Metrics for expq2 (section 3.11)

start0.0ms (0%)

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

analyze1.0ms (0%)

Memory

2.3MiB live, 2.3MiB 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)

sample703.0ms (16%)

Memory

26.3MiB live, 960.3MiB allocated; 177ms collecting garbage

Samples

391.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 245.0ms

ival-exp: 85.0ms (34.7% of total)

ival-expm1: 60.0ms (24.5% of total)

ival-div: 56.0ms (22.9% of total)

ival->: 31.0ms (12.6% of total)

exact: 7.0ms (2.9% of total)

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

adjust: 2.0ms (0.8% of total)

Bogosity

explain93.0ms (2.1%)

Memory

9.9MiB live, 149.7MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	176	0

Confusion

	Predicted +	Predicted -
+	176	0
-	0	80

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	176	0	0
-	0	0	80

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	80
1	176

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

49.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-div: 4.0ms (32.5% of total)

ival-exp: 4.0ms (32.5% of total)

ival-expm1: 3.0ms (24.4% 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)

preprocess271.0ms (6.2%)

Memory

17.4MiB live, 301.4MiB allocated; 51ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	21	19
2	67	19
3	213	19
4	1052	19
0	5	7
0	8	7
1	13	7
2	29	7
3	67	7
4	285	7
5	3049	7
0	8303	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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	34.8%	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify227.0ms (5.2%)

Memory

-8.7MiB live, 216.6MiB allocated; 54ms collecting garbage

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	29	15
3	67	15
4	285	15
5	3049	15
0	8303	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 (0.4%)

Memory

21.5MiB live, 21.5MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.01171875	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	40.63251974601401	(-.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 (32.2% of total)

ival-exp: 2.0ms (32.2% of total)

ival-expm1: 2.0ms (32.2% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.8MiB live, 3.8MiB 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
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))

Calls

3 calls:

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

simplify667.0ms (15.2%)

Memory

-91.1MiB live, 397.5MiB allocated; 735ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	191
1	181	191
2	559	185
3	2075	185
0	8733	147

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 15

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))

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

rewrite63.0ms (1.4%)

Memory

-3.0MiB live, 53.6MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	30	13
0	212	9

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 29

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 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (+.f64 x #s(literal 0 binary64)))
(expm1.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 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 (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))))
(+.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) (/.f64 (sinh.f64 x) (expm1.f64 x)))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 x) (cosh.f64 x)) (.f64 (sinh.f64 x) (sinh.f64 x))) (-.f64 (cosh.f64 x) (sinh.f64 x)))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (.f64 (sinh.f64 x) (sinh.f64 x)) (.f64 (cosh.f64 x) (sinh.f64 x)))))
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(exp.f64 (+.f64 x #s(literal 0 binary64)))
(exp.f64 x)

eval6.0ms (0.1%)

Memory: 8.6MiB live, 8.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 721 to 171 computations (76.3% saved)

prune4.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	51	6	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	6	58

Accuracy

100.0%

Counts

58 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
	98.6%	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) x))
▶	69.6%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
▶	69.6%	#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))))
▶	69.9%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	69.6%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Compiler

Compiled 150 to 112 computations (25.3% saved)

simplify260.0ms (5.9%)

Memory

13.3MiB live, 335.0MiB allocated; 37ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
cost-diff	0	(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(expm1.f64 x)
cost-diff	0	(exp.f64 x)
cost-diff	0	(/.f64 (exp.f64 x) (expm1.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	134
0	33	134
1	54	134
2	125	134
3	333	134
4	975	134
5	4337	134
0	8157	134

Stop Event

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

Calls

Call 1

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

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

localize56.0ms (1.3%)

Memory

14.1MiB live, 69.3MiB allocated; 9ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
accuracy	0.03125	(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	0.0546875	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
accuracy	19.46419753273586	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.00390625	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
accuracy	0.11328125	(fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	19.46527272037779	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.00390625	(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
accuracy	19.456014759486052	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	19.25688289167358	#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	0.01171875	(/.f64 (exp.f64 x) (expm1.f64 x))

