Metrics for expq2 (section 3.11)

start0.0ms (0%)

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

analyze1.0ms (0%)

Memory

4.1MiB live, 4.1MiB 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)

sample724.0ms (13.8%)

Memory

22.2MiB live, 877.5MiB allocated; 223ms collecting garbage

Samples

517.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 353.0ms

ival-expm1: 181.0ms (51.3% of total)

ival-exp: 75.0ms (21.3% of total)

ival-div: 54.0ms (15.3% of total)

ival->: 30.0ms (8.5% of total)

exact: 6.0ms (1.7% of total)

ival-assert: 4.0ms (1.1% of total)

adjust: 2.0ms (0.6% of total)

Bogosity

explain69.0ms (1.3%)

Memory

-6.8MiB live, 187.2MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
180	-	1	(0.028559506288189013)	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	-	0	-	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(exp.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	179	1

Confusion

	Predicted +	Predicted -
+	179	1
-	0	76

Precision

1.0

Recall

0.9944444444444445

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	179	1	0
-	0	0	76

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	77
1	179

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

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

ival-exp: 4.0ms (35.2% of total)

ival-div: 3.0ms (26.4% of total)

ival-expm1: 3.0ms (26.4% 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)

preprocess167.0ms (3.2%)

Memory

0.2MiB live, 137.3MiB allocated; 14ms 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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	34.1%	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify171.0ms (3.2%)

Memory

-27.9MiB live, 119.7MiB 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)

localize16.0ms (0.3%)

Memory

17.1MiB live, 17.1MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.015625	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	40.91560585766528	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

11.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-div: 2.0ms (35.5% of total)

ival-exp: 2.0ms (35.5% of total)

ival-expm1: 2.0ms (35.5% 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

2.2MiB live, 2.2MiB 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))

simplify212.0ms (4%)

Memory

4.6MiB live, 142.1MiB allocated; 35ms 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)

rewrite286.0ms (5.4%)

Memory

-8.8MiB live, 330.8MiB allocated; 33ms 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))
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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)

eval101.0ms (1.9%)

Memory: 32.1MiB live, 123.0MiB allocated; 8ms collecting garbage
Compiler: Compiled 14 895 to 1 739 computations (88.3% saved)

prune15.0ms (0.3%)

Memory

-1.6MiB live, 42.5MiB allocated; 5ms collecting garbage

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	564	8	572
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	565	8	573

Accuracy

100.0%

Counts

573 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.4%	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
▶	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
	98.9%	(/.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)))
▶	100.0%	(*.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))
▶	71.4%	#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)))))
▶	71.3%	#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))))
▶	70.4%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
	71.0%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Compiler

Compiled 202 to 154 computations (23.8% saved)

simplify156.0ms (3%)

Memory

-24.5MiB live, 163.5MiB allocated; 35ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(expm1.f64 x)
cost-diff	0	(exp.f64 x)
cost-diff	0	(/.f64 (exp.f64 x) (expm1.f64 x))
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	(pow.f64 x #s(literal 3 binary64))
cost-diff	0	(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))))
cost-diff	0	#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)))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(expm1.f64 x)
cost-diff	0	(pow.f64 (expm1.f64 x) #s(literal -1 binary64))
cost-diff	0	(exp.f64 x)
cost-diff	2	(*.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	132
0	35	134
1	53	134
2	118	130
3	334	130
4	1158	130
5	4775	130
0	8687	130

Stop Event

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

Calls

Call 1

Inputs
(*.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))
(exp.f64 x)
x
(pow.f64 (expm1.f64 x) #s(literal -1 binary64))
(expm1.f64 x)
#s(literal -1 binary64)
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(literal 1/12 binary64)
x
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
#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)))))
(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))))
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
#s(literal -1/720 binary64)
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(literal 1/12 binary64)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 x)
x
(expm1.f64 x)

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

localize81.0ms (1.5%)

Memory

10.5MiB live, 158.2MiB allocated; 15ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(expm1.f64 x)
accuracy	0.0	(exp.f64 x)
accuracy	0.015625	(/.f64 (exp.f64 x) (expm1.f64 x))
accuracy	0.00390625	(pow.f64 x #s(literal 3 binary64))
accuracy	0.02734375	(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))))
accuracy	0.1171875	(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	18.32897005605355	#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)))))
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	0.1171875	(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	18.365458694812528	#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	18.920456174920474	#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	0.0078125	(pow.f64 (expm1.f64 x) #s(literal -1 binary64))
accuracy	0.0078125	(*.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))

