Metrics for NMSE Section 6.1 mentioned, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze54.0ms (0.5%)

Memory

-16.8MiB live, 60.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.7%	92.5%	6.2%	0.1%	0%	1.2%	0%	9
93.7%	92.5%	6.2%	0.1%	0%	1.2%	0%	10
96.8%	94.9%	3.1%	0.1%	0%	1.9%	0%	11
96.8%	94.9%	3.1%	0.1%	0%	1.9%	0%	12

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample2.4s (20.3%)

Memory

74.0MiB live, 4 080.0MiB allocated

Samples

840.0ms	2 332×	1	valid
834.0ms	5 923×	0	valid
143.0ms	1 005×	0	exit
3.0ms	18×	1	exit
1.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-mult: 340.0ms (22.6% of total)

ival-exp: 339.0ms (22.5% of total)

ival-div: 254.0ms (16.9% of total)

ival-sub: 171.0ms (11.4% of total)

ival-add: 164.0ms (10.9% of total)

ival-neg: 121.0ms (8% of total)

adjust: 93.0ms (6.2% of total)

exact: 10.0ms (0.7% of total)

ival-true: 8.0ms (0.5% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

explain427.0ms (3.7%)

Memory

-1.1MiB live, 647.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
77	4	(8.110409549897334e-101 -1.4765479330052761e-8)	-	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`
0	0	-	-	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
0	0	-	-	`(exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))`
0	0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) eps)`
0	0	-	-	`(+.f64 #s(literal 1 binary64) eps)`
0	0	-	-	`(*.f64 (-.f64 #s(literal 1 binary64) eps) x)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) eps)`
0	0	-	-	`eps`
0	0	-	-	`(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))`
0	0	-	-	`(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))`
0	0	-	-	`(.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x))))`
0	0	-	-	`(neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(*.f64 (+.f64 #s(literal 1 binary64) eps) x)`
0	0	-	-	`(exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`	cancellation	81	0

Confusion

	Predicted +	Predicted -
+	78	0
-	3	175

Precision

0.9629629629629629

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	78	0	0
-	3	0	175

Precision?

0.9629629629629629

Recall?

1.0

Freqs

test

number	freq
0	175
1	81

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

118.0ms	156×	1	valid
61.0ms	356×	0	valid

Compiler

Compiled 317 to 61 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-add: 59.0ms (40.2% of total)

ival-mult: 25.0ms (17% of total)

ival-div: 23.0ms (15.7% of total)

ival-exp: 18.0ms (12.3% of total)

ival-sub: 9.0ms (6.1% of total)

adjust: 6.0ms (4.1% of total)

ival-neg: 5.0ms (3.4% of total)

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

exact: 1.0ms (0.7% of total)

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

preprocess175.0ms (1.5%)

Memory

30.7MiB live, 263.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 102×	`lower-fma.f64`
11 102×	`lower-fma.f32`
2 706×	`lower-*.f32`
2 698×	`lower-*.f64`
1 598×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	155
1	168	138
2	524	135
3	1740	135
4	4682	133
0	19	29
0	34	29
1	70	29
2	169	27
3	513	27
4	1130	27
5	3343	25
6	7591	25
0	8123	23

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

(fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) eps)) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) eps)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))

Symmetry

(abs eps)

Compiler

Compiled 31 to 19 computations (38.7% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	70.5%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))

Status

Accuracy

Program

▶

70.5%

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

Compiler

Compiled 31 to 19 computations (38.7% saved)

simplify180.0ms (1.5%)

Memory

-9.0MiB live, 204.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	128	(*.f64 (+.f64 #s(literal 1 binary64) eps) x)
cost-diff	128	(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))
cost-diff	128	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))
cost-diff	704	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))

Rules

11 102×	`lower-fma.f64`
11 102×	`lower-fma.f32`
2 706×	`lower-*.f32`
2 698×	`lower-*.f64`
1 598×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	141
0	34	141
1	70	141
2	169	131
3	513	131
4	1130	131
5	3343	129
6	7591	129
0	8123	123

Stop Event

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

Calls

Call 1

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

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

localize96.0ms (0.8%)

Memory

6.1MiB live, 162.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
accuracy	0.01171875	(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
accuracy	0.01171875	(*.f64 (+.f64 #s(literal 1 binary64) eps) x)
accuracy	18.64809640009885	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))

Samples

51.0ms	78×	1	valid
24.0ms	178×	0	valid

Compiler

Compiled 143 to 21 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-exp: 35.0ms (57.6% of total)

ival-mult: 7.0ms (11.5% of total)

ival-div: 5.0ms (8.2% of total)

ival-sub: 4.0ms (6.6% of total)

ival-add: 4.0ms (6.6% of total)

adjust: 3.0ms (4.9% of total)

ival-neg: 2.0ms (3.3% of total)

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

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

exact: 0.0ms (0% of total)

series38.0ms (0.3%)

Memory

-23.4MiB live, 48.8MiB allocated

Counts

6 → 132

Calls

Call 1

Inputs
#s(alt (/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) (patch (/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) (patch (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #<representation binary64>) () ())
#s(alt (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)) (patch (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (+.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (taylor 0 eps) (#s(alt (/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) (patch (/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* x (- 1 eps)) (taylor 0 x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor 0 x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 eps)) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal 1 binary64) eps) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 eps) (taylor 0 eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 eps) eps) (taylor 0 eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 eps) eps) (taylor 0 eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 eps) eps) (taylor 0 eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (/ 1 eps)) (taylor inf eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (/ 1 eps)) (taylor inf eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (/ 1 eps)) (taylor inf eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (/ 1 eps)) (taylor -inf eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (/ 1 eps)) (taylor -inf eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (/ 1 eps)) (taylor -inf eps) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())) ())

Calls

33 calls:

Time	Variable		Point	Expression
19.0ms	eps	@	0	(/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2)
2.0ms	x	@	-inf	(/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2)
2.0ms	eps	@	-inf	(/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2)
1.0ms	x	@	inf	(/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2)
1.0ms	x	@	0	(/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2)

simplify435.0ms (3.7%)

Memory

-105.5MiB live, 301.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 046×	`lower-fma.f64`
12 046×	`lower-fma.f32`
4 270×	`lower-*.f64`
4 270×	`lower-*.f32`
2 328×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	231	2534
1	733	2245
2	2538	1951
3	7519	1951
0	8258	1820

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 130

Calls

Call 1

Inputs
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
1
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))
(- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))
(- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (+ (* 1/2 (* (pow x 2) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))
(- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (+ (* 1/2 (* (pow x 2) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (+ (* 1/24 (* (pow x 4) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x))))))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))
(- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))
(- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps)))
(- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps)))
(- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps)))
(- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))
(- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))
(- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))
(- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))
2
(+ 2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))
(+ 2 (* x (- (+ (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))
(+ 2 (* x (- (+ (* x (- (+ (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))
(* -1 x)
(- (* eps x) x)
(- (* eps x) x)
(- (* eps x) x)
(* eps x)
(* eps (- (* -1 (/ x eps)) (* -1 x)))
(* eps (- (* -1 (/ x eps)) (* -1 x)))
(* eps (- (* -1 (/ x eps)) (* -1 x)))
(* eps x)
(* -1 (* eps (- (/ x eps) x)))
(* -1 (* eps (- (/ x eps) x)))
(* -1 (* eps (- (/ x eps) x)))
(* x (- eps 1))
(* x (- eps 1))
(* x (- eps 1))
(* x (- eps 1))
(* x (- eps 1))
(* x (- eps 1))
(* x (- eps 1))
(* x (- eps 1))
(* -1 (* x (- 1 eps)))
(* -1 (* x (- 1 eps)))
(* -1 (* x (- 1 eps)))
(* -1 (* x (- 1 eps)))
x
(+ x (* eps x))
(+ x (* eps x))
(+ x (* eps x))
(* eps x)
(* eps (+ x (/ x eps)))
(* eps (+ x (/ x eps)))
(* eps (+ x (/ x eps)))
(* eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
(* x (+ 1 eps))
x
(+ x (* -1 (* eps x)))
(+ x (* -1 (* eps x)))
(+ x (* -1 (* eps x)))
(* -1 (* eps x))
(* eps (+ (* -1 x) (/ x eps)))
(* eps (+ (* -1 x) (/ x eps)))
(* eps (+ (* -1 x) (/ x eps)))
(* -1 (* eps x))
(* -1 (* eps (+ x (* -1 (/ x eps)))))
(* -1 (* eps (+ x (* -1 (/ x eps)))))
(* -1 (* eps (+ x (* -1 (/ x eps)))))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(* x (- 1 eps))
(/ 1 eps)
(/ (+ 1 eps) eps)
(/ (+ 1 eps) eps)
(/ (+ 1 eps) eps)
1
(+ 1 (/ 1 eps))
(+ 1 (/ 1 eps))
(+ 1 (/ 1 eps))
1
(+ 1 (/ 1 eps))
(+ 1 (/ 1 eps))
(+ 1 (/ 1 eps))

