Metrics for expq2 (section 3.11)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	75.2%	24.8%	0%	0%	0%	0
0%	0%	75.2%	24.8%	0%	0%	0%	1
50%	37.6%	37.6%	24.8%	0%	0%	0%	2
75%	56.4%	18.8%	24.8%	0%	0%	0%	3
87.5%	65.8%	9.4%	24.8%	0%	0%	0%	4
93.8%	70.5%	4.7%	24.8%	0%	0%	0%	5
96.9%	72.8%	2.3%	24.8%	0%	0%	0%	6
98.4%	74%	1.2%	24.8%	0%	0%	0%	7
99.2%	74.6%	0.6%	24.8%	0%	0%	0%	8
99.6%	74.9%	0.3%	24.8%	0%	0%	0%	9
99.8%	75%	0.1%	24.8%	0%	0%	0%	10
99.9%	75.1%	0.1%	24.8%	0%	0%	0%	11
100%	75.1%	0%	24.8%	0%	0%	0%	12

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample831.0ms (13.4%)

Memory

-0.4MiB live, 932.5MiB allocated

Samples

399.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 230.0ms

ival-expm1: 76.0ms (33.1% of total)

ival-exp: 66.0ms (28.8% of total)

ival-div: 57.0ms (24.8% of total)

ival->: 21.0ms (9.1% of total)

exact: 7.0ms (3% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

explain66.0ms (1.1%)

Memory

39.0MiB live, 84.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
164	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	-	-	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
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	164	0

Confusion

	Predicted +	Predicted -
+	164	0
-	0	92

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	164	0	0
-	0	0	92

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	92
1	164

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-exp: 4.0ms (35.4% of total)

ival-div: 3.0ms (26.5% of total)

ival-expm1: 3.0ms (26.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess218.0ms (3.5%)

Memory

-15.8MiB live, 193.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	21	19
2	62	19
3	186	19
4	864	19
0	5	7
0	8	7
1	13	7
2	26	7
3	56	7
4	229	7
5	2069	7
6	6649	7
0	8741	5

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.3%	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify155.0ms (2.5%)

Memory

-28.3MiB live, 259.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f64 x)
cost-diff	0	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
cost-diff	2	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	13	15
2	26	15
3	56	15
4	229	15
5	2069	15
6	6649	15
0	8741	11

Stop Event

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

Calls

Call 1

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

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

localize15.0ms (0.2%)

Memory

16.7MiB live, 16.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.015625	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	37.81138712022363	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

11.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 2.0ms (35.4% of total)

ival-exp: 2.0ms (35.4% of total)

ival-expm1: 2.0ms (35.4% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Counts

3 → 15

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(/ 1 x)
(/ (+ 1 (* 1/2 x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(- (exp x) 1)
(/ (exp x) (- (exp x) 1))
(exp x)

Calls

3 calls:

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

simplify246.0ms (4%)

Memory

12.1MiB live, 199.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	111
1	166	111
2	530	105
3	1942	105
4	5239	105
0	8089	87

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 14

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(/ 1 x)
(/ (+ 1 (* 1/2 x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(- (exp x) 1)
(/ (exp x) (- (exp x) 1))
(exp x)

Outputs
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.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)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 x)) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/720 binary64) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(- (exp x) 1)
(expm1.f64 x)
(/ (exp x) (- (exp x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp x)
(exp.f64 x)

rewrite200.0ms (3.2%)

Memory

-22.4MiB live, 254.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	30	13
2	177	13
3	1809	13
0	9626	9

Stop Event

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

Counts

3 → 466

Calls

Call 1

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

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

eval111.0ms (1.8%)

Memory: -2.4MiB live, 145.0MiB allocated
Compiler: Compiled 14 895 to 1 739 computations (88.3% saved)

prune12.0ms (0.2%)

Memory

36.1MiB live, 36.1MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	563	9	572
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	564	9	573

Accuracy

100.0%

Counts

573 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.8%	(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 x))) (.f64 #s(literal 2 binary64) (expm1.f64 x)))
	39.3%	(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
	38.4%	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
▶	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	99.1%	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/720 binary64) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
▶	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
▶	65.0%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Compiler

Compiled 234 to 176 computations (24.8% saved)

simplify178.0ms (2.9%)

Memory

-15.7MiB live, 127.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) (cosh.f64 x))
cost-diff	0	(sinh.f64 x)
cost-diff	4	(fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
cost-diff	4	(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 x))) (.f64 #s(literal 2 binary64) (expm1.f64 x)))
cost-diff	0	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
cost-diff	0	(exp.f64 x)
cost-diff	0	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(expm1.f64 x)
cost-diff	0	(exp.f64 x)
cost-diff	0	(/.f64 (exp.f64 x) (expm1.f64 x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	131
0	46	122
1	81	119
2	220	119
3	817	119
4	6247	119
0	8853	119

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 x)
x
(expm1.f64 x)
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(literal 1/12 binary64)
x
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(exp.f64 x)
x
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 x))) (.f64 #s(literal 2 binary64) (expm1.f64 x)))
(fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
#s(literal 2 binary64)
(sinh.f64 x)
x
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
(cosh.f64 x)
(*.f64 #s(literal 2 binary64) (expm1.f64 x))
(expm1.f64 x)

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 x)
x
(expm1.f64 x)
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(literal 1/12 binary64)
x
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(exp.f64 x)
x
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 x))) (.f64 #s(literal 2 binary64) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
(*.f64 #s(literal 2 binary64) (exp.f64 x))
#s(literal 2 binary64)
(sinh.f64 x)
x
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
(*.f64 (cosh.f64 x) #s(literal 2 binary64))
(cosh.f64 x)
(*.f64 #s(literal 2 binary64) (expm1.f64 x))
(expm1.f64 x)

localize72.0ms (1.2%)

Memory

4.4MiB live, 91.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(cosh.f64 x)
accuracy	0.00390625	(sinh.f64 x)
accuracy	0.015625	(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 x))) (.f64 #s(literal 2 binary64) (expm1.f64 x)))
accuracy	0.27469365559146774	(fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
accuracy	0.0	(exp.f64 x)
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	0.015625	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
accuracy	0.7944683730749016	#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.0078125	(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	0.0078125	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
accuracy	0.5775281710559734	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	1.3003014453242276	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
accuracy	0.0	(expm1.f64 x)
accuracy	0.0	(exp.f64 x)
accuracy	0.015625	(/.f64 (exp.f64 x) (expm1.f64 x))