Samples

43.0ms

256×

valid

Compiler

Compiled 119 to 19 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 11.0ms (36.6% of total)

const: 6.0ms (20% of total)

ival-div: 4.0ms (13.3% of total)

ival-add: 3.0ms (10% of total)

ival-exp: 2.0ms (6.7% of total)

ival-expm1: 2.0ms (6.7% of total)

ival-sub: 1.0ms (3.3% 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)

series14.0ms (0.3%)

Memory

-35.5MiB live, 8.1MiB allocated; 12ms collecting garbage

Counts

13 → 43

Calls

Call 1

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

Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (+ (* (* x x) -1/720) 1/12) #s(hole binary64 1/12))
#s(approx (+ (* (* x x) -1/720) 1/12) #s(hole binary64 (+ 1/12 (* -1/720 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 1/2))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (+ 1/2 (/ 1 x))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* 1/12 x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* x (+ 1/12 (* 1/2 (/ 1 x))))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1/720 (pow x 3))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (* 1/12 (/ 1 (pow x 2)))) 1/720))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))) 1/720))))
#s(approx (+ (* (* x x) -1/720) 1/12) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* (* x x) -1/720) 1/12) #s(hole binary64 (* (pow x 2) (- (* 1/12 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (- 1/720 (* 1/12 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/720 (* -1 (/ (+ 1/12 (* 1/2 (/ 1 x))) (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -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
10.0ms	x	@	-inf	((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (/ (exp x) (- (exp x) 1)) (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (+ (* (* x x) -1/720) 1/12) (* x x))
2.0ms	x	@	inf	((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (/ (exp x) (- (exp x) 1)) (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (+ (* (* x x) -1/720) 1/12) (* x x))
1.0ms	x	@	0	((/ (exp x) (- (exp x) 1)) (exp x) (- (exp x) 1) (/ (exp x) (- (exp x) 1)) (/ 1 x) (/ (exp x) (- (exp x) 1)) (- (/ 1 x) -1/2) (/ (exp x) (- (exp x) 1)) (+ (* 1/12 x) (- (/ 1 x) -1/2)) (/ (exp x) (- (exp x) 1)) (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) (+ (* (* x x) -1/720) 1/12) (* x x))

Time

Variable

Point

Expression

10.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify138.0ms (3.1%)

Memory

16.5MiB live, 160.1MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	142	748
1	375	742
2	1310	712
3	6496	708
0	8150	627

Stop Event

1×	iter limit
1×	node limit

Counts

43 → 43

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (+ (* (* x x) -1/720) 1/12) #s(hole binary64 1/12))
#s(approx (+ (* (* x x) -1/720) 1/12) #s(hole binary64 (+ 1/12 (* -1/720 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 1/2))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (+ 1/2 (/ 1 x))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* 1/12 x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* x (+ 1/12 (* 1/2 (/ 1 x))))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1/720 (pow x 3))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (* 1/12 (/ 1 (pow x 2)))) 1/720))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))) 1/720))))
#s(approx (+ (* (* x x) -1/720) 1/12) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* (* x x) -1/720) 1/12) #s(hole binary64 (* (pow x 2) (- (* 1/12 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (- 1/720 (* 1/12 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/720 (* -1 (/ (+ 1/12 (* 1/2 (/ 1 x))) (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) -1/720) 1/12) x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (- (+ 1/720 (* -1 (/ (+ 1/2 (/ 1 x)) (pow x 3)))) (* 1/12 (/ 1 (pow x 2))))))))

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

rewrite76.0ms (1.7%)

Memory

15.8MiB live, 60.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	100
0	33	100
1	127	100
0	946	100