Outputs
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(.f64 (fma.f64 (.f64 (exp.f64 (neg.f64 x)) (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64))))) (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
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(fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) x #s(literal 2 binary64))
(+ 2 (* x (- (+ (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))) x #s(literal 2 binary64))
(+ 2 (* x (- (+ (* x (- (+ (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps) (.f64 (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/6 binary64)) x)) x (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))) x #s(literal 2 binary64))
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(* -1 x)
(neg.f64 x)
(- (* eps x) x)
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(- (* eps x) x)
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(- (* eps x) x)
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* eps x)
(*.f64 eps x)
(* eps (- (* -1 (/ x eps)) (* -1 x)))
(*.f64 (-.f64 x (/.f64 x eps)) eps)
(* eps (- (* -1 (/ x eps)) (* -1 x)))
(*.f64 (-.f64 x (/.f64 x eps)) eps)
(* eps (- (* -1 (/ x eps)) (* -1 x)))
(*.f64 (-.f64 x (/.f64 x eps)) eps)
(* eps x)
(*.f64 eps x)
(* -1 (* eps (- (/ x eps) x)))
(*.f64 (-.f64 x (/.f64 x eps)) eps)
(* -1 (* eps (- (/ x eps) x)))
(*.f64 (-.f64 x (/.f64 x eps)) eps)
(* -1 (* eps (- (/ x eps) x)))
(*.f64 (-.f64 x (/.f64 x eps)) eps)
(* x (- eps 1))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* x (- eps 1))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* x (- eps 1))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* x (- eps 1))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* x (- eps 1))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* x (- eps 1))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* x (- eps 1))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* x (- eps 1))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* -1 (* x (- 1 eps)))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* -1 (* x (- 1 eps)))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* -1 (* x (- 1 eps)))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(* -1 (* x (- 1 eps)))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
x
(+ x (* eps x))
(fma.f64 eps x x)
(+ x (* eps x))
(fma.f64 eps x x)
(+ x (* eps x))
(fma.f64 eps x x)
(* eps x)
(*.f64 eps x)
(* eps (+ x (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) x) eps)
(* eps (+ x (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) x) eps)
(* eps (+ x (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) x) eps)
(* eps x)
(*.f64 eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))
(*.f64 (+.f64 (/.f64 x eps) x) eps)
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))
(*.f64 (+.f64 (/.f64 x eps) x) eps)
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))
(*.f64 (+.f64 (/.f64 x eps) x) eps)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
(* x (+ 1 eps))
(fma.f64 eps x x)
x
(+ x (* -1 (* eps x)))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(+ x (* -1 (* eps x)))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(+ x (* -1 (* eps x)))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* eps (+ (* -1 x) (/ x eps)))
(*.f64 (-.f64 (/.f64 x eps) x) eps)
(* eps (+ (* -1 x) (/ x eps)))
(*.f64 (-.f64 (/.f64 x eps) x) eps)
(* eps (+ (* -1 x) (/ x eps)))
(*.f64 (-.f64 (/.f64 x eps) x) eps)
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* -1 (* eps (+ x (* -1 (/ x eps)))))
(*.f64 (-.f64 (/.f64 x eps) x) eps)
(* -1 (* eps (+ x (* -1 (/ x eps)))))
(*.f64 (-.f64 (/.f64 x eps) x) eps)
(* -1 (* eps (+ x (* -1 (/ x eps)))))
(*.f64 (-.f64 (/.f64 x eps) x) eps)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(* x (- 1 eps))
(*.f64 (-.f64 #s(literal 1 binary64) eps) x)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ (+ 1 eps) eps)
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps)
(/ (+ 1 eps) eps)
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps)
(/ (+ 1 eps) eps)
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps)
1
#s(literal 1 binary64)
(+ 1 (/ 1 eps))
(+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(+ 1 (/ 1 eps))
(+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(+ 1 (/ 1 eps))
(+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (/ 1 eps))
(+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(+ 1 (/ 1 eps))
(+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(+ 1 (/ 1 eps))
(+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))

rewrite202.0ms (1.7%)

Memory

3.0MiB live, 388.8MiB allocated

Rules

4 830×	`lower-fma.f64`
4 830×	`lower-fma.f32`
3 930×	`lower-/.f32`
3 926×	`lower-/.f64`
3 926×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	77
0	34	77
1	131	73
2	932	72
0	8931	66

Stop Event

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

Counts

6 → 454

Calls

Call 1

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

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

eval120.0ms (1%)

Memory: 32.7MiB live, 225.6MiB allocated
Compiler: Compiled 30 258 to 2 344 computations (92.3% saved)

prune103.0ms (0.9%)

Memory

-11.9MiB live, 263.1MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	578	6	584
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	579	6	585

Accuracy

100.0%

Counts

585 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.2%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
▶	47.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
	44.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps) (.f64 (*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/6 binary64)) x)) x (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal 1 binary64)))
▶	99.3%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
▶	59.5%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
▶	47.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

Compiler

Compiled 424 to 176 computations (58.5% saved)

simplify133.0ms (1.1%)

Memory

9.2MiB live, 243.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	320	(*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))
cost-diff	384	(+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))
cost-diff	384	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps))
cost-diff	2368	(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
cost-diff	0	(exp.f64 (neg.f64 x))
cost-diff	0	(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
cost-diff	512	(.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
cost-diff	320	(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64))
cost-diff	384	(+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))
cost-diff	2368	(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
cost-diff	0	(exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x))
cost-diff	0	(+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)))
cost-diff	0	(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))

Rules

9 418×	`lower-fma.f32`
9 410×	`lower-fma.f64`
3 240×	`lower-*.f32`
3 224×	`lower-*.f64`
2 154×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	686
0	93	684
1	200	679
2	600	607
3	2350	463
4	6163	463
0	8213	449

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)))
(exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x))
(*.f64 (-.f64 #s(literal -1 binary64) eps) x)
(-.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
eps
x
(exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(-.f64 eps #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1 binary64)
eps
(+.f64 #s(literal 1 binary64) eps)
(+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))
(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
(-.f64 eps #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
(.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))
(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x))
(exp.f64 (neg.f64 x))
(neg.f64 x)
x
(+.f64 (+.f64 x #s(literal 2 binary64)) x)
(+.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))
#s(literal 1/4 binary64)
(fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))
(-.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
eps
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps))
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps)
(+.f64 #s(literal 1 binary64) eps)
#s(literal 1 binary64)
(*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))
(+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))
(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
(-.f64 eps #s(literal 1 binary64))
x
(*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1/2 binary64)

Outputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x)))))
(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)))
(exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x))
(*.f64 (-.f64 #s(literal -1 binary64) eps) x)
(-.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
eps
x
(exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(-.f64 eps #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(literal 0 binary64) x #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 #s(literal 0 binary64) x #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
x
#s(literal 1/2 binary64)
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
#s(literal 0 binary64)
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1 binary64)
eps
(+.f64 #s(literal 1 binary64) eps)
(-.f64 eps #s(literal -1 binary64))
(+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))
(-.f64 eps (/.f64 #s(literal 1 binary64) eps))
(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
(-.f64 eps #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 (+.f64 x #s(literal 1 binary64)) (exp.f64 (neg.f64 x))))
(.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))
(*.f64 (+.f64 x #s(literal 1 binary64)) (exp.f64 (neg.f64 x)))
(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))
(exp.f64 (neg.f64 x))
(neg.f64 x)
x
(+.f64 (+.f64 x #s(literal 2 binary64)) x)
(fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))
(+.f64 x #s(literal 2 binary64))
(+.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps))) #s(literal 0 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps))) #s(literal 0 binary64)) x #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(fma.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps))) #s(literal 0 binary64))
(.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))
(.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps))) #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps)))
(-.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
eps
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps))
(-.f64 (/.f64 #s(literal 1 binary64) eps) eps)
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps)
(/.f64 (-.f64 eps #s(literal -1 binary64)) eps)
(+.f64 #s(literal 1 binary64) eps)
(-.f64 eps #s(literal -1 binary64))
#s(literal 1 binary64)
(*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps))
(+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))
(-.f64 eps (/.f64 #s(literal 1 binary64) eps))
(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
(-.f64 eps #s(literal 1 binary64))
x
(*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))
#s(literal 0 binary64)
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
#s(literal 0 binary64)
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1/2 binary64)

localize367.0ms (3.1%)

Memory

21.7MiB live, 846.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	3.3880168386269713	(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
accuracy	4.719002247307508	(fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
accuracy	19.062124285596475	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
accuracy	26.83322641620269	(fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))
accuracy	0	(exp.f64 (neg.f64 x))
accuracy	0.0078125	(+.f64 (+.f64 x #s(literal 2 binary64)) x)
accuracy	0.0078125	(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x))
accuracy	25.932197318679826	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
accuracy	0.0078125	(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
accuracy	0.01171875	(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
accuracy	3.3880168386269713	(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
accuracy	33.89132174740991	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
accuracy	33.89132174740991	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
accuracy	0	(exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x))
accuracy	0.01171875	(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
accuracy	0.01171875	(*.f64 (-.f64 #s(literal -1 binary64) eps) x)
accuracy	0.4724826064934252	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))

Samples

230.0ms	239×	1	valid
20.0ms	17×	2	valid

Compiler

Compiled 594 to 56 computations (90.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 205.0ms

ival-exp: 48.0ms (23.4% of total)

ival-mult: 47.0ms (23% of total)

adjust: 41.0ms (20% of total)

ival-add: 23.0ms (11.2% of total)

ival-div: 23.0ms (11.2% of total)

ival-sub: 18.0ms (8.8% of total)

ival-neg: 4.0ms (2% of total)

exact: 1.0ms (0.5% of total)

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

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

series59.0ms (0.5%)

Memory

-44.5MiB live, 129.8MiB allocated

Counts

23 → 420

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))) (patch #s(approx (/ (- ( (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))) (patch (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))) #<representation binary64>) () ())
#s(alt (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (patch (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) (patch (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (patch (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64))) (patch #s(approx (/ (- ( (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) (patch (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #<representation binary64>) () ())
#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (patch (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal -1 binary64) eps) x) (patch (.f64 (-.f64 #s(literal -1 binary64) eps) x) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 eps #s(literal 1 binary64)) x) (patch (.f64 (-.f64 eps #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (patch (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (patch (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 (+.f64 x #s(literal 2 binary64)) x) (patch (+.f64 (+.f64 x #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) (patch (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #<representation binary64>) () ())
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Outputs
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#s(alt (* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())