Samples

32.0ms	166×	0	valid
23.0ms	89×	1	exit
1.0ms	1×	2	valid

Compiler

Compiled 129 to 25 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 9.0ms (23.1% of total)

ival-cosh: 8.0ms (20.6% of total)

ival-div: 5.0ms (12.9% of total)

adjust: 4.0ms (10.3% of total)

const: 4.0ms (10.3% of total)

ival-add: 3.0ms (7.7% of total)

ival-exp: 2.0ms (5.1% of total)

ival-sinh: 2.0ms (5.1% of total)

ival-sub: 1.0ms (2.6% of total)

ival-expm1: 1.0ms (2.6% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

18.4MiB live, 18.4MiB allocated

Counts

16 → 40

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 x)
(expm1.f64 x)
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 (exp.f64 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 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 x))) (.f64 #s(literal 2 binary64) (expm1.f64 x)))
(fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
(sinh.f64 x)
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
(cosh.f64 x)

Outputs
(/ 1 x)
(/ (+ 1 (* 1/2 x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
2
(+ 2 (* 2 x))
(+ 2 (* x (+ 2 x)))
(+ 2 (* x (+ 2 (* x (+ 1 (* 1/3 x))))))
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(/ (exp x) (- (exp x) 1))
(exp x)
(- (exp x) 1)
(* 1/12 x)
(* x (+ 1/12 (* 1/2 (/ 1 x))))
(* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (/ 1 x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 2 (exp x))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(+ (exp x) (/ 1 (exp x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (+ (* 2 (sinh x)) (* 2 (cosh x))) (* 2 (- (exp x) 1))) (+ (* 2 (sinh x)) (* 2 (cosh x))) (sinh x) (* 2 (cosh x)) (cosh x))
4.0ms	x	@	inf	((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (+ (* 2 (sinh x)) (* 2 (cosh x))) (* 2 (- (exp x) 1))) (+ (* 2 (sinh x)) (* 2 (cosh x))) (sinh x) (* 2 (cosh x)) (cosh x))
2.0ms	x	@	0	((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (+ (* 2 (sinh x)) (* 2 (cosh x))) (* 2 (- (exp x) 1))) (+ (* 2 (sinh x)) (* 2 (cosh x))) (sinh x) (* 2 (cosh x)) (cosh x))

Time

Variable

Point

Expression

5.0ms

-inf

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (+ (* 2 (sinh x)) (* 2 (cosh x))) (* 2 (- (exp x) 1))) (+ (* 2 (sinh x)) (* 2 (cosh x))) (sinh x) (* 2 (cosh x)) (cosh x))

4.0ms

inf

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (+ (* 2 (sinh x)) (* 2 (cosh x))) (* 2 (- (exp x) 1))) (+ (* 2 (sinh x)) (* 2 (cosh x))) (sinh x) (* 2 (cosh x)) (cosh x))

2.0ms

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (+ (* 2 (sinh x)) (* 2 (cosh x))) (* 2 (- (exp x) 1))) (+ (* 2 (sinh x)) (* 2 (cosh x))) (sinh x) (* 2 (cosh x)) (cosh x))

simplify141.0ms (2.3%)

Memory

-19.3MiB live, 128.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	338
1	464	338
2	1584	315
3	5118	315
0	8375	271

Stop Event

1×	iter limit
1×	node limit

Counts

40 → 39

Calls

Call 1

Inputs
(/ 1 x)
(/ (+ 1 (* 1/2 x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
2
(+ 2 (* 2 x))
(+ 2 (* x (+ 2 x)))
(+ 2 (* x (+ 2 (* x (+ 1 (* 1/3 x))))))
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(/ (exp x) (- (exp x) 1))
(exp x)
(- (exp x) 1)
(* 1/12 x)
(* x (+ 1/12 (* 1/2 (/ 1 x))))
(* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (/ 1 x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 2 (exp x))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(+ (exp x) (/ 1 (exp x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))

Outputs
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 x)) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.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)
2
#s(literal 2 binary64)
(+ 2 (* 2 x))
(fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))
(+ 2 (* x (+ 2 x)))
(fma.f64 (+.f64 #s(literal 2 binary64) x) x #s(literal 2 binary64))
(+ 2 (* x (+ 2 (* x (+ 1 (* 1/3 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64))
(* x (+ 1 (* 1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) x)
(+ 2 (pow x 2))
(fma.f64 x x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/360 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 2 binary64))
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(/ (exp x) (- (exp x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp x)
(exp.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(* x (+ 1/12 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/12 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* 2 (exp x))
(*.f64 #s(literal 2 binary64) (exp.f64 x))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #s(literal 1/2 binary64))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(fma.f64 #s(literal 1/2 binary64) (exp.f64 x) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))

rewrite314.0ms (5.1%)

Memory

-19.9MiB live, 170.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	104
0	46	95
1	156	92
2	1192	92
0	9105	92

Stop Event

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

Counts

16 → 952

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 x)
(expm1.f64 x)
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 (exp.f64 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 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 x))) (.f64 #s(literal 2 binary64) (expm1.f64 x)))
(fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
(sinh.f64 x)
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
(cosh.f64 x)

