Metrics for Kahan's exp quotient

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample586.0ms (60.2%)

Memory

-6.9MiB live, 862.9MiB allocated; 256ms collecting garbage

Samples

385.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-expm1: 108.0ms (69.5% of total)

ival-div!: 46.0ms (29.6% of total)

adjust: 2.0ms (1.3% of total)

Bogosity

preprocess41.0ms (4.2%)

Memory

-22.2MiB live, 68.5MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	48	20
2	211	20
3	1294	20

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.5%	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series6.0ms (0.6%)

Memory

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	147

Stop Event

1×	iter-limit

Counts

5 → 14

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable	Point
1.0ms	x	-inf
1.0ms	x	inf
0.0ms	x	0

rewrite67.0ms (6.9%)

Memory

23.7MiB live, 118.9MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	45	14
0	398	10

Stop Event

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

Counts

5 → 77

Calls

Call 1

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

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

eval11.0ms (1.1%)

Memory: -14.8MiB live, 31.0MiB allocated; 4ms collecting garbage
Compiler: Compiled 1 032 to 270 computations (73.8% saved)

prune3.0ms (0.3%)

Memory

10.7MiB live, 10.7MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Accuracy

100.0%

Counts

88 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (expm1.f64 x) x)
▶	55.3%	#s(approx (/ (- (exp x) 1) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
▶	55.4%	#s(approx (/ (- (exp x) 1) x) #s(literal 1 binary64))

Compiler

Compiled 24 to 20 computations (16.7% saved)

series7.0ms (0.7%)

Memory

-28.8MiB live, 17.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	127

Stop Event

1×	iter-limit

Counts

9 → 12

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable	Point
1.0ms	x	-inf
1.0ms	x	inf
0.0ms	x	0

rewrite54.0ms (5.5%)

Memory

38.5MiB live, 91.3MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
0	15	33
1	73	33
0	645	31

Stop Event

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

Counts

9 → 108

Calls

Call 1

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

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

eval12.0ms (1.2%)

Memory: -13.8MiB live, 32.6MiB allocated; 3ms collecting garbage
Compiler: Compiled 1 568 to 343 computations (78.1% saved)

prune4.0ms (0.4%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	111	3	114

Accuracy

100.0%

Counts

114 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
▶	55.3%	#s(approx (/ (- (exp x) 1) x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓	55.4%	#s(approx (/ (- (exp x) 1) x) #s(literal 1 binary64))

Compiler

Compiled 23 to 19 computations (17.4% saved)

series3.0ms (0.3%)

Memory

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	80

Stop Event

1×	iter-limit

Counts

5 → 8

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable	Point
1.0ms	x	-inf
0.0ms	x	inf
0.0ms	x	0

rewrite85.0ms (8.7%)

Memory

-10.2MiB live, 83.6MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
0	10	18
1	63	18
0	616	16

Stop Event

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

Counts

5 → 35

Calls

Call 1

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

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

eval4.0ms (0.4%)

Memory: 12.4MiB live, 12.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 693 to 139 computations (79.9% saved)

prune9.0ms (0.9%)

Memory

-33.0MiB live, 17.7MiB allocated; 4ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	37	4	41

Accuracy

100.0%

Counts

41 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	55.3%	#s(approx (/ (- (exp x) 1) x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
▶	3.7%	#s(approx (/ (- (exp x) 1) x) #s(approx (+ (* x 1/2) 1) (*.f64 #s(literal 1/2 binary64) x)))
✓	55.4%	#s(approx (/ (- (exp x) 1) x) #s(literal 1 binary64))

Compiler

Compiled 39 to 31 computations (20.5% saved)

series4.0ms (0.4%)

Memory

11.1MiB live, 11.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	79

Stop Event

1×	iter-limit

Counts

5 → 8

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable	Point
1.0ms	x	-inf
1.0ms	x	inf
0.0ms	x	0

rewrite44.0ms (4.5%)

Memory

-0.3MiB live, 46.2MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
0	12	30
1	65	30
0	618	26

Stop Event

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

Counts

5 → 9

Calls

Call 1

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

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

eval1.0ms (0.1%)

Memory: 3.0MiB live, 3.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 187 to 56 computations (70.1% saved)

prune2.0ms (0.2%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	11	0	11
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	11	4	15

Accuracy

100.0%

Counts

15 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	55.3%	#s(approx (/ (- (exp x) 1) x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓	3.7%	#s(approx (/ (- (exp x) 1) x) #s(approx (+ (* x 1/2) 1) (*.f64 #s(literal 1/2 binary64) x)))
✓	55.4%	#s(approx (/ (- (exp x) 1) x) #s(literal 1 binary64))

Compiler

Compiled 39 to 31 computations (20.5% saved)

regimes12.0ms (1.2%)

Memory

-26.2MiB live, 20.7MiB allocated; 1ms collecting garbage

Accuracy

Total -33.5b remaining (-117.3%)

Threshold costs -33.5b (-117.3%)

Counts

4 → 1

6 → 1

Calls

Call 1

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

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

Call 2

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

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

Calls

4 calls:

5.0ms	x
2.0ms	x
2.0ms	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
1.0ms	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Results

Accuracy	Segments	Branch
55.4%	1	`(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)`
55.4%	1	`x`
100.0%	1	`(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)`
100.0%	1	`x`

Compiler

Compiled 71 to 35 computations (50.7% saved)

derivations2.0ms (0.2%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 12 to 9 computations (25% saved)

preprocess18.0ms (1.8%)

Memory: 40.0MiB live, 40.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 40 to 26 computations (35% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0.1%)

sample586.0ms (60.2%)

preprocess41.0ms (4.2%)

series6.0ms (0.6%)

rewrite67.0ms (6.9%)

eval11.0ms (1.1%)

prune3.0ms (0.3%)

series7.0ms (0.7%)

rewrite54.0ms (5.5%)

eval12.0ms (1.2%)

prune4.0ms (0.4%)

series3.0ms (0.3%)

rewrite85.0ms (8.7%)

eval4.0ms (0.4%)

prune9.0ms (0.9%)

series4.0ms (0.4%)

rewrite44.0ms (4.5%)

eval1.0ms (0.1%)

prune2.0ms (0.2%)

regimes12.0ms (1.2%)

derivations2.0ms (0.2%)

preprocess18.0ms (1.8%)

end0.0ms (0%)

Profiling