Calls

105 calls:

Time	Variable		Point	Expression
9.0ms	x	@	0	(* (- eps 1) x)
3.0ms	eps	@	-inf	(+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))
2.0ms	x	@	inf	(* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2)
2.0ms	x	@	0	(+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2))
1.0ms	eps	@	inf	(+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))

simplify230.0ms (2%)

Memory

24.6MiB live, 338.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 512×	`lower-fma.f64`
13 512×	`lower-fma.f32`
5 516×	`lower-*.f64`
5 516×	`lower-*.f32`
4 440×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	428	7893
1	1425	7136
2	4525	6652
0	8822	6279

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 418

Calls

Call 1

Inputs
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
1
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(exp (* -1 x))
(+ (exp (* -1 x)) (* 1/2 (* eps (+ (* -1 (* x (exp (* -1 x)))) (* x (exp (* -1 x)))))))
(+ (exp (* -1 x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (* -1 x))))) (* 1/2 (+ (* -1 (* x (exp (* -1 x)))) (* x (exp (* -1 x))))))))
(+ (exp (* -1 x)) (* eps (+ (* 1/2 (+ (* -1 (* x (exp (* -1 x)))) (* x (exp (* -1 x))))) (* eps (+ (* 1/2 (* eps (+ (* -1/6 (* (pow x 3) (exp (* -1 x)))) (* 1/6 (* (pow x 3) (exp (* -1 x))))))) (* 1/2 (* (pow x 2) (exp (* -1 x)))))))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1)))))
1
(+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1))))
(+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)))))
(+ 1 (* x (+ (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)) (* x (+ (* 1/2 (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))) (* 1/2 (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 2 (exp (* -1 x)))
(+ (* 2 (exp (* -1 x))) (* eps (+ (* -1 (* x (exp (* -1 x)))) (* x (exp (* -1 x))))))
(+ (* 2 (exp (* -1 x))) (* eps (+ (* -1 (* x (exp (* -1 x)))) (+ (* eps (* (pow x 2) (exp (* -1 x)))) (* x (exp (* -1 x)))))))
(+ (* 2 (exp (* -1 x))) (* eps (+ (* -1 (* x (exp (* -1 x)))) (+ (* eps (+ (* eps (+ (* -1/6 (* (pow x 3) (exp (* -1 x)))) (* 1/6 (* (pow x 3) (exp (* -1 x)))))) (* (pow x 2) (exp (* -1 x))))) (* x (exp (* -1 x)))))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1))))
(+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1))))
(+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1))))
(+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1))))
2
(+ 2 (* x (- (+ eps (* -1 (+ 1 eps))) 1)))
(+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))) 1)))
(+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (+ (* 1/2 (pow (- eps 1) 2)) (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))))))) 1)))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1))))
(exp (* -1 x))
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1
(- 1 (/ 1 eps))
(- 1 (/ 1 eps))
(- 1 (/ 1 eps))
(/ 1 eps)
(/ (+ 1 (* -1 eps)) eps)
(/ (+ 1 (* -1 eps)) eps)
(/ (+ 1 (* -1 eps)) eps)
-1
(- (/ 1 eps) 1)
(- (/ 1 eps) 1)
(- (/ 1 eps) 1)
-1
(- (/ 1 eps) 1)
(- (/ 1 eps) 1)
(- (/ 1 eps) 1)
2
(+ 2 (* 2 x))
(+ 2 (* 2 x))
(+ 2 (* 2 x))
(* 2 x)
(* x (+ 2 (* 2 (/ 1 x))))
(* x (+ 2 (* 2 (/ 1 x))))
(* x (+ 2 (* 2 (/ 1 x))))
(* 2 x)
(* x (+ 2 (* 2 (/ 1 x))))
(* x (+ 2 (* 2 (/ 1 x))))
(* x (+ 2 (* 2 (/ 1 x))))
-2
(- (* 2 (pow eps 2)) 2)
(- (* 2 (pow eps 2)) 2)
(- (* 2 (pow eps 2)) 2)
(* 2 (pow eps 2))
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))
(* 2 (pow eps 2))
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
1
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* -1/2 x)
(+ (* -1/2 x) (* 1/2 (* (pow eps 2) x)))
(+ (* -1/2 x) (* 1/2 (* (pow eps 2) x)))
(+ (* -1/2 x) (* 1/2 (* (pow eps 2) x)))
(* 1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* 1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)))
(+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))
(+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))
(+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))
(* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))

Outputs
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(.f64 (fma.f64 (.f64 (exp.f64 (neg.f64 x)) (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64))))) (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x))))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
(.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/120 binary64))) (fma.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64)))))) (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)))))) (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/720 binary64) (.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/5040 binary64))) (fma.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64)) (.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 6 binary64)))))) (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/120 binary64))) (fma.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64))))))) (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64))))))) (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x)))) #s(literal 1/2 binary64)))
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))
(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) eps) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) eps) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) eps) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))
(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) eps) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) eps) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) eps) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))) #s(literal 1 binary64))
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))))) x (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))))) #s(literal 1 binary64))
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))))) x (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 #s(literal 1 binary64) eps) eps) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))))) x (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))))) x #s(literal 1 binary64))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) #s(literal 1/2 binary64))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) #s(literal 1/2 binary64))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
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(fma.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))) (*.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64)))
(* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))))
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(.f64 (fma.f64 (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/4 binary64) (*.f64 (/.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) x) #s(literal 1/2 binary64))) x)
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(.f64 (fma.f64 (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/4 binary64) (*.f64 (/.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) x) #s(literal 1/2 binary64))) x)
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(.f64 (fma.f64 (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/4 binary64) (*.f64 (/.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) x) #s(literal 1/2 binary64))) x)
(* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))))
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))
(.f64 (fma.f64 (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/4 binary64) (*.f64 (/.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) x) #s(literal 1/2 binary64))) x)
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))
(.f64 (fma.f64 (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/4 binary64) (*.f64 (/.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) x) #s(literal 1/2 binary64))) x)
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))
(.f64 (fma.f64 (fma.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/4 binary64) (*.f64 (/.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) x) #s(literal 1/2 binary64))) x)

rewrite248.0ms (2.1%)

Memory

-2.9MiB live, 341.0MiB allocated

Rules

4 070×	`lower-*.f32`
4 052×	`lower-*.f64`
3 962×	`lower-fma.f32`
3 952×	`lower-fma.f64`
3 134×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	490
0	93	490
1	402	477
2	3965	477
0	8128	461

Stop Event

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

Counts

23 → 569

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)))
(exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))))
(+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
(.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x))
(exp.f64 (neg.f64 x))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps))
(*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(*.f64 (-.f64 #s(literal -1 binary64) eps) x)
(*.f64 (-.f64 eps #s(literal 1 binary64)) x)
(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(+.f64 (+.f64 x #s(literal 2 binary64)) x)
(fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64)))

Outputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))
(/.f64 (.f64 (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x) #s(literal 3 binary64))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (.f64 x #s(literal 3 binary64))))) #s(literal 1/2 binary64)) (+.f64 (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (exp.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) x (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))))) (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x) #s(literal 3 binary64))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (.f64 x #s(literal 3 binary64)))))) (+.f64 (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (exp.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) x (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x)))))
(fma.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(fma.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) (.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x))))
(fma.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) #s(literal 1/2 binary64) (.f64 (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x)) #s(literal 1/2 binary64)))
(fma.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) #s(literal 1/2 binary64) (.f64 (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)) #s(literal 1/2 binary64)))
(+.f64 (.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) #s(literal 1/2 binary64)) (.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) #s(literal 1/2 binary64)))
(+.f64 (.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) #s(literal 1/2 binary64)) (.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))) (.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x))))
(+.f64 (.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x))) (.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(.f64 (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x)))))
(.f64 (+.f64 (exp.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x) #s(literal 3 binary64))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (.f64 x #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (exp.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) x (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))))))
(pow.f64 (/.f64 (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))) (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (exp.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) x (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x)))) (+.f64 (exp.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x) #s(literal 3 binary64))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (*.f64 x #s(literal 3 binary64)))))) #s(literal -1 binary64))
(/.f64 (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x)))) (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x))))
(/.f64 (neg.f64 (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))))) (neg.f64 (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x)))))
(/.f64 (neg.f64 (+.f64 (exp.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x) #s(literal 3 binary64))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (.f64 x #s(literal 3 binary64)))))) (neg.f64 (+.f64 (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (exp.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) x (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))))))
(/.f64 (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x)))) (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))))
(/.f64 (+.f64 (exp.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x) #s(literal 3 binary64))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (.f64 x #s(literal 3 binary64))))) (+.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))) (exp.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) x (*.f64 (-.f64 eps #s(literal 1 binary64)) x))))))
(/.f64 (+.f64 (exp.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x) #s(literal 3 binary64))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (.f64 x #s(literal 3 binary64))))) (+.f64 (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (exp.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) x (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x))) (-.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x))) (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 (exp.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 x x))) (exp.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) x (.f64 (-.f64 eps #s(literal 1 binary64)) x)))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 x x)))) (+.f64 (exp.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) x) #s(literal 3 binary64))) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (*.f64 x #s(literal 3 binary64)))))))
(fma.f64 (exp.f64 (.f64 eps x)) (exp.f64 (neg.f64 x)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)))
(fma.f64 (exp.f64 (.f64 x eps)) (exp.f64 (neg.f64 x)) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)))
(fma.f64 (pow.f64 (exp.f64 eps) x) (exp.f64 (neg.f64 x)) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)))
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(fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 x #s(literal 1/4 binary64)) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (-.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) eps) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64))))))
(fma.f64 x (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (-.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) eps) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64))))) (*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (-.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) eps) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)))) x) (.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (-.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) eps) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)))) x)) #s(literal 1/16 binary64)) (fma.f64 (.f64 x #s(literal 1/4 binary64)) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (-.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) eps) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)))) (.f64 #s(literal -1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)))))) (/.f64 (.f64 (.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps))) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)))) #s(literal 1/4 binary64)) (fma.f64 (.f64 x #s(literal 1/4 binary64)) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (-.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) eps) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)))) (.f64 #s(literal -1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)))))))
(+.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (-.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) eps) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64))))) (.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64)))
(+.f64 (.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 1/4 binary64)) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (-.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) eps) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64))))))

eval320.0ms (2.7%)

