Metrics for expq2 (section 3.11)

start0.0ms (0%)

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

analyze1.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated; 0ms collecting garbage

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)

sample735.0ms (12.9%)

Memory

-26.0MiB live, 880.2MiB allocated; 199ms collecting garbage

Samples

493.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 274.0ms

ival-exp: 131.0ms (47.9% of total)

ival-div: 58.0ms (21.2% of total)

ival-expm1: 53.0ms (19.4% of total)

ival->: 21.0ms (7.7% of total)

exact: 6.0ms (2.2% of total)

ival-assert: 3.0ms (1.1% of total)

adjust: 2.0ms (0.7% of total)

Bogosity

explain68.0ms (1.2%)

Memory

44.6MiB live, 182.7MiB allocated; 8ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
167	-	-	`(-.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	167	0

Confusion

	Predicted +	Predicted -
+	167	0
-	0	89

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	167	0	0
-	0	0	89

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	89
1	167

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

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 (34.9% of total)

ival-div: 3.0ms (26.2% of total)

ival-expm1: 3.0ms (26.2% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess200.0ms (3.5%)

Memory

-7.5MiB live, 192.1MiB allocated; 30ms collecting garbage

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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.1%	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify139.0ms (2.4%)

Memory

-12.3MiB live, 171.2MiB allocated; 28ms collecting garbage

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)

localize30.0ms (0.5%)

Memory

-13.4MiB live, 43.9MiB allocated; 8ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	38.45494897063316	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

16.0ms

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 (35.1% of total)

ival-exp: 2.0ms (35.1% of total)

ival-expm1: 2.0ms (35.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

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))

simplify164.0ms (2.9%)

Memory

5.0MiB live, 135.2MiB allocated; 28ms collecting garbage

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)

rewrite285.0ms (5%)

Memory

-11.6MiB live, 326.6MiB allocated; 44ms collecting garbage

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))))
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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)

eval79.0ms (1.4%)

Memory: 10.2MiB live, 107.3MiB allocated; 13ms collecting garbage
Compiler: Compiled 14 895 to 1 739 computations (88.3% saved)

prune12.0ms (0.2%)

Memory

-14.1MiB live, 33.1MiB allocated; 2ms collecting garbage

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	565	7	572
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	566	7	573

Accuracy

100.0%

Counts

573 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	37.6%	(/.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))
	99.8%	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
	66.1%	#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)))))
▶	66.2%	#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))))
▶	66.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	66.3%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Compiler

Compiled 188 to 142 computations (24.5% saved)

simplify213.0ms (3.7%)

Memory

38.4MiB live, 179.5MiB allocated; 28ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
cost-diff	0	(exp.f64 x)
cost-diff	0	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
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	(-.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 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: 0 (0.0ms)

Iter	Nodes	Cost
0	20	112
0	31	112
1	41	112
2	66	112
3	113	112
4	337	112
5	2146	112
6	5446	112
0	9253	112

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

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

localize56.0ms (1%)

Memory

-25.8MiB live, 113.0MiB allocated; 9ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
accuracy	21.80282643980994	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
accuracy	38.45494897063316	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.0	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
accuracy	0.1015625	(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	21.62510811508034	#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	0.0	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
accuracy	21.570028049270988	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	21.633692148315994	#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	0.00390625	(/.f64 (exp.f64 x) (expm1.f64 x))

Samples

40.0ms

256×

valid

Compiler

Compiled 94 to 14 computations (85.1% saved)

Precisions

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

const: 13.0ms (46.9% of total)

ival-exp: 4.0ms (14.4% of total)

ival-div: 3.0ms (10.8% of total)

ival-add: 2.0ms (7.2% of total)

ival-mult: 2.0ms (7.2% of total)

ival-expm1: 2.0ms (7.2% of total)

ival-sub: 1.0ms (3.6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Counts

12 → 21

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	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 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (exp x))
1.0ms	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 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (exp x))
1.0ms	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 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (/ (exp x) (- (exp x) 1)) (- (exp x) 1) (exp x))

