Metrics for expax (section 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze18.0ms (0.3%)

Memory

14.8MiB live, 14.8MiB 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)

sample1.1s (18.7%)

Memory

5.6MiB live, 550.1MiB allocated

Samples

730.0ms	8 256×	0	valid
13.0ms	314×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 441.0ms

ival-mult: 262.0ms (59.4% of total)

ival-expm1: 146.0ms (33.1% of total)

ival->: 22.0ms (5% of total)

exact: 8.0ms (1.8% of total)

ival-assert: 4.0ms (0.9% of total)

Bogosity

explain72.0ms (1.2%)

Memory

1.8MiB live, 115.2MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`	cancellation	134	0

Confusion

	Predicted +	Predicted -
+	134	0
-	0	122

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	134	0	0
-	0	1	121

Precision?

0.9925925925925926

Recall?

1.0

Freqs

test

number	freq
0	122
1	134

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

28.0ms

512×

valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-exp: 4.0ms (33% of total)

ival-mult: 4.0ms (33% of total)

ival-expm1: 3.0ms (24.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess16.0ms (0.3%)

Memory

24.6MiB live, 24.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs
(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

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.6%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 6 to 6 computations (0% saved)

simplify3.0ms (0%)

Memory

3.3MiB live, 3.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize32.0ms (0.5%)

Memory

-32.9MiB live, 18.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a x)
accuracy	0.02838588492458946	(exp.f64 (*.f64 a x))
accuracy	30.332561332980568	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Samples

26.0ms

256×

valid

Compiler

Compiled 34 to 14 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-exp: 15.0ms (76% of total)

ival-mult: 3.0ms (15.2% of total)

ival-expm1: 2.0ms (10.1% 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

4.7MiB live, 4.7MiB allocated

Counts

3 → 72

Calls

Call 1

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

Inputs

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

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

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

Outputs
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf a) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 a x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (exp.f64 (*.f64 a x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (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)))

simplify215.0ms (3.6%)

Memory

-6.9MiB live, 107.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

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

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

rewrite71.0ms (1.2%)

Memory

6.7MiB live, 87.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 111

Calls

Call 1

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

Outputs
#<batchref>
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#<batchref>

eval22.0ms (0.4%)

Memory: 5.7MiB live, 44.0MiB allocated
Compiler: Compiled 3 512 to 343 computations (90.2% saved)

prune10.0ms (0.2%)

Memory

-8.0MiB live, 31.3MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	174	9	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	9	184

Accuracy

100.0%

Counts

184 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	20.3%	(-.f64 #s(approx (exp (* a x)) (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))) #s(literal 1 binary64))
▶	18.8%	(-.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))
▶	20.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
▶	18.3%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 x a))
	66.7%	#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)))
	67.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
	61.0%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
	67.0%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 280 to 200 computations (28.6% saved)

simplify53.0ms (0.9%)

Memory

23.3MiB live, 64.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	212
0	49	212
1	87	212
2	146	212
3	310	212
4	700	212
5	1433	212
6	1669	212
7	1739	212
8	1811	212
9	1951	212
10	2061	212
11	2061	212
12	2061	212
13	2212	212
0	2212	212

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize76.0ms (1.3%)

Memory

5.4MiB live, 121.8MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.3359375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	1.428165466834202	(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	21.112758896644753	#s(approx (exp (* a x)) (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)))
accuracy	30.332561332980568	(-.f64 #s(approx (exp (* a x)) (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))) #s(literal 1 binary64))
accuracy	1.4278771399345533	(fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))
accuracy	10.995447098033353	(.f64 (.f64 a a) x)
accuracy	21.14415818453837	#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	30.332561332980568	(-.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	21.35098398928095	#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
accuracy	30.332561332980568	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	21.582843514815302	#s(approx (exp (* a x)) #s(literal 1 binary64))
accuracy	30.332561332980568	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(*.f64 x a)
accuracy	0.022684980164287515	(expm1.f64 (*.f64 x a))

