Metrics for expax (section 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze17.0ms (0.3%)

Memory

37.3MiB live, 37.3MiB allocated

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)

sample885.0ms (13.4%)

Memory

-13.5MiB live, 724.6MiB allocated

Samples

630.0ms	8 256×	0	valid
14.0ms	304×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 223.0ms

ival-mult: 102.0ms (45.8% of total)

ival-expm1: 61.0ms (27.4% of total)

ival->: 49.0ms (22% of total)

exact: 7.0ms (3.1% of total)

ival-assert: 4.0ms (1.8% of total)

Bogosity

explain64.0ms (1%)

Memory

33.5MiB live, 72.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
117	1	(-9.912615776335613e-270 1.3766328419543502e-54)	-	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
0	0	-	-	`a`
0	0	-	-	`(exp.f64 (*.f64 a x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 a x)`
0	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	118	0

Confusion

	Predicted +	Predicted -
+	117	0
-	1	138

Precision

0.9915254237288136

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	0	0
-	1	0	138

Precision?

0.9915254237288136

Recall?

1.0

Freqs

test

number	freq
0	138
1	118

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 42 to 22 computations (47.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-exp: 4.0ms (34.9% of total)

ival-mult: 4.0ms (34.9% of total)

ival-expm1: 3.0ms (26.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess19.0ms (0.3%)

Memory

-28.2MiB live, 15.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	42	36
2	73	34
3	108	34
4	141	34
5	165	34
6	204	34
7	226	34
8	240	34
9	251	34
10	252	34
0	6	6
0	9	6
1	17	6
2	20	6
0	20	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

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 x a))

Symmetry

(sort a x)

Compiler

Compiled 6 to 6 computations (0% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.4%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 6 to 6 computations (0% saved)

simplify3.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-6144	(exp.f64 (*.f64 a x))
cost-diff	0	(*.f64 a x)
cost-diff	6336	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	9	16
1	17	16
2	20	16
0	20	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

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

localize16.0ms (0.2%)

Memory

18.5MiB live, 18.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a x)
accuracy	0.020195019536884032	(exp.f64 (*.f64 a x))
accuracy	27.230365264735624	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Samples

12.0ms

256×

valid

Compiler

Compiled 18 to 8 computations (55.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-exp: 2.0ms (36.4% of total)

ival-mult: 2.0ms (36.4% of total)

ival-expm1: 2.0ms (36.4% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs
#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())
#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())

Inputs

#s(alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())

#s(alt (*.f64 a x) (patch (*.f64 a x) #<representation binary64>) () ())

#s(alt (exp.f64 (*.f64 a x)) (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())

Outputs
#s(alt (* a x) (taylor 0 a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))) (taylor 0 a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a x)) (taylor 0 a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2)))))) (taylor 0 a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))) (taylor 0 a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor inf a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor inf a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor inf a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor inf a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor inf a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor inf a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor inf a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor inf a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor inf a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor inf a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor inf a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor inf a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf a) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf a) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf a) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ a (* 1/2 (* (pow a 2) x)))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3)))))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a x)) (taylor 0 x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x))))) (taylor 0 x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))) (taylor 0 x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor inf x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor inf x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor inf x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor inf x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor inf x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor inf x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor inf x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor inf x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf x) (#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt (exp.f64 (.f64 a x)) (patch (exp.f64 (.f64 a x)) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify205.0ms (3.1%)

Memory

-11.1MiB live, 63.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	432
1	195	432
2	526	424
3	1045	424
4	1672	424
5	1873	424
6	1900	424
7	1920	424
8	1934	424
9	1937	424
10	1937	424
11	2619	420
12	3094	420
13	4061	420
14	4062	420
15	4062	420
16	4190	420
17	4190	420
18	6071	416
19	6279	416
20	6321	416
21	6335	416
22	6335	416
23	6511	416
24	6849	416
25	6849	416
26	7408	416
0	7408	360

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

Inputs
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* a x)
(* a x)
(* a x)
(* a x)
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* a x)
(* a x)
(* a x)
(* a x)
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))

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

rewrite62.0ms (0.9%)

Memory

0.1MiB live, 37.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
0	9	13
1	30	13
2	152	13
0	1346	11

Stop Event

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

Counts

3 → 111

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
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#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval38.0ms (0.6%)

Memory: 2.9MiB live, 44.8MiB allocated
Compiler: Compiled 3 200 to 339 computations (89.4% saved)

prune12.0ms (0.2%)

Memory

-16.2MiB live, 20.8MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	176	7	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	7	184

Accuracy

100.0%

Counts

184 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	24.3%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
▶	22.8%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 x a))
	65.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
	66.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
▶	61.8%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
▶	66.6%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 134 to 106 computations (20.9% saved)

simplify10.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(.f64 (.f64 a a) x)
cost-diff	0	(fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a)
cost-diff	0	(.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
cost-diff	0	(fma.f64 x a #s(literal 1 binary64))
cost-diff	0	#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	0	(*.f64 x a)
cost-diff	0	#s(approx (- (exp (* a x)) 1) (*.f64 x a))
cost-diff	0	#s(approx (exp (* a x)) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	(*.f64 x a)
cost-diff	0	(expm1.f64 (*.f64 x a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	112
0	31	108
1	52	108
2	75	108
3	115	108
4	157	108
5	173	108
6	192	108
7	192	108
8	259	108
9	261	108
0	261	108

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize41.0ms (0.6%)

Memory

16.4MiB live, 53.2MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a a)
accuracy	1.4428482423582345	(.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)
accuracy	6.031173579992508	(.f64 (.f64 a a) x)
accuracy	22.134001700856427	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
accuracy	0	(fma.f64 x a #s(literal 1 binary64))
accuracy	21.872853375281892	#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
accuracy	27.230365264735624	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0	(*.f64 x a)
accuracy	21.383766887641624	#s(approx (- (exp (* a x)) 1) (*.f64 x a))
accuracy	21.81900086498602	#s(approx (exp (* a x)) #s(literal 1 binary64))
accuracy	27.230365264735624	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(*.f64 x a)
accuracy	0.028007519536884032	(expm1.f64 (*.f64 x a))

Samples

30.0ms

256×

valid

Compiler

Compiled 90 to 17 computations (81.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 11.0ms (59.3% of total)

ival-exp: 3.0ms (16.2% of total)

ival-expm1: 3.0ms (16.2% of total)

ival-add: 2.0ms (10.8% of total)

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

exact: 0.0ms (0% of total)

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

series41.0ms (0.6%)