Time

Variable

Point

Expression

1.0ms

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

1.0ms

-inf

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

1.0ms

inf

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

simplify177.0ms (3.1%)

Memory

40.4MiB live, 224.4MiB allocated; 28ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	153
1	214	153
2	667	140
3	2274	140
4	6433	140
0	8408	120

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 20

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

rewrite241.0ms (4.2%)

Memory

-8.6MiB live, 356.9MiB allocated; 75ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	84
0	31	84
1	111	84
2	754	84
0	8410	84

Stop Event

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

Counts

12 → 382

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

Outputs
(.f64 (/.f64 (neg.f64 (exp.f64 x)) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (neg.f64 (exp.f64 x)) (expm1.f64 (.f64 #s(literal 3 binary64) x))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 (.f64 #s(literal 3 binary64) x)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 3 binary64) x))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))))
(.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 3 binary64) 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 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(/.f64 (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (expm1.f64 (.f64 #s(literal 3 binary64) x)))
(/.f64 (.f64 (/.f64 (exp.f64 x) (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 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (expm1.f64 x))
(/.f64 (.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 3 binary64) x))) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)))) (-.f64 (*.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 (exp.f64 x) (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 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (expm1.f64 (.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) (/.f64 (cosh.f64 x) (expm1.f64 x))) (.f64 (/.f64 (sinh.f64 x) (expm1.f64 x)) (/.f64 (sinh.f64 x) (expm1.f64 x)))) (-.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) (/.f64 (sinh.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))) (fma.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) (/.f64 (cosh.f64 x) (expm1.f64 x)) (-.f64 (.f64 (/.f64 (sinh.f64 x) (expm1.f64 x)) (/.f64 (sinh.f64 x) (expm1.f64 x))) (.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) (/.f64 (sinh.f64 x) (expm1.f64 x))))))
(/.f64 (.f64 (exp.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))) (.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(/.f64 (.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)))) (.f64 (expm1.f64 (.f64 #s(literal 3 binary64) x)) (-.f64 (.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 1 binary64))))
(/.f64 (.f64 (exp.f64 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)))) (.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)) (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 (fma.f64 (cosh.f64 x) (expm1.f64 x) (.f64 (expm1.f64 x) (sinh.f64 x))) (.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (sinh.f64 x) (-.f64 (sinh.f64 x) (cosh.f64 x)) (pow.f64 (cosh.f64 x) #s(literal 2 binary64))) (expm1.f64 x)))
(/.f64 (neg.f64 (exp.f64 x)) (neg.f64 (expm1.f64 x)))
(/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(neg.f64 (/.f64 (neg.f64 (exp.f64 x)) (expm1.f64 x)))
(fma.f64 (/.f64 (cosh.f64 x) (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)) (/.f64 (sinh.f64 x) (expm1.f64 x)))
(fma.f64 (/.f64 (cosh.f64 x) (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (sinh.f64 x) (expm1.f64 x)))
(fma.f64 (/.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (.f64 (exp.f64 x) (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x)))))
(fma.f64 (/.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 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 (exp.f64 x) (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x)))))
(fma.f64 (/.f64 (sinh.f64 x) (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)) (/.f64 (cosh.f64 x) (expm1.f64 x)))
(fma.f64 (/.f64 (sinh.f64 x) (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (cosh.f64 x) (expm1.f64 x)))
(fma.f64 (/.f64 (sinh.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (cosh.f64 x) (expm1.f64 x)))
(fma.f64 (/.f64 (cosh.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (sinh.f64 x) (expm1.f64 x)))
(fma.f64 (/.f64 (sinh.f64 x) (expm1.f64 (*.f64 #s(literal 3 binary64) x))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (cosh.f64 x) (expm1.f64 x)))
(fma.f64 (/.f64 (cosh.f64 x) (expm1.f64 (*.f64 #s(literal 3 binary64) x))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (sinh.f64 x) (expm1.f64 x)))
(fma.f64 (/.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (.f64 (exp.f64 x) (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x)))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (cosh.f64 x) (.f64 (/.f64 (exp.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (+.f64 (sinh.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) #s(literal 1 binary64) (.f64 (/.f64 (exp.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (exp.f64 x)))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (exp.f64 x) (.f64 (/.f64 (exp.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 1 binary64)))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 3 binary64) x))) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (.f64 (/.f64 (exp.f64 x) (expm1.f64 (*.f64 #s(literal 3 binary64) x))) (exp.f64 x)))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 #s(literal 3 binary64) x))) (+.f64 #s(literal 1 binary64) (exp.f64 x)) (.f64 (/.f64 (exp.f64 x) (expm1.f64 (*.f64 #s(literal 3 binary64) x))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))
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(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (.f64 (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))) (.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (pow.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (fma.f64 (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (fma.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (pow.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 #s(literal -1 binary64) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(literal 1 binary64)))) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1 binary64)))) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 9 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 6 binary64))) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (neg.f64 (fma.f64 #s(literal -1 binary64) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (neg.f64 (neg.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(neg.f64 (neg.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (pow.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (pow.f64 (+.f64 (+.f64 (pow.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))

