Metrics for expax (section 3.5)

start0.0ms (0%)

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

analyze17.0ms (1.6%)

Memory

25.2MiB live, 25.2MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75.9%	68.7%	21.9%	0.1%	0%	9.4%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
86%	71.8%	11.7%	0.1%	0%	16.4%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.4%	73.4%	6%	0.1%	0%	20.5%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 12 to 7 computations (41.7% saved)

sample593.0ms (55.7%)

Memory

17.0MiB live, 618.3MiB allocated; 207ms collecting garbage

Samples

385.0ms	8 256×	0	valid
13.0ms	324×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-expm1: 82.0ms (54.1% of total)

ival-mult!: 66.0ms (43.6% of total)

adjust: 1.0ms (0.7% of total)

ival->: 1.0ms (0.7% of total)

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

Bogosity

preprocess84.0ms (7.9%)

Memory

4.5MiB live, 48.8MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	42
1	46	42
2	87	42
3	283	42
4	3581	42

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.5%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Symmetry

(sort a x)

Compiler

Compiled 12 to 12 computations (0% saved)

series5.0ms (0.5%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Counts

6 → 17

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite131.0ms (12.3%)

Memory

-24.7MiB live, 171.3MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	314
0	86	314
1	480	314
0	4421	271

Stop Event

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

Counts

23 → 55

Calls

Call 1

Inputs
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(exp.f64 (*.f64 a x))
(*.f64 a x)
a
x
#s(literal 1 binary64)
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* a x)))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* a (+ x (* 1/2 (* a (pow x 2)))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))))
#s(approx (exp (* a x)) #s(hole binary64 1))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* a x))))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))))
#s(approx a #s(hole binary64 a))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (- (exp (* a x)) 1)))
#s(approx (exp (* a x)) #s(hole binary64 (exp (* a x))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* x (+ a (* 1/2 (* (pow a 2) x))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))))
#s(approx x #s(hole binary64 x))

Outputs
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 2 binary64)))) (neg.f64 (-.f64 (exp.f64 (*.f64 x a)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 3 binary64)))) (neg.f64 (+.f64 (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64)) (exp.f64 (.f64 (*.f64 x a) #s(literal 2 binary64))))))
(/.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 2 binary64))) (-.f64 (exp.f64 (*.f64 x a)) #s(literal -1 binary64)))
(/.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 3 binary64))) (+.f64 (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64)) (exp.f64 (.f64 (*.f64 x a) #s(literal 2 binary64)))))
(fma.f64 (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64))
(fma.f64 (exp.f64 (*.f64 x a)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x a)) #s(literal -1 binary64))
(expm1.f64 (fma.f64 x a #s(literal 0 binary64)))
(expm1.f64 (*.f64 (log.f64 (exp.f64 a)) x))
(expm1.f64 (*.f64 x a))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 x a) #s(literal 2 binary64))) (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64))))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 x a) #s(literal 3 binary64))) (+.f64 (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64)) (exp.f64 (.f64 (.f64 x a) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64)) (exp.f64 (.f64 (.f64 x a) #s(literal 2 binary64))))))
(-.f64 (exp.f64 (*.f64 x a)) #s(literal 1 binary64))
(+.f64 (cosh.f64 (.f64 x a)) (-.f64 (sinh.f64 (.f64 x a)) #s(literal 1 binary64)))
(+.f64 (exp.f64 (*.f64 x a)) #s(literal -1 binary64))
(*.f64 (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64))))
(.f64 (exp.f64 (.f64 x a)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (exp.f64 (.f64 x a)))
(pow.f64 (exp.f64 x) a)
(pow.f64 (exp.f64 a) x)
(/.f64 (.f64 (exp.f64 (.f64 x a)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 x a)) (cosh.f64 (.f64 x a))) (.f64 (sinh.f64 (.f64 x a)) (sinh.f64 (.f64 x a)))) (-.f64 (cosh.f64 (.f64 x a)) (sinh.f64 (.f64 x a))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 x a)) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 x a)) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 x a)) (cosh.f64 (.f64 x a)) (-.f64 (.f64 (sinh.f64 (.f64 x a)) (sinh.f64 (.f64 x a))) (.f64 (cosh.f64 (.f64 x a)) (sinh.f64 (.f64 x a))))))
(exp.f64 (fma.f64 x a #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 a)) x))
(exp.f64 (*.f64 x a))
(+.f64 (sinh.f64 (.f64 x a)) (cosh.f64 (.f64 x a)))
(+.f64 (cosh.f64 (.f64 x a)) (sinh.f64 (.f64 x a)))
(.f64 (.f64 #s(literal 1 binary64) x) a)
(.f64 (.f64 #s(literal 1 binary64) a) x)
(.f64 (.f64 x a) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x a))
(*.f64 x a)
(*.f64 a x)
(/.f64 (.f64 #s(literal 2 binary64) (.f64 x a)) #s(literal 2 binary64))
a
x
#s(literal 1 binary64)
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) a) #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))) a x) a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) a) #s(literal 1/24 binary64))) a (.f64 (.f64 x x) #s(literal 1/2 binary64))) a x) a))
#s(approx (exp (* a x)) #s(literal 1 binary64))
#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) a) #s(literal 1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a #s(literal 1 binary64)))
#s(approx a a)
#s(approx (- (exp (* a x)) 1) (expm1.f64 (*.f64 x a)))
#s(approx (exp (* a x)) (exp.f64 (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 a a) a) x) #s(literal 1/6 binary64) (.f64 (.f64 a a) #s(literal 1/2 binary64))) x a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 a a) a) #s(literal 1/6 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 a a) a) a) x) #s(literal 1/24 binary64))) x (.f64 (.f64 a a) #s(literal 1/2 binary64))) x a) x))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 a a) a) x) #s(literal 1/6 binary64) (.f64 (*.f64 a a) #s(literal 1/2 binary64))) x a) x #s(literal 1 binary64)))
#s(approx x x)