Memory

-19.2MiB live, 18.7MiB allocated

Counts

13 → 300

Calls

Call 1

Inputs
#s(alt (expm1.f64 (.f64 x a)) (patch (expm1.f64 (.f64 x a)) #<representation binary64>) () ())
#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (exp (* a x)) #s(literal 1 binary64)) (patch #s(approx (exp (* a x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (exp (* a x)) 1) (.f64 x a)) (patch #s(approx (- (exp ( a x)) 1) (*.f64 x a)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x a #s(literal 1 binary64)) (patch (fma.f64 x a #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) (patch (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) (patch (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) #<representation binary64>) () ())
#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())
#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())

Outputs
#s(alt (* a x) (taylor 0 a) (#s(alt (expm1.f64 (.f64 x a)) (patch (expm1.f64 (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (expm1.f64 (.f64 x a)) (patch (expm1.f64 (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt (expm1.f64 (.f64 x a)) (patch (expm1.f64 (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))) (taylor 0 a) (#s(alt (expm1.f64 (.f64 x a)) (patch (expm1.f64 (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 a) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x a #s(literal 1 binary64)) (patch (fma.f64 x a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 a) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x a #s(literal 1 binary64)) (patch (fma.f64 x a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) (pow x 2))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) (patch (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) (patch (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) (patch (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) (patch (.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) (patch (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) (patch (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) (patch (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) (patch (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	a	@	inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (* a a))
2.0ms	x	@	-inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (* a a))
1.0ms	a	@	-inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (* a a))
1.0ms	x	@	inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (* a a))
1.0ms	a	@	0	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (* a a))

simplify461.0ms (7%)

Memory

-24.7MiB live, 263.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	2132
1	318	2132
2	823	2104
3	2493	2104
4	6842	2104
0	8433	1806

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 298

Calls

Call 1

Inputs
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
1
(+ 1 (* a x))
(+ 1 (* a x))
(+ 1 (* a x))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
a
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* a (+ x (/ 1 a)))
(* a (+ x (/ 1 a)))
(* a (+ x (/ 1 a)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* -1 (* a (- (* -1 x) (/ 1 a))))
(* -1 (* a (- (* -1 x) (/ 1 a))))
(* -1 (* a (- (* -1 x) (/ 1 a))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
1
(+ 1 (* a x))
(+ 1 (* a x))
(+ 1 (* a x))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
a
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* x (+ a (/ 1 x)))
(* x (+ a (/ 1 x)))
(* x (+ a (/ 1 x)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) x))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* a x)
(* a x)
(* a x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* -1 (* x (- (* -1 a) (/ 1 x))))
(* -1 (* x (- (* -1 a) (/ 1 x))))
(* -1 (* x (- (* -1 a) (/ 1 x))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) x))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)

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

rewrite189.0ms (2.9%)

Memory

-5.5MiB live, 150.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	98
0	31	94
1	121	94
2	727	94
3	6903	94
0	8442	94

Stop Event

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

Counts

13 → 554

Calls

Call 1

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

Outputs
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eval113.0ms (1.7%)

Memory: -7.3MiB live, 143.8MiB allocated
Compiler: Compiled 17 064 to 1 866 computations (89.1% saved)

prune31.0ms (0.5%)

Memory

24.8MiB live, 63.8MiB allocated

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	914	6	920
Fresh	0	2	2
Picked	1	4	5
Done	0	0	0
Total	915	12	927

Accuracy

100.0%

Counts

927 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	23.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	24.3%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
▶	24.3%	(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	22.8%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
▶	33.3%	(exp.f64 (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
	65.4%	#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
	65.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
▶	66.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
▶	65.4%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
	22.2%	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a a) x) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
✓	66.6%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 223 to 175 computations (21.5% saved)

simplify50.0ms (0.8%)

Memory

-13.5MiB live, 25.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal -1 binary64))
cost-diff	448	(.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64))
cost-diff	6336	(log.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal -1 binary64)))
cost-diff	12800	(exp.f64 (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
cost-diff	0	(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
cost-diff	0	(fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))
cost-diff	0	#s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	0	(.f64 (.f64 a x) a)
cost-diff	0	(fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a)
cost-diff	0	(.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x)
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
cost-diff	0	(*.f64 a x)
cost-diff	0	#s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	128	(+.f64 (*.f64 a x) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
cost-diff	0	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	256
0	62	258
1	109	255
2	195	245
3	325	245
4	762	245
5	1116	245
6	1560	245
7	1898	245
8	2061	245
9	2089	245
10	2309	245
11	2350	245
12	2359	245
13	2359	245
14	2561	245
0	2561	242

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize132.0ms (2%)

Memory

-16.9MiB live, 109.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.020195019536884032	(expm1.f64 (*.f64 a x))
accuracy	0.078125	(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal -1 binary64))
accuracy	1.4235144263679453	(exp.f64 (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
accuracy	6.053327352601546	(log.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal -1 binary64)))
accuracy	0	(*.f64 x a)
accuracy	0.00390625	(fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))
accuracy	0.4210640954791848	#s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64)))
accuracy	15.204724457463252	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0	(.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x)
accuracy	0	(*.f64 a x)
accuracy	0.0390625	(.f64 (.f64 a x) a)
accuracy	0.4228070609601263	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
accuracy	0	(*.f64 a x)
accuracy	0.00390625	(+.f64 (*.f64 a x) #s(literal 1 binary64))
accuracy	0.42735442871393164	#s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64)))
accuracy	15.204724457463252	(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0	(*.f64 x a)
accuracy	0.00390625	(.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))
accuracy	0.11328125	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.4153640850166813	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))

Samples

47.0ms	165×	0	invalid
45.0ms	91×	0	valid

Compiler

Compiled 221 to 33 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-mult: 50.0ms (68.2% of total)

ival-add: 7.0ms (9.5% of total)

ival-exp: 4.0ms (5.5% of total)

const: 4.0ms (5.5% of total)

ival-pow: 4.0ms (5.5% of total)

ival-expm1: 2.0ms (2.7% of total)

ival-log: 2.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series165.0ms (2.5%)

Memory

20.3MiB live, 170.4MiB allocated

Counts

24 → 564

Calls

Call 1

Inputs
#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (patch (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) #<representation binary64>) () ())
#s(alt (+.f64 (.f64 a x) #s(literal 1 binary64)) (patch (+.f64 (.f64 a x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (exp (* a x)) (+.f64 (.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp ( a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (exp (* a x)) (+.f64 (.f64 a x) #s(literal 1 binary64))) (patch #s(approx (exp ( a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 a x) (patch (.f64 a x) #<representation binary64>) () ())
#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x) (patch (.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) (patch (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) #<representation binary64>) () ())
#s(alt (.f64 (.f64 a x) a) (patch (.f64 (.f64 a x) a) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) (patch (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) #<representation binary64>) () ())
#s(alt (exp.f64 (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) (patch (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) (patch (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (expm1.f64 (.f64 a x)) (patch (expm1.f64 (.f64 a x)) #<representation binary64>) () ())