Outputs
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (exp.f64 x)) (*.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x)))) (/.f64 (-.f64 (sinh.f64 x) (cosh.f64 x)) (expm1.f64 x)))
(.f64 (/.f64 (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64))))) (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (sinh.f64 x) #s(literal 2 binary64)))))) (/.f64 (exp.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 #s(literal 2 binary64) (neg.f64 (expm1.f64 x))) (/.f64 (neg.f64 (exp.f64 x)) #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal -2 binary64) (expm1.f64 x)) (/.f64 (exp.f64 x) #s(literal -2 binary64)))
(.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (/.f64 #s(literal 2 binary64) (expm1.f64 x)) (/.f64 (exp.f64 x) #s(literal 2 binary64)))
(*.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (expm1.f64 x)))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (exp.f64 x)) (expm1.f64 x)))
(*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 x))))
(.f64 #s(literal 2 binary64) (/.f64 (exp.f64 x) (.f64 #s(literal 2 binary64) (expm1.f64 x))))
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (exp.f64 x) (expm1.f64 x)))
(/.f64 (+.f64 (pow.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (sinh.f64 x) (expm1.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (sinh.f64 x) (expm1.f64 x)) #s(literal 2 binary64)) (*.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) (/.f64 (sinh.f64 x) (expm1.f64 x))))))
(/.f64 (neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) (exp.f64 x)) (expm1.f64 x))) #s(literal -2 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (sinh.f64 x) (expm1.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (sinh.f64 x) (cosh.f64 x)) (expm1.f64 x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 (sinh.f64 x) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (sinh.f64 x) (expm1.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) #s(literal 2 binary64)) (*.f64 (/.f64 (sinh.f64 x) (expm1.f64 x)) (/.f64 (cosh.f64 x) (expm1.f64 x)))))))
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(/.f64 (neg.f64 (fma.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64))))) #s(literal -4 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))) #s(literal -2 binary64))
(/.f64 (fma.f64 #s(literal 1 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x)) (.f64 (exp.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (pow.f64 (cosh.f64 x) #s(literal 2 binary64))))) (.f64 (exp.f64 x) (-.f64 (sinh.f64 x) (cosh.f64 x))))
(/.f64 (fma.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)) (exp.f64 x)) (exp.f64 (+.f64 x (neg.f64 x))))
(/.f64 (fma.f64 #s(literal 1 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 (exp.f64 x) (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))))) (.f64 (exp.f64 x) (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 1 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 (exp.f64 x) (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))))) (.f64 (exp.f64 x) (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 (+.f64 #s(literal 4 binary64) (.f64 (exp.f64 x) (fma.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64)))))) (*.f64 (exp.f64 x) #s(literal 4 binary64)))
(/.f64 (+.f64 #s(literal 4 binary64) (.f64 (exp.f64 x) (fma.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 (sinh.f64 x) #s(literal 2 binary64)))))) (*.f64 (exp.f64 x) #s(literal 4 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x))) #s(literal 2 binary64)) (.f64 (exp.f64 x) (.f64 (.f64 #s(literal 2 binary64) (exp.f64 x)) (.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x)))))) (.f64 (exp.f64 x) (.f64 (*.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x))) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64))))) #s(literal 2 binary64)) (.f64 (exp.f64 x) (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64))))) (.f64 (exp.f64 x) (.f64 (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (sinh.f64 x) #s(literal 2 binary64))))) #s(literal 2 binary64))))
(/.f64 (+.f64 #s(literal -2 binary64) (.f64 (exp.f64 x) (.f64 #s(literal -2 binary64) (exp.f64 x)))) (*.f64 (exp.f64 x) #s(literal -2 binary64)))
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (exp.f64 x) (.f64 #s(literal 2 binary64) (exp.f64 x)))) (*.f64 #s(literal 2 binary64) (exp.f64 x)))
(/.f64 (fma.f64 (neg.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal -2 binary64) (.f64 #s(literal -2 binary64) (neg.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64))))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64) (.f64 #s(literal -2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))) #s(literal -4 binary64))
(/.f64 (fma.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal -2 binary64) (.f64 #s(literal 2 binary64) (neg.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64))))) #s(literal -4 binary64))
(/.f64 (fma.f64 (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (pow.f64 (cosh.f64 x) #s(literal 2 binary64))) (exp.f64 x) (.f64 (-.f64 (sinh.f64 x) (cosh.f64 x)) #s(literal 1 binary64))) (.f64 (-.f64 (sinh.f64 x) (cosh.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (exp.f64 x) (.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64))) (.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 (fma.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (exp.f64 x) (.f64 (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)))) #s(literal 1 binary64))) (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))))
(/.f64 (fma.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (exp.f64 x) (.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 1 binary64))) (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))))
(/.f64 (fma.f64 (fma.f64 (.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64)))) (exp.f64 x) #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (exp.f64 x)))
(/.f64 (fma.f64 (fma.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 (sinh.f64 x) #s(literal 2 binary64)))) (exp.f64 x) #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (exp.f64 x)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) (exp.f64 x)) (.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x)))) (exp.f64 x) (.f64 (.f64 (.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x))) #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (.f64 (*.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x))) #s(literal 2 binary64)) (exp.f64 x)))
(/.f64 (fma.f64 (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64))) (exp.f64 x) (.f64 (.f64 (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64))))) #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (.f64 (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (sinh.f64 x) #s(literal 2 binary64))))) #s(literal 2 binary64)) (exp.f64 x)))
(/.f64 (fma.f64 (.f64 #s(literal -2 binary64) (exp.f64 x)) (exp.f64 x) #s(literal -2 binary64)) (.f64 #s(literal -2 binary64) (exp.f64 x)))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (exp.f64 x)) (exp.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (exp.f64 x)))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))) (*.f64 (sinh.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (pow.f64 (cosh.f64 x) #s(literal 2 binary64))) (-.f64 (cosh.f64 x) (cosh.f64 x)))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (pow.f64 (cosh.f64 x) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x (neg.f64 x))))))
(/.f64 (fma.f64 (cosh.f64 x) #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 (fma.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))) #s(literal 4 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (exp.f64 x)) (.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x)))) (-.f64 (sinh.f64 x) (cosh.f64 x)) (exp.f64 (neg.f64 (neg.f64 (neg.f64 x)))))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (exp.f64 x)) (.f64 #s(literal 2 binary64) (-.f64 (sinh.f64 x) (cosh.f64 x)))) (-.f64 (sinh.f64 x) (cosh.f64 x)) (exp.f64 (neg.f64 x)))
(fma.f64 (/.f64 (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64))))) (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64)))))) (exp.f64 x) (exp.f64 (neg.f64 (neg.f64 (neg.f64 x)))))
(fma.f64 (/.f64 (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64))))) (fma.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64)))))) (exp.f64 x) (exp.f64 (neg.f64 x)))
(fma.f64 (cosh.f64 x) #s(literal 1 binary64) (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 (cosh.f64 x) #s(literal 1 binary64) (cosh.f64 x))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (cosh.f64 x))
(fma.f64 #s(literal 2 binary64) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 (neg.f64 (neg.f64 x)))))
(fma.f64 #s(literal 2 binary64) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) (exp.f64 (neg.f64 (neg.f64 (neg.f64 x)))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) (exp.f64 (neg.f64 x)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) (exp.f64 (neg.f64 (neg.f64 (neg.f64 x)))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (.f64 (sinh.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (cosh.f64 x) (cosh.f64 x))) (/.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (cosh.f64 x) (cosh.f64 x))))
(+.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (pow.f64 (cosh.f64 x) #s(literal 2 binary64))))) (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (pow.f64 (cosh.f64 x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x (neg.f64 x)))))) (/.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x (neg.f64 x)))))))
(+.f64 (/.f64 (.f64 (.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal 4 binary64)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (cosh.f64 x) (cosh.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 (neg.f64 (neg.f64 x)))))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(*.f64 (cosh.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (cosh.f64 x) #s(literal 2 binary64))) (.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (cosh.f64 x) #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))) (.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))))))
(/.f64 (fma.f64 #s(literal 2 binary64) (exp.f64 x) (*.f64 #s(literal 2 binary64) (exp.f64 (neg.f64 x)))) #s(literal 4 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(/.f64 (fma.f64 (cosh.f64 x) #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal 4 binary64))
(/.f64 (neg.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal -2 binary64))
(/.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))
(cosh.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cosh.f64 (neg.f64 (neg.f64 x)))
(cosh.f64 (neg.f64 x))
(cosh.f64 x)
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (cosh.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)))

eval155.0ms (2.5%)