Stop Event

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

Counts

13 → 121

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 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 (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))))
(+.f64 (/.f64 (cosh.f64 x) (expm1.f64 x)) (/.f64 (sinh.f64 x) (expm1.f64 x)))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 x) (cosh.f64 x)) (.f64 (sinh.f64 x) (sinh.f64 x))) (-.f64 (cosh.f64 x) (sinh.f64 x)))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (.f64 (sinh.f64 x) (sinh.f64 x)) (.f64 (cosh.f64 x) (sinh.f64 x)))))
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(exp.f64 (+.f64 x #s(literal 0 binary64)))
(exp.f64 x)
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (+.f64 x #s(literal 0 binary64)))
(expm1.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
#s(approx (/ (exp x) (- (exp x) 1)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (+.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (+.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal -1/8 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (pow.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 1/12 binary64) x (pow.f64 x #s(literal -1 binary64)))) #s(literal 1/4 binary64)) (+.f64 (fma.f64 #s(literal 1/12 binary64) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/144 binary64) (.f64 x x))) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x)))
(/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/12 binary64) x (pow.f64 x #s(literal -1 binary64))) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (pow.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 1/12 binary64) x (pow.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 (fma.f64 #s(literal 1/12 binary64) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/144 binary64) (.f64 x x)) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/1728 binary64) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/144 binary64) (.f64 x x) (.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/144 binary64) (.f64 x x)) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/12 binary64) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/1728 binary64) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/144 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/12 binary64) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/1728 binary64) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/144 binary64) (.f64 x x) (.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x)))))
(fma.f64 #s(literal 1/12 binary64) x (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(fma.f64 x #s(literal 1/12 binary64) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/144 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/12 binary64) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/12 binary64) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))))
(-.f64 (fma.f64 #s(literal 1/12 binary64) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64))
(-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/12 binary64) x))
(-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (*.f64 (neg.f64 x) #s(literal 1/12 binary64)))
(-.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/12 binary64) x)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/144 binary64) (.f64 x x) (.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 #s(literal 1/12 binary64) x))))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/144 binary64) (.f64 x x) (.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x))))))
(+.f64 (*.f64 #s(literal 1/12 binary64) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(+.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x))
#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))))
(/.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64)))) #s(literal 1/4 binary64)) (+.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x)))
(/.f64 (-.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 2 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.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)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 3 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 2 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.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))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 3 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 2 binary64)) (.f64 (.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))))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 3 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 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 x (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 2 binary64)) (-.f64 (.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)))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.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)))))
(-.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x (pow.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64))
(-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (neg.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64))) x))
(-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (neg.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64))))
(-.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x)))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 3 binary64)) (fma.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) #s(literal 2 binary64)))))
(+.f64 (.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)))
(+.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/12 binary64)) x))
(/.f64 (-.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 #s(literal 1/12 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/144 binary64))) (neg.f64 (-.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/12 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/1728 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (.f64 (*.f64 x x) #s(literal -1/8640 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (-.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/12 binary64)))
(/.f64 (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/1728 binary64)) (+.f64 #s(literal 1/144 binary64) (-.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (*.f64 x x) #s(literal -1/8640 binary64)))))
(/.f64 (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/1728 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (.f64 (*.f64 x x) #s(literal -1/8640 binary64))))
(fma.f64 (*.f64 #s(literal -1/720 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1/12 binary64))
(fma.f64 (*.f64 #s(literal -1/720 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1/12 binary64))
(fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/12 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal -1/720 binary64)) #s(literal 1/12 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 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))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64))
(fma.f64 x (*.f64 #s(literal -1/720 binary64) x) #s(literal 1/12 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/12 binary64))) (/.f64 #s(literal 1/144 binary64) (-.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/12 binary64))))
(-.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/720 binary64) (.f64 x x)))
(-.f64 #s(literal 1/12 binary64) (.f64 (neg.f64 (.f64 x x)) #s(literal -1/720 binary64)))
(-.f64 #s(literal 1/12 binary64) (.f64 (neg.f64 x) (.f64 #s(literal -1/720 binary64) x)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (.f64 (.f64 x x) #s(literal -1/8640 binary64)))) (/.f64 #s(literal 1/1728 binary64) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (.f64 (.f64 x x) #s(literal -1/8640 binary64)))))
(+.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/12 binary64))
(+.f64 #s(literal 1/12 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval45.0ms (1%)

Memory: -17.7MiB live, 27.3MiB allocated; 7ms collecting garbage
Compiler: Compiled 4 903 to 689 computations (85.9% saved)

prune8.0ms (0.2%)

Memory

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

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	211	9	220

Accuracy

100.0%

Counts

220 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	98.6%	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) x))
✓	69.6%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
✓	69.6%	#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))))
▶	2.8%	#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))))
✓	69.9%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	69.6%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	3.1%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
▶	3.4%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))