Outputs
#s(alt (* a x) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 a) (#s(alt (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* a x))) (taylor 0 a) (#s(alt (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))) (taylor 0 a) (#s(alt (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (log (/ 1 (- (exp (* a x)) 1)))) (taylor -inf x) (#s(alt (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 (- (exp (* a x)) 1)))) (taylor -inf x) (#s(alt (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 (- (exp (* a x)) 1)))) (taylor -inf x) (#s(alt (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 (- (exp (* a x)) 1)))) (taylor -inf x) (#s(alt (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (- (exp (* a x)) 1)) (taylor -inf x) (#s(alt (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) (patch (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (- (exp (* a x)) 1)) (taylor -inf x) (#s(alt (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) (patch (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (- (exp (* a x)) 1)) (taylor -inf x) (#s(alt (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) (patch (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (- (exp (* a x)) 1)) (taylor -inf x) (#s(alt (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) (patch (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf x) (#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf x) (#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf x) (#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor -inf x) (#s(alt (.f64 x a) (patch (.f64 x a) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* a x)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 a) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 a) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 a) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (expm1.f64 (.f64 a x)) (patch (expm1.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (expm1.f64 (.f64 a x)) (patch (expm1.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (expm1.f64 (.f64 a x)) (patch (expm1.f64 (.f64 a x)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (expm1.f64 (.f64 a x)) (patch (expm1.f64 (.f64 a x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
46.0ms	x	@	-inf	((- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (+ (* a x) 1) (- (exp (* a x)) 1) (exp (* a x)) (* a x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (* (+ (* 1/2 (* x a)) 1) a) (exp (* (log (pow (- (exp (* a x)) 1) -1)) -1)) (log (pow (- (exp (* a x)) 1) -1)) (* (log (pow (- (exp (* a x)) 1) -1)) -1) (pow (- (exp (* a x)) 1) -1) (* 1/6 x) (* x a) (+ (* 1/2 (* x a)) 1) (- (exp (* a x)) 1))
35.0ms	a	@	-inf	((- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (+ (* a x) 1) (- (exp (* a x)) 1) (exp (* a x)) (* a x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (* (+ (* 1/2 (* x a)) 1) a) (exp (* (log (pow (- (exp (* a x)) 1) -1)) -1)) (log (pow (- (exp (* a x)) 1) -1)) (* (log (pow (- (exp (* a x)) 1) -1)) -1) (pow (- (exp (* a x)) 1) -1) (* 1/6 x) (* x a) (+ (* 1/2 (* x a)) 1) (- (exp (* a x)) 1))
35.0ms	a	@	inf	((- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (+ (* a x) 1) (- (exp (* a x)) 1) (exp (* a x)) (* a x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (* (+ (* 1/2 (* x a)) 1) a) (exp (* (log (pow (- (exp (* a x)) 1) -1)) -1)) (log (pow (- (exp (* a x)) 1) -1)) (* (log (pow (- (exp (* a x)) 1) -1)) -1) (pow (- (exp (* a x)) 1) -1) (* 1/6 x) (* x a) (+ (* 1/2 (* x a)) 1) (- (exp (* a x)) 1))
19.0ms	x	@	inf	((- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (+ (* a x) 1) (- (exp (* a x)) 1) (exp (* a x)) (* a x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (* (+ (* 1/2 (* x a)) 1) a) (exp (* (log (pow (- (exp (* a x)) 1) -1)) -1)) (log (pow (- (exp (* a x)) 1) -1)) (* (log (pow (- (exp (* a x)) 1) -1)) -1) (pow (- (exp (* a x)) 1) -1) (* 1/6 x) (* x a) (+ (* 1/2 (* x a)) 1) (- (exp (* a x)) 1))
5.0ms	a	@	0	((- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (+ (* a x) 1) (- (exp (* a x)) 1) (exp (* a x)) (* a x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (* (+ (* 1/2 (* x a)) 1) a) (exp (* (log (pow (- (exp (* a x)) 1) -1)) -1)) (log (pow (- (exp (* a x)) 1) -1)) (* (log (pow (- (exp (* a x)) 1) -1)) -1) (pow (- (exp (* a x)) 1) -1) (* 1/6 x) (* x a) (+ (* 1/2 (* x a)) 1) (- (exp (* a x)) 1))

simplify225.0ms (3.4%)

Memory

8.5MiB live, 278.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	357	5090
1	1254	4976
2	4365	4816
0	8087	4196