eval5.0ms (0.5%)

Memory: 10.9MiB live, 10.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 365 to 172 computations (52.9% saved)

prune2.0ms (0.2%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Accuracy

100.0%

Counts

50 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	21.6%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 x a))
▶	71.1%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 19 to 19 computations (0% saved)

series3.0ms (0.3%)

Memory

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

Counts

8 → 17

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	-inf	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1)
1.0ms	x	@	-inf	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1)
0.0ms	a	@	inf	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1)
0.0ms	x	@	inf	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1)
0.0ms	a	@	0	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1)

rewrite115.0ms (10.8%)

Memory

-10.7MiB live, 45.4MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	332
0	88	312
1	511	312
0	4549	289

Stop Event

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

Counts

25 → 62

Calls

Call 1

Inputs
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(*.f64 x a)
x
a
(expm1.f64 (*.f64 x a))
(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (exp (* a x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* a x)))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* a (+ x (* 1/2 (* a (pow x 2)))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))))
#s(approx a #s(hole binary64 a))
#s(approx (exp (* a x)) #s(hole binary64 1))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* a x))))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (- (exp (* a x)) 1)))
#s(approx (exp (* a x)) #s(hole binary64 (exp (* a x))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* x (+ a (* 1/2 (* (pow a 2) x))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))))
#s(approx (exp (* a x)) #s(hole binary64 (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))))