eval109.0ms (1.9%)

Memory: 0.6MiB live, 153.4MiB allocated; 34ms collecting garbage
Compiler: Compiled 15 286 to 1 492 computations (90.2% saved)

prune20.0ms (0.4%)

Memory

-8.1MiB live, 37.9MiB allocated; 4ms collecting garbage

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	504	5	509
Fresh	1	1	2
Picked	0	5	5
Done	0	0	0
Total	505	11	516

Accuracy

100.0%

Counts

516 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	37.6%	(/.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))
▶	99.8%	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
▶	66.1%	#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))))
✓	66.2%	#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))))
▶	30.4%	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
✓	66.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	66.3%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	28.9%	#s(approx (/ (exp x) (- (exp x) 1)) (sqrt.f64 (pow.f64 x #s(literal -2 binary64))))
▶	2.9%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
▶	3.1%	#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 254 to 186 computations (26.8% saved)

simplify137.0ms (2.4%)

Memory

37.9MiB live, 174.7MiB allocated; 25ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
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(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	#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 #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 #s(literal 1/6 binary64) x #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 (fma.f64 #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	33	198
0	50	198
1	76	198
2	174	198
3	472	198
4	1336	198
5	4533	198
0	8600	184

Stop Event

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

Calls

Call 1

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

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

localize165.0ms (2.9%)

Memory

-26.9MiB live, 123.5MiB allocated; 108ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	31.219834111668245	(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
accuracy	43.00724011796106	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	0.02734375	(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	21.699745409194676	#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	0.3125	(*.f64 #s(literal 1/12 binary64) x)
accuracy	21.62510811508034	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
accuracy	40.679309743283156	#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
accuracy	21.570028049270988	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
accuracy	40.96097151364796	#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
accuracy	0.03125	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.0390625	(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.09765625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	21.340043988777893	#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))

Samples

146.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 140 to 27 computations (80.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 104.0ms

ival-div: 55.0ms (53% of total)

ival-mult: 18.0ms (17.4% of total)

const: 11.0ms (10.6% of total)

ival-add: 7.0ms (6.7% of total)

ival-pow: 6.0ms (5.8% of total)

ival-exp: 3.0ms (2.9% of total)

ival-expm1: 2.0ms (1.9% of total)

adjust: 1.0ms (1% of total)

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

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated; 0ms collecting garbage

Counts

17 → 46

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify138.0ms (2.4%)

Memory

-6.7MiB live, 130.1MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	381
1	358	375
2	1284	347
3	5467	343
0	8510	305

Stop Event

1×	iter limit
1×	node limit

Counts

46 → 45

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

rewrite172.0ms (3%)

Memory

14.5MiB live, 145.8MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	173
0	50	173
1	183	169
2	1236	169
0	8397	155