Samples

57.0ms

256×

valid

Compiler

Compiled 367 to 54 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 17.0ms (46.4% of total)

ival-add: 11.0ms (30% of total)

const: 4.0ms (10.9% of total)

ival-expm1: 3.0ms (8.2% of total)

ival-exp: 2.0ms (5.5% of total)

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

exact: 0.0ms (0% of total)

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

series35.0ms (0.6%)

Memory

-27.7MiB live, 52.3MiB allocated

Counts

17 → 396

Calls

Call 1

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

Outputs
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (expm1.f64 (*.f64 x a)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (expm1.f64 (*.f64 x a)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (expm1.f64 (*.f64 x a)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (expm1.f64 (*.f64 x a)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (*.f64 x a) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (*.f64 x a) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 a) (#s(alt #<batchref> (patch (*.f64 x a) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (.f64 a a) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
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) (exp (* a x)) (+ (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) 1) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (* a a) x) (* 1/6 x))
2.0ms	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) (exp (* a x)) (+ (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) 1) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (* a a) x) (* 1/6 x))
2.0ms	x	@	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) (exp (* a x)) (+ (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) 1) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (* a a) x) (* 1/6 x))
2.0ms	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) (exp (* a x)) (+ (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) 1) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (* a a) x) (* 1/6 x))
2.0ms	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) (exp (* a x)) (+ (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) 1) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (* a a) x) (* 1/6 x))

simplify198.0ms (3.3%)

Memory

27.6MiB live, 220.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	211	3108
1	707	3103
2	2339	3003
3	6186	2990
0	8501	2591

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

rewrite207.0ms (3.5%)

Memory

12.1MiB live, 292.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	177
0	49	177
1	209	177
2	1532	177
0	8086	177

Stop Event

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

Counts

17 → 405

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

Outputs
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eval197.0ms (3.3%)

Memory: -27.5MiB live, 289.9MiB allocated
Compiler: Compiled 26 736 to 1 880 computations (93% saved)

prune32.0ms (0.5%)

Memory

-1.3MiB live, 76.5MiB allocated

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	835	5	840
Fresh	2	2	4
Picked	1	4	5
Done	0	0	0
Total	838	11	849

Accuracy

100.0%

Counts

849 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	20.3%	(-.f64 #s(approx (exp (* a x)) (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))) #s(literal 1 binary64))
▶	19.1%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	20.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
▶	6.9%	(-.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))
✓	18.3%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
	62.9%	#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a))
▶	61.0%	#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
▶	67.0%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
	66.7%	#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)))
▶	67.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))

Compiler

Compiled 338 to 238 computations (29.6% saved)

simplify45.0ms (0.8%)

Memory

0.8MiB live, 43.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	305
0	63	302
1	110	302
2	192	302
3	341	302
4	701	302
5	1289	302
6	1560	302
7	1659	302
8	1751	302
9	1783	302
10	1783	302
11	1783	302
12	1971	302
0	1971	296

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize87.0ms (1.5%)

Memory

31.1MiB live, 104.2MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.1171875	(.f64 (.f64 a x) a)
accuracy	1.4278771399345533	(fma.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))
accuracy	21.14415818453837	#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x #s(literal 1 binary64)))
accuracy	30.332561332980568	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	10.995447098033353	(.f64 (.f64 a a) x)
accuracy	21.14415818453837	#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	30.332561332980568	(-.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	41.978217917728	#s(approx (+ (* (+ (* (* (* a a) x) 1/2) a) x) 1) (.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x))
accuracy	0.01171875	(fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a)
accuracy	1.4356896399345533	(.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)
accuracy	10.995447098033353	(.f64 (.f64 a a) x)
accuracy	21.58515930531674	#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
accuracy	0	(*.f64 a x)
accuracy	21.12439651230843	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
accuracy	0.08984375	(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
accuracy	0.3359375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	1.428165466834202	(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	20.716160993570117	#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

