Metrics for expm1 (example 3.7)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample424.0ms (38.8%)

Memory

-5.1MiB live, 672.5MiB allocated; 104ms collecting garbage

Samples

218.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-expm1: 90.0ms (98.3% of total)

adjust: 1.0ms (1.1% of total)

Bogosity

explain64.0ms (5.9%)

Memory

27.0MiB live, 117.1MiB allocated; 8ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.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	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

31.0ms

512×

valid

Compiler

Compiled 24 to 16 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-expm1: 18.0ms (83.3% of total)

ival-exp: 4.0ms (18.5% of total)

adjust: 0.0ms (0% of total)

preprocess114.0ms (10.5%)

Memory

-32.7MiB live, 58.6MiB allocated; 42ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	18	15
2	42	15
3	149	15
4	718	15
5	7965	15

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.3%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Compiler

Compiled 8 to 8 computations (0% saved)

series1.0ms (0.1%)

Memory

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

Counts

4 → 11

Calls

Call 1

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

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) #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 #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (exp x) #s(hole binary64 (exp x)))

Calls

3 calls:

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

rewrite212.0ms (19.4%)

Memory

17.1MiB live, 248.9MiB allocated; 45ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	117
0	40	117
1	226	117
2	2046	117
0	8915	92

Stop Event

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

Counts

15 → 63

Calls

Call 1

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

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

eval6.0ms (0.6%)

Memory: 12.0MiB live, 12.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 062 to 208 computations (80.4% saved)

prune2.0ms (0.2%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	3	60

Accuracy

100.0%

Counts

60 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.4%	(-.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 x)
▶	98.0%	#s(approx (- (exp x) 1) x)

Compiler

Compiled 16 to 14 computations (12.5% saved)

series1.0ms (0.1%)

Memory

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

Counts

8 → 15

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) x)
x
(expm1.f64 x)
(-.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(literal 1 binary64)

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 x #s(hole binary64 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 (- (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)))))

Calls

3 calls:

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

Time

Variable

Point

Expression

0.0ms

-inf

((- (exp x) 1) x (- (exp x) 1) (- (exp x) 1) (exp x) (- x -1) -1 1)

0.0ms

inf

((- (exp x) 1) x (- (exp x) 1) (- (exp x) 1) (exp x) (- x -1) -1 1)

0.0ms

((- (exp x) 1) x (- (exp x) 1) (- (exp x) 1) (exp x) (- x -1) -1 1)

rewrite88.0ms (8.1%)

Memory

-4.2MiB live, 86.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	151
0	51	147
1	276	147
0	2496	136

Stop Event

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

Counts

23 → 76

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) x)
x
(expm1.f64 x)
(-.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(literal 1 binary64)
#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 x #s(hole binary64 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 (- (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)))))

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

eval6.0ms (0.6%)

Memory: 16.2MiB live, 16.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 990 to 236 computations (76.2% saved)

prune3.0ms (0.3%)

Memory

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

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	64	3	67

Accuracy

100.0%

Counts

67 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.4%	(-.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
✓	98.0%	#s(approx (- (exp x) 1) x)

Compiler

Compiled 36 to 27 computations (25% saved)

regimes56.0ms (5.1%)

Memory

-50.7MiB live, 15.3MiB allocated; 66ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) x)
(-.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(expm1.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))

Outputs
(expm1.f64 x)

Calls

3 calls:

53.0ms	x
1.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
1.0ms	(exp.f64 x)

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes3.0ms (0.3%)

Memory

8.4MiB live, 8.4MiB allocated; 0ms collecting garbage

Accuracy

Total -58.0b remaining (-4572%)

Threshold costs -58b (-4572%)

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(approx (- (exp x) 1) x)

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.0%	1	`(exp.f64 x)`
98.0%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
98.0%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

derivations66.0ms (6%)

Memory

18.7MiB live, 69.9MiB allocated; 7ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 8 to 6 computations (25% saved)

preprocess45.0ms (4.1%)

Memory: -19.1MiB live, 27.8MiB allocated; 2ms collecting garbage
Compiler: Compiled 28 to 24 computations (14.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample424.0ms (38.8%)

explain64.0ms (5.9%)

preprocess114.0ms (10.5%)

series1.0ms (0.1%)

rewrite212.0ms (19.4%)

eval6.0ms (0.6%)

prune2.0ms (0.2%)

series1.0ms (0.1%)

rewrite88.0ms (8.1%)

eval6.0ms (0.6%)

prune3.0ms (0.3%)

regimes56.0ms (5.1%)

regimes3.0ms (0.3%)

derivations66.0ms (6%)

preprocess45.0ms (4.1%)

end0.0ms (0%)

Profiling