Metrics for expax (section 3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze19.0ms (0.3%)

Memory

1.1MiB live, 39.9MiB 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)

sample594.0ms (9.5%)

Memory

45.7MiB live, 747.6MiB allocated

Samples

348.0ms	8 256×	0	valid
34.0ms	322×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 184.0ms

ival-mult: 84.0ms (45.5% of total)

ival-expm1: 71.0ms (38.5% of total)

ival->: 21.0ms (11.4% of total)

exact: 7.0ms (3.8% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

explain68.0ms (1.1%)

Memory

6.2MiB live, 119.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
125	1	(-1.4489747332185033e-236 1.6395613537377962e-87)	0	-	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
1	0	-	1	(-8.090923331276063e+201 -9.443458002528757e-201)	`(exp.f64 (*.f64 a x))`
0	0	-	0	-	`a`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(*.f64 a x)`
0	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	126	0

Confusion

	Predicted +	Predicted -
+	125	1
-	1	129

Precision

0.9920634920634921

Recall

0.9920634920634921

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	125	1	0
-	1	0	129

Precision?

0.9921259842519685

Recall?

1.0

Freqs

test

number	freq
0	130
1	126

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

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 (36% of total)

ival-mult: 4.0ms (36% of total)

ival-expm1: 3.0ms (27% of total)

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

exact: 0.0ms (0% of total)

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

preprocess85.0ms (1.4%)

Memory

-29.2MiB live, 16.1MiB allocated

Algorithm

1×	egg-herbie

Rules

42×	`sub-neg`
40×	`exp-sum`
24×	`exp-prod`
24×	`+-commutative`
18×	`*-commutative`

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)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.8%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 6 to 6 computations (0% saved)

simplify3.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB 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))

Rules

6×	`lower-exp.f32`
4×	`exp-prod`
4×	`lower-pow.f64`
4×	`lower-+.f64`
4×	`lower-exp.f64`

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 (0.3%)

Memory

23.6MiB live, 23.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a x)
accuracy	0.01953125	(exp.f64 (*.f64 a x))
accuracy	28.294748473331065	(-.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 (36.5% of total)

ival-mult: 2.0ms (36.5% of total)

ival-expm1: 2.0ms (36.5% 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

4.8MiB live, 4.8MiB 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)))

simplify209.0ms (3.3%)

Memory

-20.8MiB live, 92.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8 560×	`lower-fma.f64`
8 560×	`lower-fma.f32`
3 428×	`associate-r`
2 992×	`lower-*.f64`
2 992×	`lower-*.f32`

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)

rewrite72.0ms (1.2%)

Memory

18.7MiB live, 58.6MiB allocated

Rules

806×	`lower-fma.f64`
806×	`lower-fma.f32`
650×	`lower-*.f32`
648×	`lower-*.f64`
594×	`lower-/.f64`

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

eval23.0ms (0.4%)

Memory: -7.2MiB live, 30.8MiB allocated
Compiler: Compiled 3 200 to 339 computations (89.4% saved)

prune9.0ms (0.1%)

Memory

17.8MiB live, 17.8MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	175	8	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	8	184

Accuracy

100.0%

Counts

184 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	18.6%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	20.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
▶	18.1%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 x a))
▶	63.2%	#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)))
	64.2%	#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)))
	59.3%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
	63.7%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 162 to 126 computations (22.2% saved)

simplify234.0ms (3.7%)

Memory

1.4MiB live, 192.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

20 738×	`lower-fma.f32`
20 726×	`lower-fma.f64`
6 136×	`lower-+.f64`
6 136×	`lower-+.f32`
5 760×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	221
0	51	219
1	89	219
2	163	219
3	398	219
4	1138	219
5	2687	219
6	4219	219
7	4668	219
8	4705	219
9	4705	219
10	7583	219
11	7583	219
12	7583	219
13	7859	219
14	7859	219
0	9774	219

Stop Event

1×	iter limit
1×	node limit
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)
(-.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)
(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))
(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)
#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)
(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
(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)
(-.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)
(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)))
#s(approx (exp (* a x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a) x #s(literal 1 binary64))
(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)
#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)))
#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 a x) #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 a x) #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))
(fma.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 #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 (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)
(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 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 a x) #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)
(*.f64 a x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

localize131.0ms (2.1%)

