Metrics for expax (section 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze21.0ms (0.3%)

Memory

-17.3MiB live, 24.2MiB 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)

sample593.0ms (7.3%)

Memory

60.3MiB live, 636.2MiB allocated

Samples

337.0ms	8 256×	0	valid
13.0ms	322×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 162.0ms

ival-mult: 66.0ms (40.6% of total)

ival-expm1: 53.0ms (32.6% of total)

ival->: 34.0ms (20.9% of total)

exact: 6.0ms (3.7% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

explain108.0ms (1.3%)

Memory

-19.4MiB live, 104.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
131	1	(-4.451667057314674e-92 1.1309548702573366e-232)	-	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
0	0	-	-	`a`
0	0	-	-	`(exp.f64 (*.f64 a x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 a x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`	cancellation	132	0

Confusion

	Predicted +	Predicted -
+	131	0
-	1	124

Precision

0.9924242424242424

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	0
-	1	0	124

Precision?

0.9924242424242424

Recall?

1.0

Freqs

test

number	freq
0	124
1	132

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 44 to 22 computations (50% saved)

Precisions

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

ival-mult: 5.0ms (38.4% of total)

ival-exp: 4.0ms (30.8% of total)

ival-expm1: 3.0ms (23.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess21.0ms (0.3%)

Memory

-1.7MiB live, 35.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort a x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.0%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0%)

Memory

7.4MiB live, 7.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 a x)
cost-diff	0	(exp.f64 (*.f64 a x))
cost-diff	192	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize23.0ms (0.3%)

Memory

-11.1MiB live, 30.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a x)
accuracy	0.014003759768442016	(exp.f64 (*.f64 a x))
accuracy	30.07484880937281	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Samples

17.0ms

256×

valid

Compiler

Compiled 18 to 8 computations (55.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (58.8% of total)

ival-exp: 3.0ms (29.4% of total)

ival-expm1: 2.0ms (19.6% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

3 → 72

Calls

Call 1

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

Outputs
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))>
#<alt (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>

Calls

18 calls:

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

simplify287.0ms (3.5%)

Memory

1.6MiB live, 193.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8 560×	`lower-fma.f64`
8 560×	`lower-fma.f32`
3 454×	`associate-r`
2 992×	`lower-*.f64`
2 992×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	432
1	195	432
2	526	424
3	1050	424
4	1650	424
5	1848	424
6	1875	424
7	1895	424
8	1909	424
9	1912	424
10	1912	424
11	2607	420
12	3082	420
13	4049	420
14	4050	420
15	4050	420
16	4178	420
17	4178	420
18	6095	416
19	6319	416
20	6361	416
21	6375	416
22	6375	416
23	6551	416
24	6889	416
25	6889	416
26	7463	416
0	7463	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))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
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))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* 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))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(exp (* a x))
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)

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

rewrite86.0ms (1.1%)

Memory

-20.1MiB live, 105.2MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 111

Calls

Call 1

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

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

eval19.0ms (0.2%)

Memory: 32.6MiB live, 32.6MiB allocated
Compiler: Compiled 3 258 to 325 computations (90% saved)

prune25.0ms (0.3%)

Memory

-16.9MiB live, 59.3MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

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

Accuracy

100.0%

Counts

184 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
	53.0%	(-.f64 (pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 1 binary64))
▶	20.5%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 a x))
	65.2%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 a (.f64 x x)) (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)))
▶	64.3%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x)))
▶	64.3%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
	68.9%	#s(approx (- (exp (* a x)) 1) (*.f64 a x))

Compiler

Compiled 198 to 122 computations (38.4% saved)

simplify486.0ms (6%)

Memory

2.1MiB live, 348.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x x)
cost-diff	0	(*.f64 a (+.f64 x x))
cost-diff	0	(expm1.f64 (*.f64 a (+.f64 x x)))
cost-diff	7808	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
cost-diff	0	(.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x)
cost-diff	0	(.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x x))
cost-diff	0	(fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
cost-diff	0	(.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
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 a x)
cost-diff	0	(expm1.f64 (*.f64 a x))