Stop Event

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

Counts

17 → 294

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (.f64 (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))) (.f64 (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))) (-.f64 (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))))
(/.f64 (+.f64 (pow.f64 (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (-.f64 (.f64 (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))) (.f64 (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (exp.f64 x)))) (neg.f64 (neg.f64 (neg.f64 #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 (fma.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)) (.f64 #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)) (sinh.f64 x))) (.f64 #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(/.f64 (neg.f64 (neg.f64 (exp.f64 x))) (neg.f64 (neg.f64 #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 (neg.f64 (exp.f64 x)) (neg.f64 #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 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(neg.f64 (/.f64 (neg.f64 (exp.f64 x)) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(neg.f64 (/.f64 (exp.f64 x) (neg.f64 #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 (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(+.f64 (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))) (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(/.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 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (sinh.f64 x) (cosh.f64 x)))))
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x))) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 x) (*.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (*.f64 (cosh.f64 x) (sinh.f64 x))))))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 x)))) #s(literal 4 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (*.f64 (cosh.f64 x) (sinh.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(-.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))))
(+.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (cosh.f64 x) (sinh.f64 x))))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (.f64 (cosh.f64 x) (sinh.f64 x))))))
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(exp.f64 x)
#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (*.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))) (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)))) (-.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (*.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64))) (.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))) (-.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 #s(literal 1 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (-.f64 (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64))) (.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (.f64 x #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 3 binary64))) (fma.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)) (-.f64 (.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))) (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x)) (neg.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) x)) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(/.f64 (neg.f64 (.f64 x (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 x (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) x) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)))
(/.f64 (.f64 x (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))
(fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x (.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
(fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (.f64 x #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (*.f64 #s(literal 1 binary64) x))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
(+.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (*.f64 x #s(literal 1 binary64)))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 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))
#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 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/12 binary64) x)
(.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))
(.f64 #s(literal 1/6 binary64) (fabs.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/12 binary64))
(sqrt.f64 (.f64 #s(literal 1/144 binary64) (.f64 x x)))
(fabs.f64 (neg.f64 (*.f64 #s(literal 1/12 binary64) x)))
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(/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (.f64 (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))) (.f64 (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(fma.f64 x (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))) (pow.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) x))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))))
(+.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))) (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) #s(literal -1 binary64)))
(+.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))

eval68.0ms (1.2%)

Memory: 12.9MiB live, 71.3MiB allocated; 8ms collecting garbage
Compiler: Compiled 13 577 to 1 611 computations (88.1% saved)

prune10.0ms (0.2%)

Memory

-21.7MiB live, 23.0MiB allocated; 4ms collecting garbage

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	357	2	359
Fresh	1	0	1
Picked	2	3	5
Done	0	5	5
Total	360	10	370

Accuracy

100.0%

Counts

370 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	37.6%	(/.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))
▶	72.8%	(/.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 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
▶	87.8%	(/.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)))
✓	66.1%	#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))))
✓	66.2%	#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))))
✓	66.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	66.3%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	2.9%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
✓	3.1%	#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 157 to 111 computations (29.3% saved)

simplify117.0ms (2%)

Memory

11.8MiB live, 101.1MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
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 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
cost-diff	0	(*.f64 (fma.f64 (fma.f64 #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 #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 #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	16	145
0	27	145
1	41	145
2	93	145
3	262	145
4	764	145
5	2520	145
6	6607	145
0	8056	137

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

localize75.0ms (1.3%)

Memory

-11.5MiB live, 43.2MiB allocated; 6ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0390625	(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.09765625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	21.340043988777893	#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))
accuracy	21.751378842167796	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy	0.0390625	(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.09765625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	21.340043988777893	#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))
accuracy	22.089984998653055	#s(approx (exp x) #s(literal 1 binary64))