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 560

Calls

Call 1

Inputs
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(* 1/2 a)
(* a (+ 1/2 (* 1/6 (* a x))))
(* a (+ 1/2 (* 1/6 (* a x))))
(* a (+ 1/2 (* 1/6 (* a x))))
1
(+ 1 (* a x))
(+ 1 (* a x))
(+ 1 (* a x))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
a
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
a
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(+ (log (/ 1 x)) (* -1 (log a)))
(+ (log (/ 1 x)) (+ (* -1 (log a)) (* -1/2 (* a x))))
(+ (log (/ 1 x)) (+ (* -1 (log a)) (* a (+ (* -1/2 x) (* 1/2 (* a (+ (* -2 (* x (+ (* -1/4 x) (* 1/6 x)))) (* -1/4 (pow x 2)))))))))
(+ (log (/ 1 x)) (+ (* -1 (log a)) (* a (+ (* -1/2 x) (* a (+ (* 1/6 (* a (+ (* -6 (* x (+ (* -1/2 (* x (+ (* -1/4 x) (* 1/6 x)))) (+ (* -1/12 (pow x 2)) (* 1/24 (pow x 2)))))) (+ (* -3 (* (pow x 2) (+ (* -1/4 x) (* 1/6 x)))) (* -1/4 (pow x 3)))))) (* 1/2 (+ (* -2 (* x (+ (* -1/4 x) (* 1/6 x)))) (* -1/4 (pow x 2))))))))))
(* -1 (+ (log (/ 1 x)) (* -1 (log a))))
(+ (* -1 (+ (log (/ 1 x)) (* -1 (log a)))) (* 1/2 (* a x)))
(+ (* -1 (+ (log (/ 1 x)) (* -1 (log a)))) (* a (+ (* -1/2 (* a (+ (* -2 (* x (+ (* -1/4 x) (* 1/6 x)))) (* -1/4 (pow x 2))))) (* 1/2 x))))
(+ (* -1 (+ (log (/ 1 x)) (* -1 (log a)))) (* a (+ (* 1/2 x) (* a (+ (* -1/2 (+ (* -2 (* x (+ (* -1/4 x) (* 1/6 x)))) (* -1/4 (pow x 2)))) (* -1/6 (* a (+ (* -6 (* x (+ (* -1/2 (* x (+ (* -1/4 x) (* 1/6 x)))) (+ (* -1/12 (pow x 2)) (* 1/24 (pow x 2)))))) (+ (* -3 (* (pow x 2) (+ (* -1/4 x) (* 1/6 x)))) (* -1/4 (pow x 3)))))))))))
(/ 1 (* a x))
(/ (+ (* -1/2 a) (/ 1 x)) a)
(/ (+ (* a (- (* -1 (* a (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)
(/ (+ (* a (- (* a (- (* -1 (* a (+ (* -1/2 (* x (+ (* -1/4 x) (* 1/6 x)))) (+ (* -1/12 (pow x 2)) (* 1/24 (pow x 2)))))) (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)
(* a x)
(* a x)
(* a x)
(* a x)
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* 1/6 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* a x)
(* a (+ x (/ 1 a)))
(* a (+ x (/ 1 a)))
(* a (+ x (/ 1 a)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* a x)
(* a x)
(* a x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow a 2)) (/ x a))))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow a 2)) (/ x a))))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(* a x)
(* a x)
(* a x)
(* a x)
(* 1/2 (* a x))
(* a (+ (* 1/2 x) (/ 1 a)))
(* a (+ (* 1/2 x) (/ 1 a)))
(* a (+ (* 1/2 x) (/ 1 a)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(* 1/6 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* a x)
(* -1 (* a (- (* -1 x) (/ 1 a))))
(* -1 (* a (- (* -1 x) (/ 1 a))))
(* -1 (* a (- (* -1 x) (/ 1 a))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* a x)
(* a x)
(* a x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* -1 (/ (- (* -1 x) (/ 1 a)) a)) (* 1/2 (pow x 2))))
(* (pow a 2) (+ (* -1 (/ (- (* -1 x) (/ 1 a)) a)) (* 1/2 (pow x 2))))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(* a x)
(* a x)
(* a x)
(* a x)
(* 1/2 (* a x))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
(* -1 (* a (- (* -1/2 x) (/ 1 a))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(* 1/2 a)
(+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))
(+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))
(+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))
1
(+ 1 (* a x))
(+ 1 (* a x))
(+ 1 (* a x))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
a
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
a
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(+ (log (/ 1 a)) (* -1 (log x)))
(+ (log (/ 1 a)) (+ (* -1 (log x)) (* -1/2 (* a x))))
(+ (log (/ 1 a)) (+ (* -1 (log x)) (* x (+ (* -1/2 a) (* 1/2 (* x (+ (* -2 (* a (+ (* -1/4 a) (* 1/6 a)))) (* -1/4 (pow a 2)))))))))
(+ (log (/ 1 a)) (+ (* -1 (log x)) (* x (+ (* -1/2 a) (* x (+ (* 1/6 (* x (+ (* -6 (* a (+ (* -1/2 (* a (+ (* -1/4 a) (* 1/6 a)))) (+ (* -1/12 (pow a 2)) (* 1/24 (pow a 2)))))) (+ (* -3 (* (pow a 2) (+ (* -1/4 a) (* 1/6 a)))) (* -1/4 (pow a 3)))))) (* 1/2 (+ (* -2 (* a (+ (* -1/4 a) (* 1/6 a)))) (* -1/4 (pow a 2))))))))))
(* -1 (+ (log (/ 1 a)) (* -1 (log x))))
(+ (* -1 (+ (log (/ 1 a)) (* -1 (log x)))) (* 1/2 (* a x)))
(+ (* -1 (+ (log (/ 1 a)) (* -1 (log x)))) (* x (+ (* -1/2 (* x (+ (* -2 (* a (+ (* -1/4 a) (* 1/6 a)))) (* -1/4 (pow a 2))))) (* 1/2 a))))
(+ (* -1 (+ (log (/ 1 a)) (* -1 (log x)))) (* x (+ (* 1/2 a) (* x (+ (* -1/2 (+ (* -2 (* a (+ (* -1/4 a) (* 1/6 a)))) (* -1/4 (pow a 2)))) (* -1/6 (* x (+ (* -6 (* a (+ (* -1/2 (* a (+ (* -1/4 a) (* 1/6 a)))) (+ (* -1/12 (pow a 2)) (* 1/24 (pow a 2)))))) (+ (* -3 (* (pow a 2) (+ (* -1/4 a) (* 1/6 a)))) (* -1/4 (pow a 3)))))))))))
(/ 1 (* a x))
(/ (+ (* -1/2 x) (/ 1 a)) x)
(/ (+ (* x (- (* -1 (* x (+ (* -1/4 a) (* 1/6 a)))) 1/2)) (/ 1 a)) x)
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (* a (+ (* -1/4 a) (* 1/6 a)))) (+ (* -1/12 (pow a 2)) (* 1/24 (pow a 2)))))) (+ (* -1/4 a) (* 1/6 a)))) 1/2)) (/ 1 a)) x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* a x)
(* a x)
(* a x)
(* a x)
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(+ 1 (* 1/2 (* a x)))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* 1/6 (* (pow a 2) x))
(* x (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* x (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* x (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* a x)
(* x (+ a (/ 1 x)))
(* x (+ a (/ 1 x)))
(* x (+ a (/ 1 x)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* a x)
(* a x)
(* a x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) x))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (+ (/ 1 (pow x 2)) (/ a x))))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (+ (/ 1 (pow x 2)) (/ a x))))
(* 1/2 (* (pow a 2) x))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* a x)
(* a x)
(* a x)
(* a x)
(* 1/2 (* a x))
(* x (+ (* 1/2 a) (/ 1 x)))
(* x (+ (* 1/2 a) (/ 1 x)))
(* x (+ (* 1/2 a) (/ 1 x)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* 1/6 (* (pow a 2) x))
(* -1 (* x (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (* x (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (* x (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* a x)
(* -1 (* x (- (* -1 a) (/ 1 x))))
(* -1 (* x (- (* -1 a) (/ 1 x))))
(* -1 (* x (- (* -1 a) (/ 1 x))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* a x)
(* a x)
(* a x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) x))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 a) (/ 1 x)) x)) (* 1/2 (pow a 2))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 a) (/ 1 x)) x)) (* 1/2 (pow a 2))))
(* 1/2 (* (pow a 2) x))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(log (/ 1 (- (exp (* a x)) 1)))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(* -1 (log (/ 1 (- (exp (* a x)) 1))))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* a x)
(* a x)
(* a x)
(* a x)
(* 1/2 (* a x))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(* -1 (* x (- (* -1/2 a) (/ 1 x))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)

