (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) (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))))
(* -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)))))
(* -1/3 (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)
(/ (- (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))))
(* 2/15 (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))))))
(* 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 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)))))
(/ (- (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))))
(.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)
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 (* -1/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* -1/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 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))
(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))))
(.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)
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) (- (* 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)
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))
-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))
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)))
(* -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))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(* -1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* (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)
(/ (- (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)))
(* 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 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 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))
(/ (- (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) (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)))
(* -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)))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(* -1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* (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)
(/ (- (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)))
(* 2/15 (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)))
(* 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 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))
(/ (- (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)))

rewrite164.0ms (2.1%)

Memory

-11.1MiB live, 228.0MiB 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)))))
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(/.f64 (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 (-.f64 (neg.f64 x) x))) (pow.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 x))))
(/.f64 (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64)))) (.f64 (neg.f64 (+.f64 (-.f64 (exp.f64 (-.f64 (neg.f64 x) x)) #s(literal -1 binary64)) (exp.f64 (+.f64 x x)))) (.f64 #s(literal -2 binary64) (cosh.f64 x))))
(/.f64 (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (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 (exp.f64 (.f64 x #s(literal 3 binary64))) (exp.f64 (.f64 (neg.f64 x) #s(literal 3 binary64)))) (.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 (.f64 #s(literal -2 binary64) (sinh.f64 x)) (.f64 #s(literal -2 binary64) (cosh.f64 x)))
(/.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)))))

eval96.0ms (1.2%)

Memory: -2.8MiB live, 153.7MiB allocated
Compiler: Compiled 15 800 to 1 451 computations (90.8% saved)

prune163.0ms (2.1%)

Memory

5.2MiB live, 162.7MiB 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 #s(literal -1/3 binary64) (.f64 x x)) x 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)

simplify235.0ms (3%)

Memory

17.9MiB live, 218.2MiB 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 #s(literal -1/3 binary64) (.f64 x x))
cost-diff	0	(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
cost-diff	0	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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

20 982×	`lower-fma.f32`
20 980×	`lower-fma.f64`
2 994×	`lower-+.f64`
2 994×	`lower-+.f32`
2 542×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	105
0	27	105
1	57	105
2	96	103
3	158	103
4	233	103
5	451	103
6	709	103
7	1022	103
8	1488	103
9	3463	103
10	6376	103
0	8180	95

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 #s(literal -1/3 binary64) (.f64 x x)) x x))
(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
(.f64 #s(literal -1/3 binary64) (.f64 x x))
#s(literal -1/3 binary64)
(*.f64 x 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)
#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 #s(literal -1/3 binary64) (.f64 x x)) x x))
(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
(.f64 #s(literal -1/3 binary64) (.f64 x x))
#s(literal -1/3 binary64)
(*.f64 x x)
x

localize214.0ms (2.7%)

Memory

-4.3MiB live, 201.2MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
accuracy	0.18359375	(.f64 #s(literal -1/3 binary64) (.f64 x x))
accuracy	2.1556312679819576	#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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

108.0ms	102×	2	valid
89.0ms	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: 153.0ms

ival-exp: 87.0ms (56.8% of total)

ival-add: 23.0ms (15% of total)

ival-mult: 14.0ms (9.1% of total)

adjust: 12.0ms (7.8% of total)

const: 9.0ms (5.9% of total)

ival-div: 4.0ms (2.6% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.3%)

Memory

-29.0MiB live, 12.3MiB 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 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 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 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 x (taylor 0 x) (#s(alt #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.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 0 x) (#s(alt (.f64 x x) (patch (.f64 x 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 (* 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 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 (/ (- (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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 3)) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/3)) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.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 (/ (- (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 (* 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 (* 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 (/ (- (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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x x)) (patch #s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) (patch (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/3 binary64) (.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

3 calls:

Time

Variable

Point

Expression

18.0ms

inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 (* x x)) x) x) (* -1/3 (* x x)) (* x x))

2.0ms

-inf

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 (* x x)) x) x) (* -1/3 (* x x)) (* x x))

1.0ms

((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) -1/3) (* x x)) 1) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 (* x x)) x) x) (* -1/3 (* x x)) (* x x))

simplify142.0ms (1.8%)

Memory

27.1MiB live, 144.0MiB allocated

Algorithm

1×	egg-herbie

Rules

7 934×	`lower-fma.f64`
7 934×	`lower-fma.f32`
3 174×	`lower-*.f64`
3 174×	`lower-*.f32`
1 698×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	746
1	167	710
2	412	710
3	1227	710
4	3078	710
5	5708	710
0	8279	669

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

rewrite317.0ms (4%)

Memory

-24.7MiB live, 227.1MiB allocated

Rules

4 558×	`lower-fma.f32`
4 556×	`lower-fma.f64`
4 548×	`lower-*.f32`
4 542×	`lower-*.f64`
4 404×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	101
0	27	79
1	125	77
2	914	77
0	8609	69