Samples

62.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 127 to 21 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-div: 18.0ms (37.8% of total)

ival-pow: 11.0ms (23.1% of total)

const: 6.0ms (12.6% of total)

ival-mult: 5.0ms (10.5% of total)

ival-exp: 2.0ms (4.2% of total)

ival-add: 2.0ms (4.2% of total)

ival-expm1: 2.0ms (4.2% of total)

ival-sub: 1.0ms (2.1% 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)

series6.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated; 0ms collecting garbage

Counts

13 → 33

Calls

Call 1

Inputs
(*.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))
(exp.f64 x)
(pow.f64 (expm1.f64 x) #s(literal -1 binary64))
(expm1.f64 x)
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
#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)))))
(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))))
(pow.f64 x #s(literal 3 binary64))
(/.f64 (exp.f64 x) (expm1.f64 x))

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((* (exp x) (pow (- (exp x) 1) -1)) (exp x) (pow (- (exp x) 1) -1) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* (pow x 3) -1/720) (+ (* 1/12 x) (- (/ 1 x) -1/2))) (pow x 3) (/ (exp x) (- (exp x) 1)))
2.0ms	x	@	inf	((* (exp x) (pow (- (exp x) 1) -1)) (exp x) (pow (- (exp x) 1) -1) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* (pow x 3) -1/720) (+ (* 1/12 x) (- (/ 1 x) -1/2))) (pow x 3) (/ (exp x) (- (exp x) 1)))
1.0ms	x	@	0	((* (exp x) (pow (- (exp x) 1) -1)) (exp x) (pow (- (exp x) 1) -1) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* (pow x 3) -1/720) (+ (* 1/12 x) (- (/ 1 x) -1/2))) (pow x 3) (/ (exp x) (- (exp x) 1)))

Time

Variable

Point

Expression

3.0ms

-inf

((* (exp x) (pow (- (exp x) 1) -1)) (exp x) (pow (- (exp x) 1) -1) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* (pow x 3) -1/720) (+ (* 1/12 x) (- (/ 1 x) -1/2))) (pow x 3) (/ (exp x) (- (exp x) 1)))

2.0ms

inf

((* (exp x) (pow (- (exp x) 1) -1)) (exp x) (pow (- (exp x) 1) -1) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* (pow x 3) -1/720) (+ (* 1/12 x) (- (/ 1 x) -1/2))) (pow x 3) (/ (exp x) (- (exp x) 1)))

1.0ms

((* (exp x) (pow (- (exp x) 1) -1)) (exp x) (pow (- (exp x) 1) -1) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* (pow x 3) -1/720) (+ (* 1/12 x) (- (/ 1 x) -1/2))) (pow x 3) (/ (exp x) (- (exp x) 1)))

simplify136.0ms (2.6%)

Memory

-11.8MiB live, 209.1MiB allocated; 36ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	305
1	334	299
2	1153	281
3	4842	278
0	8216	253

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 32

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))))))
(/ (+ 1 (* -1/2 x)) x)
(/ (+ 1 (* x (- (* 1/12 x) 1/2))) x)
(/ (+ 1 (* x (- (* x (+ 1/12 (* -1/720 (pow x 2)))) 1/2))) 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)))))))
(pow x 3)
(/ (exp x) (- (exp x) 1))
(exp x)
(/ 1 (- (exp x) 1))
(- (exp x) 1)
(* 1/12 x)
(* x (+ 1/12 (* 1/2 (/ 1 x))))
(* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (/ 1 x))
(* -1/720 (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 (* 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))))))

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

rewrite562.0ms (10.7%)

Memory

-53.3MiB live, 359.4MiB allocated; 778ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	94
0	35	96
1	125	92
2	869	92
0	8265	92

Stop Event

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

Counts

13 → 364

Calls

Call 1

Inputs
(*.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))
(exp.f64 x)
(pow.f64 (expm1.f64 x) #s(literal -1 binary64))
(expm1.f64 x)
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
#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)))))
(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))))
(pow.f64 x #s(literal 3 binary64))
(/.f64 (exp.f64 x) (expm1.f64 x))

