Metrics for Kahan's exp quotient

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample506.0ms (18.3%)

Memory

20.7MiB live, 731.2MiB allocated; 96ms collecting garbage

Samples

310.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 135.0ms

ival-expm1: 66.0ms (48.8% of total)

ival-div: 64.0ms (47.3% of total)

ival-assert: 3.0ms (2.2% of total)

adjust: 2.0ms (1.5% of total)

Bogosity

explain73.0ms (2.7%)

Memory

2.6MiB live, 100.8MiB allocated; 7ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
128	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	-	-	`(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(exp.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	128	1

Confusion

	Predicted +	Predicted -
+	128	1
-	0	127

Precision

1.0

Recall

0.9922480620155039

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	1	0
-	0	0	127

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 38 to 19 computations (50% saved)

Precisions

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

ival-exp: 6.0ms (42% of total)

ival-div: 4.0ms (28% of total)

ival-expm1: 3.0ms (21% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess355.0ms (12.9%)

Memory

-45.1MiB live, 259.6MiB allocated; 61ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	32	21
2	78	21
3	247	21
4	1225	21
0	5	6
0	8	6
1	16	6
2	32	6
3	76	6
4	299	6
5	3046	6
0	8497	4

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Outputs
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
(/.f64 (expm1.f64 x) x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

series3.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Counts

5 → 16

Calls

Call 1

Inputs
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
x
#s(literal 1 binary64)

Outputs
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 1))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* x (+ 1/2 (* 1/6 x))))))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx x #s(hole binary64 x))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (/ (- (exp x) 1) x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (exp x) #s(hole binary64 (exp x)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ (- (exp x) 1) x) (- (exp x) 1) (exp x) x 1)
1.0ms	x	@	inf	((/ (- (exp x) 1) x) (- (exp x) 1) (exp x) x 1)
0.0ms	x	@	0	((/ (- (exp x) 1) x) (- (exp x) 1) (exp x) x 1)

rewrite203.0ms (7.4%)

Memory

20.5MiB live, 209.7MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	192
0	49	192
1	240	192
2	2096	192
0	8129	147

Stop Event

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

Counts

21 → 104

Calls

Call 1

Inputs
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
x
#s(literal 1 binary64)
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 1))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* x (+ 1/2 (* 1/6 x))))))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx x #s(hole binary64 x))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (/ (- (exp x) 1) x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (exp x) #s(hole binary64 (exp x)))