Outputs
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64))) a x) a)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* a x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* a (+ 1/2 (* 1/6 (* a x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64)) a)
(* a (+ 1/2 (* 1/6 (* a x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64)) a)
(* a (+ 1/2 (* 1/6 (* a x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64)) a)
1
#s(literal 1 binary64)
(+ 1 (* a x))
(fma.f64 x a #s(literal 1 binary64))
(+ 1 (* a x))
(fma.f64 x a #s(literal 1 binary64))
(+ 1 (* a x))
(fma.f64 x a #s(literal 1 binary64))
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
1
#s(literal 1 binary64)
(+ 1 (* a x))
(fma.f64 x a #s(literal 1 binary64))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x a) #s(literal 1/2 binary64))) a x) a #s(literal 1 binary64))
(* a x)
(*.f64 x a)
(* a x)
(*.f64 x a)
(* a x)
(*.f64 x a)
(* a x)
(*.f64 x a)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x)
a
(* a (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
(* a (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
(* a (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
1
#s(literal 1 binary64)
(+ 1 (* a x))
(fma.f64 x a #s(literal 1 binary64))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
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rewrite190.0ms (2.9%)

Memory

7.4MiB live, 169.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	223
0	62	225
1	217	218
2	1412	212
0	8340	209

Stop Event

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

Counts

24 → 787

Calls

Call 1

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

Outputs
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eval186.0ms (2.8%)

Memory: 10.5MiB live, 230.3MiB allocated
Compiler: Compiled 30 947 to 3 653 computations (88.2% saved)

prune52.0ms (0.8%)

Memory

17.2MiB live, 103.6MiB allocated

Pruning

21 alts after pruning (13 fresh and 8 done)

	Pruned	Kept	Total
New	1 450	11	1 461
Fresh	1	2	3
Picked	1	4	5
Done	0	4	4
Total	1 452	21	1 473

Accuracy

100.0%

Counts

1 473 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	44.7%	(pow.f64 (pow.f64 (expm1.f64 (*.f64 x a)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
▶	24.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))
✓	23.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	24.3%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
✓	24.3%	(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
	4.8%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
	4.9%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
✓	22.8%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
	42.7%	(exp.f64 (log.f64 (expm1.f64 (*.f64 x a))))
	65.4%	#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
▶	66.6%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))))
▶	65.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
▶	65.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
✓	66.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
✓	65.4%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
	62.5%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64))) x #s(literal 1 binary64)) (.f64 x a)))
	66.6%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x))
	23.2%	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)) (*.f64 x a)))
▶	22.2%	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
✓	66.6%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 418 to 322 computations (23% saved)

simplify336.0ms (5.1%)

Memory

14.3MiB live, 231.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (*.f64 x a) #s(literal 1/2 binary64)) x)
cost-diff	0	(fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (*.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
cost-diff	0	#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))
cost-diff	0	(.f64 (.f64 (*.f64 x a) #s(literal 1/2 binary64)) a)
cost-diff	0	(.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)
cost-diff	0	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
cost-diff	320	(fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))
cost-diff	0	(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
cost-diff	0	(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x)
cost-diff	0	(.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))))
cost-diff	320	(fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	387
0	72	381
1	138	379
2	292	379
3	618	379
4	1589	379
5	3018	379
6	3067	379
7	3088	379
8	3108	379
9	3108	379
10	4805	379
11	4805	379
12	4818	379
13	4818	379
14	5108	379
15	5202	379
16	5202	379
0	8298	364

Stop Event

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

Calls

Call 1

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

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

localize178.0ms (2.7%)

Memory

-22.1MiB live, 239.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2616829043420723	(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (*.f64 x a) #s(literal 1/2 binary64)) x)
accuracy	0.3203125	(*.f64 #s(literal 1/24 binary64) x)
accuracy	1.4180211914848613	(fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (*.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64))
accuracy	21.99657863911636	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
accuracy	0.1328125	(/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))
accuracy	0.140625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))
accuracy	21.872853375281892	#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
accuracy	27.230365264735624	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.0078125	(fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))
accuracy	0.12890625	(.f64 (.f64 (*.f64 x a) #s(literal 1/2 binary64)) a)
accuracy	4.044529996942342	(.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)
accuracy	22.134001700856427	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
accuracy	1.4428482423582345	(.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x)
accuracy	6.031173579992508	(.f64 (.f64 a a) x)
accuracy	22.134001700856427	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
accuracy	40.34802588771311	#s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64)))
accuracy	0.16863251953688405	(.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))
accuracy	0.3203125	(*.f64 #s(literal 1/6 binary64) x)
accuracy	1.4665006432731755	(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x)
accuracy	21.37267084678604	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))))

Samples

150.0ms

256×

valid

Compiler

Compiled 300 to 42 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-add: 71.0ms (54.5% of total)

ival-mult: 45.0ms (34.5% of total)

const: 7.0ms (5.4% of total)

ival-div: 3.0ms (2.3% of total)

ival-exp: 2.0ms (1.5% of total)

ival-expm1: 2.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series47.0ms (0.7%)

Memory

3.9MiB live, 41.5MiB allocated

Counts

23 → 528

Calls

Call 1

Inputs
#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) (patch (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) #<representation binary64>) () ())
#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)))) (patch #s(approx (- (exp ( a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a)))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) (patch (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())
#s(alt #s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x) (patch (.f64 #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) (patch #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) (patch (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) (patch #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) (patch (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/24 binary64) x) (patch (.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())