Memory

7.6MiB live, 126.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.2734375	(*.f64 #s(literal 1/24 binary64) x)
accuracy	0.4868896419316846	(.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	0.7296836366816313	(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	23.53661215574031	#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	1.19457115705365	(fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))
accuracy	8.11863921778364	(.f64 (.f64 a a) x)
accuracy	23.430415988393378	#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)))
accuracy	28.294748473331065	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0	(fma.f64 x a #s(literal 1 binary64))
accuracy	23.55337032214192	#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
accuracy	28.294748473331065	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	23.69472021442764	#s(approx (exp (* a x)) #s(literal 1 binary64))
accuracy	28.294748473331065	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(*.f64 x a)
accuracy	0.03125	(expm1.f64 (*.f64 x a))

Samples

84.0ms

256×

valid

Compiler

Compiled 181 to 29 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-mult: 42.0ms (64.8% of total)

ival-add: 12.0ms (18.5% of total)

const: 6.0ms (9.3% of total)

ival-expm1: 3.0ms (4.6% of total)

ival-exp: 2.0ms (3.1% of total)

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

exact: 0.0ms (0% of total)

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

series30.0ms (0.5%)

Memory

-28.4MiB live, 47.0MiB allocated

Counts

17 → 396

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 (-.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 (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<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 #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 (.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 (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>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (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>) () ())) ())
#s(alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (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>) () ())) ())
#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 #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 1 (taylor 0 a) (#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 (+ 1 (* a x)) (taylor 0 a) (#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 (+ 1 (* a (+ x (* 1/2 (* a (pow x 2)))))) (taylor 0 a) (#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 (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))) (taylor 0 a) (#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 (* a x) (taylor 0 a) (#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 (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#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 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))) (taylor 0 a) (#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 (* 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 #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 1 (taylor 0 a) (#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 (+ 1 (* a x)) (taylor 0 a) (#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 (+ 1 (* a (+ x (* 1/2 (* a (pow x 2)))))) (taylor 0 a) (#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 (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))) (taylor 0 a) (#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 1 (taylor 0 a) (#s(alt (fma.f64 x a #s(literal 1 binary64)) (patch (fma.f64 x a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a x)) (taylor 0 a) (#s(alt (fma.f64 x a #s(literal 1 binary64)) (patch (fma.f64 x a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a x)) (taylor 0 a) (#s(alt (fma.f64 x a #s(literal 1 binary64)) (patch (fma.f64 x a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a x)) (taylor 0 a) (#s(alt (fma.f64 x a #s(literal 1 binary64)) (patch (fma.f64 x a #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a x) (taylor 0 a) (#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* a (+ x (* 1/2 (* a (pow x 2))))) (taylor 0 a) (#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(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 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(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 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 a) (#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a x)) (taylor 0 a) (#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2)))))) (taylor 0 a) (#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))) (taylor 0 a) (#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 a) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a x)) (taylor 0 a) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2)))))) (taylor 0 a) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2)))))) (taylor 0 a) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 a) (#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 (* a (+ 1 (* 1/2 (* a x)))) (taylor 0 a) (#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 (* a (+ 1 (* 1/2 (* a x)))) (taylor 0 a) (#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 (* a (+ 1 (* 1/2 (* a x)))) (taylor 0 a) (#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 (* a x) (taylor 0 a) (#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 (* 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 (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>) () ())) ())
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#s(alt (- (exp (* a x)) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* a x)) (taylor -inf x) (#s(alt #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) (patch #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a 2) (pow x 2))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (- (* -1 a) (/ 1 x)) x)) (* 1/2 (pow a 2)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (- (* -1 a) (/ 1 x)) x)) (* 1/2 (pow a 2)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) #<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 (- (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 (* (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
4.0ms	a	@	0	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (+ (* (* (* a a) x) 1/2) a) (- (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) (* (* a a) x) (* 1/24 x))
3.0ms	a	@	-inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (+ (* (* (* a a) x) 1/2) a) (- (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) (* (* a a) x) (* 1/24 x))
3.0ms	x	@	-inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (+ (* (* (* a a) x) 1/2) a) (- (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) (* (* a a) x) (* 1/24 x))
3.0ms	x	@	inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (+ (* (* (* a a) x) 1/2) a) (- (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) (* (* a a) x) (* 1/24 x))
2.0ms	a	@	inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (+ (* (* (* a a) x) 1/2) a) (- (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) (* (* a a) x) (* 1/24 x))

simplify183.0ms (2.9%)