Outputs
(*.f64 (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (expm1.f64 x) x))
(*.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (/.f64 (expm1.f64 x) x))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64)))) (neg.f64 (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal -2 binary64)) (*.f64 (/.f64 (exp.f64 x) x) (pow.f64 x #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (expm1.f64 x)))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (-.f64 (.f64 (exp.f64 x) x) x)) (neg.f64 (.f64 x x)))
(/.f64 (-.f64 (.f64 (neg.f64 (exp.f64 x)) (neg.f64 x)) (.f64 (neg.f64 x) #s(literal -1 binary64))) (*.f64 x x))
(/.f64 (-.f64 (.f64 (neg.f64 (exp.f64 x)) x) (.f64 (neg.f64 x) #s(literal 1 binary64))) (*.f64 (neg.f64 x) x))
(/.f64 (-.f64 (.f64 (exp.f64 x) (neg.f64 x)) (.f64 x #s(literal -1 binary64))) (*.f64 x (neg.f64 x)))
(/.f64 (-.f64 (neg.f64 (exp.f64 x)) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))) (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal -2 binary64)) (*.f64 (/.f64 (exp.f64 x) x) (pow.f64 x #s(literal -1 binary64))))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (*.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x)))
(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 x))) (neg.f64 (neg.f64 x)))
(/.f64 (-.f64 (.f64 (exp.f64 x) x) x) (.f64 x x))
(/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (expm1.f64 x) x)
(neg.f64 (/.f64 (neg.f64 (expm1.f64 x)) x))
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(fma.f64 (/.f64 (exp.f64 x) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (exp.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x))
(fma.f64 (/.f64 (exp.f64 x) x) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 x) x) (/.f64 #s(literal -1 binary64) x))
(-.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 2 binary64)) (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x)) (/.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x)))
(-.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal -2 binary64)) (.f64 (/.f64 (exp.f64 x) x) (pow.f64 x #s(literal -1 binary64)))))) (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 x) x) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal -2 binary64)) (.f64 (/.f64 (exp.f64 x) x) (pow.f64 x #s(literal -1 binary64)))))))
(-.f64 (/.f64 (.f64 (exp.f64 x) x) (.f64 x x)) (/.f64 x (*.f64 x x)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x) (/.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) x) (/.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64)) x))
(-.f64 (/.f64 (exp.f64 x) x) (pow.f64 x #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x)) (/.f64 #s(literal -1 binary64) (.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) x)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)) (/.f64 #s(literal -1 binary64) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))
(+.f64 (/.f64 (cosh.f64 x) x) (/.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) x))
(+.f64 (/.f64 (exp.f64 x) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (expm1.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (expm1.f64 x) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) (-.f64 (sinh.f64 x) #s(literal 1 binary64))) (.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (neg.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 2 binary64) (.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))) (.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (cosh.f64 x) (sinh.f64 x)))) #s(literal 2 binary64))) (.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (*.f64 (cosh.f64 x) (sinh.f64 x)))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 (/.f64 (neg.f64 (exp.f64 x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 (/.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)) (/.f64 (neg.f64 (exp.f64 x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 (/.f64 (fabs.f64 (exp.f64 x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 (/.f64 (fabs.f64 (exp.f64 x)) #s(literal 1 binary64)) (/.f64 (fabs.f64 (exp.f64 x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (exp.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) #s(literal 1 binary64)) (/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(expm1.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(pow.f64 (exp.f64 #s(literal 1 binary64)) x)
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (sinh.f64 x) (cosh.f64 x)))))
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x))) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 x) (*.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (*.f64 (cosh.f64 x) (sinh.f64 x))))))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 x)))) #s(literal 4 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (*.f64 (cosh.f64 x) (sinh.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(-.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))))
(exp.f64 x)
(+.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (cosh.f64 x) (sinh.f64 x))))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (cosh.f64 x) (sinh.f64 x))))))
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
x
#s(literal 1 binary64)
#s(approx (/ (- (exp x) 1) x) #s(literal 1 binary64))
#s(approx (/ (- (exp x) 1) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (/ (- (exp x) 1) x) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (- (exp x) 1) x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (- (exp x) 1) x)
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx x x)
#s(approx (/ (- (exp x) 1) x) (/.f64 (expm1.f64 x) x))
#s(approx (- (exp x) 1) (expm1.f64 x))
#s(approx (exp x) (exp.f64 x))

eval10.0ms (0.4%)

Memory: 15.8MiB live, 15.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 698 to 363 computations (78.6% saved)

prune64.0ms (2.3%)

Memory

6.2MiB live, 53.1MiB allocated; 3ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	2	107

Accuracy

100.0%

Counts

107 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.9%	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
▶	73.8%	(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))

Status

Accuracy

Program

✓

52.9%

(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

▶

73.8%

(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))

Compiler

Compiled 24 to 17 computations (29.2% saved)

series12.0ms (0.4%)

Memory

-35.2MiB live, 21.2MiB allocated; 3ms collecting garbage

Counts

12 → 42

Calls

Call 1

Inputs
(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))
(neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))
(expm1.f64 (*.f64 x #s(literal 3 binary64)))
(*.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x))
(*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)
(fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(exp.f64 x)
(-.f64 (exp.f64 x) #s(literal -1 binary64))
#s(literal -1 binary64)

