Metrics for expax (section 3.5)

start0.0ms (0%)

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

analyze27.0ms (1.9%)

Memory

-2.0MiB live, 42.4MiB allocated; 7ms 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)

sample608.0ms (43.1%)

Memory

-8.1MiB live, 892.4MiB allocated; 62ms collecting garbage

Samples

351.0ms	8 256×	0	valid
14.0ms	292×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-mult: 79.0ms (52.5% of total)

ival-expm1: 65.0ms (43.2% of total)

adjust: 2.0ms (1.3% of total)

ival->: 2.0ms (1.3% of total)

ival-assert: 2.0ms (1.3% of total)

exact: 1.0ms (0.7% of total)

Bogosity

explain70.0ms (5%)

Memory

8.1MiB live, 102.3MiB allocated; 5ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
131	-	-	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
0	-	-	`a`
0	-	-	`(exp.f64 (*.f64 a x))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 a x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`	cancellation	131	0

Confusion

	Predicted +	Predicted -
+	131	0
-	0	125

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	0
-	0	0	125

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	125
1	131

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms

512×

valid

Compiler

Compiled 42 to 22 computations (47.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 5.0ms (38.9% of total)

ival-exp: 4.0ms (31.2% of total)

ival-expm1: 3.0ms (23.4% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess233.0ms (16.5%)

Memory

-6.8MiB live, 218.4MiB allocated; 64ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	42
1	45	42
2	81	42
3	219	42
4	977	42
0	6	6
0	9	6
1	17	6
2	35	6
3	84	6
4	297	6
5	2733	6
0	8456	4

Stop Event

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

Calls

Call 1

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

Outputs
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (-.f64 (*.f64 x a) #s(literal 0 binary64)))

Symmetry

(sort a x)

Compiler

Compiled 6 to 6 computations (0% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.8%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 6 to 6 computations (0% saved)

series5.0ms (0.4%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Counts

6 → 18

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 x) #s(hole binary64 (* a x)))
#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	@	0	((- (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	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)
1.0ms	x	@	0	((- (exp (* a x)) 1) (exp (* a x)) (* a x) a x 1)

rewrite162.0ms (11.5%)

Memory

-6.9MiB live, 137.6MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	321
0	87	321
1	479	321
0	4482	278

Stop Event

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

Counts

24 → 56

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

eval6.0ms (0.4%)

Memory: 9.5MiB live, 9.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 865 to 183 computations (78.8% saved)

prune9.0ms (0.6%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Accuracy

100.0%

Counts

55 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))
▶	66.3%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 17 to 15 computations (11.8% saved)

series3.0ms (0.2%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Counts

8 → 20

Calls

Call 1

Inputs
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(*.f64 x a)
x
a
(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))
(fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64))
#s(literal 1 binary64)
#s(literal 0 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 (* x a) #s(hole binary64 (* a x)))
#s(approx a #s(hole binary64 a))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* a x)))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* a (+ x (* 1/2 (* a (pow x 2)))))))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 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 (+ (* (* x a) 1) 0) #s(hole binary64 (* a x)))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (- (exp (* a x)) 1)))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (- (exp (* a x)) 1)))
#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 (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* x (+ a (* 1/2 (* (pow a 2) x))))))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))))

Calls

6 calls:

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

rewrite46.0ms (3.3%)

Memory

-12.8MiB live, 30.8MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	419
0	94	364
0	470	340

Stop Event

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

Counts

28 → 57

Calls

Call 1

Inputs
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(*.f64 x a)
x
a
(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))
(fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64))
#s(literal 1 binary64)
#s(literal 0 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 (* x a) #s(hole binary64 (* a x)))
#s(approx a #s(hole binary64 a))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* a x)))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* a (+ x (* 1/2 (* a (pow x 2)))))))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 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 (+ (* (* x a) 1) 0) #s(hole binary64 (* a x)))
#s(approx (- (exp (* a x)) 1) #s(hole binary64 (- (exp (* a x)) 1)))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (- (exp (* a x)) 1)))
#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 (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* x (+ a (* 1/2 (* (pow a 2) x))))))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))))
#s(approx (- (exp (+ (* (* x a) 1) 0)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))))