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

eval66.0ms (1.3%)

Memory: -10.8MiB live, 132.4MiB allocated; 12ms collecting garbage
Compiler: Compiled 17 473 to 1 720 computations (90.2% saved)

prune15.0ms (0.3%)

Memory

-5.8MiB live, 41.3MiB allocated; 2ms collecting garbage

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	498	8	506
Fresh	1	2	3
Picked	2	3	5
Done	0	0	0
Total	501	13	514

Accuracy

100.0%

Counts

514 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.4%	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	100.0%	(*.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
	77.5%	(.f64 (exp.f64 x) #s(approx (pow (- (exp x) 1) -1) (/.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
✓	71.3%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
	3.0%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
▶	33.0%	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
	70.4%	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
✓	70.4%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	71.0%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	39.3%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))))
▶	3.6%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
	71.4%	#s(approx (* (exp x) (pow (- (exp x) 1) -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))))

Compiler

Compiled 376 to 278 computations (26.1% saved)

simplify129.0ms (2.5%)

Memory

34.8MiB live, 126.3MiB allocated; 20ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	189
0	45	189
1	66	187
2	115	187
3	224	187
4	696	187
5	3911	187
0	8769	183

Stop Event

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

Calls

Call 1

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

localize68.0ms (1.3%)

Memory

-14.0MiB live, 122.7MiB allocated; 13ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	28.244521356554156	(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
accuracy	42.91776358250998	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
accuracy	0.02734375	(-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64))
accuracy	0.1171875	(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
accuracy	18.365458694812528	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))))
accuracy	20.665220962941184	(*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 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	18.547886344100267	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	0.33984375	(*.f64 #s(literal 1/12 binary64) x)
accuracy	18.365458694812528	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
accuracy	43.99834108371078	#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
accuracy	0.0	(expm1.f64 x)
accuracy	0.0	(exp.f64 x)
accuracy	0.0078125	(/.f64 #s(literal 1 binary64) (expm1.f64 x))
accuracy	0.0078125	(*.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))

Samples

47.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 139 to 22 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 8.0ms (24.2% of total)

ival-div: 7.0ms (21.2% of total)

ival-pow: 6.0ms (18.1% of total)

const: 4.0ms (12.1% of total)

ival-sub: 3.0ms (9.1% of total)

ival-exp: 2.0ms (6% of total)

ival-expm1: 2.0ms (6% of total)

ival-add: 1.0ms (3% of total)

ival-neg: 1.0ms (3% 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)

series8.0ms (0.2%)

Memory

17.1MiB live, 17.1MiB allocated; 0ms collecting garbage

Counts

19 → 36

Calls

Call 1

Inputs
(*.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(exp.f64 x)
(/.f64 #s(literal 1 binary64) (expm1.f64 x))
(expm1.f64 x)
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64))))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))
(neg.f64 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))
(*.f64 x x)
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 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))))))
(/ (+ 1 (* -1/2 x)) x)
(/ (+ 1 (* x (- (* 1/12 x) 1/2))) x)
(/ (+ 1 (* x (- (* x (+ 1/12 (* -1/720 (pow x 2)))) 1/2))) 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 x)
(pow x 2)
(/ -1 (pow x 2))
(/ (- (* -1/2 x) 1) (pow x 2))
(/ (- (* x (- (* -1/12 x) 1/2)) 1) (pow x 2))
(/ (exp x) (- (exp x) 1))
(exp x)
(/ 1 (- (exp x) 1))
(- (exp x) 1)
(* x (+ 1/12 (* 1/2 (/ 1 x))))
(* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (/ 1 x))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (/ 1 x)) x))
-1/12
(* -1 (+ 1/12 (* 1/2 (/ 1 x))))
(- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)
(* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))
(/ -1 x)

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

simplify138.0ms (2.6%)

Memory

-14.3MiB live, 129.0MiB allocated; 24ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	258
1	268	257
2	821	237
3	2971	231
4	7539	230
0	8144	207

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 35

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

rewrite198.0ms (3.8%)