65.0ms

256×

valid

Compiler

Compiled 516 to 74 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 23.0ms (53.2% of total)

ival-add: 11.0ms (25.4% of total)

const: 4.0ms (9.2% of total)

ival-expm1: 3.0ms (6.9% of total)

ival-exp: 2.0ms (4.6% of total)

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

exact: 0.0ms (0% of total)

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

series41.0ms (0.7%)

Memory

-3.3MiB live, 81.2MiB allocated

Counts

20 → 468

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	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) (* a x) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (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) (exp (* a x)) (+ (* (+ (* (* (* a x) a) 1/2) a) x) 1) (+ (* (* (* a x) a) 1/2) a) (* 1/6 x) (* (* a x) a))
4.0ms	x	@	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) (* a x) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (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) (exp (* a x)) (+ (* (+ (* (* (* a x) a) 1/2) a) x) 1) (+ (* (* (* a x) a) 1/2) a) (* 1/6 x) (* (* a x) 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) (* a x) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (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) (exp (* a x)) (+ (* (+ (* (* (* a x) a) 1/2) a) x) 1) (+ (* (* (* a x) a) 1/2) a) (* 1/6 x) (* (* a x) 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) (* a x) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (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) (exp (* a x)) (+ (* (+ (* (* (* a x) a) 1/2) a) x) 1) (+ (* (* (* a x) a) 1/2) a) (* 1/6 x) (* (* a x) a))
2.0ms	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) (* a x) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (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) (exp (* a x)) (+ (* (+ (* (* (* a x) a) 1/2) a) x) 1) (+ (* (* (* a x) a) 1/2) a) (* 1/6 x) (* (* a x) a))

simplify322.0ms (5.5%)

Memory

-48.0MiB live, 157.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	195	3932
1	662	3904
2	2088	3836
3	4164	3832
0	8429	3396

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 464

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
(+ 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))))))))
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))))
(* (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)
(* 1/6 (* (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)
(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)
(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)))
(* (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)
(* 1/6 (* (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)
(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)
(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)))
(* (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)
(* 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
(+ 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))))))))
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)))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(- (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)
(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)
(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)))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(- (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)
(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)
(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)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)
(* (pow a 2) x)

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

rewrite223.0ms (3.8%)

Memory

14.6MiB live, 211.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	257
0	63	254
1	229	254
2	1173	254
0	8238	248

Stop Event

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

Counts

20 → 492

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

Outputs
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eval134.0ms (2.3%)

Memory: -24.6MiB live, 248.2MiB allocated
Compiler: Compiled 36 228 to 2 096 computations (94.2% saved)

prune109.0ms (1.8%)

Memory

-3.3MiB live, 74.9MiB allocated

Pruning

15 alts after pruning (6 fresh and 9 done)

	Pruned	Kept	Total
New	1 016	5	1 021
Fresh	1	1	2
Picked	0	5	5
Done	0	4	4
Total	1 017	15	1 032

Accuracy

100.0%

Counts

1 032 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	20.3%	(-.f64 #s(approx (exp (* a x)) (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))) #s(literal 1 binary64))
✓	19.1%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	20.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
✓	6.9%	(-.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))
✓	18.3%	(-.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 a a) x) #s(literal 1/2 binary64) a) x))
▶	66.3%	#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) x) a))
✓	67.0%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
▶	17.8%	#s(approx (- (exp (* x a)) 1) #s(approx (* (+ (* (* (* a a) x) 1/2) a) x) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x a)) x) a)))
	66.7%	#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)))
✓	67.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
▶	66.3%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 #s(literal 1/2 binary64) a)) x #s(literal 1 binary64)) (.f64 x a)))
▶	67.6%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x) a))
▶	18.8%	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64)) a) x)) (.f64 x a)))

Compiler

Compiled 455 to 321 computations (29.5% saved)

simplify53.0ms (0.9%)

Memory

11.0MiB live, 49.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	401
0	75	401
1	134	401
2	242	399
3	415	399
4	855	399
5	1188	399
6	1764	399
7	2184	399
8	2356	399
9	2384	399
10	2569	399
11	2613	399
12	2622	399
13	2622	399
14	2797	399
0	2797	389