Outputs
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(.f64 (.f64 x a) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x a))
(.f64 x (.f64 a #s(literal 1 binary64)))
(*.f64 x a)
(*.f64 a x)
(/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 x a) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 x a) (.f64 x a) (-.f64 #s(literal 0 binary64) (.f64 (*.f64 x a) #s(literal 0 binary64)))))
(fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x a) #s(literal 0 binary64))
(fma.f64 x (*.f64 a #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 x a #s(literal 0 binary64))
(fma.f64 a x #s(literal 0 binary64))
(+.f64 (*.f64 x a) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x a))
x
a
(/.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 a) x) (pow.f64 (exp.f64 a) x)) #s(literal 1 binary64)) (fma.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (pow.f64 (exp.f64 a) x) (pow.f64 (exp.f64 a) x) (+.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 a) x))))
(expm1.f64 (*.f64 x a))
(-.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))
(.f64 (.f64 x a) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x a))
(.f64 x (.f64 a #s(literal 1 binary64)))
(*.f64 x a)
(*.f64 a x)
(/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 x a) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 x a) (.f64 x a) (-.f64 #s(literal 0 binary64) (.f64 (*.f64 x a) #s(literal 0 binary64)))))
(fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x a) #s(literal 0 binary64))
(fma.f64 x (*.f64 a #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 x a #s(literal 0 binary64))
(fma.f64 a x #s(literal 0 binary64))
(+.f64 (*.f64 x a) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x a))
#s(literal 1 binary64)
#s(literal 0 binary64)
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 x x) a) #s(literal 1/2 binary64) x) a))
#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 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a))
#s(approx (* x a) (*.f64 x a))
#s(approx a a)
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 x x) a) #s(literal 1/2 binary64) x) a))
#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 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a))
#s(approx (* x a) (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (expm1.f64 (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (expm1.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 (pow.f64 a #s(literal 4 binary64)) x) #s(literal 1/24 binary64) (.f64 (.f64 (.f64 a a) a) #s(literal 1/6 binary64))) x (.f64 (*.f64 a a) #s(literal 1/2 binary64))) x a) x))
#s(approx x x)
#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 (pow.f64 a #s(literal 4 binary64)) x) #s(literal 1/24 binary64) (.f64 (.f64 (.f64 a a) a) #s(literal 1/6 binary64))) x (.f64 (*.f64 a a) #s(literal 1/2 binary64))) x a) x))

eval6.0ms (0.4%)

Memory: 7.9MiB live, 7.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 683 to 146 computations (78.6% saved)

prune12.0ms (0.9%)

Memory

14.6MiB live, 14.6MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	51	3	54

Accuracy

100.0%

Counts

54 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.5%	(expm1.f64 (fma.f64 (/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64)))
✓	100.0%	(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))
✓	66.3%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Status

Accuracy

Program

▶

59.5%

(expm1.f64 (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 x a) (*.f64 x a)) #s(literal 0 binary64)) (-.f64 (*.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64)))

✓

100.0%

(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))

✓

66.3%

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

Compiler

Compiled 36 to 26 computations (27.8% saved)

series25.0ms (1.8%)

Memory

-34.5MiB live, 13.3MiB allocated; 17ms collecting garbage

Counts

11 → 16

Calls

Call 1

Inputs
(expm1.f64 (fma.f64 (/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64)))
(fma.f64 (/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64))
(/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64)))
(-.f64 (.f64 (.f64 x a) (*.f64 x a)) #s(literal 0 binary64))
(.f64 (.f64 x a) (*.f64 x a))
(*.f64 x a)
x
a
#s(literal 0 binary64)
(-.f64 (*.f64 x a) #s(literal 0 binary64))
#s(literal 1 binary64)