Memory

-5.2MiB live, 144.2MiB allocated; 55ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	168
0	45	166
1	149	162
2	921	162
0	8322	158

Stop Event

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

Counts

19 → 404

Calls

Call 1

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

Outputs
(.f64 (.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)))
(.f64 (.f64 (exp.f64 x) (pow.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (.f64 (exp.f64 x) (pow.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (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 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 x)))
(.f64 (pow.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (exp.f64 x)))
(.f64 (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) (.f64 (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) (exp.f64 x)))
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 1 binary64))
(*.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (exp.f64 x))
(*.f64 #s(literal 1 binary64) (/.f64 (exp.f64 x) (expm1.f64 x)))
(.f64 (exp.f64 x) (.f64 #s(literal 1 binary64) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(*.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))
(/.f64 (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (expm1.f64 (.f64 x #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (.f64 (sinh.f64 x) (-.f64 (sinh.f64 x) (cosh.f64 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) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 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 3 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.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 x #s(literal 3 binary64)))) (-.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 x #s(literal 3 binary64)))) (+.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (*.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))))))
(/.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64)))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (.f64 (sinh.f64 x) (-.f64 (sinh.f64 x) (cosh.f64 x)))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (exp.f64 (neg.f64 x)))
(/.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) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))) (.f64 (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))) (-.f64 (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (cosh.f64 x)) (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (cosh.f64 x))) (.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (sinh.f64 x)) (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (sinh.f64 x)))) (-.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (cosh.f64 x)) (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (sinh.f64 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) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (-.f64 (.f64 (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))) (.f64 (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (cosh.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (sinh.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (cosh.f64 x)) (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (cosh.f64 x)) (-.f64 (.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (sinh.f64 x)) (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (sinh.f64 x))) (.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (cosh.f64 x)) (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (sinh.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 (fma.f64 (cosh.f64 x) (expm1.f64 x) (.f64 (expm1.f64 x) (sinh.f64 x))) (.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (neg.f64 (exp.f64 x)) (neg.f64 (expm1.f64 x)))
(/.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (exp.f64 (neg.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(neg.f64 (*.f64 (exp.f64 x) (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (exp.f64 x)))
(neg.f64 (/.f64 (neg.f64 (exp.f64 x)) (expm1.f64 x)))
(fma.f64 (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(fma.f64 (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(fma.f64 (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)) (*.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(fma.f64 (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(fma.f64 (.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(fma.f64 (.f64 (cosh.f64 x) (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)) (*.f64 (sinh.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(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)))
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(/.f64 (-.f64 (.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 3 binary64)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64) (+.f64 #s(literal 1/144 binary64) (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64))))) (.f64 (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64) (+.f64 #s(literal 1/144 binary64) (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64)))) #s(literal 1/1728 binary64))) (*.f64 (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64) (+.f64 #s(literal 1/144 binary64) (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64) (+.f64 #s(literal 1/144 binary64) (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64))))))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 3 binary64)) #s(literal 1/1728 binary64))) (neg.f64 (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64) (+.f64 #s(literal 1/144 binary64) (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (+.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 3 binary64)) #s(literal 1/1728 binary64)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64) (+.f64 #s(literal 1/144 binary64) (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64)))))
(neg.f64 (neg.f64 (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64)) (+.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64))) (/.f64 #s(literal 1/144 binary64) (+.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 3 binary64)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64) (+.f64 #s(literal 1/144 binary64) (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64))))) (/.f64 #s(literal 1/1728 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64) (+.f64 #s(literal 1/144 binary64) (pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/12 binary64)))
(-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal 1/12 binary64))

eval54.0ms (1%)

Memory: -11.1MiB live, 76.3MiB allocated; 10ms collecting garbage
Compiler: Compiled 12 315 to 1 796 computations (85.4% saved)

prune14.0ms (0.3%)

Memory

35.8MiB live, 35.8MiB allocated; 0ms collecting garbage

Pruning

15 alts after pruning (8 fresh and 7 done)

	Pruned	Kept	Total
New	435	3	438
Fresh	0	5	5
Picked	1	4	5
Done	0	3	3
Total	436	15	451