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize99.0ms (1.7%)

Memory

23.3MiB live, 102.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.09375	(fma.f64 #s(literal 1/6 binary64) (*.f64 x a) #s(literal 1/2 binary64))
accuracy	1.435977966834202	(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 x a) #s(literal 1/2 binary64)) a) x)
accuracy	20.716160993570117	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64)) a) x)) (.f64 x a)))
accuracy	41.89870748272419	#s(approx (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 x a) #s(literal 1/2 binary64)) a) x))
accuracy	0	(*.f64 x a)
accuracy	0.0390625	(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) x)
accuracy	2.617409386180029	(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) x) a)
accuracy	21.58515930531674	#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) x) a))
accuracy	0.046875	(.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 #s(literal 1/2 binary64) a)) x #s(literal 1 binary64)) (.f64 x a))
accuracy	1.428165466834202	(fma.f64 #s(approx (* (+ (* (* 1/6 x) a) 1/2) a) (*.f64 #s(literal 1/2 binary64) a)) x #s(literal 1 binary64))
accuracy	20.716160993570117	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 #s(literal 1/2 binary64) a)) x #s(literal 1 binary64)) (.f64 x a)))
accuracy	21.984810920464678	#s(approx (* (+ (* (* 1/6 x) a) 1/2) a) (*.f64 #s(literal 1/2 binary64) a))
accuracy	0.1171875	(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x a)) x)
accuracy	6.539863098848968	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x a)) x) a)
accuracy	21.58515930531674	#s(approx (- (exp (* x a)) 1) #s(approx (* (+ (* (* (* a a) x) 1/2) a) x) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x a)) x) a)))
accuracy	32.53912117662463	#s(approx (* (+ (* (* (* a a) x) 1/2) a) x) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x a)) x) a))
accuracy	0.3359375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	1.418947880335639	(.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	1.428165466834202	(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	20.716160993570117	#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))

Samples

74.0ms

256×

valid

Compiler

Compiled 697 to 89 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 33.0ms (64.3% of total)

ival-add: 8.0ms (15.6% of total)

const: 7.0ms (13.6% of total)

ival-expm1: 3.0ms (5.8% of total)

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

exact: 0.0ms (0% of total)

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

series46.0ms (0.8%)

Memory

-22.1MiB live, 53.8MiB allocated

Counts

23 → 540

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	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) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (* (* (* 1/2 (* x a)) x) a) (* (* 1/2 (* x a)) 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) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* x a)) 1) (* (* (+ (* 1/2 (* x a)) 1) x) a) (* (+ (* 1/2 (* x a)) 1) x) (+ (* 1/2 (* x a)) 1) (- (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) x) (* 1/6 x) (* x a) (+ (* 1/6 (* x a)) 1/2))
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) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (* (* (* 1/2 (* x a)) x) a) (* (* 1/2 (* x a)) 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) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* x a)) 1) (* (* (+ (* 1/2 (* x a)) 1) x) a) (* (+ (* 1/2 (* x a)) 1) x) (+ (* 1/2 (* x a)) 1) (- (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) x) (* 1/6 x) (* x a) (+ (* 1/6 (* x a)) 1/2))
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) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (* (* (* 1/2 (* x a)) x) a) (* (* 1/2 (* x a)) 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) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* x a)) 1) (* (* (+ (* 1/2 (* x a)) 1) x) a) (* (+ (* 1/2 (* x a)) 1) x) (+ (* 1/2 (* x a)) 1) (- (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) x) (* 1/6 x) (* x a) (+ (* 1/6 (* x a)) 1/2))
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) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (* (* (* 1/2 (* x a)) x) a) (* (* 1/2 (* x a)) 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) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* x a)) 1) (* (* (+ (* 1/2 (* x a)) 1) x) a) (* (+ (* 1/2 (* x a)) 1) x) (+ (* 1/2 (* x a)) 1) (- (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) x) (* 1/6 x) (* x a) (+ (* 1/6 (* x a)) 1/2))
3.0ms	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) x) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (* (* (* 1/2 (* x a)) x) a) (* (* 1/2 (* x a)) 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) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* x a)) 1) (* (* (+ (* 1/2 (* x a)) 1) x) a) (* (+ (* 1/2 (* x a)) 1) x) (+ (* 1/2 (* x a)) 1) (- (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) x) (* 1/6 x) (* x a) (+ (* 1/6 (* x a)) 1/2))

simplify158.0ms (2.7%)