Memory

33.6MiB live, 188.7MiB allocated

Algorithm

1×	egg-herbie

Rules

20 954×	`lower-fma.f64`
20 954×	`lower-fma.f32`
5 792×	`lower-*.f64`
5 792×	`lower-*.f32`
3 606×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	317	3586
1	1038	3548
2	3340	3462
0	8272	3054

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 394

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

rewrite175.0ms (2.8%)

Memory

-2.9MiB live, 153.6MiB allocated

Rules

5 064×	`lower-*.f32`
5 052×	`lower-*.f64`
4 514×	`lower-/.f64`
4 514×	`lower-/.f32`
4 362×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	182
0	51	180
1	216	180
2	1479	180
0	8370	180

Stop Event

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

Counts

17 → 450

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

Outputs
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eval188.0ms (3%)

Memory: -20.1MiB live, 182.1MiB allocated
Compiler: Compiled 21 247 to 2 216 computations (89.6% saved)

prune33.0ms (0.5%)

Memory

-4.0MiB live, 74.2MiB allocated

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	919	7	926
Fresh	1	2	3
Picked	1	4	5
Done	0	0	0
Total	921	13	934

Accuracy

100.0%

Counts

934 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	20.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))))
✓	18.6%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	20.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
	4.3%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
✓	18.1%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
	61.0%	#s(approx (- (exp (* x a)) 1) (.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))
▶	63.7%	#s(approx (- (exp (* x a)) 1) (*.f64 x a))
	63.2%	#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))))
▶	64.2%	#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)))
▶	59.3%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
	62.8%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 x a)))
▶	63.2%	#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 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) x) a))

Compiler

Compiled 283 to 211 computations (25.4% saved)

simplify338.0ms (5.4%)

Memory

31.6MiB live, 269.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

38 044×	`lower-fma.f32`
38 030×	`lower-fma.f64`
9 468×	`lower-+.f64`
9 468×	`lower-+.f32`
3 970×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	312
0	67	308
1	121	308
2	235	308
3	533	308
4	1541	308
5	3196	308
6	3235	308
7	3259	308
8	3283	308
9	3283	308
10	5372	308
11	5372	308
12	5385	308
13	5385	308
14	5781	308
15	5911	308
16	5911	308
0	9730	300

Stop Event

1×	iter limit
1×	node limit
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)
#s(approx (- (exp (* x a)) 1) (*.f64 x a))
(*.f64 x a)
x
a
#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)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #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 a x #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 a x #s(literal 1 binary64)))
(fma.f64 a x #s(literal 1 binary64))
a
x
#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 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) 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 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) x) a)
(.f64 (fma.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 #s(literal 1 binary64)) x)
(fma.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 #s(literal 1 binary64))
(.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)
(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))
(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 a x)
#s(literal 1/2 binary64)
#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)
#s(approx (- (exp (* x a)) 1) (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(*.f64 x a)
x
a
#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)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.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(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #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 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)) (fma.f64 a x #s(literal 1 binary64)))
#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
(fma.f64 a x #s(literal 1 binary64))
(fma.f64 x a #s(literal 1 binary64))
a
x
#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 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) 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)) 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 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) 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)) x) a)
(.f64 (fma.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 #s(literal 1 binary64)) 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)) x)
(fma.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 #s(literal 1 binary64))
(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 a x) #s(literal 1/2 binary64)) x)
(.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 a x) #s(literal 1/2 binary64))
(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 a x)
(*.f64 x a)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

localize112.0ms (1.8%)

Memory

10.4MiB live, 86.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.7296836366816313	(fma.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 #s(literal 1 binary64))
accuracy	0.9674199778424419	(.f64 (fma.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 #s(literal 1 binary64)) x)
accuracy	1.1602356363637185	(.f64 (.f64 (fma.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 #s(literal 1 binary64)) x) a)
accuracy	23.53661215574031	#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 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) x) a))
accuracy	0.12890625	(/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64)))
accuracy	0.5202349204931405	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))))
accuracy	23.55337032214192	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
accuracy	28.294748473331065	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0	(*.f64 a a)
accuracy	1.19066490705365	(.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)
accuracy	8.11863921778364	(.f64 (.f64 a a) x)
accuracy	23.813727858529457	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
accuracy	0	(*.f64 x a)
accuracy	23.223451406888017	#s(approx (- (exp (* x a)) 1) (*.f64 x a))
accuracy	0.05859375	(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
accuracy	0.2734375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	1.183197726218307	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
accuracy	22.920022300083165	#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