Memory: 6.6MiB live, 506.8MiB allocated
Compiler: Compiled 56 251 to 3 621 computations (93.6% saved)

prune698.0ms (6%)

Memory

10.7MiB live, 483.9MiB allocated

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	1 293	16	1 309
Fresh	1	0	1
Picked	3	2	5
Done	0	0	0
Total	1 297	18	1 315

Accuracy

100.0%

Counts

1 315 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps)) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
	38.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 (.f64 eps eps) eps #s(literal -1 binary64)) eps (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) eps))) #s(literal 1 binary64)))
▶	42.4%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))
▶	73.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
▶	76.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
	46.2%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
	68.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 #s(approx (exp ( (- -1 eps) x)) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
✓	59.5%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
	54.7%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
	46.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
	14.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
	75.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	44.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)) (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
▶	46.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
	70.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (exp.f64 (neg.f64 x))))
	54.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶	15.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
✓	47.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

Compiler

Compiled 740 to 381 computations (48.5% saved)

simplify162.0ms (1.4%)

Memory

-45.1MiB live, 212.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f64 (neg.f64 x))
cost-diff	0	(*.f64 (exp.f64 (neg.f64 x)) x)
cost-diff	0	#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
cost-diff	256	(fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64)))
cost-diff	704	(fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))
cost-diff	1088	(/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps))
cost-diff	2368	(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps)))
cost-diff	0	(.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64)))
cost-diff	0	(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
cost-diff	0	(.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64))))
cost-diff	0	(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))

Rules

9 638×	`lower-fma.f32`
9 628×	`lower-fma.f64`
3 406×	`lower-*.f32`
3 390×	`lower-*.f64`
1 706×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	802
0	114	773
1	253	760
2	691	702
3	2453	528
4	5897	512
0	8383	493

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64))))
(.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))
x
(fma.f64 (*.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64)))
(.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))
(.f64 (.f64 eps x) eps)
(*.f64 eps x)
eps
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps)))
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1 binary64)
eps
(+.f64 #s(literal 1 binary64) eps)
(/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps))
(fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64)))
(fma.f64 eps eps #s(literal -1 binary64))
#s(literal -1 binary64)
(*.f64 (+.f64 eps #s(literal 1 binary64)) eps)
(+.f64 eps #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x))
(*.f64 (exp.f64 (neg.f64 x)) x)
(exp.f64 (neg.f64 x))
(neg.f64 x)
x

Outputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64))))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))
(.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)
x
(fma.f64 (*.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
eps
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x)) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x)) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64)))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x))
(.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))
(.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x)
(.f64 (.f64 eps x) eps)
(.f64 (.f64 x eps) eps)
(*.f64 eps x)
(*.f64 x eps)
eps
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
x
#s(literal 1/2 binary64)
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps)))
#s(literal 0 binary64)
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1 binary64)
eps
(+.f64 #s(literal 1 binary64) eps)
(-.f64 eps #s(literal -1 binary64))
(/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps))
(-.f64 eps (/.f64 #s(literal 1 binary64) eps))
(fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64)))
(*.f64 (fma.f64 eps eps #s(literal -1 binary64)) (-.f64 eps #s(literal -1 binary64)))
(fma.f64 eps eps #s(literal -1 binary64))
#s(literal -1 binary64)
(*.f64 (+.f64 eps #s(literal 1 binary64)) eps)
(fma.f64 eps eps eps)
(+.f64 eps #s(literal 1 binary64))
(-.f64 eps #s(literal -1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x))
(*.f64 (exp.f64 (neg.f64 x)) x)
(exp.f64 (neg.f64 x))
(neg.f64 x)
x

localize377.0ms (3.2%)

Memory

11.0MiB live, 841.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 (neg.f64 x))
accuracy	0.0078125	(*.f64 (exp.f64 (neg.f64 x)) x)
accuracy	25.932197318679826	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
accuracy	38.43381955992134	#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x))
accuracy	0.0390625	(fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64)))
accuracy	3.38801683862697	(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps)))
accuracy	22.317331219012832	(/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps))
accuracy	33.89132174740991	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))
accuracy	0.12109375	(.f64 (.f64 eps x) eps)
accuracy	2.3862727461862376	(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
accuracy	19.062124285596475	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
accuracy	28.13350455598668	#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64)))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.4724826064934252	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
accuracy	34.02662498666572	#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x))
accuracy	0	#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64))))
accuracy	2.3862727461862376	(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64))
accuracy	4.719002247307508	(.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))
accuracy	19.062124285596475	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))

Samples

163.0ms	162×	1	valid
131.0ms	94×	2	valid

Compiler

Compiled 580 to 74 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 250.0ms

ival-mult: 71.0ms (28.4% of total)

adjust: 59.0ms (23.6% of total)

ival-add: 39.0ms (15.6% of total)

ival-exp: 33.0ms (13.2% of total)

ival-div: 23.0ms (9.2% of total)

ival-sub: 20.0ms (8% of total)

ival-neg: 4.0ms (1.6% of total)

exact: 1.0ms (0.4% of total)

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

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

series89.0ms (0.8%)

Memory

9.6MiB live, 130.4MiB allocated

Counts

21 → 420

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)) (patch (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)) #<representation binary64>) () ())
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Outputs
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#s(alt (+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) (taylor 0 x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) (taylor inf x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) (taylor inf x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) (taylor inf x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) (taylor inf x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

105 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	0	(* (* (* eps x) eps) 1/2)
3.0ms	x	@	inf	(* (* (* eps x) eps) 1/2)
2.0ms	eps	@	-inf	(+ (* (- (/ 1 eps) 1) (+ 1 eps)) (/ (+ (* (+ (* eps eps) -1) eps) (+ (* eps eps) -1)) (* (+ eps 1) eps)))
2.0ms	eps	@	inf	(+ (* (- (/ 1 eps) 1) (+ 1 eps)) (/ (+ (* (+ (* eps eps) -1) eps) (+ (* eps eps) -1)) (* (+ eps 1) eps)))
2.0ms	x	@	0	(+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (/ (+ (* (+ (* eps eps) -1) eps) (+ (* eps eps) -1)) (* (+ eps 1) eps)))) 1)

simplify318.0ms (2.7%)

Memory

-4.0MiB live, 325.3MiB allocated

Algorithm

1×	egg-herbie

Rules

13 266×	`lower-fma.f64`
13 266×	`lower-fma.f32`
5 778×	`lower-*.f64`
5 778×	`lower-*.f32`
4 210×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	396	9601
1	1314	8843
2	4372	8124
0	8653	7616

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 417

Calls

Call 1

Inputs
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
1
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(* 1/2 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* 1/2 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
1
(+ 1 (* 1/2 (* x (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)))))
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(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))

Outputs
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
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rewrite180.0ms (1.5%)

Memory

18.3MiB live, 334.0MiB allocated

Rules

4 992×	`lower-fma.f32`
4 978×	`lower-fma.f64`
4 844×	`lower-*.f32`
4 828×	`lower-*.f64`
2 332×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	745
0	114	745
1	530	646
2	5517	646
0	8433	629

Stop Event

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

Counts

21 → 348

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64))))
(.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64)))
(.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps)))
(/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (*.f64 (+.f64 eps #s(literal 1 binary64)) eps))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64))
(fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x))
(*.f64 (exp.f64 (neg.f64 x)) x)
(exp.f64 (neg.f64 x))
(.f64 (.f64 eps x) eps)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))

Outputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x) (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x (-.f64 #s(literal 1 binary64) (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x)))))
(pow.f64 (/.f64 (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x (-.f64 #s(literal 1 binary64) (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x))) (fma.f64 (.f64 (.f64 (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x) (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x)) (-.f64 #s(literal 1 binary64) (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x #s(literal -1 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x) (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(literal 1 binary64))) (neg.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x) #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x))) x (-.f64 #s(literal 1 binary64) (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) eps #s(literal -1/2 binary64)) x)) x)))))
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(/.f64 (fma.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (fma.f64 eps eps #s(literal -1 binary64)))) (.f64 (.f64 eps eps) eps) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (fma.f64 eps eps #s(literal -1 binary64))))) (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) (-.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)) (.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps) (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (.f64 (+.f64 eps #s(literal 1 binary64)) (fma.f64 eps eps #s(literal -1 binary64))) (-.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps) (fma.f64 eps eps #s(literal -1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) (-.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)) (.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)) eps)) (fma.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (fma.f64 eps eps #s(literal -1 binary64)))) (.f64 (.f64 eps eps) eps) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (fma.f64 eps eps #s(literal -1 binary64)))))))
(fma.f64 (/.f64 (.f64 (+.f64 eps #s(literal 1 binary64)) (fma.f64 eps eps #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 eps eps))) (-.f64 #s(literal 1 binary64) eps) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 (/.f64 (.f64 (+.f64 eps #s(literal 1 binary64)) (fma.f64 eps eps #s(literal -1 binary64))) (fma.f64 eps eps #s(literal -1 binary64))) (-.f64 eps #s(literal 1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 (/.f64 (.f64 (+.f64 eps #s(literal 1 binary64)) (fma.f64 eps eps #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) eps #s(literal 1 binary64))) (fma.f64 eps (-.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 (/.f64 (.f64 (+.f64 eps #s(literal 1 binary64)) (fma.f64 eps eps #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) eps #s(literal 1 binary64))) (fma.f64 eps eps (-.f64 #s(literal 1 binary64) eps)) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)))
(fma.f64 (fma.f64 (.f64 (.f64 eps eps) eps) eps #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 1 binary64))) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64)))
(fma.f64 (fma.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 eps eps) eps) eps (-.f64 #s(literal 1 binary64) (.f64 eps (neg.f64 eps))))) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 (.f64 eps eps) #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)))
(fma.f64 (fma.f64 eps eps eps) (-.f64 eps #s(literal 1 binary64)) (fma.f64 eps eps #s(literal -1 binary64)))
(fma.f64 (.f64 (+.f64 eps #s(literal 1 binary64)) (fma.f64 eps eps #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps #s(literal 1 binary64))) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 eps #s(literal 1 binary64)) eps) (fma.f64 eps eps #s(literal -1 binary64)))
(fma.f64 (+.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(fma.f64 eps (+.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64))
(fma.f64 eps (fma.f64 eps eps #s(literal -1 binary64)) (fma.f64 eps eps #s(literal -1 binary64)))
(fma.f64 eps eps (+.f64 #s(literal -1 binary64) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)))
(fma.f64 #s(literal 1 binary64) (.f64 eps eps) (+.f64 #s(literal -1 binary64) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)))
(-.f64 (/.f64 (.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)) eps) (-.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps) (fma.f64 eps eps #s(literal -1 binary64)))) (/.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) (fma.f64 eps eps #s(literal -1 binary64))) (-.f64 (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps) (fma.f64 eps eps #s(literal -1 binary64)))))
(+.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps #s(literal -1 binary64)) (*.f64 eps eps))
(+.f64 (*.f64 eps (+.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)) #s(literal -1 binary64))
(+.f64 (fma.f64 eps eps #s(literal -1 binary64)) (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps))
(+.f64 (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps) (fma.f64 eps eps #s(literal -1 binary64)))
(+.f64 (.f64 eps eps) (+.f64 #s(literal -1 binary64) (.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)))
(+.f64 #s(literal -1 binary64) (*.f64 eps (+.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x))
(*.f64 (exp.f64 (neg.f64 x)) x)
(*.f64 x (exp.f64 (neg.f64 x)))
(/.f64 x (exp.f64 x))
(*.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(pow.f64 (/.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) x)
(pow.f64 (exp.f64 x) #s(literal -1 binary64))
(pow.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) x))
(exp.f64 (*.f64 (log.f64 (exp.f64 x)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 x))
(.f64 (.f64 eps eps) x)
(.f64 (.f64 x eps) eps)
(.f64 x (.f64 eps eps))
(.f64 eps (.f64 x eps))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (/.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps)) #s(literal 1 binary64)))

eval130.0ms (1.1%)

Memory: -1.1MiB live, 308.2MiB allocated
Compiler: Compiled 21 798 to 1 368 computations (93.7% saved)

prune120.0ms (1%)

Memory

18.9MiB live, 340.2MiB allocated

Pruning

23 alts after pruning (18 fresh and 5 done)

	Pruned	Kept	Total
New	755	10	765
Fresh	3	8	11
Picked	2	3	5
Done	0	2	2
Total	760	23	783

Accuracy

100.0%

Counts

783 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.5%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) x) (fma.f64 (*.f64 eps eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) x #s(literal 1 binary64)))
▶	42.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
✓	73.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
▶	76.2%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
	46.2%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
	48.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x)) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x)) x #s(literal -1 binary64))))
	68.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 #s(approx (exp ( (- -1 eps) x)) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
✓	59.5%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
	46.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
	33.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))
	15.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (/ (+ (* (+ (* eps eps) -1) eps) (+ (* eps eps) -1)) (* (+ eps 1) eps)))) 1) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (+.f64 #s(literal 1 binary64) eps) (/.f64 eps (+.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 eps eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) eps))))) (.f64 x #s(literal 1/2 binary64)))))
▶	14.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
	75.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	44.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x)) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
	44.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)) (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
✓	46.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
	70.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (exp.f64 (neg.f64 x))))
▶	2.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
	54.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
✓	15.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
▶	10.7%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
	3.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
✓	47.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

Compiler

Compiled 872 to 426 computations (51.1% saved)

simplify132.0ms (1.1%)

Memory

-29.3MiB live, 202.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
cost-diff	128	(-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
cost-diff	320	(.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
cost-diff	640	(fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
cost-diff	448	(.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))
cost-diff	2368	(fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))
cost-diff	0	#s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)
cost-diff	0	#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (- 1 x) (neg.f64 x))
cost-diff	0	#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x)))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
cost-diff	0	(.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64)))
cost-diff	0	(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))

Rules

9 822×	`lower-fma.f32`
9 810×	`lower-fma.f64`
3 128×	`lower-*.f32`
3 104×	`lower-*.f64`
2 410×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	1054
0	129	1040
1	298	995
2	881	897
3	3119	687
4	7050	687
0	8419	644

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64)))
(.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) x)
(*.f64 eps eps)
eps
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x)))
#s(approx (- 1 x) (neg.f64 x))
(neg.f64 x)
x
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x))
(*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)
#s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))))
(.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))
(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
(-.f64 eps #s(literal 1 binary64))
eps
#s(literal 1 binary64)
(-.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
(-.f64 eps (/.f64 #s(literal 1 binary64) eps))
(/.f64 #s(literal 1 binary64) eps)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x)
(fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (*.f64 eps eps) eps) #s(literal -1/8 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 (*.f64 eps eps) eps))
#s(literal 1/8 binary64)
(.f64 (.f64 eps eps) eps)
(*.f64 eps eps)
eps
#s(literal -1/8 binary64)
x
(fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 eps eps) eps) eps)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

Outputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64)))
(.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) x)
(*.f64 eps eps)
eps
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x)))
#s(approx (- 1 x) (neg.f64 x))
(neg.f64 x)
x
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x))
#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) x))
(*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)
(*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) x)
#s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))
#s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (-.f64 x x)))
#s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))))
#s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (-.f64 x x))
(.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))
(-.f64 x x)
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
x
#s(literal 1/2 binary64)
(fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))
#s(literal 0 binary64)
(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
(-.f64 eps #s(literal 1 binary64))
eps
#s(literal 1 binary64)
(-.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
(-.f64 eps (/.f64 #s(literal 1 binary64) eps))
(/.f64 #s(literal 1 binary64) eps)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (/.f64 x (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) #s(literal 1/4 binary64))) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/8 binary64)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (/.f64 x (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) #s(literal 1/4 binary64))) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/8 binary64)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (/.f64 x (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) #s(literal 1/4 binary64))) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/8 binary64)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))
(.f64 (/.f64 x (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) #s(literal 1/4 binary64))) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/8 binary64)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x)
(.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/8 binary64)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x)
(fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (*.f64 eps eps) eps) #s(literal -1/8 binary64))
(fma.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/8 binary64)) (.f64 (*.f64 eps eps) eps) #s(literal -1/8 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 (*.f64 eps eps) eps))
(.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(.f64 (.f64 eps eps) eps)
(*.f64 eps eps)
eps
#s(literal -1/8 binary64)
x
(fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) #s(literal 1/4 binary64))
(.f64 (.f64 (*.f64 eps eps) eps) eps)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(.f64 #s(literal -1/4 binary64) (.f64 eps eps))
(.f64 (.f64 eps eps) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

localize706.0ms (6%)

Memory

18.8MiB live, 650.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.9362901535400543	(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x)
accuracy	2.3862727461862376	(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64))
accuracy	19.062124285596475	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
accuracy	25.88752775962235	(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))
accuracy	0.01171875	(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
accuracy	3.38801683862697	(fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))
accuracy	33.89132174740991	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
accuracy	61.99859042974503	#s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))))
accuracy	0.0078125	(*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)
accuracy	19.346119635066348	#s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy	25.932197318679826	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
accuracy	38.43381955992134	#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x))
accuracy	0	(neg.f64 x)
accuracy	0.4724826064934252	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
accuracy	34.02662498666572	#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x)))
accuracy	38.859343521226684	#s(approx (- 1 x) (neg.f64 x))
accuracy	2.3862727461862376	(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
accuracy	6.647497797111652	(.f64 (.f64 eps eps) x)
accuracy	19.062124285596475	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
accuracy	28.13350455598668	#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64)))

Samples

507.0ms	223×	2	valid
54.0ms	33×	3	valid

Compiler

Compiled 669 to 83 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 467.0ms

ival-mult: 188.0ms (40.3% of total)

adjust: 81.0ms (17.4% of total)

ival-div: 63.0ms (13.5% of total)

ival-sub: 54.0ms (11.6% of total)

ival-add: 42.0ms (9% of total)

ival-exp: 33.0ms (7.1% of total)

ival-neg: 4.0ms (0.9% of total)

exact: 1.0ms (0.2% of total)

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

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

series118.0ms (1%)

