Metrics for expq2 (section 3.11)

start0.0ms (0%)

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

analyze2.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample817.0ms (21.8%)

Memory

6.1MiB live, 578.4MiB allocated; 160ms collecting garbage

Samples

554.0ms	8 255×	0	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 284.0ms

ival-exp: 135.0ms (47.6% of total)

ival-expm1: 78.0ms (27.5% of total)

ival-div!: 68.0ms (24% of total)

adjust: 2.0ms (0.7% of total)

Bogosity

preprocess127.0ms (3.4%)

Memory

-25.0MiB live, 70.2MiB allocated; 42ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	29	26
2	98	26
3	397	26
4	5419	26

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	33.9%	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Compiler

Compiled 12 to 10 computations (16.7% saved)

series3.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Counts

5 → 16

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) 1)
1.0ms	x	@	inf	((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) 1)
1.0ms	x	@	0	((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) 1)

rewrite815.0ms (21.8%)

Memory

30.5MiB live, 725.0MiB allocated; 226ms collecting garbage

Counts

21 → 21

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

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

eval4.0ms (0.1%)

Memory: 3.9MiB live, 3.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 95 to 51 computations (46.3% saved)

prune6.0ms (0.2%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	13	8	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	8	22

Accuracy

100.0%

Counts

22 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
	32.8%	(exp.f64 x)
▶	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
▶	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
	3.2%	#s(approx (- (exp x) 1) x)
▶	3.0%	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
▶	3.3%	#s(approx (exp x) #s(literal 1 binary64))

Compiler

Compiled 106 to 100 computations (5.7% saved)

series10.0ms (0.3%)

Memory

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

Counts

17 → 45

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) (exp x) 1 (exp x) (+ x 1) (/ (exp x) (- (exp x) 1)) (/ (+ (* 1/2 x) 1) x) (+ (* 1/2 x) 1) 1/2 (/ (exp x) (- (exp x) 1)) (/ (+ (* (+ (* 1/12 x) 1/2) x) 1) x) (+ (* (+ (* 1/12 x) 1/2) x) 1) (+ (* 1/12 x) 1/2) 1/12)
3.0ms	x	@	-inf	((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) (exp x) 1 (exp x) (+ x 1) (/ (exp x) (- (exp x) 1)) (/ (+ (* 1/2 x) 1) x) (+ (* 1/2 x) 1) 1/2 (/ (exp x) (- (exp x) 1)) (/ (+ (* (+ (* 1/12 x) 1/2) x) 1) x) (+ (* (+ (* 1/12 x) 1/2) x) 1) (+ (* 1/12 x) 1/2) 1/12)
2.0ms	x	@	0	((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) (exp x) 1 (exp x) (+ x 1) (/ (exp x) (- (exp x) 1)) (/ (+ (* 1/2 x) 1) x) (+ (* 1/2 x) 1) 1/2 (/ (exp x) (- (exp x) 1)) (/ (+ (* (+ (* 1/12 x) 1/2) x) 1) x) (+ (* (+ (* 1/12 x) 1/2) x) 1) (+ (* 1/12 x) 1/2) 1/12)

Time

Variable

Point

Expression

4.0ms

inf

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

3.0ms

-inf

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

2.0ms

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

rewrite1.0s (27.1%)

Memory

-43.3MiB live, 246.2MiB allocated; 215ms collecting garbage

Counts

62 → 54

Calls

Call 1

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

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

eval5.0ms (0.1%)

Memory: 4.9MiB live, 4.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 235 to 96 computations (59.1% saved)

prune6.0ms (0.2%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	3	3
Picked	1	4	5
Done	0	0	0
Total	47	9	56

Accuracy

100.0%

Counts

56 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	70.2%	(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
▶	32.8%	(exp.f64 x)
✓	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
✓	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
▶	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	3.2%	#s(approx (- (exp x) 1) x)
✓	3.0%	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
✓	3.3%	#s(approx (exp x) #s(literal 1 binary64))
▶	3.3%	#s(literal 1/12 binary64)

Compiler

Compiled 77 to 75 computations (2.6% saved)

series2.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

Counts

9 → 21

Calls

Call 1

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ (exp x) (- (exp x) 1)) (/ 1 x) 1 x 1/12 (- (exp x) 1) (+ (/ 1 x) 1/2) 1/2 (exp x))
1.0ms	x	@	inf	((/ (exp x) (- (exp x) 1)) (/ 1 x) 1 x 1/12 (- (exp x) 1) (+ (/ 1 x) 1/2) 1/2 (exp x))
0.0ms	x	@	0	((/ (exp x) (- (exp x) 1)) (/ 1 x) 1 x 1/12 (- (exp x) 1) (+ (/ 1 x) 1/2) 1/2 (exp x))