Accuracy

100.0%

Counts

451 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.4%	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	100.0%	(*.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
▶	77.5%	(.f64 (exp.f64 x) #s(approx (pow (- (exp x) 1) -1) (/.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
▶	81.0%	(.f64 (exp.f64 x) #s(approx (/ 1 (- (exp x) 1)) (-.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x))))
✓	71.3%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
	3.0%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
✓	33.0%	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
▶	70.4%	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
✓	70.4%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	71.0%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	3.3%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
	39.2%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1/12 binary64)))))
✓	3.6%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
▶	71.4%	#s(approx (* (exp x) (pow (- (exp x) 1) -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))))

Compiler

Compiled 404 to 298 computations (26.2% saved)

simplify142.0ms (2.7%)

Memory

-18.5MiB live, 85.8MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	302
0	55	302
1	83	302
2	177	300
3	498	297
4	1599	297
5	7514	297
0	8294	280

Stop Event

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

Calls

Call 1

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

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

localize100.0ms (1.9%)

Memory

2.4MiB live, 91.8MiB allocated; 9ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0703125	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
accuracy	0.2421875	(.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x)
accuracy	2.1008461060904002	(/.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	18.510031545421896	#s(approx (pow (- (exp x) 1) -1) (/.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
accuracy	0.00390625	(pow.f64 x #s(literal -1 binary64))
accuracy	18.920456174920474	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	0.0234375	(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	0.0703125	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
accuracy	18.32897005605355	#s(approx (* (exp x) (pow (- (exp x) 1) -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	18.547886344100267	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
accuracy	44.35993347626248	#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
accuracy	0.01171875	(-.f64 (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
accuracy	0.0703125	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
accuracy	0.2421875	(.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x)
accuracy	18.510031545421896	#s(approx (/ 1 (- (exp x) 1)) (-.f64 (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x)))

Samples

80.0ms

256×

valid

Compiler

Compiled 228 to 30 computations (86.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-mult: 30.0ms (47.1% of total)

ival-pow: 9.0ms (14.1% of total)

ival-div: 8.0ms (12.6% of total)

const: 6.0ms (9.4% of total)

ival-add: 3.0ms (4.7% of total)

ival-sub: 3.0ms (4.7% of total)

ival-exp: 2.0ms (3.1% of total)

ival-expm1: 2.0ms (3.1% 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)

series5.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Counts

16 → 34

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify160.0ms (3%)

Memory

-2.3MiB live, 178.5MiB allocated; 26ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	350
1	308	343
2	1114	324
3	5154	317
0	8533	300

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 34

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))))))
(/ (+ 1 (* -1/2 x)) x)
(/ (+ 1 (* x (- (* 1/12 x) 1/2))) x)
(/ (+ 1 (* x (- (* x (+ 1/12 (* -1/720 (pow x 2)))) 1/2))) x)
1/12
(+ 1/12 (* -1/720 (pow x 2)))
(pow x 2)
(* 1/12 x)
(* x (+ 1/12 (* -1/720 (pow x 2))))
(/ (exp x) (- (exp x) 1))
(exp x)
(/ 1 (- (exp x) 1))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 3)))))
(* (pow x 3) (- (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4))) (+ 1/720 (/ 1/2 (pow x 3)))))
1/2
(+ 1/2 (/ 1 x))
(* (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 (* (pow x 3) (- 1/720 (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ 1/720 (/ 1/2 (pow x 3))) (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ 1/720 (* -1 (/ (- (/ 1 x) 1/2) (pow x 3)))) (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/720 (* -1 (/ (+ 1/12 (* 1/2 (/ 1 x))) (pow x 2))))))
(* -1 (* (pow x 3) (- (+ 1/720 (* -1 (/ (+ 1/2 (/ 1 x)) (pow x 3)))) (* 1/12 (/ 1 (pow x 2))))))

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

rewrite185.0ms (3.5%)

Memory

26.3MiB live, 170.5MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	212
0	55	212
1	193	210
2	1329	210
0	8598	196

Stop Event

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

Counts

16 → 315

Calls

Call 1

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

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

eval111.0ms (2.1%)

Memory: -6.8MiB live, 94.4MiB allocated; 22ms collecting garbage
Compiler: Compiled 22 534 to 2 274 computations (89.9% saved)

prune23.0ms (0.4%)