Memory

1.7MiB live, 92.0MiB allocated

Counts

25 → 480

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))) (patch #s(approx (/ (- ( (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) (patch (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) (patch #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x)))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x)))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))) (patch #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x))) (patch #s(approx (/ (- ( (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)) (patch #s(approx ( (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x) (patch (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x) #<representation binary64>) () ())
#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) (patch (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))) (patch (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))))) (patch #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))))) #<representation binary64>) () ())
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Outputs
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#s(alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) (taylor inf eps) (#s(alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))) (patch #s(approx (/ (- ( (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)) (patch (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)) (patch (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (- (* -1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))) (/ 1 x)) x)) (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)) (patch (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (- (* -1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))) (/ 1 x)) x)) (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)) (patch (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/8 x) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 x) (* 1/8 (* (pow eps 6) x))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 x) (* 1/8 (* (pow eps 6) x))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 x) (* 1/8 (* (pow eps 6) x))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (* (pow eps 6) x)) (taylor inf eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x))) (taylor inf eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x))) (taylor inf eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x))) (taylor inf eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (* (pow eps 6) x)) (taylor -inf eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/8 (pow eps 6)) 1/8)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #<representation binary64>) () ())) ())

Calls

120 calls:

Time	Variable		Point	Expression
31.0ms	x	@	0	(/ (* (+ (* (* 1/8 (* (* eps eps) eps)) (* (* eps eps) eps)) -1/8) x) (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))))
2.0ms	x	@	0	(* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps))))
1.0ms	eps	@	0	(+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))
1.0ms	eps	@	inf	(+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))
1.0ms	x	@	inf	(/ (* (+ (* (* 1/8 (* (* eps eps) eps)) (* (* eps eps) eps)) -1/8) x) (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))))

simplify332.0ms (2.8%)

Memory

-6.8MiB live, 260.4MiB allocated

Algorithm

1×	egg-herbie

Rules

14 132×	`lower-fma.f64`
14 132×	`lower-fma.f32`
6 002×	`lower-*.f64`
6 002×	`lower-*.f32`
4 210×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	411	9635
1	1382	8861
2	4588	8172
0	9254	7661

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 479

Calls

Call 1

Inputs
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
1
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(* 1/2 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* 1/2 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
1
(+ 1 (* 1/2 (* x (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)))))
(+ 1 (* x (+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))))
(+ 1 (* x (+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))))
(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (+ (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (+ (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (/ 1 (pow x 2)))))
(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))) (/ 1 x)) x)) (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))) (/ 1 x)) x)) (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))
(* -1/2 x)
(+ (* -1/2 x) (* 1/2 (* (pow eps 2) x)))
(+ (* -1/2 x) (* 1/2 (* (pow eps 2) x)))
(+ (* -1/2 x) (* 1/2 (* (pow eps 2) x)))
(* 1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* 1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)))
(+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))
(+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))
(+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))
(* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* x (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))
(* -1 (* x (+ (* -1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (* -1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (* (pow eps 2) x))
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
1
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
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(exp (* -1 x))
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(+ (exp (* -1 x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (* -1 x))))) (* 1/2 (+ (* -1 (* x (exp (* -1 x)))) (* x (exp (* -1 x))))))))
(+ (exp (* -1 x)) (* eps (+ (* 1/2 (+ (* -1 (* x (exp (* -1 x)))) (* x (exp (* -1 x))))) (* eps (+ (* 1/2 (* eps (+ (* -1/6 (* (pow x 3) (exp (* -1 x)))) (* 1/6 (* (pow x 3) (exp (* -1 x))))))) (* 1/2 (* (pow x 2) (exp (* -1 x)))))))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 (* -1 eps))))) (exp (* x (- (* -1 eps) 1)))))
1
(+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1))))
(+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)))))
(+ 1 (* x (+ (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)) (* x (+ (* 1/2 (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))) (* 1/2 (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
(* 1/2 (+ (exp (* -1 (* x (+ 1 eps)))) (exp (* x (- eps 1)))))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
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(+ (* -1/2 x) (* 1/2 (* (pow eps 2) x)))
(+ (* -1/2 x) (* (pow eps 2) (- (* -1 (* (pow eps 2) (+ (* -1/2 x) (* 1/2 x)))) (* -1/2 x))))
(+ (* -1/2 x) (* (pow eps 2) (- (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/2 x) (* 1/2 x))) (+ (* -1/2 x) (* 1/2 x)))) (* -1/2 x))))
(* 1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1/2 x) (* 1/2 x)) (pow eps 4))) (* 1/2 x)) (* 1/2 (/ x (pow eps 2)))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 6))) (+ (* 1/2 x) (* 1/2 (/ x (pow eps 6))))) (+ (* -1/2 (/ x (pow eps 4))) (+ (* 1/2 (/ x (pow eps 2))) (* 1/2 (/ x (pow eps 4)))))))
(* 1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/2 x)))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1/2 x) (* 1/2 x)) (pow eps 4))) (* 1/2 x)) (* 1/2 (/ x (pow eps 2)))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 6))) (+ (* 1/2 x) (* 1/2 (/ x (pow eps 6))))) (+ (* -1/2 (/ x (pow eps 4))) (+ (* 1/2 (/ x (pow eps 2))) (* 1/2 (/ x (pow eps 4)))))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(/ (* x (- (* 1/8 (pow eps 6)) 1/8)) (- (+ 1/4 (* 1/4 (pow eps 4))) (* -1/4 (pow eps 2))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2)))))
(* 1/2 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* 1/2 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))
1
(+ 1 (* 1/2 (* x (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)))))
(+ 1 (* x (+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))))
(+ 1 (* x (+ (* 1/4 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) (* 1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))))))
(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (+ (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (+ (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x)) (/ 1 (pow x 2)))))
(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))) (/ 1 x)) x)) (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))) (/ 1 x)) x)) (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))
(* -1/8 x)
(+ (* -1/8 x) (* 1/8 (* (pow eps 6) x)))
(+ (* -1/8 x) (* 1/8 (* (pow eps 6) x)))
(+ (* -1/8 x) (* 1/8 (* (pow eps 6) x)))
(* 1/8 (* (pow eps 6) x))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(* 1/8 (* (pow eps 6) x))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(* x (- (* 1/8 (pow eps 6)) 1/8))

Outputs
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))
(.f64 (fma.f64 (.f64 (exp.f64 (neg.f64 x)) (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64))))) (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x))))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))
(.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/120 binary64))) (fma.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64)))))) (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)))))) (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x))))))
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/720 binary64) (.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/5040 binary64))) (fma.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64)) (.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 6 binary64)))))) (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/120 binary64))) (fma.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64))))))) (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64))))))) (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (exp.f64 (neg.f64 x)))) #s(literal 1/2 binary64)))
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))
(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (fma.f64 eps x (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 eps x (neg.f64 x))) eps) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (fma.f64 eps x (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 eps x (neg.f64 x))) eps) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (fma.f64 eps x (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 eps x (neg.f64 x))) eps) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (fma.f64 eps x (neg.f64 x)))) #s(literal 1/2 binary64))
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))
(.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (fma.f64 eps x (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 eps x (neg.f64 x))) eps) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (fma.f64 eps x (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 eps x (neg.f64 x))) eps) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (fma.f64 eps x (neg.f64 x)))) #s(literal 1/2 binary64))
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))
(.f64 (+.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 eps x (neg.f64 x))) eps) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 #s(literal -1 binary64) eps) x)))) (exp.f64 (fma.f64 eps x (neg.f64 x)))) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))) #s(literal 1 binary64))
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))))) x (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))))) #s(literal 1 binary64))
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (.f64 (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))))) x (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))))) x (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (.f64 (-.f64 eps #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))))) x #s(literal 1 binary64))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (fma.f64 eps x (neg.f64 x))))) #s(literal 1/2 binary64))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (fma.f64 eps x (neg.f64 x))))) #s(literal 1/2 binary64))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (fma.f64 eps x (neg.f64 x))))) #s(literal 1/2 binary64))
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))
(.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (fma.f64 eps x (neg.f64 x))))) #s(literal 1/2 binary64))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
(.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (fma.f64 eps x (neg.f64 x))))) #s(literal 1/2 binary64))
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))
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(.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)))))
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (* 1/2 (/ (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps)) x))))
(.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/4 binary64) (.f64 (/.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) x) #s(literal 1/2 binary64))) (.f64 x x))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))) (/ 1 x)) x)) (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))
(.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/4 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (neg.f64 x))) (*.f64 x x))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (- (+ eps (* (+ 1 eps) (- (/ 1 eps) 1))) (/ 1 eps))) (/ 1 x)) x)) (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))))
(.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) eps) (.f64 (-.f64 eps (/.f64 #s(literal 1 binary64) eps)) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/4 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (neg.f64 x))) (*.f64 x x))
(* -1/8 x)
(*.f64 #s(literal -1/8 binary64) x)
(+ (* -1/8 x) (* 1/8 (* (pow eps 6) x)))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(+ (* -1/8 x) (* 1/8 (* (pow eps 6) x)))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(+ (* -1/8 x) (* 1/8 (* (pow eps 6) x)))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* 1/8 (* (pow eps 6) x))
(.f64 (.f64 (pow.f64 eps #s(literal 6 binary64)) x) #s(literal 1/8 binary64))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64))))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64))))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64))))) (pow.f64 eps #s(literal 6 binary64)))
(* 1/8 (* (pow eps 6) x))
(.f64 (.f64 (pow.f64 eps #s(literal 6 binary64)) x) #s(literal 1/8 binary64))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64))))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64))))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/8 (/ x (pow eps 6))) (* 1/8 x)))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64))))) (pow.f64 eps #s(literal 6 binary64)))
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)
(* x (- (* 1/8 (pow eps 6)) 1/8))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64)) x)

rewrite478.0ms (4.1%)