Memory: 36.8MiB live, 125.8MiB allocated
Compiler: Compiled 30 428 to 3 363 computations (88.9% saved)

prune60.0ms (1%)

Memory

-4.3MiB live, 45.1MiB allocated

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	960	5	965
Fresh	1	3	4
Picked	2	3	5
Done	0	0	0
Total	963	11	974

Accuracy

100.0%

Counts

974 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.3%	(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
	38.4%	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	64.5%	(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
▶	82.0%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
✓	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
	3.0%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
✓	65.0%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	3.4%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))

Compiler

Compiled 302 to 212 computations (29.8% saved)

simplify123.0ms (2%)

Memory

10.9MiB live, 101.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (exp.f64 x))
cost-diff	0	(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
cost-diff	2	(-.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	6	(/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x))))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
cost-diff	0	(*.f64 #s(literal 1/12 binary64) x)
cost-diff	0	#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
cost-diff	0	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
cost-diff	0	#s(approx (exp x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	211
0	53	205
1	78	205
2	133	205
3	334	205
4	1194	199
0	8436	181

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
#s(literal 1/12 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal -1/2 binary64)
(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #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 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x))))
(sqrt.f64 (exp.f64 x))
(exp.f64 x)
x
(sqrt.f64 (exp.f64 (neg.f64 x)))
(exp.f64 (neg.f64 x))
(neg.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
#s(literal 1/12 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal -1/2 binary64)
(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #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 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x))))
(exp.f64 x)
(sqrt.f64 (exp.f64 x))
(exp.f64 x)
x
(sqrt.f64 (exp.f64 (neg.f64 x)))
(pow.f64 (exp.f64 x) #s(literal -1/2 binary64))
(exp.f64 (neg.f64 x))
(neg.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
#s(literal 1 binary64)

localize74.0ms (1.2%)

Memory

1.6MiB live, 100.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.015625	(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	0.23338629664385482	(sqrt.f64 (exp.f64 x))
accuracy	0.2334474325901241	(sqrt.f64 (exp.f64 (neg.f64 x)))
accuracy	37.81138712022363	(-.f64 (exp.f64 x) #s(literal 1 binary64))
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	0.015625	(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
accuracy	22.522948645385462	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy	22.851239981327765	#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.0078125	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
accuracy	22.340194714418068	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	0.29296875	(*.f64 #s(literal 1/12 binary64) x)
accuracy	22.32363818218908	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
accuracy	40.53629773775477	#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	0.015625	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
accuracy	22.851239981327765	#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
accuracy	22.887182822145153	#s(approx (exp x) #s(literal 1 binary64))

Samples

56.0ms

256×

valid

Compiler

Compiled 147 to 24 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-div: 6.0ms (21.1% of total)

ival-exp: 4.0ms (14.1% of total)

ival-mult: 4.0ms (14.1% of total)

const: 4.0ms (14.1% of total)

ival-add: 3.0ms (10.5% of total)

ival-sqrt: 3.0ms (10.5% of total)

ival-expm1: 1.0ms (3.5% of total)

ival-sub: 1.0ms (3.5% of total)

ival-neg: 1.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory

-29.9MiB live, 16.3MiB allocated

Counts

19 → 39

Calls

Call 1

Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #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 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (exp.f64 x))
(sqrt.f64 (exp.f64 (neg.f64 x)))

Outputs
(/ 1 x)
(/ (+ 1 (* 1/2 x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/12 x)
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/8 x))))
(+ 1 (* x (+ 1/2 (* x (+ 1/8 (* 1/48 x))))))
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 1/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 1/8 (* -1/48 x))) 1/2)))
(/ (exp x) (- (exp x) 1))
(exp x)
(- (exp x) 1)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* x (+ 1/12 (* 1/2 (/ 1 x))))
(* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (/ 1 x))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(sqrt (/ (exp x) (exp (neg x))))
(* (sqrt (/ (exp x) (exp (neg x)))) (/ 1 (- (exp x) 1)))
(sqrt (exp x))
(sqrt (exp (neg x)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))
(sqrt (/ (exp x) (exp (* -1 x))))
(* (sqrt (/ (exp x) (exp (* -1 x)))) (/ 1 (- (exp x) 1)))
(sqrt (exp (* -1 x)))

Calls

3 calls:

Time

Variable

Point

Expression

6.0ms

-inf

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (* 1/12 x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ 1 x) (/ (exp x) (- (exp x) 1)) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (+ (* 1/2 x) 1) (/ (sqrt (exp x)) (sqrt (exp (neg x)))) (- (exp x) 1) (/ (/ (sqrt (exp x)) (sqrt (exp (neg x)))) (- (exp x) 1)) (sqrt (exp x)) (sqrt (exp (neg x))))

5.0ms

inf

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (* 1/12 x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ 1 x) (/ (exp x) (- (exp x) 1)) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (+ (* 1/2 x) 1) (/ (sqrt (exp x)) (sqrt (exp (neg x)))) (- (exp x) 1) (/ (/ (sqrt (exp x)) (sqrt (exp (neg x)))) (- (exp x) 1)) (sqrt (exp x)) (sqrt (exp (neg x))))

1.0ms

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (* 1/12 x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ 1 x) (/ (exp x) (- (exp x) 1)) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (+ (* 1/2 x) 1) (/ (sqrt (exp x)) (sqrt (exp (neg x)))) (- (exp x) 1) (/ (/ (sqrt (exp x)) (sqrt (exp (neg x)))) (- (exp x) 1)) (sqrt (exp x)) (sqrt (exp (neg x))))

simplify485.0ms (7.8%)

Memory

-39.8MiB live, 247.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	285
1	364	271
2	1083	264
3	4817	256
0	8261	218