Memory

-4.0MiB live, 40.9MiB allocated; 4ms collecting garbage

Pruning

16 alts after pruning (4 fresh and 12 done)

	Pruned	Kept	Total
New	506	1	507
Fresh	0	3	3
Picked	0	5	5
Done	0	7	7
Total	506	16	522

Accuracy

100.0%

Counts

522 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.4%	(/.f64 (exp.f64 x) (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
	81.0%	(.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x))) #s(approx (/ 1 (- (exp x) 1)) (-.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x))))
✓	100.0%	(*.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
✓	77.5%	(.f64 (exp.f64 x) #s(approx (pow (- (exp x) 1) -1) (/.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
✓	81.0%	(.f64 (exp.f64 x) #s(approx (/ 1 (- (exp x) 1)) (-.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x))))
✓	71.3%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
	3.0%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
✓	33.0%	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
✓	70.4%	#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
✓	70.4%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	71.0%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	3.3%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
	39.2%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1/12 binary64)))))
✓	3.6%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
✓	71.4%	#s(approx (* (exp x) (pow (- (exp x) 1) -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))))

Compiler

Compiled 626 to 294 computations (53% saved)

regimes19.0ms (0.4%)

Memory

-19.1MiB live, 25.1MiB allocated; 5ms collecting garbage

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
#s(approx (* (exp x) (pow (- (exp x) 1) -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)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1/12 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x 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)))
#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) #s(approx (/ 1 (- (exp x) 1)) (-.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 (exp.f64 x) #s(approx (pow (- (exp x) 1) -1) (/.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x))) #s(approx (/ 1 (- (exp x) 1)) (-.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(*.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))

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

Calls

3 calls:

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

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

18.6MiB live, 18.6MiB allocated; 0ms collecting garbage

Counts

17 → 1

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
#s(approx (* (exp x) (pow (- (exp x) 1) -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)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1/12 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x 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)))
#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) #s(approx (/ 1 (- (exp x) 1)) (-.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 (exp.f64 x) #s(approx (pow (- (exp x) 1) -1) (/.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x))) #s(approx (/ 1 (- (exp x) 1)) (-.f64 (-.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #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)))
3.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
98.9%	1	`(exp.f64 x)`
98.9%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
98.9%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes13.0ms (0.2%)

Memory

-25.7MiB live, 18.6MiB allocated; 3ms collecting garbage

Counts

13 → 2

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
#s(approx (* (exp x) (pow (- (exp x) 1) -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)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1/12 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (*.f64 x 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)))
#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) (pow (- (exp x) 1) -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	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
4.0ms	x
3.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
98.3%	2	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
99.4%	2	`(exp.f64 x)`
99.4%	2	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes9.0ms (0.2%)

Memory

18.8MiB live, 18.8MiB allocated; 0ms collecting garbage

Counts

11 → 2

Calls

Call 1

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

Outputs

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

#s(approx (* (exp x) (pow (- (exp x) 1) -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:

4.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
2.0ms	(exp.f64 x)

Results

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

Compiler

Compiled 10 to 8 computations (20% saved)

regimes9.0ms (0.2%)

Memory

9.9MiB live, 9.9MiB 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)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
#s(approx (* (exp x) (pow (- (exp x) 1) -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)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1/12 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/12 binary64)))))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))

Outputs
#s(approx (* (exp x) (pow (- (exp x) 1) -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:

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
71.4%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
71.4%	1	`(exp.f64 x)`
71.4%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes6.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms 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)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (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)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
71.3%	1	`x`
71.3%	1	`(exp.f64 x)`
71.3%	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

7.4MiB live, 7.4MiB 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)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
71.0%	1	`x`
71.0%	1	`(exp.f64 x)`
71.0%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes44.0ms (0.8%)

Memory

-50.2MiB live, 6.7MiB allocated; 5ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

40.0ms	(exp.f64 x)
2.0ms	x
1.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
70.4%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
70.4%	1	`(exp.f64 x)`
70.4%	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

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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
3.6%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
3.6%	1	`x`
3.6%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes3.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB 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
3.3%	1	`x`
3.3%	1	`(exp.f64 x)`
3.3%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 8 computations (20% saved)

bsearch14.0ms (0.3%)

Memory

13.0MiB live, 13.0MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-45428.53515971034	-0.16898460191183964