Outputs
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 1))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 (+ 1 (* x (+ 1/2 (* 1/6 x))))))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (* -3 x)))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (* x (- (* -9/2 x) 3))))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (* x (- (* x (- (* -9/2 x) 9/2)) 3))))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (* x (- (* x (- (* x (- (* -27/8 x) 9/2)) 9/2)) 3))))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (* 3 x)))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (* x (+ 3 (* 9/2 x)))))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (* x (+ 3 (* x (+ 9/2 (* 9/2 x)))))))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (* x (+ 3 (* x (+ 9/2 (* x (+ 9/2 (* 27/8 x)))))))))
#s(approx (* x 3) #s(hole binary64 (* 3 x)))
#s(approx x #s(hole binary64 x))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* -3 x)))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* x (- (* -3 x) 3))))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* x (- (* x (- (* -5/2 x) 3)) 3))))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* x (- (* x (- (* x (- (* -3/2 x) 5/2)) 3)) 3))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* 3 x)))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* x (+ 3 (* 3 x)))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* x (+ 3 (* x (+ 3 (* 5/2 x)))))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* x (+ 3 (* x (+ 3 (* x (+ 5/2 (* 3/2 x)))))))))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 3))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 (+ 3 (* 3 x))))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 (+ 3 (* x (+ 3 (* 5/2 x))))))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 (+ 3 (* x (+ 3 (* x (+ 5/2 (* 3/2 x))))))))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) -1) #s(hole binary64 2))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 x)))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 (* x (+ 1 (* 1/2 x))))))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 (* -1 (/ (- 1 (exp (* 3 x))) (* x (+ 1 (+ (exp x) (pow (exp x) 2))))))))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (- 1 (exp (* 3 x)))))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (- (exp (* 3 x)) 1)))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* -1 (* x (+ 1 (+ (exp x) (pow (exp x) 2)))))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* x (+ 1 (+ (exp x) (pow (exp x) 2))))))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 (+ 1 (+ (exp x) (pow (exp x) 2)))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 1 (exp x))))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) (neg (- (exp (* x 3)) 1)) (- (exp (* x 3)) 1) (* x 3) x 3 (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) (+ (* (exp x) (exp x)) (- (exp x) -1)) (exp x) (- (exp x) -1) -1)
4.0ms	x	@	-inf	((/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) (neg (- (exp (* x 3)) 1)) (- (exp (* x 3)) 1) (* x 3) x 3 (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) (+ (* (exp x) (exp x)) (- (exp x) -1)) (exp x) (- (exp x) -1) -1)
3.0ms	x	@	inf	((/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) (neg (- (exp (* x 3)) 1)) (- (exp (* x 3)) 1) (* x 3) x 3 (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) (+ (* (exp x) (exp x)) (- (exp x) -1)) (exp x) (- (exp x) -1) -1)

Time

Variable

Point

Expression

4.0ms

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

4.0ms

-inf

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

3.0ms

inf

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

rewrite211.0ms (7.6%)

Memory

31.1MiB live, 260.7MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	168	769
0	184	753
1	914	741
0	7852	680

Stop Event

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

Counts

54 → 251

Calls

Call 1

Inputs
(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))
(neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))
(expm1.f64 (*.f64 x #s(literal 3 binary64)))
(*.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x))
(*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)
(fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(exp.f64 x)
(-.f64 (exp.f64 x) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 1))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 (+ 1 (* x (+ 1/2 (* 1/6 x))))))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (* -3 x)))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (* x (- (* -9/2 x) 3))))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (* x (- (* x (- (* -9/2 x) 9/2)) 3))))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (* x (- (* x (- (* x (- (* -27/8 x) 9/2)) 9/2)) 3))))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (* 3 x)))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (* x (+ 3 (* 9/2 x)))))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (* x (+ 3 (* x (+ 9/2 (* 9/2 x)))))))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (* x (+ 3 (* x (+ 9/2 (* x (+ 9/2 (* 27/8 x)))))))))
#s(approx (* x 3) #s(hole binary64 (* 3 x)))
#s(approx x #s(hole binary64 x))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* -3 x)))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* x (- (* -3 x) 3))))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* x (- (* x (- (* -5/2 x) 3)) 3))))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* x (- (* x (- (* x (- (* -3/2 x) 5/2)) 3)) 3))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* 3 x)))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* x (+ 3 (* 3 x)))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* x (+ 3 (* x (+ 3 (* 5/2 x)))))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* x (+ 3 (* x (+ 3 (* x (+ 5/2 (* 3/2 x)))))))))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 3))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 (+ 3 (* 3 x))))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 (+ 3 (* x (+ 3 (* 5/2 x))))))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 (+ 3 (* x (+ 3 (* x (+ 5/2 (* 3/2 x))))))))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) -1) #s(hole binary64 2))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 x)))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 (* x (+ 1 (* 1/2 x))))))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) #s(hole binary64 (* -1 (/ (- 1 (exp (* 3 x))) (* x (+ 1 (+ (exp x) (pow (exp x) 2))))))))
#s(approx (neg (- (exp (* x 3)) 1)) #s(hole binary64 (- 1 (exp (* 3 x)))))
#s(approx (- (exp (* x 3)) 1) #s(hole binary64 (- (exp (* 3 x)) 1)))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) #s(hole binary64 (* -1 (* x (+ 1 (+ (exp x) (pow (exp x) 2)))))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) #s(hole binary64 (* x (+ 1 (+ (exp x) (pow (exp x) 2))))))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(hole binary64 (+ 1 (+ (exp x) (pow (exp x) 2)))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 1 (exp x))))