67.0ms

256×

valid

Compiler

Compiled 265 to 38 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 25.0ms (52.5% of total)

ival-add: 7.0ms (14.7% of total)

const: 6.0ms (12.6% of total)

ival-div: 3.0ms (6.3% of total)

ival-expm1: 3.0ms (6.3% of total)

ival-exp: 2.0ms (4.2% of total)

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

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

exact: 0.0ms (0% of total)

series55.0ms (0.9%)

Memory

-3.9MiB live, 34.0MiB allocated

Counts

20 → 456

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

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	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) (- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (/ 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) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (* 1/6 x) (* a a))
3.0ms	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) (- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (/ 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) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (* 1/6 x) (* a a))
3.0ms	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) (- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (/ 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) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (* 1/6 x) (* a a))
2.0ms	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) (- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (/ 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) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (* 1/6 x) (* a a))
2.0ms	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) (- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (/ 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) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (* 1/6 x) (* a a))

simplify417.0ms (6.7%)

Memory

5.2MiB live, 205.6MiB allocated

Algorithm

1×	egg-herbie

Rules

25 112×	`lower-fma.f64`
25 112×	`lower-fma.f32`
7 120×	`lower-*.f64`
7 120×	`lower-*.f32`
4 310×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	392	4685
1	1328	4642
2	4709	4484
0	8391	3969

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 452

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

rewrite153.0ms (2.5%)

Memory

4.8MiB live, 233.1MiB allocated

Rules

5 106×	`lower-*.f32`
5 082×	`lower-*.f64`
4 758×	`lower-fma.f32`
4 744×	`lower-fma.f64`
4 344×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	244
0	67	240
1	250	240
2	1563	240
0	8359	232

Stop Event

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

Counts

20 → 537

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

Outputs
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eval149.0ms (2.4%)

Memory: 0.5MiB live, 273.7MiB allocated
Compiler: Compiled 22 826 to 2 438 computations (89.3% saved)

prune47.0ms (0.7%)

Memory

-22.3MiB live, 100.9MiB allocated

Pruning

19 alts after pruning (12 fresh and 7 done)

	Pruned	Kept	Total
New	1 021	9	1 030
Fresh	1	3	4
Picked	2	3	5
Done	0	4	4
Total	1 024	19	1 043

Accuracy

100.0%

Counts

1 043 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
	64.0%	(/.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)) x (/.f64 #s(literal 1 binary64) a)) x)))
	63.9%	(/.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)))
▶	68.4%	(/.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)))
	68.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) a (/.f64 #s(literal 1 binary64) x)) a)))
✓	18.6%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	20.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
▶	4.3%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
✓	18.1%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
✓	63.7%	#s(approx (- (exp (* x a)) 1) (*.f64 x a))
▶	64.2%	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a) (*.f64 x a)))
	63.2%	#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))))
	64.2%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) (.f64 x a) #s(literal 1 binary64)) (.f64 x a)))
✓	59.3%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
	62.8%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 x a)))
✓	63.2%	#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 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) x) a))
▶	64.2%	#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)) x) a))
▶	62.8%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a))

Compiler

Compiled 409 to 308 computations (24.7% saved)

simplify110.0ms (1.8%)

Memory

27.6MiB live, 63.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

3 124×	`lower-fma.f32`
3 114×	`lower-fma.f64`
1 670×	`lower-*.f32`
1 646×	`lower-*.f64`
1 440×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	458
0	78	454
1	138	454
2	274	454
3	578	451
4	1380	451
5	2060	451
6	2864	451
7	3733	451
8	4421	451
9	4487	451
10	4498	451
11	4509	451
12	4509	451
13	4509	451
14	4840	451
15	5065	451
16	5066	451
0	5066	426

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize124.0ms (2%)