Samples

44.0ms

256×

valid

Compiler

Compiled 100 to 18 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-add: 17.0ms (49.9% of total)

ival-mult: 7.0ms (20.6% of total)

const: 3.0ms (8.8% of total)

ival-div: 2.0ms (5.9% of total)

ival-exp: 2.0ms (5.9% of total)

ival-expm1: 2.0ms (5.9% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Counts

9 → 29

Calls

Call 1

Inputs
(/.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)))
#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 (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) (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 (fma.f64 #s(literal 1/6 binary64) x #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))
(fma.f64 #s(literal 1/6 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 (* 1/2 x))
1/2
(+ 1/2 (* 1/6 x))
(/ (exp x) (- (exp x) 1))
(exp x)
(- (exp x) 1)
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify145.0ms (2.5%)

Memory

33.3MiB live, 118.8MiB allocated; 14ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	199
1	255	197
2	819	192
3	3708	192
0	8371	164

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

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 (* 1/2 x))
1/2
(+ 1/2 (* 1/6 x))
(/ (exp x) (- (exp x) 1))
(exp x)
(- (exp x) 1)
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))

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

rewrite507.0ms (8.9%)

Memory

-86.5MiB live, 167.6MiB allocated; 839ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	96
0	27	96
1	104	96
2	732	96
0	8047	90

Stop Event

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

Counts

9 → 227

Calls

Call 1

Inputs
(/.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)))
#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 (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) (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 (fma.f64 #s(literal 1/6 binary64) x #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))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))

Outputs
(/.f64 (neg.f64 #s(approx (exp x) #s(literal 1 binary64))) (neg.f64 #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(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 #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))
(neg.f64 (neg.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))
(neg.f64 (neg.f64 #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 (/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) x x) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) x x) (+.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 6 binary64)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (-.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64))) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 x (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64))) x) (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(/.f64 (.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) x) (neg.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) x) (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(/.f64 (.f64 x (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (.f64 x (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))) (-.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (-.f64 (.f64 x x) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) x x)) (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x)) (neg.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) x x) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) #s(literal 1 binary64) x)
(fma.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))) x (.f64 (pow.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) x))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) x)
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
(fma.f64 x (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 x (pow.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 x (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
(-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (*.f64 #s(literal -1 binary64) x))
(-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
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(/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))) (.f64 (.f64 x x) (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 3 binary64))) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64)))) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64)) (.f64 (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64)) #s(literal 1/8 binary64))) (.f64 (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 4 binary64)) #s(literal 1/16 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 6 binary64)) #s(literal 1/64 binary64)) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/144 binary64) #s(literal 1/16 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 6 binary64)) #s(literal 1/64 binary64)) (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(/.f64 (+.f64 #s(literal 1/512 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 9 binary64))) (.f64 (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 6 binary64)) #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/1728 binary64))) (fma.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64)))
(neg.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal -1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 (pow.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 6 binary64)))) (fma.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)) (-.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 4 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 6 binary64)))) (fma.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)) (-.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3/2 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 #s(literal 1/216 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/216 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) x) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (.f64 #s(literal 1/6 binary64) x) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 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 #s(literal 1/6 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))))
(-.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))
(+.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) x) #s(literal 1/12 binary64)) #s(literal 1/4 binary64))))
(+.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 (neg.f64 x)) #s(literal 1/6 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))

eval80.0ms (1.4%)

Memory: -17.5MiB live, 86.8MiB allocated; 11ms collecting garbage
Compiler: Compiled 14 710 to 1 431 computations (90.3% saved)

prune13.0ms (0.2%)

Memory

23.4MiB live, 23.4MiB allocated; 0ms collecting garbage

Pruning

14 alts after pruning (5 fresh and 9 done)

	Pruned	Kept	Total
New	347	5	352
Fresh	0	0	0
Picked	1	1	2
Done	0	8	8
Total	348	14	362

Accuracy

100.0%

Counts

362 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	37.6%	(/.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))
✓	72.8%	(/.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 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
	87.8%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)))
	35.7%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) x))))
	90.7%	(/.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)))
	87.8%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x #s(literal 1 binary64)) x)))
	81.1%	(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
✓	66.1%	#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))))
✓	66.2%	#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))))
✓	66.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	66.3%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	2.9%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
✓	3.1%	#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 623 to 272 computations (56.3% saved)

regimes18.0ms (0.3%)