Rules

16 280×	`lower-fma.f32`
16 272×	`lower-fma.f64`
5 134×	`lower-+.f32`
5 130×	`lower-+.f64`
2 994×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	230
0	57	221
1	121	221
2	291	221
3	809	221
4	2027	221
5	3558	221
6	5604	221
7	5990	221
8	7862	221
0	8297	221

Stop Event

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

Calls

Call 1

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

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

localize93.0ms (1.1%)

Memory

25.6MiB live, 150.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
accuracy	0.014003759768442016	(expm1.f64 (*.f64 a (+.f64 x x)))
accuracy	0.014003759768442016	(exp.f64 (*.f64 a x))
accuracy	0.015625	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
accuracy	0.3515625	(*.f64 x #s(literal 1/24 binary64))
accuracy	0.9793933225553222	(.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x))
accuracy	4.313869592946435	(fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x)
accuracy	20.294237130866314	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x)))
accuracy	0.0078125	(.f64 #s(literal 1/2 binary64) (.f64 x x))
accuracy	0.9730907896375589	(.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))
accuracy	5.4177278485836835	(fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
accuracy	20.46349797868629	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
accuracy	20.37212660336736	#s(approx (exp (* a x)) #s(literal 1 binary64))
accuracy	30.07484880937281	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(*.f64 a x)
accuracy	0.014003759768442016	(expm1.f64 (*.f64 a x))

Samples

60.0ms

256×

valid

Compiler

Compiled 221 to 31 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 21.0ms (48.1% of total)

const: 9.0ms (20.6% of total)

ival-add: 7.0ms (16% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.3%)

Memory

1.4MiB live, 39.8MiB allocated

Counts

19 → 420

Calls

Call 1

Inputs
#<alt (expm1.f64 (*.f64 a x))>
#<alt (*.f64 a x)>
#<alt (-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))>
#<alt #s(approx (exp (* a x)) #s(literal 1 binary64))>
#<alt #s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))>
#<alt (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))>
#<alt (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)>
#<alt (.f64 #s(literal 1/2 binary64) (.f64 x x))>
#<alt #s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x)))>
#<alt (.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x))>
#<alt (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x)>
#<alt (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))>
#<alt (/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))>
#<alt (expm1.f64 (*.f64 a (+.f64 x x)))>
#<alt (*.f64 a (+.f64 x x))>
#<alt (+.f64 x x)>
#<alt (*.f64 x #s(literal 1/24 binary64))>
#<alt (exp.f64 (*.f64 a x))>
#<alt (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>

Outputs
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))>
#<alt (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))>
#<alt (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))>
#<alt (* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 (* a x))))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt (* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))>
#<alt (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))>
#<alt (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (* a x)>
#<alt (* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (* 2 (* a x))>
#<alt (* a (+ (* 2 x) (* 2 (* a (pow x 2)))))>
#<alt (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2))))))>
#<alt (* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 2/3 (* a (pow x 4))) (* 4/3 (pow x 3))))))))>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (* 2 (* a x))>
#<alt (* x (+ (* 2 a) (* 2 (* (pow a 2) x))))>
#<alt (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2))))))>
#<alt (* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 2/3 (* (pow a 4) x)) (* 4/3 (pow a 3))))))))>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (- (exp (* 2 (* a x))) 1)>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 (* a x))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))>
#<alt (+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt 1>
#<alt (+ 1 (* a x))>
#<alt (+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt (exp (* a x))>
#<alt 2>
#<alt (+ 2 (* a x))>
#<alt (+ 2 (* a (+ x (* 1/2 (* a (pow x 2))))))>
#<alt (+ 2 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt 2>
#<alt (+ 2 (* a x))>
#<alt (+ 2 (* x (+ a (* 1/2 (* (pow a 2) x)))))>
#<alt (+ 2 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>
#<alt (+ 1 (exp (* a x)))>

Calls

105 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* a (+ (* a (* 1/2 (* x x))) x))
3.0ms	x	@	0	(/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1))
1.0ms	a	@	0	(* a (+ (* a (* x (* x (+ (* (* a x) (+ (* a (* x 1/24)) 1/6)) 1/2)))) x))
1.0ms	a	@	0	(* a (+ (* a (* 1/2 (* x x))) x))
1.0ms	a	@	0	(/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1))

simplify343.0ms (4.2%)