Stop Event

1×	iter limit
1×	node limit

Counts

39 → 38

Calls

Call 1

Inputs
(/ 1 x)
(/ (+ 1 (* 1/2 x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/12 x)
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/8 x))))
(+ 1 (* x (+ 1/2 (* x (+ 1/8 (* 1/48 x))))))
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 1/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 1/8 (* -1/48 x))) 1/2)))
(/ (exp x) (- (exp x) 1))
(exp x)
(- (exp x) 1)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* x (+ 1/12 (* 1/2 (/ 1 x))))
(* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (/ 1 x))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(sqrt (/ (exp x) (exp (neg x))))
(* (sqrt (/ (exp x) (exp (neg x)))) (/ 1 (- (exp x) 1)))
(sqrt (exp x))
(sqrt (exp (neg x)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))
(sqrt (/ (exp x) (exp (* -1 x))))
(* (sqrt (/ (exp x) (exp (* -1 x)))) (/ 1 (- (exp x) 1)))
(sqrt (exp (* -1 x)))

Outputs
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 x)) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.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)
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/8 x))))
(fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (+ 1/8 (* 1/48 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/48 binary64) x #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* 1/8 x) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/8 (* -1/48 x))) 1/2)))
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) x #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(/ (exp x) (- (exp x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp x)
(exp.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1/12 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/12 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt (/ (exp x) (exp (neg x))))
(fabs.f64 (exp.f64 x))
(* (sqrt (/ (exp x) (exp (neg x)))) (/ 1 (- (exp x) 1)))
(/.f64 (fabs.f64 (exp.f64 x)) (expm1.f64 x))
(sqrt (exp x))
(sqrt.f64 (exp.f64 x))
(sqrt (exp (neg x)))
(pow.f64 (exp.f64 x) #s(literal -1/2 binary64))
(* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))
(*.f64 (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)) (neg.f64 x))
(sqrt (/ (exp x) (exp (* -1 x))))
(fabs.f64 (exp.f64 x))
(* (sqrt (/ (exp x) (exp (* -1 x)))) (/ 1 (- (exp x) 1)))
(/.f64 (fabs.f64 (exp.f64 x)) (expm1.f64 x))
(sqrt (exp (* -1 x)))
(pow.f64 (exp.f64 x) #s(literal -1/2 binary64))

rewrite188.0ms (3%)

Memory

-5.7MiB live, 222.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	170
0	53	168
1	159	166
2	951	160
0	8349	144

Stop Event

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

Counts

19 → 329

Calls

Call 1

Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #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 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (exp.f64 x))
(sqrt.f64 (exp.f64 (neg.f64 x)))

Outputs
(/.f64 (neg.f64 #s(approx (exp x) #s(literal 1 binary64))) (neg.f64 #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(neg.f64 (/.f64 (neg.f64 #s(approx (exp x) #s(literal 1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
#s(approx (exp x) #s(literal 1 binary64))
(neg.f64 (neg.f64 #s(approx (exp x) #s(literal 1 binary64))))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(neg.f64 (neg.f64 #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (.f64 (.f64 #s(literal 1/2 binary64) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (.f64 (.f64 #s(literal 1/2 binary64) x) x))) (-.f64 x (.f64 (.f64 #s(literal 1/2 binary64) x) x)))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (.f64 x x)) (-.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x)))) (-.f64 x (.f64 x (.f64 #s(literal 1/2 binary64) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (.f64 (.f64 #s(literal 1/2 binary64) x) x) (-.f64 (.f64 x x) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (.f64 (.f64 #s(literal 1/2 binary64) x) x)) (.f64 x (.f64 (.f64 #s(literal 1/2 binary64) x) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x)) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (.f64 x (.f64 x (.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) x)) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) x x)) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) x) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64) x)
(fma.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64) x)
(fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))) x (.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x x)
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) x) x)
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/2 binary64) x)) x)
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 x (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) x (.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) x) x)))
(fma.f64 #s(literal 1 binary64) x (.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(fma.f64 #s(literal 1 binary64) x (.f64 x (.f64 #s(literal 1/2 binary64) x)))
(fma.f64 x (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))) (.f64 x (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))))
(fma.f64 x (*.f64 #s(literal 1/2 binary64) x) x)
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 x (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) x) x)))
(fma.f64 x #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/2 binary64) x)))
(-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (neg.f64 x))
(-.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(-.f64 x (.f64 (.f64 #s(literal -1/2 binary64) x) x))
(-.f64 x (.f64 (neg.f64 x) (.f64 #s(literal 1/2 binary64) x)))
(+.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64)) x)
(+.f64 (.f64 (.f64 x (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)) x)
(+.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))) x) (.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) x))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) x) x)) x)
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal 1/2 binary64) x))) x)
(+.f64 (.f64 x (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))) (.f64 x (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) x)
(+.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) x)
(+.f64 x (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64)))
(+.f64 x (.f64 (.f64 x (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(+.f64 x (.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) x) x)))
(+.f64 x (.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal 1/2 binary64) x))))
(+.f64 x (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(+.f64 x (.f64 x (.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
(*.f64 x #s(literal 1/12 binary64))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))) (.f64 (/.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))) (.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))))) (+.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))) (*.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/8 binary64))) (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)) #s(literal 2 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
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(pow.f64 (exp.f64 (neg.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (exp.f64 x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 x) #s(literal -1/2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (/.f64 x #s(literal 2 binary64))) (cosh.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (sinh.f64 (/.f64 x #s(literal -2 binary64))) (sinh.f64 (/.f64 x #s(literal -2 binary64))))) (-.f64 (cosh.f64 (/.f64 x #s(literal 2 binary64))) (sinh.f64 (/.f64 x #s(literal -2 binary64)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (/.f64 x #s(literal 2 binary64))) (cosh.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 (.f64 (sinh.f64 (/.f64 x #s(literal -2 binary64))) (sinh.f64 (/.f64 x #s(literal -2 binary64)))) (.f64 (cosh.f64 (/.f64 x #s(literal 2 binary64))) (sinh.f64 (/.f64 x #s(literal -2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (*.f64 (sinh.f64 x) (exp.f64 x)))))
(/.f64 (hypot.f64 (pow.f64 (cosh.f64 x) #s(literal 3/2 binary64)) (pow.f64 (sinh.f64 (neg.f64 x)) #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (*.f64 (sinh.f64 (neg.f64 x)) (-.f64 (sinh.f64 (neg.f64 x)) (cosh.f64 x))))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (exp.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (exp.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (exp.f64 x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (exp.f64 (neg.f64 x)))
(-.f64 (cosh.f64 (/.f64 x #s(literal 2 binary64))) (sinh.f64 (/.f64 x #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 #s(literal -1/2 binary64) x)) (sinh.f64 (.f64 #s(literal -1/2 binary64) x)))
(+.f64 (cosh.f64 (/.f64 x #s(literal 2 binary64))) (sinh.f64 (/.f64 x #s(literal -2 binary64))))
(exp.f64 (*.f64 #s(literal -1/2 binary64) x))
(exp.f64 (/.f64 x #s(literal -2 binary64)))

eval73.0ms (1.2%)