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

0.0ms

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

rewrite756.0ms (20.2%)

Memory

-24.5MiB live, 215.0MiB allocated; 44ms collecting garbage

Counts

30 → 28

Calls

Call 1

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

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

eval3.0ms (0.1%)

Memory: 2.4MiB live, 2.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 93 to 54 computations (41.9% saved)

prune5.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	0	0
Picked	0	5	5
Done	0	4	4
Total	21	9	30

Accuracy

100.0%

Counts

30 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	70.2%	(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓	32.8%	(exp.f64 x)
✓	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
✓	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
✓	70.2%	#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	3.2%	#s(approx (- (exp x) 1) x)
✓	3.0%	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
✓	3.3%	#s(approx (exp x) #s(literal 1 binary64))
✓	3.3%	#s(literal 1/12 binary64)

Compiler

Compiled 99 to 80 computations (19.2% saved)

regimes11.0ms (0.3%)

Memory

17.5MiB live, 17.5MiB allocated; 0ms collecting garbage

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

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
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 9 to 8 computations (11.1% saved)

regimes10.0ms (0.3%)

Memory

-32.1MiB live, 13.9MiB allocated; 2ms collecting garbage

Counts

9 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`(exp.f64 x)`
98.8%	2	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
100.0%	2	`x`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes5.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated; 0ms collecting garbage

Counts

8 → 2

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.7%	2	`(exp.f64 x)`
99.7%	2	`x`

Compiler

Compiled 3 to 3 computations (0% saved)

regimes7.0ms (0.2%)

Memory

14.0MiB live, 14.0MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

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
70.2%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
70.2%	1	`(exp.f64 x)`
70.2%	1	`x`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes5.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
3.3%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
3.3%	1	`(exp.f64 x)`
3.3%	1	`x`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes7.0ms (0.2%)

Memory

-39.5MiB live, 6.8MiB allocated; 4ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/12 binary64)

Outputs
#s(literal 1/12 binary64)

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
3.3%	1	`x`
3.3%	1	`(exp.f64 x)`
3.3%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 9 to 8 computations (11.1% saved)

bsearch13.0ms (0.3%)

Memory

21.7MiB live, 21.7MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-2312227.5051023993	-0.00011193456652643685

Samples

6.0ms

160×

valid

Compiler

Compiled 160 to 168 computations (-5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-exp: 2.0ms (57.3% of total)

ival-expm1: 1.0ms (28.7% of total)

ival-div!: 1.0ms (28.7% of total)

adjust: 0.0ms (0% of total)

bsearch12.0ms (0.3%)

Memory

19.6MiB live, 19.6MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-2312227.5051023993	-0.00011193456652643685

Samples

6.0ms

144×

valid

Compiler

Compiled 80 to 98 computations (-22.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-exp: 2.0ms (57.3% of total)

ival-expm1: 1.0ms (28.7% of total)

ival-div!: 1.0ms (28.7% of total)

adjust: 0.0ms (0% of total)

derivations2.0ms (0%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 33 to 25 computations (24.2% saved)

preprocess100.0ms (2.7%)

Memory: -21.6MiB live, 113.2MiB allocated; 31ms collecting garbage
Compiler: Compiled 45 to 36 computations (20% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze2.0ms (0%)

sample817.0ms (21.8%)

preprocess127.0ms (3.4%)

series3.0ms (0.1%)

rewrite815.0ms (21.8%)

eval4.0ms (0.1%)

prune6.0ms (0.2%)

series10.0ms (0.3%)

rewrite1.0s (27.1%)

eval5.0ms (0.1%)

prune6.0ms (0.2%)

series2.0ms (0.1%)

rewrite756.0ms (20.2%)

eval3.0ms (0.1%)

prune5.0ms (0.1%)

regimes11.0ms (0.3%)

regimes10.0ms (0.3%)

regimes5.0ms (0.1%)

regimes7.0ms (0.2%)

regimes5.0ms (0.1%)

regimes7.0ms (0.2%)

bsearch13.0ms (0.3%)

bsearch12.0ms (0.3%)

derivations2.0ms (0%)

preprocess100.0ms (2.7%)

end0.0ms (0%)

Profiling