Memory

-19.9MiB live, 175.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.05859375	(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
accuracy	0.2734375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	1.191010226218307	(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x)
accuracy	22.920022300083165	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a) (*.f64 x a)))
accuracy	0.48672066134615866	(.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)) x)
accuracy	0.7295732387004853	(.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)) x) a)
accuracy	1.183197726218307	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
accuracy	22.920022300083165	#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)) x) a))
accuracy	8.11863921778364	(.f64 (.f64 a a) x)
accuracy	23.430415988393378	#s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x)))
accuracy	28.294748473331065	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
accuracy	39.99908663230937	#s(approx (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))
accuracy	0.9674199778424419	(.f64 #s(approx (+ ( (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x)
accuracy	1.1602356363637185	(.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a)
accuracy	16.385734760214657	#s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)))
accuracy	23.53661215574031	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a))
accuracy	0.00390625	(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a))
accuracy	0.1640625	(/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)) x)
accuracy	0.5202349204931405	(/.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)))
accuracy	19.683542610139014	#s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)) x))

Samples

95.0ms

256×

valid

Compiler

Compiled 314 to 48 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 37.0ms (50.3% of total)

ival-add: 18.0ms (24.5% of total)

ival-div: 8.0ms (10.9% of total)

const: 6.0ms (8.2% of total)

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

ival-expm1: 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)

series39.0ms (0.6%)

Memory

10.6MiB live, 48.2MiB allocated

Counts

22 → 516

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (/ (+ (* -1/2 x) (/ 1 a)) x) (+ (* -1/2 x) (/ 1 a)) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (* (* (* (* a a) x) 1/2) x) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) a) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (+ (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* x a)) (- (exp (* a x)) 1) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* (+ (* (* 1/6 x) a) 1/2) a) (* (* a a) x) (* 1/6 x))
3.0ms	a	@	-inf	((/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (/ (+ (* -1/2 x) (/ 1 a)) x) (+ (* -1/2 x) (/ 1 a)) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (* (* (* (* a a) x) 1/2) x) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) a) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (+ (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* x a)) (- (exp (* a x)) 1) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* (+ (* (* 1/6 x) a) 1/2) a) (* (* a a) x) (* 1/6 x))
3.0ms	x	@	inf	((/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (/ (+ (* -1/2 x) (/ 1 a)) x) (+ (* -1/2 x) (/ 1 a)) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (* (* (* (* a a) x) 1/2) x) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) a) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (+ (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* x a)) (- (exp (* a x)) 1) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* (+ (* (* 1/6 x) a) 1/2) a) (* (* a a) x) (* 1/6 x))
3.0ms	a	@	inf	((/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (/ (+ (* -1/2 x) (/ 1 a)) x) (+ (* -1/2 x) (/ 1 a)) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (* (* (* (* a a) x) 1/2) x) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) a) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (+ (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* x a)) (- (exp (* a x)) 1) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* (+ (* (* 1/6 x) a) 1/2) a) (* (* a a) x) (* 1/6 x))
2.0ms	a	@	0	((/ 1 (/ 1 (- (exp (* a x)) 1))) (/ 1 (- (exp (* a x)) 1)) (/ (+ (* -1/2 x) (/ 1 a)) x) (+ (* -1/2 x) (/ 1 a)) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) a) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) x) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (* (* (* (* a a) x) 1/2) x) (- (exp (* a x)) 1) (* (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) a) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (+ (* (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* x a)) (* x a)) (- (exp (* a x)) 1) (* (* (+ (* (* 1/6 x) a) 1/2) a) x) (* (+ (* (* 1/6 x) a) 1/2) a) (* (* a a) x) (* 1/6 x))

simplify217.0ms (3.5%)

Memory

5.7MiB live, 206.2MiB allocated

Algorithm

1×	egg-herbie

Rules

17 528×	`lower-fma.f64`
17 528×	`lower-fma.f32`
7 382×	`lower-*.f64`
7 382×	`lower-*.f32`
3 504×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	420	5802
1	1427	5679
2	5111	5485
0	8274	4935

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 512

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

rewrite175.0ms (2.8%)

Memory

22.2MiB live, 208.9MiB allocated

Rules

6 772×	`lower-fma.f32`
6 762×	`lower-fma.f64`
4 212×	`lower-*.f32`
4 188×	`lower-*.f64`
3 328×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	389
0	78	385
1	301	377
2	2127	377
0	8201	349

Stop Event

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

Counts

22 → 367

Calls

Call 1

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

Outputs
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eval119.0ms (1.9%)

Memory: 1.7MiB live, 192.9MiB allocated
Compiler: Compiled 19 404 to 2 016 computations (89.6% saved)

prune39.0ms (0.6%)