Memory

-16.8MiB live, 499.0MiB allocated

Algorithm

1×	egg-herbie

Rules

20 526×	`lower-fma.f64`
20 526×	`lower-fma.f32`
5 738×	`lower-+.f64`
5 738×	`lower-+.f32`
5 400×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	365	4235
1	1199	4104
2	3651	4066
0	8213	3634

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 416

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

Outputs
(* a x)
(*.f64 a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 x (fma.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 a a)) a))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 a (fma.f64 a (fma.f64 a (.f64 a (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (.f64 x (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 a x))
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(* a x)
(*.f64 a x)
(* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))
(.f64 x (fma.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 a a)) a))
(* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 a (.f64 a a)) #s(literal 5/12 binary64) (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 (.f64 a a) #s(literal -1/2 binary64))))) (.f64 #s(literal 1/2 binary64) (*.f64 a a))) a))
(* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(.f64 x (fma.f64 x (fma.f64 a (.f64 a #s(literal 1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 (.f64 a a) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 a (.f64 a a)) #s(literal 5/12 binary64) (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 (.f64 a a) #s(literal -1/2 binary64))))) (.f64 a #s(literal -1/2 binary64)))) (fma.f64 (.f64 a (.f64 a a)) #s(literal 5/12 binary64) (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 (*.f64 a a) #s(literal -1/2 binary64)))))))) a))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64)))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* a (+ (* 2 x) (* 2 (* a (pow x 2)))))
(.f64 (.f64 x #s(literal 2 binary64)) (fma.f64 a (*.f64 a x) a))
(* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2))))))
(.f64 a (fma.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 4/3 binary64)) x #s(literal 2 binary64))) (*.f64 x #s(literal 2 binary64))))
(* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 2/3 (* a (pow x 4))) (* 4/3 (pow x 3))))))))
(.f64 a (fma.f64 a (fma.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 4/3 binary64)) x #s(literal 2 binary64)) (.f64 (.f64 a (.f64 (.f64 x x) (.f64 x x))) (.f64 a #s(literal 2/3 binary64)))) (.f64 x #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* x (+ (* 2 a) (* 2 (* (pow a 2) x))))
(.f64 (.f64 x #s(literal 2 binary64)) (fma.f64 a (*.f64 a x) a))
(* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2))))))
(.f64 x (fma.f64 x (fma.f64 a (.f64 a #s(literal 2 binary64)) (.f64 (.f64 a (.f64 x (.f64 a a))) #s(literal 4/3 binary64))) (*.f64 a #s(literal 2 binary64))))
(* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 2/3 (* (pow a 4) x)) (* 4/3 (pow a 3))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 a (.f64 (.f64 a a) #s(literal 4/3 binary64)) (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 x #s(literal 2/3 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 a (*.f64 a x) a))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(- (exp (* 2 (* a x))) 1)
(expm1.f64 (.f64 x (.f64 a #s(literal 2 binary64))))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 (* a x))
(.f64 x (.f64 a #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
1
#s(literal 1 binary64)
(+ 1 (* a x))
(fma.f64 a x #s(literal 1 binary64))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(fma.f64 a (fma.f64 x (.f64 a (.f64 x #s(literal 1/2 binary64))) x) #s(literal 1 binary64))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x) #s(literal 1 binary64))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
1
#s(literal 1 binary64)
(+ 1 (* a x))
(fma.f64 a x #s(literal 1 binary64))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(fma.f64 a (fma.f64 x (.f64 a (.f64 x #s(literal 1/2 binary64))) x) #s(literal 1 binary64))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(fma.f64 x (fma.f64 x (fma.f64 a (.f64 a #s(literal 1/2 binary64)) (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (*.f64 a a))))) a) #s(literal 1 binary64))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
(exp (* a x))
(exp.f64 (*.f64 a x))
2
#s(literal 2 binary64)
(+ 2 (* a x))
(fma.f64 a x #s(literal 2 binary64))
(+ 2 (* a (+ x (* 1/2 (* a (pow x 2))))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a a)) a) #s(literal 2 binary64))
(+ 2 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x) #s(literal 2 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
2
#s(literal 2 binary64)
(+ 2 (* a x))
(fma.f64 a x #s(literal 2 binary64))
(+ 2 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a a)) a) #s(literal 2 binary64))
(+ 2 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(fma.f64 x (fma.f64 x (fma.f64 a (.f64 a #s(literal 1/2 binary64)) (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (*.f64 a a))))) a) #s(literal 2 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+ 1 (exp (* a x)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

rewrite122.0ms (1.5%)