Memory

-29.4MiB live, 16.6MiB allocated; 3ms collecting garbage

Counts

20 → 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)) (/.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)) (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 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) #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(approx (+ ( 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) 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) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x 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))))
(/.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 (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 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) x))))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (sqrt.f64 (pow.f64 x #s(literal -2 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 (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)))))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

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

Calls

3 calls:

8.0ms	(exp.f64 x)
6.0ms	x
4.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Results

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

Compiler

Compiled 10 to 8 computations (20% saved)

regimes13.0ms (0.2%)

Memory

21.8MiB live, 21.8MiB allocated; 0ms collecting garbage

Counts

18 → 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)) (/.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)) (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 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) #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(approx (+ ( 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) 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) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x 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))))
(/.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 (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 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) x))))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (sqrt.f64 (pow.f64 x #s(literal -2 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 (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)))))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))

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

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
99.8%	1	`(exp.f64 x)`
99.8%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
99.8%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes13.0ms (0.2%)

Memory

19.0MiB live, 19.0MiB allocated; 0ms collecting garbage

Counts

17 → 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)) (/.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)) (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 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) #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(approx (+ ( 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) 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) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x 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))))
(/.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 (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 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) x))))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (sqrt.f64 (pow.f64 x #s(literal -2 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 (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)))))

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:

5.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
3.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.9%	2	`(exp.f64 x)`
98.6%	2	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
99.9%	2	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes14.0ms (0.2%)

Memory

-24.8MiB live, 20.2MiB allocated; 4ms collecting garbage

Counts

15 → 3

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

Outputs

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

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

Calls

3 calls:

7.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
3.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
90.7%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
90.7%	1	`(exp.f64 x)`
96.5%	3	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes7.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated; 0ms collecting garbage

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
90.7%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
90.7%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes8.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated; 0ms collecting garbage

Counts

10 → 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)) (/.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)) (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 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) #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(approx (+ ( 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) 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) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x 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))))

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

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
87.8%	1	`(exp.f64 x)`
87.8%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
87.8%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes9.0ms (0.2%)

Memory

-37.2MiB live, 9.3MiB allocated; 2ms collecting garbage

Counts

6 → 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)) (/.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)) (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 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) #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 (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))

Calls

3 calls:

5.0ms	x
2.0ms	(exp.f64 x)
2.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
81.1%	1	`(exp.f64 x)`
81.1%	1	`x`
81.1%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes6.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated; 0ms collecting garbage

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)) (/.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)) (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) #s(literal -1/2 binary64)))

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
66.3%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
66.3%	1	`(exp.f64 x)`
66.3%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

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

Results

Accuracy	Segments	Branch
66.2%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
66.2%	1	`(exp.f64 x)`
66.2%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated; 0ms collecting garbage

Counts

2 → 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)))

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:

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
3.1%	1	`x`
3.1%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
3.1%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes3.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated; 0ms collecting garbage

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
2.9%	1	`(exp.f64 x)`
2.9%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
2.9%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

bsearch14.0ms (0.2%)

Memory

14.4MiB live, 14.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-15279.313998126725	-0.1725953458677501

Samples

7.0ms

144×

valid

Compiler

Compiled 298 to 233 computations (21.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-exp: 2.0ms (50.4% of total)

ival-div: 1.0ms (25.2% of total)

ival-expm1: 1.0ms (25.2% of total)

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

adjust: 0.0ms (0% of total)

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

bsearch20.0ms (0.4%)

Memory

-34.9MiB live, 16.3MiB allocated; 6ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
4.0ms	-15279.313998126725	-0.1725953458677501
15.0ms	-4.484298572872623e+105	-1.0854776130768828e+98