Stop Event

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

Counts

7 → 67

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 #s(literal -1/3 binary64) (.f64 x x)) x x))
(fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)
(.f64 #s(literal -1/3 binary64) (.f64 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 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x)))))))
(.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/9 binary64) (.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 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x))))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x x))
(.f64 x (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #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 (.f64 (.f64 (.f64 (.f64 x x) x) x) #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 (.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 (.f64 (.f64 (.f64 x x) x) x) #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 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 (.f64 (.f64 x x) x) x) #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 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 (.f64 (.f64 x x) x) x) #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 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 #s(literal -1/3 binary64) (*.f64 x x)) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x)))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) (.f64 (.f64 (neg.f64 x) x) (.f64 x x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (fma.f64 #s(literal 1/729 binary64) (.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))) (.f64 (neg.f64 (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) (fma.f64 (.f64 (.f64 x x) x) x (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 (.f64 (.f64 x x) x) x)))) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (.f64 (fma.f64 #s(literal 1/729 binary64) (.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))) (.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 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x))))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x) #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 #s(literal 1/729 binary64) (.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))) (-.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)) #s(literal -1/27 binary64)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 #s(literal -1/3 binary64) (*.f64 x x)) x)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/9 binary64) (.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 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x))))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 #s(literal -1/3 binary64) (.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 x x (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/9 binary64) (.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 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x)) (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 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/9 binary64) (.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 #s(literal -1/3 binary64) (.f64 x x)) x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x))))))
(neg.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x) (.f64 x (-.f64 x (.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 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x))
(fma.f64 (.f64 #s(literal -1/3 binary64) x) (.f64 x x) x)
(fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x 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 #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))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) x))) (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 x x)) (-.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #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 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal -1/3 binary64) (neg.f64 x))))
(+.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/9 binary64)) (.f64 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 #s(literal -1/3 binary64) (*.f64 x x)) x) x)
(+.f64 x (.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) x))
(.f64 (.f64 #s(literal -1/3 binary64) x) x)
(.f64 (.f64 #s(literal -1/3 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal -1/3 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal -1/3 binary64))
(.f64 x (.f64 #s(literal -1/3 binary64) x))
(*.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)))

eval47.0ms (0.6%)

Memory: -9.6MiB live, 29.2MiB allocated
Compiler: Compiled 3 114 to 226 computations (92.7% saved)

prune15.0ms (0.2%)

Memory

27.4MiB live, 27.4MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	147	4	151

Accuracy

100.0%

Counts

151 → 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 #s(literal -1/3 binary64) (.f64 x x)) x 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)

regimes14.0ms (0.2%)

Memory

-28.6MiB 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 #s(literal -1/3 binary64) (.f64 x x)) 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))
(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:

11.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
3.0ms	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%)

Memory

9.6MiB live, 9.6MiB 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 #s(literal -1/3 binary64) (.f64 x x)) 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))

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)

regimes3.0ms (0%)

Memory

7.6MiB live, 7.6MiB 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 #s(literal -1/3 binary64) (*.f64 x x)) x x))

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

6.1MiB live, 6.1MiB 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)

regimes3.0ms (0%)

Memory

6.4MiB live, 6.4MiB 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)

simplify36.0ms (0.4%)

Memory

-32.5MiB live, 12.2MiB 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 #s(literal -1/3 binary64) (.f64 x x)) x 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 #s(literal -1/3 binary64) (.f64 x x)) x 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))

soundness877.0ms (11%)

Memory

25.5MiB live, 544.7MiB allocated

Rules

12 890×	`lower-fma.f64`
12 890×	`lower-fma.f32`
8 770×	`lower-fma.f64`
8 770×	`lower-fma.f32`
4 354×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	98
0	29	76
1	132	76
2	966	76
0	8641	76
0	71	984
1	180	942
2	437	942
3	1292	942
4	3980	942
5	7740	942
0	8068	877
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	1672	414
4	2645	414
5	4176	414
6	4889	414
7	6516	414
0	8145	386

Stop Event

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

Compiler

Compiled 117 to 59 computations (49.6% saved)

preprocess45.0ms (0.6%)

Memory: -11.4MiB live, 107.2MiB 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%)

analyze0.0ms (0%)

sample4.2s (53%)

explain208.0ms (2.6%)

preprocess83.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify35.0ms (0.4%)

localize81.0ms (1%)

series4.0ms (0%)

simplify159.0ms (2%)

rewrite151.0ms (1.9%)

eval91.0ms (1.1%)

prune94.0ms (1.2%)

simplify158.0ms (2%)

localize144.0ms (1.8%)

series14.0ms (0.2%)

simplify117.0ms (1.5%)

rewrite164.0ms (2.1%)

eval96.0ms (1.2%)

prune163.0ms (2.1%)

simplify235.0ms (3%)

localize214.0ms (2.7%)

series24.0ms (0.3%)

simplify142.0ms (1.8%)

rewrite317.0ms (4%)

eval47.0ms (0.6%)

prune15.0ms (0.2%)

regimes14.0ms (0.2%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

simplify36.0ms (0.4%)

soundness877.0ms (11%)

preprocess45.0ms (0.6%)

end0.0ms (0%)

Profiling