Memory

45.4MiB live, 316.0MiB allocated

Rules

6 046×	`lower-fma.f32`
6 032×	`lower-fma.f64`
5 644×	`lower-*.f32`
5 620×	`lower-*.f64`
2 396×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	871
0	129	835
1	604	803
2	5804	803
0	9009	765

Stop Event

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

Counts

25 → 280

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))
#s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64)))
(.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x)))
#s(approx (- 1 x) (neg.f64 x))
(neg.f64 x)
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x))
(*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)
#s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))
(.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps)))))
(fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
(.f64 (.f64 eps eps) x)
(/.f64 (-.f64 eps #s(literal 1 binary64)) eps)
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))
(fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x)

Outputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) x) (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) x (-.f64 #s(literal 1 binary64) (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x)))))
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(fma.f64 x #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (/.f64 x (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)))) #s(literal 1 binary64))
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(+.f64 #s(literal 1 binary64) (.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (/.f64 x (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)))) x))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x)
(.f64 x (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)))
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(fma.f64 #s(literal -1/8 binary64) x (.f64 (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) eps) (*.f64 eps eps)) x))
(fma.f64 x (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) eps) (.f64 eps eps)) (*.f64 x #s(literal -1/8 binary64)))
(fma.f64 x #s(literal -1/8 binary64) (.f64 x (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) eps) (*.f64 eps eps))))
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(+.f64 (.f64 #s(literal -1/8 binary64) x) (.f64 (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) eps) (.f64 eps eps)) x))
(+.f64 (.f64 x (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) eps) (.f64 eps eps))) (.f64 x #s(literal -1/8 binary64)))
(+.f64 (.f64 x #s(literal -1/8 binary64)) (.f64 x (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) eps) (.f64 eps eps))))

eval189.0ms (1.6%)

Memory: -26.2MiB live, 299.5MiB allocated
Compiler: Compiled 23 573 to 1 194 computations (94.9% saved)

prune114.0ms (1%)

Memory

9.4MiB live, 328.9MiB allocated

Pruning

21 alts after pruning (13 fresh and 8 done)

	Pruned	Kept	Total
New	755	4	759
Fresh	4	9	13
Picked	2	3	5
Done	0	5	5
Total	761	21	782

Accuracy

100.0%

Counts

782 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	73.5%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64)))
✓	73.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
✓	76.2%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
	46.2%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
	48.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal -1 binary64))))
	68.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 #s(approx (exp ( (- -1 eps) x)) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
✓	59.5%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
	46.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
	33.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))
	15.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
	44.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	75.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	44.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)) (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
✓	46.6%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
	70.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (exp.f64 (neg.f64 x))))
✓	2.9%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
	54.8%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
✓	15.1%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
✓	10.7%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
	3.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
✓	47.0%	#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

Compiler

Compiled 1 276 to 371 computations (70.9% saved)

regimes49.0ms (0.4%)

Memory

-17.6MiB live, 112.3MiB allocated

Counts

37 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) x) (fma.f64 (*.f64 eps eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x)) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x)) x #s(literal -1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal -1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (/ (+ (* (+ (* eps eps) -1) eps) (+ (* eps eps) -1)) (* (+ eps 1) eps)))) 1) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (+.f64 #s(literal 1 binary64) eps) (/.f64 eps (+.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 eps eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) eps))))) (.f64 x #s(literal 1/2 binary64)))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 (.f64 eps eps) eps #s(literal -1 binary64)) eps (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)) (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x)) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (exp.f64 (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 #s(approx (exp ( (- -1 eps) x)) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps)) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps) (.f64 (*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/6 binary64)) x)) x (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))

Outputs

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

Calls

4 calls:

13.0ms	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))
13.0ms	eps
11.0ms	x
8.0ms	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`eps`
99.3%	1	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
99.3%	1	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`

Compiler

Compiled 66 to 40 computations (39.4% saved)

regimes116.0ms (1%)

Memory

-1.3MiB live, 118.4MiB allocated

Counts

35 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) x) (fma.f64 (*.f64 eps eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x)) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x)) x #s(literal -1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal -1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (/ (+ (* (+ (* eps eps) -1) eps) (+ (* eps eps) -1)) (* (+ eps 1) eps)))) 1) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (+.f64 #s(literal 1 binary64) eps) (/.f64 eps (+.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 eps eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) eps))))) (.f64 x #s(literal 1/2 binary64)))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 (.f64 eps eps) eps #s(literal -1 binary64)) eps (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)) (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x)) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (exp.f64 (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 #s(approx (exp ( (- -1 eps) x)) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))))) x (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps)) (-.f64 eps #s(literal 1 binary64))))) x (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1 binary64) eps) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) eps) (.f64 (*.f64 (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1/6 binary64)) x)) x (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal 1 binary64)))

Outputs

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

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64)))

Calls

4 calls:

84.0ms	x
11.0ms	eps
9.0ms	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))
8.0ms	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
85.1%	3	`x`
89.2%	2	`eps`
97.6%	2	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
97.6%	2	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`

Compiler

Compiled 66 to 40 computations (39.4% saved)

regimes46.0ms (0.4%)

Memory

18.0MiB live, 57.3MiB allocated

Counts

31 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) x) (fma.f64 (*.f64 eps eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x)) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x)) x #s(literal -1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal -1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (/ (+ (* (+ (* eps eps) -1) eps) (+ (* eps eps) -1)) (* (+ eps 1) eps)))) 1) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (+.f64 #s(literal 1 binary64) eps) (/.f64 eps (+.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 eps eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) eps))))) (.f64 x #s(literal 1/2 binary64)))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 (.f64 eps eps) eps #s(literal -1 binary64)) eps (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)) (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x)) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (exp.f64 (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 (exp.f64 (neg.f64 x)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 #s(approx (exp ( (- -1 eps) x)) #s(literal 1 binary64)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))

Outputs

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (exp.f64 (neg.f64 x))))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64)))

Calls

2 calls:

35.0ms

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

7.0ms

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

Results

Accuracy	Segments	Branch
96.8%	2	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
96.8%	2	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`

Compiler

Compiled 60 to 36 computations (40% saved)

regimes29.0ms (0.2%)

Memory

1.2MiB live, 80.4MiB allocated

Counts

28 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) x) (fma.f64 (*.f64 eps eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 eps #s(literal 1 binary64)))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) eps (fma.f64 eps eps #s(literal -1 binary64))) (.f64 (+.f64 eps #s(literal 1 binary64)) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x)) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) x))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) x)) x #s(literal -1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x) #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) x #s(literal -1 binary64)) (fma.f64 #s(approx (+ ( (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal -1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (/ (+ (* (+ (* eps eps) -1) eps) (+ (* eps eps) -1)) (* (+ eps 1) eps)))) 1) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (fma.f64 (+.f64 #s(literal 1 binary64) eps) (/.f64 eps (+.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 eps eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) eps))))) (.f64 x #s(literal 1/2 binary64)))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (fma.f64 (.f64 eps eps) eps #s(literal -1 binary64)) eps (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))) (.f64 (fma.f64 eps eps (+.f64 eps #s(literal 1 binary64))) eps))) #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)) (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (-.f64 eps #s(literal 1 binary64)))))) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x)) x #s(literal -2 binary64))) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) (-.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps))))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))

Outputs

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64)))

Calls

3 calls:

9.0ms

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

9.0ms

eps

7.0ms

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

Results

Accuracy	Segments	Branch
76.2%	1	`eps`
84.8%	2	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
84.8%	2	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`

Compiler

Compiled 63 to 38 computations (39.7% saved)

regimes18.0ms (0.2%)

Memory

-20.9MiB live, 56.5MiB allocated

Counts

16 → 3

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 (-.f64 eps #s(literal 1 binary64)) (-.f64 eps #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) eps)))) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) (.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps) (-.f64 eps (/.f64 #s(literal 1 binary64) eps))))))

Outputs

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 x (fma.f64 (*.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64)))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 x x))))

Calls

3 calls:

6.0ms

5.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
82.5%	3	`x`
78.8%	2	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
78.8%	2	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`

Compiler

Compiled 63 to 38 computations (39.7% saved)

regimes5.0ms (0%)

Memory

19.8MiB live, 19.8MiB allocated

Counts

12 → 3

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))

Outputs

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64)))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 x x))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
82.4%	3	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

6.1MiB live, 45.5MiB allocated

Counts

10 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))

Outputs

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 x x))))

Calls

4 calls:

4.0ms	x
4.0ms	eps
3.0ms	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))
3.0ms	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))

Results

Accuracy	Segments	Branch
66.2%	2	`eps`
73.9%	2	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
73.9%	2	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`
72.5%	4	`x`

Compiler

Compiled 66 to 40 computations (39.4% saved)

regimes16.0ms (0.1%)

Memory

-35.5MiB live, 47.0MiB allocated

Counts

9 → 3

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))

Outputs

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

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))

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

Calls

4 calls:

5.0ms	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))
4.0ms	eps
3.0ms	x
3.0ms	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
54.8%	1	`eps`
61.6%	3	`x`
54.8%	1	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
54.8%	1	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`

Compiler

Compiled 66 to 40 computations (39.4% saved)

regimes4.0ms (0%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) x)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))

Outputs

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

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
59.3%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes2.0ms (0%)

Memory

8.0MiB live, 8.1MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) #s(approx (- 1 x) (neg.f64 x))))

Outputs

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
59.3%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes6.0ms (0.1%)

Memory

-19.2MiB live, 20.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

Outputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

Calls

4 calls:

2.0ms	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))
1.0ms	x
1.0ms	eps
1.0ms	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))