Memory

4.5MiB live, 121.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	210	5312
1	745	5070
2	2350	5030
3	5920	5024
0	8462	4468

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 536

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

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

rewrite184.0ms (3.1%)

Memory

28.3MiB live, 181.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	342
0	75	342
1	230	342
2	1145	334
0	8292	324

Stop Event

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

Counts

23 → 561

Calls

Call 1

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

Outputs
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eval218.0ms (3.7%)

Memory: -8.1MiB live, 227.1MiB allocated
Compiler: Compiled 42 136 to 2 819 computations (93.3% saved)

prune48.0ms (0.8%)

Memory

-7.5MiB live, 105.8MiB allocated

Pruning

16 alts after pruning (2 fresh and 14 done)

	Pruned	Kept	Total
New	1 248	1	1 249
Fresh	0	1	1
Picked	0	5	5
Done	0	9	9
Total	1 248	16	1 264

Accuracy

100.0%

Counts

1 264 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	20.3%	(-.f64 #s(approx (exp (* a x)) (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))) #s(literal 1 binary64))
✓	19.1%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	20.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
✓	6.9%	(-.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))
✓	18.3%	(-.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 a a) x) #s(literal 1/2 binary64) a) x))
✓	66.3%	#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) x) a))
✓	67.0%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
✓	17.8%	#s(approx (- (exp (* x a)) 1) #s(approx (* (+ (* (* (* a a) x) 1/2) a) x) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x a)) x) a)))
	66.7%	#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)))
✓	67.6%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
✓	66.3%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 #s(literal 1/2 binary64) a)) x #s(literal 1 binary64)) (.f64 x a)))
✓	67.6%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x) a))
✓	18.8%	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64)) a) x)) (.f64 x a)))
	19.1%	#s(approx (- (exp (* a x)) 1) (.f64 #s(approx (+ ( (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (.f64 (.f64 #s(approx (+ (* 1/6 (* x a)) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) x) a)) a) x)) (*.f64 x a)))

Compiler

Compiled 755 to 352 computations (53.4% saved)

regimes57.0ms (1%)

Memory

11.8MiB live, 62.8MiB allocated

Counts

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

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

Calls

5 calls:

33.0ms	x
7.0ms	a
6.0ms	(*.f64 a x)
5.0ms	(exp.f64 (*.f64 a x))
5.0ms	(-.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)

regimes31.0ms (0.5%)

Memory

-17.2MiB live, 58.9MiB allocated

Counts

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

Outputs

(-.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)) 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)))

Calls

5 calls:

8.0ms	a
7.0ms	(*.f64 a x)
6.0ms	x
5.0ms	(exp.f64 (*.f64 a x))
4.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
67.6%	1	`a`
69.8%	2	`x`
71.1%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
71.1%	2	`(exp.f64 (*.f64 a x))`
71.1%	2	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes15.0ms (0.3%)

Memory

28.1MiB live, 28.1MiB allocated

Counts

18 → 2

Calls

Call 1

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

Outputs

(-.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)) 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))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
70.9%	2	`(exp.f64 (*.f64 a x))`
70.9%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
71.0%	2	`(*.f64 a x)`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes14.0ms (0.2%)

Memory

-14.1MiB live, 23.8MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

6.0ms	(*.f64 a x)
4.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
3.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
70.6%	2	`(exp.f64 (*.f64 a x))`
70.6%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
70.6%	2	`(*.f64 a x)`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes19.0ms (0.3%)

Memory

-12.5MiB live, 30.6MiB allocated

Counts

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

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

Calls

5 calls:

7.0ms	x
3.0ms	a
3.0ms	(*.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
67.0%	1	`a`
67.0%	1	`x`
67.0%	1	`(exp.f64 (*.f64 a x))`
67.0%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
67.0%	1	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes6.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB 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:

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

Results

Accuracy	Segments	Branch
18.3%	1	`x`
18.3%	1	`a`
18.3%	1	`(*.f64 a x)`
18.3%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
18.3%	1	`(exp.f64 (*.f64 a x))`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.308158726700253	-0.08379621963373791

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2292731.5464727725	-7997.530813186862

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.308158726700253	-0.08379621963373791

Compiler

Compiled 9 to 9 computations (0% saved)

simplify24.0ms (0.4%)

Memory

9.6MiB live, 47.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	206
1	78	206
2	83	206
3	86	206
4	89	206
5	93	206

Stop Event

1×

saturated

Calls

Call 1

Inputs
(expm1.f64 (*.f64 x a))
(if (<=.f64 (.f64 a x) #s(literal -5 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)) 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))))
(if (<=.f64 (.f64 a x) #s(literal -2000000 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)) 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)))
(if (<=.f64 (.f64 a x) #s(literal -5 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)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 #s(literal 1/2 binary64) a)) x #s(literal 1 binary64)) (.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 a x))
(if (<=.f64 (.f64 a x) #s(literal -5 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)) 1) (.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)) (*.f64 a x))))
(if (<=.f64 (.f64 a x) #s(literal -2000000 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)) 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)))
(if (<=.f64 (.f64 a x) #s(literal -5 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)) 1) (.f64 (fma.f64 #s(approx ( (+ (* (* 1/6 x) a) 1/2) a) (.f64 #s(literal 1/2 binary64) a)) x #s(literal 1 binary64)) (.f64 a x))))
#s(approx (- (exp (* a x)) 1) (*.f64 a x))
(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))

soundness1.5s (25.7%)

Memory

-5.2MiB live, 536.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	257
0	63	254
1	229	254
2	1173	254
0	8238	248
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
0	211	3108
1	707	3103
2	2339	3003
3	6186	2990
0	8501	2591
0	6	13
0	9	13
1	30	13
2	152	13
0	1346	11
0	195	3932
1	662	3904
2	2088	3836
3	4164	3832
0	8429	3396

Stop Event

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

Compiler

Compiled 248 to 106 computations (57.3% saved)

preprocess87.0ms (1.5%)

Memory: 7.6MiB live, 122.2MiB allocated
Remove: (sort a x)
Compiler: Compiled 456 to 164 computations (64% 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%)

analyze18.0ms (0.3%)

sample1.1s (18.7%)

explain72.0ms (1.2%)

preprocess16.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize32.0ms (0.5%)

series5.0ms (0.1%)

simplify215.0ms (3.6%)

rewrite71.0ms (1.2%)

eval22.0ms (0.4%)

prune10.0ms (0.2%)

simplify53.0ms (0.9%)

localize76.0ms (1.3%)

series35.0ms (0.6%)

simplify198.0ms (3.3%)

rewrite207.0ms (3.5%)

eval197.0ms (3.3%)

prune32.0ms (0.5%)

simplify45.0ms (0.8%)

localize87.0ms (1.5%)

series41.0ms (0.7%)

simplify322.0ms (5.5%)

rewrite223.0ms (3.8%)

eval134.0ms (2.3%)

prune109.0ms (1.8%)

simplify53.0ms (0.9%)

localize99.0ms (1.7%)

series46.0ms (0.8%)

simplify158.0ms (2.7%)

rewrite184.0ms (3.1%)

eval218.0ms (3.7%)

prune48.0ms (0.8%)

regimes57.0ms (1%)

regimes31.0ms (0.5%)

regimes15.0ms (0.3%)

regimes14.0ms (0.2%)

regimes19.0ms (0.3%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify24.0ms (0.4%)

soundness1.5s (25.7%)

preprocess87.0ms (1.5%)

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