Memory: -1.9MiB live, 144.4MiB allocated
Compiler: Compiled 14 486 to 1 620 computations (88.8% saved)

prune14.0ms (0.2%)

Memory

32.6MiB live, 32.6MiB allocated

Pruning

14 alts after pruning (8 fresh and 6 done)

	Pruned	Kept	Total
New	488	5	493
Fresh	0	3	3
Picked	2	3	5
Done	0	3	3
Total	490	14	504

Accuracy

100.0%

Counts

504 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.3%	(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
	38.4%	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	64.5%	(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
▶	89.4%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
	87.2%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
▶	21.3%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
▶	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
✓	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
	3.0%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
✓	65.0%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	3.3%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
✓	3.4%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))

Compiler

Compiled 368 to 261 computations (29.1% saved)

simplify112.0ms (1.8%)

Memory

-29.2MiB live, 111.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (exp.f64 x))
cost-diff	0	(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
cost-diff	2	(-.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	6	(/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
cost-diff	0	(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)
cost-diff	0	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))
cost-diff	0	#s(approx (exp x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
cost-diff	0	#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
cost-diff	0	(*.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)
cost-diff	0	#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))
cost-diff	0	#s(approx (exp x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	267
0	70	261
1	108	261
2	228	261
3	662	260
4	2211	255
0	8300	235

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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(literal 1 binary64)
#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))
(*.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)
(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))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
#s(literal 1/24 binary64)
x
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))
(.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
(*.f64 x x)
x
#s(literal -1/720 binary64)
#s(literal 1/12 binary64)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x)))
(sqrt.f64 (exp.f64 x))
(exp.f64 x)
x
(exp.f64 (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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(literal 1 binary64)
#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))
(*.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)
(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))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
#s(literal 1/24 binary64)
x
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))
(.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64))
(*.f64 x x)
x
#s(literal -1/720 binary64)
#s(literal 1/12 binary64)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x)))
(exp.f64 x)
(sqrt.f64 (exp.f64 x))
(exp.f64 x)
x
(exp.f64 (*.f64 #s(literal -1/2 binary64) x))
(pow.f64 (exp.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
#s(literal 1 binary64)

localize94.0ms (1.5%)

Memory

27.0MiB live, 116.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x)))
accuracy	0.015625	(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	0.23338629664385482	(sqrt.f64 (exp.f64 x))
accuracy	37.81138712022363	(-.f64 (exp.f64 x) #s(literal 1 binary64))
accuracy	0.0078125	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
accuracy	0.046875	(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	0.05859375	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
accuracy	22.310325065798278	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
accuracy	0.015625	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
accuracy	22.851239981327765	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))
accuracy	22.887182822145153	#s(approx (exp x) #s(literal 1 binary64))
accuracy	40.47617969232223	#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
accuracy	22.340194714418068	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
accuracy	40.73662691989616	#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
accuracy	0.05859375	(fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
accuracy	0.1015625	(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
accuracy	22.684620696722263	#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))
accuracy	22.887182822145153	#s(approx (exp x) #s(literal 1 binary64))

Samples

73.0ms

256×

valid

Compiler

Compiled 191 to 35 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 18.0ms (31.8% of total)

const: 12.0ms (21.2% of total)

ival-expm1: 8.0ms (14.1% of total)

ival-div: 6.0ms (10.6% of total)

ival-add: 6.0ms (10.6% of total)

ival-exp: 4.0ms (7.1% of total)

ival-sqrt: 2.0ms (3.5% of total)

ival-sub: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

14.1MiB live, 14.1MiB allocated

Counts

21 → 53

Calls

Call 1

Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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) 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))
(*.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) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))
(.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
(*.f64 x x)
(/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x)))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (exp.f64 x))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))

Outputs
(/ 1 x)
(/ (+ 1 (* 1/2 x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
1/12
(+ 1/12 (* -1/720 (pow x 2)))
(pow x 2)
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/8 x))))
(+ 1 (* x (+ 1/2 (* x (+ 1/8 (* 1/48 x))))))
1/6
(+ 1/6 (* 1/24 x))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(/ (exp x) (- (exp x) 1))
(exp x)
(- (exp x) 1)
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(+ 1/2 (/ 1 x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (* 1/12 (/ 1 (pow x 2)))) 1/720))
(* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))) 1/720))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/12 (/ 1 (pow x 2))) 1/720))
(* (sqrt (exp x)) (/ 1 (exp (* -1/2 x))))
(* (sqrt (exp x)) (/ 1 (* (exp (* -1/2 x)) (- (exp x) 1))))
(sqrt (exp x))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(* -1 (* (pow x 3) (- 1/720 (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/720 (* -1 (/ (+ 1/12 (* 1/2 (/ 1 x))) (pow x 2))))))
(* -1 (* (pow x 3) (- (+ 1/720 (* -1 (/ (+ 1/2 (/ 1 x)) (pow x 3)))) (* 1/12 (/ 1 (pow x 2))))))

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

inf

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (* (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (exp x) (- (exp x) 1)) (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (+ (* (* x x) -1/720) 1/12) (* x x) (/ (sqrt (exp x)) (exp (* -1/2 x))) (- (exp x) 1) (/ (/ (sqrt (exp x)) (exp (* -1/2 x))) (- (exp x) 1)) (sqrt (exp x)) (+ (* 1/24 x) 1/6) (+ (* (+ (* 1/24 x) 1/6) x) 1/2) (+ (* 1/2 x) 1) (- (/ 1 x) -1/2))

4.0ms

-inf

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (* (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (exp x) (- (exp x) 1)) (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (+ (* (* x x) -1/720) 1/12) (* x x) (/ (sqrt (exp x)) (exp (* -1/2 x))) (- (exp x) 1) (/ (/ (sqrt (exp x)) (exp (* -1/2 x))) (- (exp x) 1)) (sqrt (exp x)) (+ (* 1/24 x) 1/6) (+ (* (+ (* 1/24 x) 1/6) x) 1/2) (+ (* 1/2 x) 1) (- (/ 1 x) -1/2))