Memory

-5.3MiB live, 82.6MiB allocated

Pruning

19 alts after pruning (10 fresh and 9 done)

	Pruned	Kept	Total
New	934	5	939
Fresh	2	5	7
Picked	3	2	5
Done	0	7	7
Total	939	19	958

Accuracy

100.0%

Counts

958 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.0%	(/.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)) x (/.f64 #s(literal 1 binary64) a)) x)))
	63.9%	(/.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)))
	66.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 #s(approx (+ (* -1/2 x) (/ 1 a)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) a) x #s(literal 1 binary64)) a)) x)))
	68.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x a)) #s(literal 1/2 binary64)))))
	9.3%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64))))
✓	18.6%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	20.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
	4.4%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
✓	4.3%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))
✓	18.1%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
✓	63.7%	#s(approx (- (exp (* x a)) 1) (*.f64 x a))
	63.2%	#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))))
	64.2%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) (.f64 x a) #s(literal 1 binary64)) (.f64 x a)))
✓	59.3%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
	62.8%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 x a)))
✓	63.2%	#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 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) x) a))
✓	62.8%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a))
	64.2%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) x x)))

Compiler

Compiled 608 to 315 computations (48.2% saved)

regimes44.0ms (0.7%)

Memory

-19.8MiB live, 57.3MiB 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))
#s(approx (- (exp (* x a)) 1) (*.f64 x a))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) 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 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) (-.f64 (/.f64 #s(literal 1 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 a x #s(literal 1 binary64))) #s(literal 1 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) x x)))
#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)) x) a))
#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 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) (.f64 x a) #s(literal 1 binary64)) (.f64 x a)))
#s(approx (- (exp (* x a)) 1) (.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))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) 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 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a) (*.f64 x a)))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) a (/.f64 #s(literal 1 binary64) 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 (.f64 (fma.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 #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 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 #s(approx (+ (* -1/2 x) (/ 1 a)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) a) x #s(literal 1 binary64)) a)) x)))
#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)))
(/.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)) x (/.f64 #s(literal 1 binary64) a)) x)))
(expm1.f64 (*.f64 x a))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

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

Calls

5 calls:

9.0ms	x
9.0ms	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)

regimes40.0ms (0.6%)

Memory

12.2MiB live, 50.7MiB allocated

Counts

28 → 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))
#s(approx (- (exp (* x a)) 1) (*.f64 x a))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) 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 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) (-.f64 (/.f64 #s(literal 1 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 a x #s(literal 1 binary64))) #s(literal 1 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) x x)))
#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)) x) a))
#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 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) (.f64 x a) #s(literal 1 binary64)) (.f64 x a)))
#s(approx (- (exp (* x a)) 1) (.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))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) 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 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x) (.f64 x a) (*.f64 x a)))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 #s(literal -1/2 binary64) a (/.f64 #s(literal 1 binary64) 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 (.f64 (fma.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 #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 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 #s(approx (+ (* -1/2 x) (/ 1 a)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) a) x #s(literal 1 binary64)) a)) x)))
#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)))
(/.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)) x (/.f64 #s(literal 1 binary64) a)) x)))

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

Calls

5 calls:

9.0ms	a
8.0ms	x
8.0ms	(*.f64 a x)
6.0ms	(exp.f64 (*.f64 a x))
6.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
68.6%	1	`a`
68.6%	1	`x`
68.6%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
68.6%	1	`(exp.f64 (*.f64 a x))`
68.6%	1	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes18.0ms (0.3%)

Memory

24.5MiB live, 24.5MiB allocated

Counts

11 → 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))
#s(approx (- (exp (* x a)) 1) (*.f64 x a))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64))))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 x a)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* (* a a) x) 1/2) 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 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 x a))))

Outputs

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

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

Calls

5 calls:

4.0ms	a
4.0ms	x
4.0ms	(*.f64 a x)
3.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
3.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
63.7%	1	`a`
63.7%	1	`x`
69.2%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
69.2%	2	`(exp.f64 (*.f64 a x))`
69.2%	2	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes50.0ms (0.8%)

Memory

-41.9MiB live, 18.8MiB allocated

Counts

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

Outputs

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

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

Calls

3 calls:

45.0ms	(exp.f64 (*.f64 a x))
2.0ms	(*.f64 a x)
2.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
69.2%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
69.2%	2	`(exp.f64 (*.f64 a x))`
69.2%	2	`(*.f64 a x)`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes6.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