Compiler

Compiled 129 to 95 computations (26.4% saved)

simplify252.0ms (5.7%)

Memory

10.9MiB live, 199.4MiB allocated; 44ms collecting garbage

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	118
0	27	118
1	37	118
2	67	118
3	125	118
4	425	118
5	3417	118
0	8308	106

Stop Event

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

Calls

Call 1

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

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

localize35.0ms (0.8%)

Memory

-1.9MiB live, 44.9MiB allocated; 2ms collecting garbage

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.01171875	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) x))
accuracy	19.38509786804738	#s(approx (- (exp x) 1) x)
accuracy	0.11328125	(fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
accuracy	19.46527272037779	#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))))
accuracy	43.204875414474245	#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
accuracy	19.456014759486052	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
accuracy	43.204875414474245	#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
accuracy	0.29296875	(*.f64 #s(literal 1/12 binary64) x)
accuracy	19.46527272037779	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
accuracy	42.867032985400755	#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))

Samples

26.0ms

256×

valid

Compiler

Compiled 74 to 14 computations (81.1% saved)

Precisions

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

ival-div: 4.0ms (25.3% of total)

const: 3.0ms (19% of total)

ival-exp: 2.0ms (12.7% of total)

ival-mult: 2.0ms (12.7% of total)

ival-expm1: 2.0ms (12.7% of total)

ival-add: 1.0ms (6.3% of total)

ival-sub: 1.0ms (6.3% 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)

series3.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB allocated; 0ms collecting garbage

Counts

10 → 27

Calls

Call 1

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

Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (* 1/12 x) #s(hole binary64 (* 1/12 x)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* 1/12 x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* x (+ 1/12 (* 1/2 (/ 1 x))))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 1/2))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (+ 1/2 (/ 1 x))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify185.0ms (4.2%)

Memory

-15.2MiB live, 87.1MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	365
1	246	365
2	734	346
3	2510	346
4	7234	346
0	8188	298

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (* 1/12 x) #s(hole binary64 (* 1/12 x)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* 1/12 x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* x (+ 1/12 (* 1/2 (/ 1 x))))))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* x (+ 1/12 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 1/2))
#s(approx (- (/ 1 x) -1/2) #s(hole binary64 (+ 1/2 (/ 1 x))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/12)))))

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

rewrite46.0ms (1%)

Memory

24.9MiB live, 24.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	104
0	27	104
1	97	104
0	706	92

Stop Event

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

Counts

10 → 36

Calls

Call 1

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

Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))
#s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
(*.f64 x #s(literal 1/12 binary64))
#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
#s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (pow.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 2 binary64))) (-.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (.f64 #s(literal 1/12 binary64) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 2 binary64)) (pow.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/12 binary64) x) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/144 binary64) (.f64 x x) (.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (-.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 2 binary64)) (pow.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/12 binary64) x) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 2 binary64)) (.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x)))))
(/.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/144 binary64) (.f64 x x) (.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (-.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x)))))
(fma.f64 #s(literal 1/12 binary64) x #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/12 binary64) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/12 binary64) x) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/12 binary64) x) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))))
(-.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/12 binary64) x))
(-.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (*.f64 (neg.f64 x) #s(literal 1/12 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/144 binary64) (.f64 x x) (.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (-.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (.f64 #s(literal 1/12 binary64) x))))) (/.f64 (pow.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/144 binary64) (.f64 x x) (.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (-.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x))))))
(+.f64 #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/12 binary64) x))
(+.f64 (*.f64 #s(literal 1/12 binary64) x) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (neg.f64 (exp.f64 x))) (neg.f64 (neg.f64 #s(approx (- (exp x) 1) x))))
(/.f64 (neg.f64 (exp.f64 x)) (neg.f64 #s(approx (- (exp x) 1) x)))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) x))
(neg.f64 (/.f64 (neg.f64 (exp.f64 x)) #s(approx (- (exp x) 1) x)))
(neg.f64 (/.f64 (exp.f64 x) (neg.f64 #s(approx (- (exp x) 1) x))))
(+.f64 (/.f64 (cosh.f64 x) #s(approx (- (exp x) 1) x)) (/.f64 (sinh.f64 x) #s(approx (- (exp x) 1) x)))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(/.f64 (-.f64 (.f64 (cosh.f64 x) (cosh.f64 x)) (.f64 (sinh.f64 x) (sinh.f64 x))) (-.f64 (cosh.f64 x) (sinh.f64 x)))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (.f64 (sinh.f64 x) (sinh.f64 x)) (.f64 (cosh.f64 x) (sinh.f64 x)))))
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(exp.f64 (+.f64 x #s(literal 0 binary64)))
(exp.f64 x)
#s(approx (- (exp x) 1) x)

eval49.0ms (1.1%)