Outputs
#s(alt (* a x) (taylor 0 a) (#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) (patch (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) (patch (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) (patch (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) (patch (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)))) (patch #s(approx (- (exp ( a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a)))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)))) (patch #s(approx (- (exp ( a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a)))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)))) (patch #s(approx (- (exp ( a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a)))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)))) (patch #s(approx (- (exp ( a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) (pow x 2))) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) (patch (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) (patch (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) (patch (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) (patch (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* a x)) (taylor 0 a) (#s(alt (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())) ())
#s(alt (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))) (taylor 0 a) (#s(alt (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())) ())
#s(alt (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))) (taylor 0 a) (#s(alt (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())) ())
#s(alt (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))) (taylor 0 a) (#s(alt (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x)) (patch #s(approx (- (exp ( a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x) (patch (.f64 #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x) (patch (.f64 #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x) (patch (.f64 #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) x) (patch (.f64 #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 a) (#s(alt #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) (patch #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* 1/2 (* a x)))) (taylor 0 a) (#s(alt #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) (patch #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* 1/2 (* a x)))) (taylor 0 a) (#s(alt #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) (patch #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* 1/2 (* a x)))) (taylor 0 a) (#s(alt #s(approx (+ (* (* (* a x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64))) (patch #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) (patch (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) (patch (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) (patch (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) (patch (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) (patch #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) (patch #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) (patch #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))) (taylor 0 a) (#s(alt #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) (patch #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) (pow x 2))) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) (pow x 2))) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) (pow x 2))) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) (pow x 2))) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) (patch (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) (patch (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) (patch (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) (patch (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) x)) (taylor 0 a) (#s(alt (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) (patch (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (* (pow a 2) x)) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) (patch (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (- (exp (* a x)) 1)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (- (exp (* a x)) 1)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (- (exp (* a x)) 1)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (- (exp (* a x)) 1)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a))) (patch #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (* (pow a 4) (pow x 4))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) (patch (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (.f64 x a)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (* (pow a 3) (pow x 3))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1/6 (/ (pow a 2) x)) (* -1/24 (pow a 3))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))) x)) (* -1/24 (pow a 3))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (* (pow a 2) (pow x 3))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1/6 (/ a x)) (* -1/24 (pow a 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 a) (* 1/2 (/ 1 x))) x)) (* -1/24 (pow a 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 a) (* 1/2 (/ 1 x))) x)) (* -1/24 (pow a 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) x) (patch (.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 a a) x) (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) x) (patch (.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) x) (patch (.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) x) (patch (.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) x) (patch (.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	((+ (* x a) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a))) (- (exp (* a x)) 1) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* (* a a) x) 1/2) (+ (* x a) (* (* (* (* x a) 1/2) a) x)) (- (exp (* a x)) 1) (* (* (* (* x a) 1/2) a) x) (* (* (* x a) 1/2) a) (/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (* (* a a) x) (* 1/24 x))
4.0ms	x	@	-inf	((+ (* x a) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a))) (- (exp (* a x)) 1) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* (* a a) x) 1/2) (+ (* x a) (* (* (* (* x a) 1/2) a) x)) (- (exp (* a x)) 1) (* (* (* (* x a) 1/2) a) x) (* (* (* x a) 1/2) a) (/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (* (* a a) x) (* 1/24 x))
4.0ms	a	@	inf	((+ (* x a) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a))) (- (exp (* a x)) 1) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* (* a a) x) 1/2) (+ (* x a) (* (* (* (* x a) 1/2) a) x)) (- (exp (* a x)) 1) (* (* (* (* x a) 1/2) a) x) (* (* (* x a) 1/2) a) (/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (* (* a a) x) (* 1/24 x))
3.0ms	a	@	-inf	((+ (* x a) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a))) (- (exp (* a x)) 1) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* (* a a) x) 1/2) (+ (* x a) (* (* (* (* x a) 1/2) a) x)) (- (exp (* a x)) 1) (* (* (* (* x a) 1/2) a) x) (* (* (* x a) 1/2) a) (/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (* (* a a) x) (* 1/24 x))
3.0ms	a	@	0	((+ (* x a) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a))) (- (exp (* a x)) 1) (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* (* a a) x) 1/2) (+ (* x a) (* (* (* (* x a) 1/2) a) x)) (- (exp (* a x)) 1) (* (* (* (* x a) 1/2) a) x) (* (* (* x a) 1/2) a) (/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (* (* a a) x) (* 1/24 x))

simplify302.0ms (4.6%)

Memory

20.1MiB live, 167.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	367	5486
1	1226	5432
2	4259	5260
0	8389	4738

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 526

Calls

Call 1

Inputs
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(* 1/2 (* a x))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
a
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* a (+ 1 (* 1/2 (* a x))))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(/ 1 (* a x))
(/ (+ (* -1/2 a) (/ 1 x)) a)
(/ (+ (* a (- (* -1 (* a (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)
(/ (+ (* a (- (* a (- (* -1 (* a (+ (* -1/2 (* x (+ (* -1/4 x) (* 1/6 x)))) (+ (* -1/12 (pow x 2)) (* 1/24 (pow x 2)))))) (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(+ 1 (* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))))
(* 1/2 x)
(+ (* 1/6 (* a (pow x 2))) (* 1/2 x))
(+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))
(+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (+ (* 1/2 (/ x (pow a 2))) (/ 1 (pow a 3))))))
(* 1/24 (* (pow a 2) (pow x 3)))
(* (pow a 2) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))
(* (pow a 2) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* (pow a 2) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 2) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))) a)) (* -1/24 (pow x 3)))))
(* 1/24 (* (pow a 2) (pow x 3)))
(* (pow a 2) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ x a)) (* -1/6 (pow x 2))) a)) (* 1/24 (pow x 3))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ x a)) (* -1/6 (pow x 2))) a)) (* 1/24 (pow x 3))))
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))
(* (pow x 2) (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))
(* (pow x 2) (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))
(* 1/2 (* a x))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
a
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(+ a (* 1/2 (* (pow a 2) x)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(/ 1 (* a x))
(/ (+ (* -1/2 x) (/ 1 a)) x)
(/ (+ (* x (- (* -1 (* x (+ (* -1/4 a) (* 1/6 a)))) 1/2)) (/ 1 a)) x)
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (* a (+ (* -1/4 a) (* 1/6 a)))) (+ (* -1/12 (pow a 2)) (* 1/24 (pow a 2)))))) (+ (* -1/4 a) (* 1/6 a)))) 1/2)) (/ 1 a)) x)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2)))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 (* a x))))
(* x (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))
(* x (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) x))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))
(* 1/24 (* (pow a 2) (pow x 3)))
(* (pow x 3) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 3) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* (pow x 3) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* 1/2 (* (pow a 2) x))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(* 1/2 (* (pow a 2) x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(/ 1 (- (exp (* a x)) 1))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 (/ (pow a 2) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))) x)) (* -1/24 (pow a 3)))))
(* 1/24 (* (pow a 2) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 (/ a x)) (* -1/24 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 a) (* 1/2 (/ 1 x))) x)) (* -1/24 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 a) (* 1/2 (/ 1 x))) x)) (* -1/24 (pow a 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)

Outputs
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
(* 1/2 (* (pow a 2) (pow x 2)))
(.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x)
(* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(.f64 (.f64 a a) (.f64 (.f64 x x) (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))))
(* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(.f64 (.f64 a a) (.f64 (.f64 x x) (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))))
(* (pow a 2) (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(.f64 (.f64 a a) (.f64 (.f64 x x) (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))))
(* 1/2 (* a x))
(.f64 #s(literal 1/2 binary64) (.f64 x a))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64)) x) a)
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64)) x) a)
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64)) x) a)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
a
(* a (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a)
(* a (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a)
(* a (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a)
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
(* 1/2 (* (pow a 2) (pow x 2)))
(.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x)
(* 1/2 (* (pow a 2) (pow x 2)))
(.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x)
(* 1/2 (* (pow a 2) (pow x 2)))
(.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x)
(* 1/2 (* (pow a 2) (pow x 2)))
(.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x)
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
(/ 1 (* a x))
(/.f64 #s(literal 1 binary64) (*.f64 x a))
(/ (+ (* -1/2 a) (/ 1 x)) a)
(/.f64 (fma.f64 #s(literal -1/2 binary64) a (/.f64 #s(literal 1 binary64) x)) a)
(/ (+ (* a (- (* -1 (* a (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)
(/.f64 (fma.f64 (fma.f64 (*.f64 x a) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) a (/.f64 #s(literal 1 binary64) x)) a)
(/ (+ (* a (- (* a (- (* -1 (* a (+ (* -1/2 (* x (+ (* -1/4 x) (* 1/6 x)))) (+ (* -1/12 (pow x 2)) (* 1/24 (pow x 2)))))) (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 (neg.f64 a) (.f64 x (fma.f64 x #s(literal -1/24 binary64) (.f64 (.f64 #s(literal -1/12 binary64) x) #s(literal -1/2 binary64)))))) a #s(literal -1/2 binary64)) a (/.f64 #s(literal 1 binary64) x)) a)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
1
#s(literal 1 binary64)
(+ 1 (* a x))
(fma.f64 x a #s(literal 1 binary64))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x #s(literal 1 binary64))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a #s(literal 1 binary64))
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* a x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64)) x) a #s(literal 1 binary64))
(+ 1 (* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))))
(fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 (.f64 a a) #s(literal 1/24 binary64)) x (.f64 #s(literal 1/6 binary64) a)) x #s(literal 1/2 binary64)) x) a #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/6 (* a (pow x 2))) (* 1/2 x))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64)) x)
(+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))
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(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)

rewrite302.0ms (4.6%)