Outputs
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(.f64 (.f64 #s(literal 1 binary64) a) x)
(.f64 (.f64 #s(literal 1 binary64) x) a)
(.f64 #s(literal 1 binary64) (.f64 x a))
(.f64 (.f64 x a) #s(literal 1 binary64))
(*.f64 x a)
(*.f64 a x)
(/.f64 (.f64 #s(literal 2 binary64) (.f64 x a)) #s(literal 2 binary64))
x
a
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 2 binary64)))) (neg.f64 (-.f64 (exp.f64 (*.f64 x a)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 3 binary64)))) (neg.f64 (+.f64 (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64)) (exp.f64 (.f64 (*.f64 x a) #s(literal 2 binary64))))))
(/.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 2 binary64))) (-.f64 (exp.f64 (*.f64 x a)) #s(literal -1 binary64)))
(/.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 3 binary64))) (+.f64 (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64)) (exp.f64 (.f64 (*.f64 x a) #s(literal 2 binary64)))))
(fma.f64 (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (exp.f64 x) (/.f64 a #s(literal 2 binary64))) (pow.f64 (exp.f64 x) (/.f64 a #s(literal 2 binary64))) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x a)) #s(literal -1 binary64))
(fma.f64 (exp.f64 (*.f64 x a)) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (fma.f64 x a #s(literal 0 binary64)))
(expm1.f64 (*.f64 (log.f64 (exp.f64 a)) x))
(expm1.f64 (*.f64 (log.f64 (exp.f64 x)) a))
(expm1.f64 (*.f64 x a))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 x a) #s(literal 2 binary64))) (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64))))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 x a) #s(literal 3 binary64))) (+.f64 (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64)) (exp.f64 (.f64 (.f64 x a) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (exp.f64 (.f64 x a)) #s(literal -1 binary64)) (exp.f64 (.f64 (.f64 x a) #s(literal 2 binary64))))))
(-.f64 (exp.f64 (*.f64 x a)) #s(literal 1 binary64))
(+.f64 (cosh.f64 (.f64 x a)) (-.f64 (sinh.f64 (.f64 x a)) #s(literal 1 binary64)))
(+.f64 (exp.f64 (*.f64 x a)) #s(literal -1 binary64))
(/.f64 (neg.f64 (fma.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64))) (neg.f64 (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(approx (exp ( a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64))) #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(/.f64 (fma.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 #s(approx (exp ( a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64))) #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(-.f64 (/.f64 (.f64 #s(approx (exp ( a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64))) (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 (.f64 (.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64))) #s(approx (exp (* a x)) #s(literal 1 binary64))) (fma.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(approx (exp (* a x)) #s(literal 1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(+.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(approx (exp ( a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) #s(literal 1 binary64)))
#s(approx (exp (* a x)) #s(literal 1 binary64))
(/.f64 (.f64 #s(approx (exp ( a x)) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
#s(literal 1 binary64)
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) a) #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))) a x) a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) a) #s(literal 1/24 binary64))) a (.f64 (.f64 x x) #s(literal 1/2 binary64))) a x) a))
#s(approx a a)
(.f64 #s(approx (exp ( a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) #s(literal 1 binary64)))
#s(approx (exp (* a x)) #s(literal 1 binary64))
(/.f64 (.f64 #s(approx (exp ( a x)) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) a) #s(literal 1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a #s(literal 1 binary64)))
#s(approx (- (exp (* a x)) 1) (expm1.f64 (*.f64 x a)))
#s(approx (exp (* a x)) (exp.f64 (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 a a) a) x) #s(literal 1/6 binary64) (.f64 (.f64 a a) #s(literal 1/2 binary64))) x a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 a a) a) #s(literal 1/6 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 a a) a) a) x) #s(literal 1/24 binary64))) x (.f64 (.f64 a a) #s(literal 1/2 binary64))) x a) x))
#s(approx x x)
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 a a) a) x) #s(literal 1/6 binary64) (.f64 (*.f64 a a) #s(literal 1/2 binary64))) x a) x #s(literal 1 binary64)))

eval5.0ms (0.5%)

Memory: 5.6MiB live, 5.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 447 to 174 computations (61.1% saved)

prune8.0ms (0.8%)

Memory

-41.7MiB live, 3.9MiB allocated; 3ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	55	3	58

Accuracy

100.0%

Counts

58 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	21.6%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
✓	71.1%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 37 to 34 computations (8.1% saved)

regimes10.0ms (0.9%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

Outputs
(expm1.f64 (*.f64 x a))

Calls

5 calls:

4.0ms	x
2.0ms	a
2.0ms	(*.f64 a x)
1.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
1.0ms	(exp.f64 (*.f64 a x))

Results

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

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes6.0ms (0.6%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
71.1%	1	`(*.f64 a x)`
71.1%	1	`(exp.f64 (*.f64 a x))`
71.1%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
71.1%	1	`a`
71.1%	1	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes5.0ms (0.5%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
21.6%	1	`(exp.f64 (*.f64 a x))`
21.6%	1	`(*.f64 a x)`
21.6%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
21.6%	1	`a`
21.6%	1	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

derivations49.0ms (4.6%)

Memory

-4.8MiB live, 39.1MiB allocated; 4ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 15 to 12 computations (20% saved)

preprocess27.0ms (2.5%)

Memory: 6.9MiB live, 51.5MiB allocated; 5ms collecting garbage
Remove: (sort a x)
Compiler: Compiled 63 to 60 computations (4.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze17.0ms (1.6%)

sample593.0ms (55.7%)

preprocess84.0ms (7.9%)

series5.0ms (0.5%)

rewrite131.0ms (12.3%)

eval5.0ms (0.5%)

prune2.0ms (0.2%)

series3.0ms (0.3%)

rewrite115.0ms (10.8%)

eval5.0ms (0.5%)

prune8.0ms (0.8%)

regimes10.0ms (0.9%)

regimes6.0ms (0.6%)

regimes5.0ms (0.5%)

derivations49.0ms (4.6%)

preprocess27.0ms (2.5%)

end0.0ms (0%)

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