Outputs
(/.f64 (/.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x))) (neg.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))) x)
(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))) x)
(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (/.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x))) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)))
(/.f64 (expm1.f64 (.f64 #s(literal 9 binary64) x)) (.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)))
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#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 3/2 binary64) x #s(literal 5/2 binary64)) x #s(literal 3 binary64)) x #s(literal 3 binary64)) x))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) #s(literal 3 binary64))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) (fma.f64 #s(literal 3 binary64) x #s(literal 3 binary64)))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) (fma.f64 (fma.f64 #s(literal 5/2 binary64) x #s(literal 3 binary64)) x #s(literal 3 binary64)))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 3/2 binary64) x #s(literal 5/2 binary64)) x #s(literal 3 binary64)) x #s(literal 3 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (- (exp x) -1) #s(literal 2 binary64))
#s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x))
#s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
#s(approx (- (exp x) -1) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
#s(approx (/ (neg (- (exp (* x 3)) 1)) (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) x)))
#s(approx (neg (- (exp (* x 3)) 1)) (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64))))
#s(approx (- (exp (* x 3)) 1) (expm1.f64 (*.f64 #s(literal 3 binary64) x)))
#s(approx (neg (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x)) (*.f64 (neg.f64 x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))))
#s(approx (* (+ (* (exp x) (exp x)) (- (exp x) -1)) x) (*.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x))
#s(approx (+ (* (exp x) (exp x)) (- (exp x) -1)) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))
#s(approx (exp x) (exp.f64 x))
#s(approx (- (exp x) -1) (-.f64 (exp.f64 x) #s(literal -1 binary64)))

eval32.0ms (1.2%)

Memory: -33.6MiB live, 59.8MiB allocated; 5ms collecting garbage
Compiler: Compiled 7 416 to 1 328 computations (82.1% saved)

prune788.0ms (28.5%)

Memory

4.8MiB live, 1 017.6MiB allocated; 67ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	302	3	305

Accuracy

100.0%

Counts

305 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.7%	(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))
✓	52.9%	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
✓	73.8%	(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))

Status

Accuracy

Program

▶

73.7%

(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))

✓

52.9%

(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

✓

73.8%

(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))

Compiler

Compiled 39 to 28 computations (28.2% saved)

series5.0ms (0.2%)

Memory

8.2MiB live, 8.2MiB allocated; 0ms collecting garbage

Counts

11 → 32

Calls

Call 1

Inputs
(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x)
(expm1.f64 (*.f64 #s(literal 3 binary64) x))
(*.f64 #s(literal 3 binary64) x)
#s(literal 3 binary64)
x
(fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
#s(literal -1 binary64)
#s(literal 1 binary64)

Outputs
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 1))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* 1/6 x))))))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 3))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 (+ 3 (* 9/2 x))))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 (+ 3 (* x (+ 9/2 (* 9/2 x))))))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 (+ 3 (* x (+ 9/2 (* x (+ 9/2 (* 27/8 x))))))))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (* 3 x)))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (* x (+ 3 (* 9/2 x)))))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (* x (+ 3 (* x (+ 9/2 (* 9/2 x)))))))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (* x (+ 3 (* x (+ 9/2 (* x (+ 9/2 (* 27/8 x)))))))))
#s(approx (* 3 x) #s(hole binary64 (* 3 x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 3))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 (+ 3 (* 3 x))))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 (+ 3 (* x (+ 3 (* 5/2 x))))))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 (+ 3 (* x (+ 3 (* x (+ 5/2 (* 3/2 x))))))))
#s(approx (- (exp x) -1) #s(hole binary64 2))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 x)))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 (* x (+ 1 (* 1/2 x))))))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 (/ (- (exp (* 3 x)) 1) (* x (+ 1 (* (exp x) (+ 1 (exp x))))))))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 (/ (- (exp (* 3 x)) 1) x)))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (- (exp (* 3 x)) 1)))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 (+ 1 (* (exp x) (+ 1 (exp x))))))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 1 (exp x))))
#s(approx (exp x) #s(hole binary64 (exp x)))