Memory

8.8MiB live, 199.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	316
0	72	310
1	264	300
2	1768	300
0	8370	289

Stop Event

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

Counts

23 → 459

Calls

Call 1

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

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eval169.0ms (2.6%)

Memory: -8.9MiB live, 304.4MiB allocated
Compiler: Compiled 21 089 to 2 019 computations (90.4% saved)

prune44.0ms (0.7%)

Memory

-5.6MiB live, 120.1MiB allocated

Pruning

24 alts after pruning (13 fresh and 11 done)

	Pruned	Kept	Total
New	980	5	985
Fresh	0	8	8
Picked	2	3	5
Done	0	8	8
Total	982	24	1 006

Accuracy

100.0%

Counts

1 006 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	44.7%	(pow.f64 (pow.f64 (expm1.f64 (*.f64 x a)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
	66.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
	66.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 (fma.f64 (*.f64 x a) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) a (/.f64 #s(literal 1 binary64) x)) a)))
	71.2%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)) x)))
✓	23.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	24.3%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
✓	24.3%	(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
	4.8%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
	4.9%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
✓	22.8%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
	42.7%	(exp.f64 (log.f64 (expm1.f64 (*.f64 x a))))
	65.4%	#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
	65.6%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 a x) #s(literal 1/2 binary64)) x) a) (.f64 a x))))
✓	66.6%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))))
✓	65.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
✓	65.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
✓	66.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
✓	65.4%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
	62.5%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64))) x #s(literal 1 binary64)) (.f64 x a)))
	66.6%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x))
	23.2%	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)) (*.f64 x a)))
	22.3%	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64))) x))
✓	66.6%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 640 to 350 computations (45.3% saved)

regimes43.0ms (0.7%)

Memory

10.2MiB live, 89.7MiB allocated

Counts

30 → 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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a a) x) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64))) 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 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64))) x #s(literal 1 binary64)) (.f64 x a)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)) x)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 a x) #s(literal 1/2 binary64)) x) a) (.f64 a x))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 (fma.f64 (*.f64 x a) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) a (/.f64 #s(literal 1 binary64) x)) a)))
(expm1.f64 (*.f64 x a))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(exp.f64 (log.f64 (expm1.f64 (*.f64 x a))))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 x a)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(exp.f64 (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal -1 binary64))) #s(literal -1 binary64)))

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

Calls

5 calls:

10.0ms	x
8.0ms	a
8.0ms	(*.f64 a x)
8.0ms	(exp.f64 (*.f64 a x))
7.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Results

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

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes36.0ms (0.5%)

Memory

1.8MiB live, 79.7MiB allocated

Counts

25 → 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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a a) x) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64))) 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 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64))) x #s(literal 1 binary64)) (.f64 x a)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)) x)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 a x) #s(literal 1/2 binary64)) x) a) (.f64 a x))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 (fma.f64 (*.f64 x a) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) a (/.f64 #s(literal 1 binary64) x)) a)))

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

Calls

5 calls:

8.0ms	x
8.0ms	(*.f64 a x)
7.0ms	a
6.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
6.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
71.2%	1	`a`
71.2%	1	`x`
71.2%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
71.2%	1	`(exp.f64 (*.f64 a x))`
71.2%	1	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes37.0ms (0.6%)

Memory

-24.8MiB live, 64.6MiB allocated

Counts

21 → 2

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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a a) x) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64))) 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 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64))) x #s(literal 1 binary64)) (.f64 x a)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))))

Outputs

#s(approx (- (exp (* a x)) 1) (fma.f64 x a (*.f64 (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (*.f64 x a))))

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

Calls

5 calls:

11.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
7.0ms	x
6.0ms	a
6.0ms	(*.f64 a x)
5.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
66.6%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
66.6%	1	`(exp.f64 (*.f64 a x))`
66.6%	1	`(*.f64 a x)`
66.6%	1	`a`
68.2%	2	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes7.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

20 → 2

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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a a) x) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64))) 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 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64))) x #s(literal 1 binary64)) (.f64 x a)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))

Outputs

#s(approx (- (exp (* a x)) 1) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a)))

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
68.2%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes6.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

18 → 2

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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a a) x) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64))) 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 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64))) x #s(literal 1 binary64)) (.f64 x a)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x))

Outputs

#s(approx (- (exp (* a x)) 1) (*.f64 (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
68.2%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes26.0ms (0.4%)

Memory

4.8MiB live, 43.7MiB allocated

Counts

17 → 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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (+.f64 (*.f64 a x) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a a) x) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (* a x) a) 1/2) a) (.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64))) 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 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))
#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64))) x #s(literal 1 binary64)) (.f64 x a)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))))

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

Calls

5 calls:

6.0ms	x
5.0ms	a
5.0ms	(*.f64 a x)
4.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
4.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
66.6%	1	`a`
66.6%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
66.6%	1	`(exp.f64 (*.f64 a x))`
66.6%	1	`(*.f64 a x)`
66.6%	1	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes8.0ms (0.1%)

Memory

-25.1MiB live, 13.3MiB allocated

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:

3.0ms	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
22.8%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
22.8%	1	`(exp.f64 (*.f64 a x))`
22.8%	1	`(*.f64 a x)`
22.8%	1	`a`
22.8%	1	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

bsearch11.0ms (0.2%)

Memory

17.0MiB live, 17.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	6.181448981428226e+203	4.4421967147196405e+206

Samples

4.0ms

128×

valid

Compiler

Compiled 257 to 209 computations (18.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-mult: 1.0ms (52.6% of total)

ival-expm1: 1.0ms (52.6% of total)

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

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

bsearch2.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	6.181448981428226e+203	4.4421967147196405e+206

Compiler

Compiled 241 to 209 computations (13.3% saved)

bsearch1.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	6.181448981428226e+203	4.4421967147196405e+206