Results

Accuracy	Segments	Branch
47.0%	1	`(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))`
47.0%	1	`(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x)))))`
47.0%	1	`eps`
47.0%	1	`x`

Compiler

Compiled 66 to 40 computations (39.4% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.000000005377993	4.0

Compiler

Compiled 34 to 24 computations (29.4% saved)

bsearch0.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.000000005377993	4.0

Compiler

Compiled 34 to 24 computations (29.4% saved)

bsearch0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.000000005377993	4.0

Compiler

Compiled 34 to 24 computations (29.4% saved)

bsearch63.0ms (0.5%)

Memory

-1.6MiB live, 160.6MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
21.0ms	1.4834151309619652e+80	2.2673527404881785e+86
34.0ms	0.0002266995649232964	45.50137771694417

Samples

25.0ms	235×	0	valid
18.0ms	53×	1	valid

Compiler

Compiled 430 to 258 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 9.0ms (25.2% of total)

ival-exp: 7.0ms (19.6% of total)

ival-sub: 5.0ms (14% of total)

ival-div: 5.0ms (14% of total)

ival-add: 3.0ms (8.4% of total)

ival-neg: 3.0ms (8.4% of total)

adjust: 2.0ms (5.6% of total)

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

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

exact: 0.0ms (0% of total)

bsearch58.0ms (0.5%)

Memory

-3.4MiB live, 77.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
28.0ms	1.4834151309619652e+80	2.2673527404881785e+86
26.0ms	45.50137771694417	3835.869159180065

Samples

9.0ms	27×	1	valid
8.0ms	76×	0	valid
4.0ms	9×	2	valid

Compiler

Compiled 377 to 223 computations (40.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-exp: 4.0ms (24.5% of total)

ival-mult: 3.0ms (18.4% of total)

ival-sub: 2.0ms (12.3% of total)

adjust: 2.0ms (12.3% of total)

ival-div: 2.0ms (12.3% of total)

ival-neg: 1.0ms (6.1% of total)

ival-add: 1.0ms (6.1% of total)

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

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

exact: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.0	+inf

Compiler

Compiled 34 to 24 computations (29.4% saved)

bsearch53.0ms (0.4%)

Memory

29.9MiB live, 107.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	predicate-same
1×	narrow-enough

Steps

Time	Left	Right
7.0ms	8.807065050631937e+214	6.822504901551658e+215
42.0ms	0.0002266995649232964	45.50137771694417

Samples

28.0ms	47×	1	valid
14.0ms	113×	0	valid

Compiler

Compiled 235 to 144 computations (38.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 19.0ms (51% of total)

ival-div: 5.0ms (13.4% of total)

ival-exp: 5.0ms (13.4% of total)

ival-sub: 3.0ms (8.1% of total)

adjust: 2.0ms (5.4% of total)

ival-neg: 2.0ms (5.4% of total)

ival-add: 2.0ms (5.4% of total)

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

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

exact: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0002266995649232964	45.50137771694417

Compiler

Compiled 169 to 105 computations (37.9% saved)

bsearch23.0ms (0.2%)

Memory

-30.0MiB live, 51.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	45.50137771694417	3835.869159180065

Samples

6.0ms	35×	0	valid
6.0ms	11×	2	valid
5.0ms	18×	1	valid

Compiler

Compiled 118 to 80 computations (32.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-div: 3.0ms (21.9% of total)

ival-exp: 3.0ms (21.9% of total)

ival-mult: 2.0ms (14.6% of total)

adjust: 1.0ms (7.3% of total)

ival-sub: 1.0ms (7.3% of total)

ival-neg: 1.0ms (7.3% of total)

ival-add: 1.0ms (7.3% of total)

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

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

exact: 0.0ms (0% of total)

simplify41.0ms (0.3%)

Memory

10.6MiB live, 50.0MiB allocated

Algorithm

1×	egg-herbie

Rules

334×	`distribute-lft-neg-in_binary64`
176×	`neg-mul-1_binary64`
166×	`neg-sub0_binary64`
124×	`sub-neg_binary64`
118×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	1867
1	226	1867
2	268	1859
3	321	1859
4	366	1859
5	476	1859
6	580	1859
7	675	1859
8	775	1859
9	866	1859
10	942	1859
11	1000	1859
12	1042	1859
13	1061	1859
14	1064	1859

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
(if (<=.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 1125899909870165/562949953421312 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64))))
(if (<=.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 1125899909870165/562949953421312 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (exp.f64 (neg.f64 x)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64))))
(if (<=.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 1125899909870165/562949953421312 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/2 binary64))) x #s(literal 1 binary64))) #s(approx (/ (- ( (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64))))
(if (<=.f64 x #s(literal 45 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 x (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps #s(literal -1/2 binary64)))) x #s(literal 1 binary64))) (if (<=.f64 x #s(literal 149999999999999993457896567777726746186226871542399193716254503645915184980033536 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))))
(if (<=.f64 x #s(literal 780 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/2 binary64))) x #s(literal 1 binary64))) (if (<=.f64 x #s(literal 149999999999999993457896567777726746186226871542399193716254503645915184980033536 binary64)) #s(approx (/ (- ( (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x))))))
(if (<=.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 5 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) x) 1) (.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 x x)))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x))) (if (<=.f64 x #s(literal 99999999999999990660396936451049407652789096389402106318690169014230827417515340183487244380298106827518051036015414262787762879627804165648934234223216948652905993920546904997130825691790753915825536773603473752064 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (* (exp (neg x)) (+ (+ x 2) x)) 1/2) (*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) x)))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* (+ (exp (* (- -1 eps) x)) (exp (* (- eps 1) x))) 1/2) (-.f64 #s(literal 1 binary64) x))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64)))))
(if (<=.f64 x #s(literal 550 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* x 1/2) (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1)))) 1) #s(approx (* (* x 1/2) (+ (* (/ (- eps 1) eps) (- -1 eps)) (- eps (/ 1 eps)))) #s(literal 0 binary64)))))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

Outputs
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (.f64 (-.f64 #s(literal -1 binary64) eps) x)) (exp.f64 (*.f64 (-.f64 eps #s(literal 1 binary64)) x)))))
(if (<=.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 1125899909870165/562949953421312 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) #s(literal 1/2 binary64))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(approx (+ (* (* 1/4 (+ (* (- -1 eps) (- (/ (+ 1 eps) eps) (+ 1 eps))) (* (+ (/ (- eps 1) eps) (- eps 1)) (- eps 1)))) x) (* (+ (* (- (/ 1 eps) 1) (+ 1 eps)) (+ (/ (- eps 1) eps) (- eps 1))) 1/2)) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal -1/8 binary64)) x) #s(approx (+ (* (* (* (* eps eps) eps) eps) 1/4) (- 1/4 (* (* (* eps eps) 1/2) -1/2))) #s(literal 1/4 binary64)))) x #s(literal 1 binary64))))
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#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))

soundness1.4s (11.7%)

Memory

11.8MiB live, 1 250.7MiB allocated

Rules

14 132×	`lower-fma.f64`
14 132×	`lower-fma.f32`
13 512×	`lower-fma.f64`
13 512×	`lower-fma.f32`
13 266×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	396	9601
1	1314	8843
2	4372	8124
0	8653	7616
0	428	7893
1	1425	7136
2	4525	6652
0	8822	6279
0	411	9635
1	1382	8861
2	4588	8172
0	9254	7661
0	231	2534
1	733	2245
2	2538	1951
3	7519	1951
0	8258	1820
0	82	745
0	114	745
1	530	646
2	5517	646
0	8433	629

Stop Event

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

Compiler

Compiled 603 to 246 computations (59.2% saved)

preprocess75.0ms (0.6%)

Memory: -20.1MiB live, 175.9MiB allocated
Remove: (abs eps)
Compiler: Compiled 872 to 254 computations (70.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze54.0ms (0.5%)

sample2.4s (20.3%)

explain427.0ms (3.7%)

preprocess175.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify180.0ms (1.5%)

localize96.0ms (0.8%)

series38.0ms (0.3%)

simplify435.0ms (3.7%)

rewrite202.0ms (1.7%)

eval120.0ms (1%)

prune103.0ms (0.9%)

simplify133.0ms (1.1%)

localize367.0ms (3.1%)

series59.0ms (0.5%)

simplify230.0ms (2%)

rewrite248.0ms (2.1%)

eval320.0ms (2.7%)

prune698.0ms (6%)

simplify162.0ms (1.4%)

localize377.0ms (3.2%)

series89.0ms (0.8%)

simplify318.0ms (2.7%)

rewrite180.0ms (1.5%)

eval130.0ms (1.1%)

prune120.0ms (1%)

simplify132.0ms (1.1%)

localize706.0ms (6%)

series118.0ms (1%)

simplify332.0ms (2.8%)

rewrite478.0ms (4.1%)

eval189.0ms (1.6%)

prune114.0ms (1%)

regimes49.0ms (0.4%)

regimes116.0ms (1%)

regimes46.0ms (0.4%)

regimes29.0ms (0.2%)

regimes18.0ms (0.2%)

regimes5.0ms (0%)

regimes15.0ms (0.1%)

regimes16.0ms (0.1%)

regimes4.0ms (0%)

regimes2.0ms (0%)

regimes6.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch63.0ms (0.5%)

bsearch58.0ms (0.5%)

bsearch0.0ms (0%)

bsearch53.0ms (0.4%)

bsearch1.0ms (0%)

bsearch23.0ms (0.2%)

simplify41.0ms (0.3%)

soundness1.4s (11.7%)

preprocess75.0ms (0.6%)

end0.0ms (0%)

Profiling