Samples

10.0ms

176×

valid

Compiler

Compiled 1 171 to 656 computations (44% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 1.0ms (26.9% of total)

ival-exp: 1.0ms (26.9% of total)

ival-expm1: 1.0ms (26.9% of total)

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

adjust: 0.0ms (0% of total)

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

simplify84.0ms (1.5%)

Memory

-7.6MiB live, 37.2MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	281
1	100	281
2	138	281
3	197	281
4	422	281
5	2132	281

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 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(if (<=.f64 x #s(literal -15/4 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 x #s(literal -10500000000000000815831766655872649178879125871197860277834278179049830808884244966648174743689294249984 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) (.f64 #s(literal 1/6 binary64) x)) x #s(literal 1 binary64)) x))) (if (<=.f64 x #s(literal -4278419646001971/1125899906842624 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) 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))))))
(/.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) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x #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 #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 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(if (<=.f64 x #s(literal -15/4 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 x #s(literal -15/4 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)))))
(if (<=.f64 x #s(literal -10500000000000000815831766655872649178879125871197860277834278179049830808884244966648174743689294249984 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) (.f64 #s(literal 1/6 binary64) x)) x #s(literal 1 binary64)) x))) (if (<=.f64 x #s(literal -4278419646001971/1125899906842624 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) 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))))))
(if (<=.f64 x #s(literal -10500000000000000815831766655872649178879125871197860277834278179049830808884244966648174743689294249984 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) (.f64 #s(literal 1/6 binary64) x)) x #s(literal 1 binary64)) x))) (if (<=.f64 x #s(literal -4278419646001971/1125899906842624 binary64)) (/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) 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 (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 (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 #s(approx (+ ( 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) (.f64 (fma.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x #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 (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)))

derivations1.2s (21.9%)

Memory

47.1MiB live, 747.9MiB allocated; 82ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	153
1	214	153
2	667	140
3	2274	140
4	6433	140
0	8408	120
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	104	381
1	358	375
2	1284	347
3	5467	343
0	8510	305
0	68	199
1	255	197
2	819	192
3	3708	192
0	8371	164
0	16	96
0	27	96
1	104	96
2	732	96
0	8047	90

Stop Event

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

Compiler

Compiled 281 to 83 computations (70.5% saved)

preprocess78.0ms (1.4%)

Memory: -1.3MiB live, 87.6MiB allocated; 10ms collecting garbage
Compiler: Compiled 588 to 188 computations (68% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0%)

sample735.0ms (12.9%)

explain68.0ms (1.2%)

preprocess200.0ms (3.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify139.0ms (2.4%)

localize30.0ms (0.5%)

series2.0ms (0%)

simplify164.0ms (2.9%)

rewrite285.0ms (5%)

eval79.0ms (1.4%)

prune12.0ms (0.2%)

simplify213.0ms (3.7%)

localize56.0ms (1%)

series3.0ms (0%)

simplify177.0ms (3.1%)

rewrite241.0ms (4.2%)

eval109.0ms (1.9%)

prune20.0ms (0.4%)

simplify137.0ms (2.4%)

localize165.0ms (2.9%)

series8.0ms (0.1%)

simplify138.0ms (2.4%)

rewrite172.0ms (3%)

eval68.0ms (1.2%)

prune10.0ms (0.2%)

simplify117.0ms (2%)

localize75.0ms (1.3%)

series4.0ms (0.1%)

simplify145.0ms (2.5%)

rewrite507.0ms (8.9%)

eval80.0ms (1.4%)

prune13.0ms (0.2%)

regimes18.0ms (0.3%)

regimes13.0ms (0.2%)

regimes13.0ms (0.2%)

regimes14.0ms (0.2%)

regimes7.0ms (0.1%)

regimes8.0ms (0.1%)

regimes9.0ms (0.2%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch14.0ms (0.2%)

bsearch20.0ms (0.4%)

simplify84.0ms (1.5%)

derivations1.2s (21.9%)

preprocess78.0ms (1.4%)

end0.0ms (0%)

Profiling