Outputs
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* a x)))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* a (+ x (* 1/2 (* a (pow x 2)))))))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 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 (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0) #s(hole binary64 (* a x)))
#s(approx (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) #s(hole binary64 (* a x)))
#s(approx (- (* (* x a) (* x a)) 0) #s(hole binary64 (* (pow a 2) (pow x 2))))
#s(approx (* (* x a) (* x a)) #s(hole binary64 (* (pow a 2) (pow x 2))))
#s(approx (* x a) #s(hole binary64 (* a x)))
#s(approx a #s(hole binary64 a))
#s(approx (- (* x a) 0) #s(hole binary64 (* a x)))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (- (exp (* a x)) 1)))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* x (+ a (* 1/2 (* (pow a 2) x))))))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 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))

Calls

6 calls:

Time	Variable		Point	Expression
19.0ms	a	@	0	((- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0) (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) (- (* (* x a) (* x a)) 0) (* (* x a) (* x a)) (* x a) x a 0 (- (* x a) 0) 1)
1.0ms	a	@	inf	((- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0) (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) (- (* (* x a) (* x a)) 0) (* (* x a) (* x a)) (* x a) x a 0 (- (* x a) 0) 1)
1.0ms	a	@	-inf	((- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0) (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) (- (* (* x a) (* x a)) 0) (* (* x a) (* x a)) (* x a) x a 0 (- (* x a) 0) 1)
1.0ms	x	@	-inf	((- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0) (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) (- (* (* x a) (* x a)) 0) (* (* x a) (* x a)) (* x a) x a 0 (- (* x a) 0) 1)
1.0ms	x	@	inf	((- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0) (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) (- (* (* x a) (* x a)) 0) (* (* x a) (* x a)) (* x a) x a 0 (- (* x a) 0) 1)

rewrite62.0ms (4.4%)

Memory

8.2MiB live, 51.1MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	458
0	107	327
0	521	313

Stop Event

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

Counts

27 → 80

Calls

Call 1

Inputs
(expm1.f64 (fma.f64 (/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64)))
(fma.f64 (/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64))
(/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64)))
(-.f64 (.f64 (.f64 x a) (*.f64 x a)) #s(literal 0 binary64))
(.f64 (.f64 x a) (*.f64 x a))
(*.f64 x a)
x
a
#s(literal 0 binary64)
(-.f64 (*.f64 x a) #s(literal 0 binary64))
#s(literal 1 binary64)
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* a x)))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* a (+ x (* 1/2 (* a (pow x 2)))))))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 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 (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0) #s(hole binary64 (* a x)))
#s(approx (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) #s(hole binary64 (* a x)))
#s(approx (- (* (* x a) (* x a)) 0) #s(hole binary64 (* (pow a 2) (pow x 2))))
#s(approx (* (* x a) (* x a)) #s(hole binary64 (* (pow a 2) (pow x 2))))
#s(approx (* x a) #s(hole binary64 (* a x)))
#s(approx a #s(hole binary64 a))
#s(approx (- (* x a) 0) #s(hole binary64 (* a x)))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (- (exp (* a x)) 1)))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* x (+ a (* 1/2 (* (pow a 2) x))))))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) #s(hole binary64 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 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))