Memory

28.7MiB live, 100.9MiB allocated

Rules

1 058×	`lower-fma.f32`
1 050×	`lower-fma.f64`
924×	`lower-*.f32`
906×	`lower-*.f64`
546×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	177
0	57	168
1	220	168
0	1607	168

Stop Event

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

Counts

19 → 299

Calls

Call 1

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

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

eval133.0ms (1.6%)

Memory: -24.3MiB live, 221.3MiB allocated
Compiler: Compiled 14 632 to 1 018 computations (93% saved)

prune72.0ms (0.9%)

Memory

22.1MiB live, 97.5MiB allocated

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	761	6	767
Fresh	1	2	3
Picked	2	3	5
Done	0	0	0
Total	764	11	775

Accuracy

100.0%

Counts

775 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.0%	(/.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
	53.0%	(-.f64 (pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	20.5%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 a x))
▶	68.9%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))
▶	60.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x)))
▶	68.3%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x)))
	68.0%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
	65.2%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 a (.f64 x x)) (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)))
▶	20.1%	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64)))))))

Compiler

Compiled 307 to 164 computations (46.6% saved)

simplify183.0ms (2.2%)

Memory

14.5MiB live, 202.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (exp.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))
cost-diff	0	(-.f64 (/.f64 (exp.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (+.f64 x x))))))
cost-diff	0	(/.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
cost-diff	448	(fma.f64 a (+.f64 x x) (*.f64 a (+.f64 x x)))
cost-diff	0	(.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64)))
cost-diff	0	(fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x)
cost-diff	0	(.f64 a (fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x)))
cost-diff	0	(*.f64 a #s(literal 1/2 binary64))
cost-diff	0	(.f64 a (.f64 a #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x)))
cost-diff	320	(fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x))
cost-diff	0	(.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (+ (* a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64))))))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64)))))))
cost-diff	0	(*.f64 a x)
cost-diff	0	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))

Rules

8 350×	`lower-fma.f32`
8 340×	`lower-fma.f64`
3 150×	`lower-*.f32`
3 126×	`lower-*.f64`
2 392×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	423
0	83	408
1	171	396
2	379	396
3	982	396
4	2583	396
5	5194	387
6	5976	387
7	7409	387
0	8175	374

Stop Event

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

Calls

Call 1

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

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

localize474.0ms (5.8%)

Memory

-14.5MiB live, 314.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (+.f64 x x)))))
accuracy	0.017910009768442016	(exp.f64 (*.f64 a (+.f64 x x)))
accuracy	0.026386279305326048	(exp.f64 (fma.f64 a (+.f64 x x) (*.f64 a (+.f64 x x))))
accuracy	30.068210138066394	(-.f64 (/.f64 (exp.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (+.f64 x x))))))
accuracy	0.47506980703421264	(fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x)
accuracy	0.9616701754959329	(fma.f64 a (.f64 x (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))
accuracy	0.9793933225553222	(.f64 a (fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x))
accuracy	20.294237130866314	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x)))
accuracy	0	(*.f64 a x)
accuracy	0	(*.f64 a #s(literal 1/2 binary64))
accuracy	13.991574040893315	(fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x))
accuracy	20.46349797868629	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x)))
accuracy	0.140625	(.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64))))
accuracy	0.9730907896375589	(.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64))))))
accuracy	20.46349797868629	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64)))))))
accuracy	42.11998664184806	#s(approx (+ (* a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64)))))
accuracy	0	(*.f64 a x)
accuracy	19.923396898904414	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))

Samples

331.0ms	84×	2	valid
52.0ms	86×	1	valid
26.0ms	86×	0	valid

Compiler

Compiled 369 to 45 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 373.0ms

const: 241.0ms (64.6% of total)

ival-exp: 52.0ms (13.9% of total)

ival-mult: 30.0ms (8% of total)

adjust: 18.0ms (4.8% of total)

ival-add: 14.0ms (3.8% of total)

ival-div: 11.0ms (3% of total)

ival-expm1: 3.0ms (0.8% of total)

ival-sub: 2.0ms (0.5% of total)