Samples

7.0ms

144×

valid

Compiler

Compiled 316 to 251 computations (20.6% saved)

Precisions

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

ival-exp: 2.0ms (51.6% of total)

ival-div: 1.0ms (25.8% of total)

ival-expm1: 1.0ms (25.8% of total)

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

adjust: 0.0ms (0% of total)

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

bsearch7.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	-45428.53515971034	-0.16898460191183964

Samples

3.0ms

64×

valid

Compiler

Compiled 334 to 260 computations (22.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-exp: 1.0ms (57.4% of total)

ival-expm1: 1.0ms (57.4% of total)

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

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

adjust: 0.0ms (0% of total)

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

simplify48.0ms (0.9%)

Memory

8.4MiB live, 52.9MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	199
1	68	199
2	105	193
3	185	193
4	621	193
5	4043	193

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) (pow (- (exp x) 1) -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 -3602879701896397/562949953421312 binary64)) #s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(approx ( (exp x) (pow (- (exp x) 1) -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) (pow (- (exp x) 1) -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 #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)) (-.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) (pow (- (exp x) 1) -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) (pow (- (exp x) 1) -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 -3602879701896397/562949953421312 binary64)) #s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(approx ( (exp x) (pow (- (exp x) 1) -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 -3602879701896397/562949953421312 binary64)) #s(approx (* (exp x) (pow (- (exp x) 1) -1)) (pow.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(approx ( (exp x) (pow (- (exp x) 1) -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)))))
#s(approx (* (exp x) (pow (- (exp x) 1) -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) (pow (- (exp x) 1) -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))))
#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))))
#s(approx (* (exp x) (pow (- (exp x) 1) -1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
#s(approx (* (exp x) (pow (- (exp x) 1) -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) (pow (- (exp x) 1) -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) (pow (- (exp x) 1) -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)))
#s(approx (* (exp x) (pow (- (exp x) 1) -1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))

derivations888.0ms (16.9%)

Memory

1.4MiB live, 515.2MiB allocated; 69ms collecting garbage

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
0	84	258
1	268	257
2	821	237
3	2971	231
4	7539	230
0	8144	207
0	103	305
1	334	299
2	1153	281
3	4842	278
0	8216	253
0	23	94
0	35	96
1	125	92
2	869	92
0	8265	92
0	5	13
0	8	13
1	30	13
2	177	13
3	1809	13
0	9626	9

Stop Event

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

Compiler

Compiled 211 to 55 computations (73.9% saved)

preprocess57.0ms (1.1%)

Memory: 9.6MiB live, 98.7MiB allocated; 10ms collecting garbage
Compiler: Compiled 448 to 132 computations (70.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0%)

sample724.0ms (13.8%)

explain69.0ms (1.3%)

preprocess167.0ms (3.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify171.0ms (3.2%)

localize16.0ms (0.3%)

series2.0ms (0%)

simplify212.0ms (4%)

rewrite286.0ms (5.4%)

eval101.0ms (1.9%)

prune15.0ms (0.3%)

simplify156.0ms (3%)

localize81.0ms (1.5%)

series6.0ms (0.1%)

simplify136.0ms (2.6%)

rewrite562.0ms (10.7%)

eval66.0ms (1.3%)

prune15.0ms (0.3%)

simplify129.0ms (2.5%)

localize68.0ms (1.3%)

series8.0ms (0.2%)

simplify138.0ms (2.6%)

rewrite198.0ms (3.8%)

eval54.0ms (1%)

prune14.0ms (0.3%)

simplify142.0ms (2.7%)

localize100.0ms (1.9%)

series5.0ms (0.1%)

simplify160.0ms (3%)

rewrite185.0ms (3.5%)

eval111.0ms (2.1%)

prune23.0ms (0.4%)

regimes19.0ms (0.4%)

regimes13.0ms (0.2%)

regimes13.0ms (0.2%)

regimes9.0ms (0.2%)

regimes9.0ms (0.2%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes44.0ms (0.8%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch14.0ms (0.3%)

bsearch7.0ms (0.1%)

simplify48.0ms (0.9%)

derivations888.0ms (16.9%)

preprocess57.0ms (1.1%)

end0.0ms (0%)

Profiling