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

rewrite153.0ms (5.6%)

Memory

13.5MiB live, 153.4MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	494
0	123	494
1	646	492
0	5714	458

Stop Event

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

Counts

43 → 161

Calls

Call 1

Inputs
(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x)
(expm1.f64 (*.f64 #s(literal 3 binary64) x))
(*.f64 #s(literal 3 binary64) x)
#s(literal 3 binary64)
x
(fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
#s(literal -1 binary64)
#s(literal 1 binary64)
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 1))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* 1/6 x))))))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 3))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 (+ 3 (* 9/2 x))))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 (+ 3 (* x (+ 9/2 (* 9/2 x))))))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 (+ 3 (* x (+ 9/2 (* x (+ 9/2 (* 27/8 x))))))))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (* 3 x)))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (* x (+ 3 (* 9/2 x)))))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (* x (+ 3 (* x (+ 9/2 (* 9/2 x)))))))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (* x (+ 3 (* x (+ 9/2 (* x (+ 9/2 (* 27/8 x)))))))))
#s(approx (* 3 x) #s(hole binary64 (* 3 x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 3))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 (+ 3 (* 3 x))))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 (+ 3 (* x (+ 3 (* 5/2 x))))))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 (+ 3 (* x (+ 3 (* x (+ 5/2 (* 3/2 x))))))))
#s(approx (- (exp x) -1) #s(hole binary64 2))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 x)))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 (* x (+ 1 (* 1/2 x))))))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) #s(hole binary64 (/ (- (exp (* 3 x)) 1) (* x (+ 1 (* (exp x) (+ 1 (exp x))))))))
#s(approx (/ (- (exp (* 3 x)) 1) x) #s(hole binary64 (/ (- (exp (* 3 x)) 1) x)))
#s(approx (- (exp (* 3 x)) 1) #s(hole binary64 (- (exp (* 3 x)) 1)))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(hole binary64 (+ 1 (* (exp x) (+ 1 (exp x))))))
#s(approx (- (exp x) -1) #s(hole binary64 (+ 1 (exp x))))
#s(approx (exp x) #s(hole binary64 (exp x)))

Outputs
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) x) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x)) #s(literal 2 binary64)))) (-.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) x) (-.f64 (pow.f64 (.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x)) #s(literal 3 binary64)) #s(literal -1 binary64))) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (pow.f64 (.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x)) #s(literal 2 binary64))))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) x) (-.f64 (pow.f64 (.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x)) #s(literal 3 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x)) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) x) (-.f64 (pow.f64 (*.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal -1 binary64)))
(/.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))) x)
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)) (/.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x))) (.f64 (pow.f64 (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) #s(literal -1 binary64)) (pow.f64 (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)) (/.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)) (fma.f64 (pow.f64 (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) #s(literal -1 binary64)) (pow.f64 (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) #s(literal -1 binary64)) (.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)) (pow.f64 (*.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))))) (neg.f64 (.f64 (neg.f64 x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)) (.f64 (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) #s(literal 1 binary64))) (.f64 (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x) (*.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)))
(/.f64 (expm1.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 2 binary64))) (.f64 (-.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) x) #s(literal -1 binary64)) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)))
(/.f64 (expm1.f64 (.f64 #s(literal 9 binary64) x)) (.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 3 binary64)) x)) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)))
(/.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (neg.f64 x)) (neg.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (.f64 (neg.f64 x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) x) (neg.f64 (neg.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)))
(neg.f64 (/.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (neg.f64 x)) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64))))
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#s(approx (- (exp (* 3 x)) 1) (*.f64 x #s(literal 3 binary64)))
#s(approx (- (exp (* 3 x)) 1) (*.f64 (fma.f64 #s(literal 9/2 binary64) x #s(literal 3 binary64)) x))
#s(approx (- (exp (* 3 x)) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 9/2 binary64) x #s(literal 9/2 binary64)) x #s(literal 3 binary64)) x))
#s(approx (- (exp (* 3 x)) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 27/8 binary64) x #s(literal 9/2 binary64)) x #s(literal 9/2 binary64)) x #s(literal 3 binary64)) x))
#s(approx (* 3 x) (*.f64 x #s(literal 3 binary64)))
#s(approx x x)
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) #s(literal 3 binary64))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) (fma.f64 x #s(literal 3 binary64) #s(literal 3 binary64)))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) (fma.f64 (fma.f64 #s(literal 5/2 binary64) x #s(literal 3 binary64)) x #s(literal 3 binary64)))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 3/2 binary64) x #s(literal 5/2 binary64)) x #s(literal 3 binary64)) x #s(literal 3 binary64)))
#s(approx (- (exp x) -1) #s(literal 2 binary64))
#s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x))
#s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
#s(approx (- (exp x) -1) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (/ (- (exp (* 3 x)) 1) x) (+ (* (- (exp x) -1) (exp x)) 1)) (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)) x)))
#s(approx (/ (- (exp (* 3 x)) 1) x) (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) x))
#s(approx (- (exp (* 3 x)) 1) (expm1.f64 (*.f64 x #s(literal 3 binary64))))
#s(approx (+ (* (- (exp x) -1) (exp x)) 1) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))
#s(approx (- (exp x) -1) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
#s(approx (exp x) (exp.f64 x))