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

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

exact: 0.0ms (0% of total)

series41.0ms (0.5%)

Memory

8.6MiB live, 49.6MiB allocated

Counts

22 → 504

Calls

Call 1

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

Outputs
#<alt (* a x)>
#<alt (* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (* a x)>
#<alt (* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 (pow a 2))>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* 1/2 a)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))>
#<alt (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))>
#<alt (* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))>
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#<alt (+ 1 (* 2 (* a x)))>
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#<alt (+ 1 (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2)))))))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt 1>
#<alt (+ 1 (* 2 (* a x)))>
#<alt (+ 1 (* x (+ (* 2 a) (* 2 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2)))))))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/2 (* a x)))>
#<alt (+ 1/2 (* a (- (* -1 (* a (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 1/2 x))))>
#<alt (+ 1/2 (* a (- (* a (- (* -1 (* a (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 1/2 x))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/2 (* a x)))>
#<alt (+ 1/2 (* x (- (* -1 (* x (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (* 1/2 a))))>
#<alt (+ 1/2 (* x (- (* x (- (* -1 (* x (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (* 1/2 a))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>

Calls

126 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(/ (- (/ (exp (+ (* a (+ x x)) (* a (+ x x)))) (+ 1 (exp (* a (+ x x))))) (/ 1 (+ 1 (exp (* a (+ x x)))))) (+ (exp (* a x)) 1))
4.0ms	x	@	inf	(* (* a x) (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2))
3.0ms	a	@	0	(/ (- (/ (exp (+ (* a (+ x x)) (* a (+ x x)))) (+ 1 (exp (* a (+ x x))))) (/ 1 (+ 1 (exp (* a (+ x x)))))) (+ (exp (* a x)) 1))
2.0ms	x	@	0	(/ (- (/ (exp (+ (* a (+ x x)) (* a (+ x x)))) (+ 1 (exp (* a (+ x x))))) (/ 1 (+ 1 (exp (* a (+ x x)))))) (+ (exp (* a x)) 1))
2.0ms	a	@	inf	(/ (- (/ (exp (+ (* a (+ x x)) (* a (+ x x)))) (+ 1 (exp (* a (+ x x))))) (/ 1 (+ 1 (exp (* a (+ x x)))))) (+ (exp (* a x)) 1))

simplify290.0ms (3.6%)

Memory

-3.5MiB live, 257.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 656×	`lower-fma.f64`
13 656×	`lower-fma.f32`
6 690×	`lower-*.f64`
6 690×	`lower-*.f32`
4 474×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	686	7632
1	2271	7022
2	7838	7006
0	8148	6524