Outputs
(/.f64 (-.f64 (.f64 (exp.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) (exp.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)))) #s(literal 1 binary64)) (fma.f64 (exp.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) #s(literal 1 binary64) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (exp.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) (exp.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))))))
(expm1.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)))
(-.f64 (exp.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x))) #s(literal 1 binary64))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)))
(/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) #s(literal 0 binary64)) (-.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) #s(literal 0 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) #s(literal 3 binary64)) #s(literal 0 binary64)) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) (-.f64 #s(literal 0 binary64) (.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64))) (neg.f64 (.f64 a x)))
(/.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) (.f64 a x))
(fma.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)) #s(literal 0 binary64))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) (/.f64 #s(literal 0 binary64) (.f64 a x)))
(+.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)))
(/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) #s(literal 0 binary64)) (-.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) #s(literal 0 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) #s(literal 3 binary64)) #s(literal 0 binary64)) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x))) (-.f64 #s(literal 0 binary64) (.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64))) (neg.f64 (.f64 a x)))
(/.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) (.f64 a x))
(fma.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)) #s(literal 0 binary64))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a x)) (/.f64 #s(literal 0 binary64) (.f64 a x)))
(+.f64 (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 a x)))
(.f64 (.f64 (*.f64 a x) x) a)
(.f64 (neg.f64 (.f64 a x)) (neg.f64 (*.f64 a x)))
(.f64 (fabs.f64 (.f64 a x)) (fabs.f64 (*.f64 a x)))
(.f64 (.f64 a a) (*.f64 x x))
(.f64 (.f64 x x) (*.f64 a a))
(.f64 (.f64 a x) (*.f64 a x))
(.f64 x (.f64 a (*.f64 a x)))
(pow.f64 (*.f64 a x) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) (pow.f64 (.f64 a x) #s(literal 2 binary64))) #s(literal 0 binary64)) (fma.f64 (.f64 a a) (*.f64 x x) #s(literal 0 binary64)))
(/.f64 (-.f64 (pow.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) (.f64 (pow.f64 (*.f64 a x) #s(literal 2 binary64)) #s(literal 0 binary64)))))
(-.f64 (pow.f64 (*.f64 a x) #s(literal 2 binary64)) #s(literal 0 binary64))
(.f64 (.f64 (*.f64 a x) x) a)
(.f64 (neg.f64 (.f64 a x)) (neg.f64 (*.f64 a x)))
(.f64 (fabs.f64 (.f64 a x)) (fabs.f64 (*.f64 a x)))
(.f64 (.f64 a a) (*.f64 x x))
(.f64 (.f64 x x) (*.f64 a a))
(.f64 (.f64 a x) (*.f64 a x))
(.f64 x (.f64 a (*.f64 a x)))
(pow.f64 (*.f64 a x) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) (pow.f64 (.f64 a x) #s(literal 2 binary64))) #s(literal 0 binary64)) (fma.f64 (.f64 a a) (*.f64 x x) #s(literal 0 binary64)))
(/.f64 (-.f64 (pow.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) (.f64 (pow.f64 (*.f64 a x) #s(literal 2 binary64)) #s(literal 0 binary64)))))
(-.f64 (pow.f64 (*.f64 a x) #s(literal 2 binary64)) #s(literal 0 binary64))
(*.f64 a x)
(*.f64 x a)
(/.f64 (-.f64 (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 (.f64 a x) x) a (+.f64 #s(literal 0 binary64) (.f64 (*.f64 a x) #s(literal 0 binary64)))))
(/.f64 (pow.f64 (*.f64 a x) #s(literal 2 binary64)) (fma.f64 a x #s(literal 0 binary64)))
(-.f64 (*.f64 a x) #s(literal 0 binary64))
x
a
#s(literal 0 binary64)
(*.f64 a x)
(*.f64 x a)
(/.f64 (-.f64 (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 (.f64 a x) x) a (+.f64 #s(literal 0 binary64) (.f64 (*.f64 a x) #s(literal 0 binary64)))))
(/.f64 (pow.f64 (*.f64 a x) #s(literal 2 binary64)) (fma.f64 a x #s(literal 0 binary64)))
(-.f64 (*.f64 a x) #s(literal 0 binary64))
#s(literal 1 binary64)
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (*.f64 a x))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (.f64 (fma.f64 (.f64 (*.f64 x x) a) #s(literal 1/2 binary64) x) a))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 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 (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a))
#s(approx (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) (*.f64 a x))
#s(approx (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) (*.f64 a x))
#s(approx (- (* (* x a) (* x a)) 0) (pow.f64 (*.f64 a x) #s(literal 2 binary64)))
#s(approx (- (* (* x a) (* x a)) 0) (pow.f64 (*.f64 a x) #s(literal 2 binary64)))
#s(approx (- (* x a) 0) (*.f64 a x))
#s(approx a a)
#s(approx (- (* x a) 0) (*.f64 a x))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (expm1.f64 (*.f64 a x)))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 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 (+ (* (/ (- (* (* x a) (* x a)) 0) (- (* x a) 0)) 1) 0)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 a #s(literal 4 binary64)) x) #s(literal 1/24 binary64) (.f64 (.f64 (.f64 a a) a) #s(literal 1/6 binary64))) x (.f64 (*.f64 a a) #s(literal 1/2 binary64))) x a) x))
#s(approx x x)