2.0ms

((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (* (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (/ (exp x) (- (exp x) 1)) (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (+ (* (* x x) -1/720) 1/12) (* x x) (/ (sqrt (exp x)) (exp (* -1/2 x))) (- (exp x) 1) (/ (/ (sqrt (exp x)) (exp (* -1/2 x))) (- (exp x) 1)) (sqrt (exp x)) (+ (* 1/24 x) 1/6) (+ (* (+ (* 1/24 x) 1/6) x) 1/2) (+ (* 1/2 x) 1) (- (/ 1 x) -1/2))

simplify186.0ms (3%)

Memory

-5.1MiB live, 137.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	130	435
1	463	423
2	1551	402
3	7513	402
0	9204	363

Stop Event

1×	iter limit
1×	node limit

Counts

53 → 52

Calls

Call 1

Inputs
(/ 1 x)
(/ (+ 1 (* 1/2 x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
1/12
(+ 1/12 (* -1/720 (pow x 2)))
(pow x 2)
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/8 x))))
(+ 1 (* x (+ 1/2 (* x (+ 1/8 (* 1/48 x))))))
1/6
(+ 1/6 (* 1/24 x))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(/ (exp x) (- (exp x) 1))
(exp x)
(- (exp x) 1)
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(+ 1/2 (/ 1 x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (* 1/12 (/ 1 (pow x 2)))) 1/720))
(* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))) 1/720))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/12 (/ 1 (pow x 2))) 1/720))
(* (sqrt (exp x)) (/ 1 (exp (* -1/2 x))))
(* (sqrt (exp x)) (/ 1 (* (exp (* -1/2 x)) (- (exp x) 1))))
(sqrt (exp x))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(* -1 (* (pow x 3) (- 1/720 (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/720 (* -1 (/ (+ 1/12 (* 1/2 (/ 1 x))) (pow x 2))))))
(* -1 (* (pow x 3) (- (+ 1/720 (* -1 (/ (+ 1/2 (/ 1 x)) (pow x 3)))) (* 1/12 (/ 1 (pow x 2))))))

Outputs
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 x)) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64)))
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/12 binary64)) x #s(literal -1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.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)
1/12
#s(literal 1/12 binary64)
(+ 1/12 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
(pow x 2)
(*.f64 x x)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/8 x))))
(fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (+ 1/8 (* 1/48 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/48 binary64) x #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* 1/24 x))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
(/ (exp x) (- (exp x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp x)
(exp.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(*.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) x) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/6 binary64)) x) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) x)) x) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64)))
(+ 1/2 (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* -1/720 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/720 binary64))
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/720))
(.f64 (-.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/720 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (* 1/12 (/ 1 (pow x 2)))) 1/720))
(fma.f64 (-.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64))
(* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))) 1/720))
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/720 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* (pow x 2) (- (* 1/12 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(* (sqrt (exp x)) (/ 1 (exp (* -1/2 x))))
(exp.f64 x)
(* (sqrt (exp x)) (/ 1 (* (exp (* -1/2 x)) (- (exp x) 1))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(sqrt (exp x))
(sqrt.f64 (exp.f64 x))
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 #s(literal 1/24 binary64) x) x)
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x)
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) x)) x) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 3) (- 1/720 (* 1/12 (/ 1 (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/12 binary64) (.f64 x x)) #s(literal -1 binary64) #s(literal -1/720 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/720 (* -1 (/ (+ 1/12 (* 1/2 (/ 1 x))) (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/720 binary64) (fma.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- (+ 1/720 (* -1 (/ (+ 1/2 (/ 1 x)) (pow x 3)))) (* 1/12 (/ 1 (pow x 2))))))
(.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/720 binary64) (/.f64 (+.f64 #s(literal 1/12 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) x)) (.f64 x x))))

rewrite226.0ms (3.6%)

Memory

-13.2MiB live, 182.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	221
0	70	221
1	228	221
2	1415	213
0	8719	193

Stop Event

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

Counts

21 → 307

Calls

Call 1

Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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) 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))
(*.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) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))
(.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
(*.f64 x x)
(/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x)))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (exp.f64 x))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))

Outputs
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (exp x) #s(literal 1 binary64))))) (neg.f64 (neg.f64 (neg.f64 #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))))))
(/.f64 (neg.f64 (neg.f64 #s(approx (exp x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 #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)))))
(/.f64 (neg.f64 #s(approx (exp x) #s(literal 1 binary64))) (neg.f64 #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))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(neg.f64 (/.f64 (neg.f64 #s(approx (exp x) #s(literal 1 binary64))) #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))))
(neg.f64 (/.f64 #s(approx (exp x) #s(literal 1 binary64)) (neg.f64 #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) 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))
(*.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)
(*.f64 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)))
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(fma.f64 x (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))) x))
(-.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 x) (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 3 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 3 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64)))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64)))))
(+.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (*.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/8 binary64))) (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)) #s(literal 2 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))

eval69.0ms (1.1%)

Memory: 21.9MiB live, 67.1MiB allocated
Compiler: Compiled 13 829 to 1 771 computations (87.2% saved)

prune38.0ms (0.6%)

Memory

-17.9MiB live, 36.1MiB allocated

Pruning

18 alts after pruning (10 fresh and 8 done)

	Pruned	Kept	Total
New	350	8	358
Fresh	1	2	3
Picked	2	3	5
Done	1	5	6
Total	354	18	372

Accuracy

100.0%

Counts

372 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	39.3%	(/.f64 (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) x)) (exp.f64 (.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
	38.4%	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	64.5%	(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
	89.4%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
	89.3%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) (*.f64 #s(literal 1/24 binary64) x)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
	87.2%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
	89.4%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 x) 1/6) x) 1/2) (.f64 (.f64 #s(literal 1/24 binary64) x) x)) x #s(literal 1 binary64)) x)))
✓	21.3%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
✓	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
	3.0%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
✓	65.0%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
✓	65.1%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	3.3%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
	17.7%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/720 binary64) (/.f64 (+.f64 #s(literal 1/12 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) x)) (.f64 x x))))))
✓	3.4%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))

Compiler

Compiled 886 to 419 computations (52.7% saved)

regimes26.0ms (0.4%)

Memory

-10.2MiB live, 33.7MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 x) 1/6) x) 1/2) (.f64 (.f64 #s(literal 1/24 binary64) x) x)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) (*.f64 #s(literal 1/24 binary64) x)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/720 binary64) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/720 binary64) (/.f64 (+.f64 #s(literal 1/12 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) x)) (.f64 x x))))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (.f64 #s(literal 2 binary64) (cosh.f64 x))) (.f64 #s(literal 2 binary64) (expm1.f64 x)))
(/.f64 (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) x)) (exp.f64 (.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 (*.f64 #s(literal -1/2 binary64) x))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))