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 500

Calls

Call 1

Inputs
(* a x)
(* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(* a x)
(* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* x (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* x (- (+ (* 2/3 (pow a 3)) (* x (- (* 1/3 (pow a 4)) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (pow a 2) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 2/3 (pow a 3)) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (pow a 2) (* 1/2 (pow a 2)))))))) (pow a 2)) (* 1/2 (pow a 2))))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* a x)
(* 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))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 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)))
(* (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)))
(* (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)))
(* 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)))
(* (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)))
(* (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)))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* 1/2 (* a (pow x 2))))
(* 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 (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)))))
x
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* 1/2 (* 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 (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 (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)))
(* 1/2 (* a (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)))
(* 1/2 (* a (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)))
(* 1/2 (* a (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)))
(* 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 (* 1/2 (* a (pow x 2)))))
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* 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)))
(* (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)))
(* 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)))
(* (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)))
(* (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)))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 (pow a 2))
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* 1/2 a)
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 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))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* 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))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))
x
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
(* 1/2 (* a x))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2))))))
(* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 2) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* 1/2 (* a x))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))
(* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 (/ (pow a 2) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* 4 (* a x))
(* a x)
(* a (+ x (* a (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* a (- (* 1/2 (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2))))))))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* a (- (+ (* 1/2 (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))) (* a (- (* 1/2 (- (+ (* -1 (* x (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1 (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/3 (pow x 4)) (* 16/3 (pow x 4))))) (+ (* 2/3 (* (pow x 3) (- (* 2 x) (* 1/2 x)))) (+ (* x (- (* 16/3 (pow x 3)) (+ (* 1/3 (pow x 3)) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x))))))) (* (pow x 2) (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))))))) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 1/2 (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2))))))))) (* 1/2 (pow x 2))))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(* a x)
(* x (+ a (* x (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* x (- (* 1/2 (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))))))) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* x (- (+ (* 1/2 (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))) (* x (- (* 1/2 (- (+ (* -1 (* a (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1 (* (pow a 2) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/3 (pow a 4)) (* 16/3 (pow a 4))))) (+ (* 2/3 (* (pow a 3) (- (* 2 a) (* 1/2 a)))) (+ (* a (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a))))))) (* (pow a 2) (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))))))) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 1/2 (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))))))) (* 1/2 (pow a 2))))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(* 2 (* a x))
(* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x)))))))
(* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (+ (* 4 (pow x 2)) (* a (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (* x (- (* 2 x) (* 1/2 x)))))))
(* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (+ (* 4 (pow x 2)) (* a (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (+ (* 16/3 (pow x 3)) (* a (- (+ (* -1 (* x (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1 (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/3 (pow x 4)) (* 16/3 (pow x 4))))) (+ (* 2/3 (* (pow x 3) (- (* 2 x) (* 1/2 x)))) (+ (* x (- (* 16/3 (pow x 3)) (+ (* 1/3 (pow x 3)) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x))))))) (* (pow x 2) (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))))))))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (* x (- (* 2 x) (* 1/2 x)))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(* 2 (* a x))
(* x (+ (* 2 a) (* x (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a)))))))
(* x (+ (* 2 a) (* x (- (+ (* -1/2 (pow a 2)) (+ (* 4 (pow a 2)) (* x (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))))) (* a (- (* 2 a) (* 1/2 a)))))))
(* x (+ (* 2 a) (* x (- (+ (* -1/2 (pow a 2)) (+ (* 4 (pow a 2)) (* x (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (+ (* 16/3 (pow a 3)) (* x (- (+ (* -1 (* a (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1 (* (pow a 2) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/3 (pow a 4)) (* 16/3 (pow a 4))))) (+ (* 2/3 (* (pow a 3) (- (* 2 a) (* 1/2 a)))) (+ (* a (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a))))))) (* (pow a 2) (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))))))))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))))) (* a (- (* 2 a) (* 1/2 a)))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
1/2
(+ 1/2 (* a (- (* 2 x) (* 1/2 x))))
(+ 1/2 (* a (- (+ (* 2 x) (* a (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))) (* 1/2 x))))
(+ 1/2 (* a (- (+ (* 2 x) (* a (- (+ (* 4 (pow x 2)) (* a (- (* 16/3 (pow x 3)) (+ (* 1/3 (pow x 3)) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))) (* 1/2 x))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
1/2
(+ 1/2 (* x (- (* 2 a) (* 1/2 a))))
(+ 1/2 (* x (- (+ (* 2 a) (* x (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))) (* 1/2 a))))
(+ 1/2 (* x (- (+ (* 2 a) (* x (- (+ (* 4 (pow a 2)) (* x (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))))) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))) (* 1/2 a))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))
(+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
1
(+ 1 (* 4 (* a x)))
(+ 1 (* a (+ (* 4 x) (* 8 (* a (pow x 2))))))
(+ 1 (* a (+ (* 4 x) (* a (+ (* 8 (pow x 2)) (* 32/3 (* a (pow x 3))))))))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
1
(+ 1 (* 4 (* a x)))
(+ 1 (* x (+ (* 4 a) (* 8 (* (pow a 2) x)))))
(+ 1 (* x (+ (* 4 a) (* x (+ (* 8 (pow a 2)) (* 32/3 (* (pow a 3) x)))))))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
1
(+ 1 (* 2 (* a x)))
(+ 1 (* a (+ (* 2 x) (* 2 (* a (pow x 2))))))
(+ 1 (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2)))))))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
1
(+ 1 (* 2 (* a x)))
(+ 1 (* x (+ (* 2 a) (* 2 (* (pow a 2) x)))))
(+ 1 (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2)))))))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
1/2
(+ 1/2 (* -1/2 (* a x)))
(+ 1/2 (* a (- (* -1 (* a (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 1/2 x))))
(+ 1/2 (* a (- (* a (- (* -1 (* a (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 1/2 x))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
1/2
(+ 1/2 (* -1/2 (* a x)))
(+ 1/2 (* x (- (* -1 (* x (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (* 1/2 a))))
(+ 1/2 (* x (- (* x (- (* -1 (* x (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (* 1/2 a))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))