eval8.0ms (0.5%)

Memory: 14.9MiB live, 14.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 692 to 291 computations (82.8% saved)

prune23.0ms (1.7%)

Memory

-11.4MiB live, 32.7MiB allocated; 8ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	71	3	74

Accuracy

100.0%

Counts

74 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	59.5%	(expm1.f64 (fma.f64 (/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64)))
✓	100.0%	(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))
✓	66.3%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Status

Accuracy

Program

✓

59.5%

(expm1.f64 (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 x a) (*.f64 x a)) #s(literal 0 binary64)) (-.f64 (*.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64)))

✓

100.0%

(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))

✓

66.3%

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

Compiler

Compiled 78 to 47 computations (39.7% saved)

regimes8.0ms (0.6%)

Memory

18.4MiB live, 18.4MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))
(expm1.f64 (fma.f64 (/.f64 (-.f64 (.f64 (.f64 x a) (.f64 x a)) #s(literal 0 binary64)) (-.f64 (.f64 x a) #s(literal 0 binary64))) #s(literal 1 binary64) #s(literal 0 binary64)))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Outputs
(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))

Calls

5 calls:

2.0ms	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)

regimes5.0ms (0.4%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

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
66.3%	1	`(*.f64 a x)`
66.3%	1	`(exp.f64 (*.f64 a x))`
66.3%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
66.3%	1	`a`
66.3%	1	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

simplify45.0ms (3.2%)

Memory

-36.0MiB live, 67.2MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	18	17
2	36	17
3	88	17
4	307	17
5	2578	17

Stop Event

1×	node limit

Calls

Call 1

Inputs
(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))
#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Outputs
(expm1.f64 (fma.f64 (*.f64 x a) #s(literal 1 binary64) #s(literal 0 binary64)))
#s(approx (- (exp (* a x)) 1) (*.f64 x a))

derivations31.0ms (2.2%)

Memory

-14.2MiB live, 31.8MiB allocated; 2ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 17 to 12 computations (29.4% saved)

preprocess16.0ms (1.2%)

Memory: 34.7MiB live, 34.7MiB allocated; 0ms collecting garbage
Remove: (sort a x)
Compiler: Compiled 60 to 50 computations (16.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze27.0ms (1.9%)

sample608.0ms (43.1%)

explain70.0ms (5%)

preprocess233.0ms (16.5%)

eval0.0ms (0%)

prune0.0ms (0%)

series5.0ms (0.4%)

rewrite162.0ms (11.5%)

eval6.0ms (0.4%)

prune9.0ms (0.6%)

series3.0ms (0.2%)

rewrite46.0ms (3.3%)

eval6.0ms (0.4%)

prune12.0ms (0.9%)

series25.0ms (1.8%)

rewrite62.0ms (4.4%)

eval8.0ms (0.5%)

prune23.0ms (1.7%)

regimes8.0ms (0.6%)

regimes5.0ms (0.4%)

simplify45.0ms (3.2%)

derivations31.0ms (2.2%)

preprocess16.0ms (1.2%)

end0.0ms (0%)

Profiling