Memory: -32.6MiB live, 13.0MiB allocated; 4ms collecting garbage
Compiler: Compiled 1 280 to 200 computations (84.4% saved)

prune5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	0	0
Picked	0	4	4
Done	0	5	5
Total	60	10	70

Accuracy

100.0%

Counts

70 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	98.6%	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) x))
▶	69.1%	(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) x))
✓	69.6%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
✓	69.6%	#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))))
✓	2.8%	#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))))
✓	69.9%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	69.6%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	3.1%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
✓	3.4%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))

Compiler

Compiled 142 to 104 computations (26.8% saved)

simplify210.0ms (4.8%)

Memory

10.6MiB live, 287.4MiB allocated; 66ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
0	11	30
1	16	30
2	29	30
3	63	30
4	243	30
5	2497	30
0	8672	26

Stop Event

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

Calls

Call 1

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

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

localize20.0ms (0.5%)

Memory

-10.8MiB live, 36.6MiB allocated; 5ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 x #s(literal -1 binary64))
accuracy	0.01171875	(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) x))
accuracy	19.38509786804738	#s(approx (- (exp x) 1) x)
accuracy	19.684083510165877	#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))

Samples

15.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 2.0ms (26.1% of total)

ival-exp: 2.0ms (26.1% of total)

ival-expm1: 2.0ms (26.1% of total)

ival-sub: 1.0ms (13% 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)

series1.0ms (0%)

Memory

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

Counts

4 → 19

Calls

Call 1

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

Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- x -1) #s(hole binary64 1))
#s(approx (- x -1) #s(hole binary64 (+ 1 x)))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- x -1) #s(hole binary64 x))
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))

Calls

3 calls:

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

simplify220.0ms (5%)

Memory

32.2MiB live, 215.5MiB allocated; 62ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	215
1	195	213
2	587	209
3	2284	209
4	7793	209
0	8012	171

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 19

Calls

Call 1

Inputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- x -1) #s(hole binary64 1))
#s(approx (- x -1) #s(hole binary64 (+ 1 x)))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- x -1) #s(hole binary64 x))
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))

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

rewrite46.0ms (1%)

Memory

-28.5MiB live, 64.5MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
0	11	28
1	45	28
0	309	24

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

4 → 14

Calls

Call 1

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

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

eval3.0ms (0.1%)

Memory: 7.3MiB live, 7.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 512 to 111 computations (78.3% saved)

prune7.0ms (0.2%)

Memory

17.8MiB live, 17.8MiB allocated; 0ms collecting garbage

Pruning

15 alts after pruning (5 fresh and 10 done)

	Pruned	Kept	Total
New	25	5	30
Fresh	0	0	0
Picked	0	1	1
Done	0	9	9
Total	25	15	40

Accuracy

100.0%

Counts

40 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	98.6%	(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) x))
	90.8%	(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
	88.9%	(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
	86.6%	(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
✓	69.1%	(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) x))
	3.1%	(/.f64 #s(approx (exp x) #s(approx (- x -1) x)) #s(approx (- (exp x) 1) x))
✓	69.6%	#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
	69.6%	#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)))))
✓	69.6%	#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))))
✓	2.8%	#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))))
✓	69.9%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	69.6%	#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	3.1%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (- (/ 1 x) -1/2) #s(literal 1/2 binary64)))
✓	3.4%	#s(approx (/ (exp x) (- (exp x) 1)) #s(approx (+ (* 1/12 x) (- (/ 1 x) -1/2)) (*.f64 #s(literal 1/12 binary64) x)))

Compiler

Compiled 489 to 245 computations (49.9% saved)

regimes17.0ms (0.4%)