5 → 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))
#s(approx (- (exp (* x a)) 1) (*.f64 x a))
(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
68.6%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
68.6%	2	`(exp.f64 (*.f64 a x))`
68.6%	2	`(*.f64 a x)`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes6.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

3 calls:

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

Results

Accuracy	Segments	Branch
63.7%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
63.7%	1	`(exp.f64 (*.f64 a x))`
63.7%	1	`(*.f64 a x)`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes8.0ms (0.1%)

Memory

-27.8MiB live, 10.8MiB 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
18.1%	1	`a`
18.1%	1	`x`
18.1%	1	`(*.f64 a x)`
18.1%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
18.1%	1	`(exp.f64 (*.f64 a x))`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6850.021387078846	-0.3827759393285982

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6850.021387078846	-0.3827759393285982

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6850.021387078846	-0.3827759393285982

Compiler

Compiled 9 to 9 computations (0% saved)

simplify28.0ms (0.4%)

Memory

3.6MiB live, 42.1MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`-commutative-binary64-.f64`
12×	`unsub-neg-binary64--.f64-neg.f64-+.f64`
10×	`neg-mul-1-binary64-*.f64-neg.f64`
8×	`+-commutative-binary64-+.f64`
8×	`sub-neg-binary64-neg.f64-+.f64--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	214
1	68	214
2	75	214
3	81	214
4	89	214
5	100	214

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)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x a)) #s(literal 1/2 binary64)))))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 x a))))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a)))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (*.f64 x a)))
#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)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x a)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 a x)) #s(literal 1/2 binary64)))))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 x a))))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64)) (.f64 a x))))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))) x) a)))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (.f64 (.f64 #s(approx (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* a x)) 1/2) x) a) 1) (fma.f64 #s(literal 1/2 binary64) (*.f64 a x) #s(literal 1 binary64))) x) a)))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (*.f64 x a)))
(if (<=.f64 (.f64 a x) #s(literal -5000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* -1/2 x) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (*.f64 a x)))
#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))

soundness1.8s (28.3%)

Memory

36.4MiB live, 734.8MiB allocated

Rules

25 112×	`lower-fma.f64`
25 112×	`lower-fma.f32`
20 954×	`lower-fma.f64`
20 954×	`lower-fma.f32`
17 528×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
0	9	13
1	30	13
2	152	13
0	1346	11
0	317	3586
1	1038	3548
2	3340	3462
0	8272	3054
0	420	5802
1	1427	5679
2	5111	5485
0	8274	4935
0	29	182
0	51	180
1	216	180
2	1479	180
0	8370	180
0	392	4685
1	1328	4642
2	4709	4484
0	8391	3969
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×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 276 to 174 computations (37% saved)

preprocess112.0ms (1.8%)

Memory: 14.2MiB live, 91.1MiB allocated
Remove: (sort a x)
Compiler: Compiled 220 to 118 computations (46.4% 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	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

start0.0ms (0%)

analyze19.0ms (0.3%)

sample594.0ms (9.5%)

explain68.0ms (1.1%)

preprocess85.0ms (1.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize16.0ms (0.3%)

series5.0ms (0.1%)

simplify209.0ms (3.3%)

rewrite72.0ms (1.2%)

eval23.0ms (0.4%)

prune9.0ms (0.1%)

simplify234.0ms (3.7%)

localize131.0ms (2.1%)

series30.0ms (0.5%)

simplify183.0ms (2.9%)

rewrite175.0ms (2.8%)

eval188.0ms (3%)

prune33.0ms (0.5%)

simplify338.0ms (5.4%)

localize112.0ms (1.8%)

series55.0ms (0.9%)

simplify417.0ms (6.7%)

rewrite153.0ms (2.5%)

eval149.0ms (2.4%)

prune47.0ms (0.7%)

simplify110.0ms (1.8%)

localize124.0ms (2%)

series39.0ms (0.6%)

simplify217.0ms (3.5%)

rewrite175.0ms (2.8%)

eval119.0ms (1.9%)

prune39.0ms (0.6%)

regimes44.0ms (0.7%)

regimes40.0ms (0.6%)

regimes18.0ms (0.3%)

regimes50.0ms (0.8%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes8.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify28.0ms (0.4%)

soundness1.8s (28.3%)

preprocess112.0ms (1.8%)

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