Calls

3 calls:

11.0ms	x
6.0ms	(exp.f64 x)
6.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Results

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

Compiler

Compiled 10 to 8 computations (20% saved)

regimes18.0ms (0.3%)

Memory

26.3MiB live, 26.3MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 x) 1/6) x) 1/2) (.f64 (.f64 #s(literal 1/24 binary64) x) x)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) (*.f64 #s(literal 1/24 binary64) x)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/720 binary64) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/720 binary64) (/.f64 (+.f64 #s(literal 1/12 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) x)) (.f64 x x))))))

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

Calls

3 calls:

7.0ms	x
5.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
5.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
99.1%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes19.0ms (0.3%)

Memory

-13.5MiB live, 29.8MiB allocated

Counts

19 → 2

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 x) 1/6) x) 1/2) (.f64 (.f64 #s(literal 1/24 binary64) x) x)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) (*.f64 #s(literal 1/24 binary64) x)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))

Outputs

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

#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))

Calls

3 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
6.0ms	x
5.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.6%	2	`x`
99.0%	2	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
99.6%	2	`(exp.f64 x)`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes15.0ms (0.2%)

Memory

26.0MiB live, 26.0MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 x) 1/6) x) 1/2) (.f64 (.f64 #s(literal 1/24 binary64) x) x)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) (*.f64 #s(literal 1/24 binary64) x)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #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) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))

Outputs

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

Calls

3 calls:

5.0ms	x
4.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
4.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
89.4%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
89.4%	1	`x`
89.4%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes13.0ms (0.2%)

Memory

-25.8MiB live, 20.0MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 1/24 x) 1/6) #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))

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

Calls

3 calls:

6.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
3.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
87.2%	1	`(exp.f64 x)`
87.2%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
87.2%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes9.0ms (0.1%)

Memory

18.9MiB live, 18.9MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))

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

Calls

3 calls:

3.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
3.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
82.0%	1	`x`
82.0%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
82.0%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes14.0ms (0.2%)

Memory

-37.4MiB live, 18.0MiB allocated

Counts

8 → 2

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x)))

Outputs

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

#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))

Calls

3 calls:

8.0ms	x
2.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
83.2%	2	`(exp.f64 x)`
83.2%	2	`x`
82.2%	2	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes8.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))

Outputs
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))

Calls

3 calls:

3.0ms	x
2.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
65.1%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
65.1%	1	`(exp.f64 x)`
65.1%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes6.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Outputs
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
65.1%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
65.1%	1	`(exp.f64 x)`
65.1%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes6.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
65.0%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
65.0%	1	`(exp.f64 x)`
65.0%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes5.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))

#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))

#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))

Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
3.4%	1	`x`
3.4%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
3.4%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes3.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))

Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
3.3%	1	`(exp.f64 x)`
3.3%	1	`x`
3.3%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 8 computations (20% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	0.10722191317902895

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch22.0ms (0.4%)

Memory

-38.3MiB live, 8.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	-1269.1682542962758	-2.232854637251648

Samples

5.0ms

128×

valid

Compiler

Compiled 306 to 240 computations (21.6% saved)

Precisions

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

ival-div: 1.0ms (31.6% of total)

ival-exp: 1.0ms (31.6% of total)

ival-expm1: 1.0ms (31.6% of total)

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

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

simplify48.0ms (0.8%)

Memory

1.4MiB live, 44.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	238
1	96	238
2	149	238
3	268	238
4	603	238
5	2395	238

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(if (<=.f64 (exp.f64 x) #s(literal 0 binary64)) (/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 x) 1/6) x) 1/2) (.f64 (.f64 #s(literal 1/24 binary64) x) x)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(if (<=.f64 x #s(literal -700 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))) #s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(if (<=.f64 (exp.f64 x) #s(literal 0 binary64)) (/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(if (<=.f64 (exp.f64 x) #s(literal 0 binary64)) (/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 x) 1/6) x) 1/2) (.f64 (.f64 #s(literal 1/24 binary64) x) x)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #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)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
(if (<=.f64 x #s(literal -700 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))) #s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64)))))
(if (<=.f64 x #s(literal -700 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)) x))) #s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 #s(literal -1/12 binary64) x #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))

soundness1.4s (22.8%)

Memory

40.2MiB live, 783.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	285
1	364	271
2	1083	264
3	4817	256
0	8261	218
0	119	338
1	464	338
2	1584	315
3	5118	315
0	8375	271
0	44	111
1	166	111
2	530	105
3	1942	105
4	5239	105
0	8089	87
0	5	13
0	8	13
1	30	13
2	177	13
3	1809	13
0	9626	9
0	130	435
1	463	423
2	1551	402
3	7513	402
0	9204	363

Stop Event

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

Compiler

Compiled 522 to 301 computations (42.3% saved)

preprocess84.0ms (1.4%)

Memory: 9.3MiB live, 106.6MiB allocated
Compiler: Compiled 502 to 184 computations (63.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample831.0ms (13.4%)

explain66.0ms (1.1%)

preprocess218.0ms (3.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify155.0ms (2.5%)

localize15.0ms (0.2%)

series2.0ms (0%)

simplify246.0ms (4%)

rewrite200.0ms (3.2%)

eval111.0ms (1.8%)

prune12.0ms (0.2%)

simplify178.0ms (2.9%)

localize72.0ms (1.2%)

series12.0ms (0.2%)

simplify141.0ms (2.3%)

rewrite314.0ms (5.1%)

eval155.0ms (2.5%)

prune60.0ms (1%)

simplify123.0ms (2%)

localize74.0ms (1.2%)

series13.0ms (0.2%)

simplify485.0ms (7.8%)

rewrite188.0ms (3%)

eval73.0ms (1.2%)

prune14.0ms (0.2%)

simplify112.0ms (1.8%)

localize94.0ms (1.5%)

series10.0ms (0.2%)

simplify186.0ms (3%)

rewrite226.0ms (3.6%)

eval69.0ms (1.1%)

prune38.0ms (0.6%)

regimes26.0ms (0.4%)

regimes18.0ms (0.3%)

regimes19.0ms (0.3%)

regimes15.0ms (0.2%)

regimes13.0ms (0.2%)

regimes9.0ms (0.1%)

regimes14.0ms (0.2%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

bsearch22.0ms (0.4%)

simplify48.0ms (0.8%)

soundness1.4s (22.8%)

preprocess84.0ms (1.4%)

end0.0ms (0%)

Profiling