Memory

-27.8MiB live, 24.0MiB allocated; 7ms collecting garbage

Counts

16 → 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))
(/.f64 #s(approx (exp x) #s(approx (- x -1) x)) #s(approx (- (exp x) 1) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) 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))))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) x))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/720 binary64) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

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

Calls

3 calls:

8.0ms	(exp.f64 x)
5.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Results

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

Compiler

Compiled 10 to 8 computations (20% saved)

regimes11.0ms (0.2%)

Memory

15.8MiB live, 15.8MiB allocated; 0ms collecting garbage

Counts

14 → 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))
(/.f64 #s(approx (exp x) #s(approx (- x -1) x)) #s(approx (- (exp x) 1) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) 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))))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 (exp.f64 x) #s(approx (- (exp x) 1) x))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/720 binary64) (fma.f64 #s(literal 1/12 binary64) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 10 to 8 computations (20% saved)

regimes10.0ms (0.2%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
90.8%	1	`(exp.f64 x)`
90.8%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
90.8%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes9.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB allocated; 0ms collecting garbage

Counts

11 → 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))
(/.f64 #s(approx (exp x) #s(approx (- x -1) x)) #s(approx (- (exp x) 1) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) 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))))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
88.9%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
88.9%	1	`(exp.f64 x)`
88.9%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes11.0ms (0.2%)

Memory

-33.7MiB live, 12.4MiB allocated; 3ms 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))
(/.f64 #s(approx (exp x) #s(approx (- x -1) x)) #s(approx (- (exp x) 1) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) 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))))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/12 binary64)) x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
86.6%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
86.6%	1	`(exp.f64 x)`
86.6%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes7.0ms (0.2%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Counts

8 → 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))
(/.f64 #s(approx (exp x) #s(approx (- x -1) x)) #s(approx (- (exp x) 1) x))
#s(approx (/ (exp x) (- (exp x) 1)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (- (exp x) 1) 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))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
69.9%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
69.9%	1	`x`
69.9%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB 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
3.4%	1	`(exp.f64 x)`
3.4%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
3.4%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes3.0ms (0.1%)

Memory

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

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 10 to 8 computations (20% saved)

simplify51.0ms (1.2%)

Memory

-22.0MiB live, 24.2MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	124
1	55	124
2	82	124
3	142	124
4	415	124
5	2826	124
6	7324	124

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

derivations487.0ms (11.1%)

Memory

49.7MiB live, 273.4MiB allocated; 36ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 124 to 46 computations (62.9% saved)

preprocess56.0ms (1.3%)

Memory: -13.7MiB live, 41.7MiB allocated; 7ms collecting garbage
Compiler: Compiled 274 to 114 computations (58.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0%)

sample703.0ms (16%)

explain93.0ms (2.1%)

preprocess271.0ms (6.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify227.0ms (5.2%)

localize16.0ms (0.4%)

series2.0ms (0%)

simplify667.0ms (15.2%)

rewrite63.0ms (1.4%)

eval6.0ms (0.1%)

prune4.0ms (0.1%)

simplify260.0ms (5.9%)

localize56.0ms (1.3%)

series14.0ms (0.3%)

simplify138.0ms (3.1%)

rewrite76.0ms (1.7%)

eval45.0ms (1%)

prune8.0ms (0.2%)

simplify252.0ms (5.7%)

localize35.0ms (0.8%)

series3.0ms (0.1%)

simplify185.0ms (4.2%)

rewrite46.0ms (1%)

eval49.0ms (1.1%)

prune5.0ms (0.1%)

simplify210.0ms (4.8%)

localize20.0ms (0.5%)

series1.0ms (0%)

simplify220.0ms (5%)

rewrite46.0ms (1%)

eval3.0ms (0.1%)

prune7.0ms (0.2%)

regimes17.0ms (0.4%)

regimes11.0ms (0.2%)

regimes10.0ms (0.2%)

regimes9.0ms (0.2%)

regimes11.0ms (0.2%)

regimes7.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify51.0ms (1.2%)

derivations487.0ms (11.1%)

preprocess56.0ms (1.3%)

end0.0ms (0%)

Profiling