Compiler

Compiled 241 to 209 computations (13.3% saved)

simplify25.0ms (0.4%)

Memory

2.4MiB live, 41.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	211
1	68	211
2	73	211
3	76	211
4	79	211
5	83	211

Stop Event

1×

saturated

Calls

Call 1

Inputs
(expm1.f64 (*.f64 x a))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)) x)))
(if (<=.f64 x #s(literal 419999999999999973562421781249042966388112643599617285130052748977054086835486711099231162971735847333838527209796222898911664315472069221240270379434598315869925389907233148024729042264671067094207858475008 binary64)) #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)))) (-.f64 #s(approx (exp ( a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64)))
(if (<=.f64 x #s(literal 419999999999999973562421781249042966388112643599617285130052748977054086835486711099231162971735847333838527209796222898911664315472069221240270379434598315869925389907233148024729042264671067094207858475008 binary64)) #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64)))
(if (<=.f64 x #s(literal 419999999999999973562421781249042966388112643599617285130052748977054086835486711099231162971735847333838527209796222898911664315472069221240270379434598315869925389907233148024729042264671067094207858475008 binary64)) #s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64)))
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))

Outputs
(expm1.f64 (*.f64 x a))
(expm1.f64 (*.f64 a x))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)) x)))
(if (<=.f64 x #s(literal 419999999999999973562421781249042966388112643599617285130052748977054086835486711099231162971735847333838527209796222898911664315472069221240270379434598315869925389907233148024729042264671067094207858475008 binary64)) #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a)))) (-.f64 #s(approx (exp ( a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64)))
(if (<=.f64 x #s(literal 419999999999999973562421781249042966388112643599617285130052748977054086835486711099231162971735847333838527209796222898911664315472069221240270379434598315869925389907233148024729042264671067094207858475008 binary64)) #s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 a x)))) (-.f64 #s(approx (exp ( a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64)))
(if (<=.f64 x #s(literal 419999999999999973562421781249042966388112643599617285130052748977054086835486711099231162971735847333838527209796222898911664315472069221240270379434598315869925389907233148024729042264671067094207858475008 binary64)) #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a))) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64)))
(if (<=.f64 x #s(literal 419999999999999973562421781249042966388112643599617285130052748977054086835486711099231162971735847333838527209796222898911664315472069221240270379434598315869925389907233148024729042264671067094207858475008 binary64)) #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 a x))) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64)))
(if (<=.f64 x #s(literal 419999999999999973562421781249042966388112643599617285130052748977054086835486711099231162971735847333838527209796222898911664315472069221240270379434598315869925389907233148024729042264671067094207858475008 binary64)) #s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) a) x)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* x a)) 1) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64)))
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (*.f64 a x))
(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))

soundness1.7s (26.1%)

Memory

-11.0MiB live, 775.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	2132
1	318	2132
2	823	2104
3	2493	2104
4	6842	2104
0	8433	1806
0	34	223
0	62	225
1	217	218
2	1412	212
0	8340	209
0	357	5090
1	1254	4976
2	4365	4816
0	8087	4196
0	367	5486
1	1226	5432
2	4259	5260
0	8389	4738
0	6	13
0	9	13
1	30	13
2	152	13
0	1346	11
0	20	98
0	31	94
1	121	94
2	727	94
3	6903	94
0	8442	94
0	63	432
1	195	432
2	526	424
3	1045	424
4	1672	424
5	1873	424
6	1900	424
7	1920	424
8	1934	424
9	1937	424
10	1937	424
11	2619	420
12	3094	420
13	4061	420
14	4062	420
15	4062	420
16	4190	420
17	4190	420
18	6071	416
19	6279	416
20	6321	416
21	6335	416
22	6335	416
23	6511	416
24	6849	416
25	6849	416
26	7408	416
0	7408	360

Stop Event

1×	fuel
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 216 to 131 computations (39.4% saved)

preprocess78.0ms (1.2%)

Memory: 28.1MiB live, 105.8MiB allocated
Remove: (sort a x)
Compiler: Compiled 292 to 126 computations (56.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	36
1	42	36
2	73	34
3	108	34
4	141	34
5	165	34
6	204	34
7	226	34
8	240	34
9	251	34
10	252	34
0	6	6
0	9	6
1	17	6
2	20	6
0	20	4

Iter	Nodes	Cost
0	20	112
0	31	108
1	52	108
2	75	108
3	115	108
4	157	108
5	173	108
6	192	108
7	192	108
8	259	108
9	261	108
0	261	108

Iter	Nodes	Cost
0	16	36
1	42	36
2	73	34
3	108	34
4	141	34
5	165	34
6	204	34
7	226	34
8	240	34
9	251	34
10	252	34
0	6	6
0	9	6
1	17	6
2	20	6
0	20	4

Iter	Nodes	Cost
0	20	112
0	31	108
1	52	108
2	75	108
3	115	108
4	157	108
5	173	108
6	192	108
7	192	108
8	259	108
9	261	108
0	261	108

start0.0ms (0%)

analyze17.0ms (0.3%)

sample885.0ms (13.4%)

explain64.0ms (1%)

preprocess19.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize16.0ms (0.2%)

series5.0ms (0.1%)

simplify205.0ms (3.1%)

rewrite62.0ms (0.9%)

eval38.0ms (0.6%)

prune12.0ms (0.2%)

simplify10.0ms (0.1%)

localize41.0ms (0.6%)

series41.0ms (0.6%)

simplify461.0ms (7%)

rewrite189.0ms (2.9%)

eval113.0ms (1.7%)

prune31.0ms (0.5%)

simplify50.0ms (0.8%)

localize132.0ms (2%)

series165.0ms (2.5%)

simplify225.0ms (3.4%)

rewrite190.0ms (2.9%)

eval186.0ms (2.8%)

prune52.0ms (0.8%)

simplify336.0ms (5.1%)

localize178.0ms (2.7%)

series47.0ms (0.7%)

simplify302.0ms (4.6%)

rewrite302.0ms (4.6%)

eval169.0ms (2.6%)

prune44.0ms (0.7%)

regimes43.0ms (0.7%)

regimes36.0ms (0.5%)

regimes37.0ms (0.6%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes26.0ms (0.4%)

regimes8.0ms (0.1%)

bsearch11.0ms (0.2%)

bsearch2.0ms (0%)

bsearch1.0ms (0%)

simplify25.0ms (0.4%)

soundness1.7s (26.1%)

preprocess78.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	36
1	42	36
2	73	34
3	108	34
4	141	34
5	165	34
6	204	34
7	226	34
8	240	34
9	251	34
10	252	34
0	6	6
0	9	6
1	17	6
2	20	6
0	20	4

Iter	Nodes	Cost
0	20	112
0	31	108
1	52	108
2	75	108
3	115	108
4	157	108
5	173	108
6	192	108
7	192	108
8	259	108
9	261	108
0	261	108