eval22.0ms (0.8%)

Memory: -12.8MiB live, 37.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 4 363 to 652 computations (85.1% saved)

prune190.0ms (6.9%)

Memory

23.2MiB live, 261.2MiB allocated; 8ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	187	3	190

Accuracy

100.0%

Counts

190 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	73.7%	(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))
✓	52.9%	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
✓	73.8%	(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))

Status

Accuracy

Program

✓

73.7%

(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))

✓

52.9%

(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

✓

73.8%

(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))

Compiler

Compiled 78 to 48 computations (38.5% saved)

regimes3.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Accuracy

Total -46.9b remaining (-1200335.9%)

Threshold costs -46.9b (-1200335.9%)

Counts

3 → 2

Calls

Call 1

Inputs

(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

(/.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) x) (fma.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (exp.f64 x) #s(literal 1 binary64)))

(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))

Outputs

(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)))

(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)`
100.0%	2	`x`

Compiler

Compiled 7 to 6 computations (14.3% saved)

bsearch13.0ms (0.5%)

Memory

-31.6MiB live, 15.9MiB allocated; 1ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
11.0ms	0.009043989712605538	7959461.94183245

Samples

6.0ms

144×

valid

Compiler

Compiled 225 to 178 computations (20.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 1.0ms (39.1% of total)

ival-expm1: 1.0ms (39.1% of total)

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

adjust: 0.0ms (0% of total)

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

simplify62.0ms (2.2%)

Memory

-3.6MiB live, 43.7MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	38	28
2	67	26
3	107	26
4	219	26
5	487	26
6	2810	26
7	6796	26

Stop Event

1×	node limit

Calls

Call 1

Inputs

(if (<=.f64 x #s(literal 5404319552844595/18014398509481984 binary64)) (/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x))) (/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x))

Outputs

(if (<=.f64 x #s(literal 5404319552844595/18014398509481984 binary64)) (/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x))) (/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x))

(if (<=.f64 x #s(literal 5404319552844595/18014398509481984 binary64)) (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) x)) (/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x))

derivations29.0ms (1.1%)

Memory

31.3MiB live, 31.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 26 to 16 computations (38.5% saved)

preprocess25.0ms (0.9%)

Memory: -18.3MiB live, 32.3MiB allocated; 6ms collecting garbage
Compiler: Compiled 108 to 66 computations (38.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0%)

sample506.0ms (18.3%)

explain73.0ms (2.7%)

preprocess355.0ms (12.9%)

eval0.0ms (0%)

prune0.0ms (0%)

series3.0ms (0.1%)

rewrite203.0ms (7.4%)

eval10.0ms (0.4%)

prune64.0ms (2.3%)

series12.0ms (0.4%)

rewrite211.0ms (7.6%)

eval32.0ms (1.2%)

prune788.0ms (28.5%)

series5.0ms (0.2%)

rewrite153.0ms (5.6%)

eval22.0ms (0.8%)

prune190.0ms (6.9%)

regimes3.0ms (0.1%)

bsearch13.0ms (0.5%)

simplify62.0ms (2.2%)

derivations29.0ms (1.1%)

preprocess25.0ms (0.9%)

end0.0ms (0%)

Profiling