Outputs
(* a x)
(*.f64 a x)
(* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))
(.f64 a (fma.f64 a (.f64 x (*.f64 x #s(literal 1/2 binary64))) x))
(* a (+ x (* a (- (+ (* a (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(.f64 a (fma.f64 a (fma.f64 a (fma.f64 (.f64 x (.f64 x x)) #s(literal 5/12 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))))) (.f64 x (*.f64 x #s(literal 1/2 binary64)))) x))
(* a (+ x (* a (- (+ (* a (- (+ (* 2/3 (pow x 3)) (* a (- (* 1/3 (pow x 4)) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (pow x 2) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 2/3 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (pow x 2) (* 1/2 (pow x 2)))))))) (pow x 2)) (* 1/2 (pow x 2))))))
(.f64 a (fma.f64 a (fma.f64 a (fma.f64 a (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/4 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 5/12 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))))) (.f64 x #s(literal 1/2 binary64))))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 5/12 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64))))))) (.f64 x (*.f64 x #s(literal 1/2 binary64)))) x))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
(/.f64 (expm1.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/ (- (exp (* 2 (* a x))) 1) (+ 1 (exp (* a x))))
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1/2
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1
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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(exp (* 2 (* a x)))
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(exp (* 2 (* a x)))
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(exp (* 2 (* a x)))
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1
#s(literal 1 binary64)
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(exp (* 2 (* a x)))
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 (* a x)))
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(/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))

rewrite269.0ms (3.3%)

Memory

-15.0MiB live, 267.0MiB allocated

Rules

5 316×	`lower-fma.f32`
5 306×	`lower-fma.f64`
2 760×	`lower-*.f32`
2 736×	`lower-*.f64`
1 642×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	347
0	83	319
1	320	258
2	2772	238
0	9480	221

Stop Event

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

Counts

22 → 1 683

Calls

Call 1

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

Outputs
#s(approx (- (exp (* a x)) 1) (*.f64 a x))
(log.f64 (exp.f64 (*.f64 a x)))
(+.f64 (*.f64 a x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 a x))
(+.f64 (log.f64 (exp.f64 (.f64 a (/.f64 x #s(literal 2 binary64))))) (log.f64 (exp.f64 (.f64 a (/.f64 x #s(literal 2 binary64))))))
(fma.f64 a x #s(literal 0 binary64))
(fma.f64 a (log.f64 (exp.f64 x)) #s(literal 0 binary64))
(fma.f64 x a #s(literal 0 binary64))
(*.f64 a x)
(*.f64 a (log.f64 (exp.f64 x)))
(*.f64 x a)
#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(.f64 #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)))) a)
#s(approx (+ (* a (* 1/2 (* x x))) x) (.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64))))
(.f64 (.f64 a x) (*.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) a))
(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) a)
(.f64 (.f64 x #s(literal 1/2 binary64)) (*.f64 a x))
(.f64 (.f64 a (*.f64 x #s(literal 1/2 binary64))) x)
(.f64 (.f64 a #s(literal 1/2 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (*.f64 a #s(literal 1/2 binary64)))
(.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64))
(.f64 (.f64 (*.f64 a x) x) #s(literal 1/2 binary64))
(.f64 (.f64 a (*.f64 x x)) #s(literal 1/2 binary64))
(+.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (*.f64 x x)))
(+.f64 (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x)) (*.f64 a x))
(-.f64 (/.f64 (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x)))) (/.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (neg.f64 x)))))
(-.f64 (/.f64 (.f64 a (.f64 x (.f64 a x))) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x)))) (/.f64 (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64)) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (*.f64 x x)))))
(fma.f64 a x (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x)))
(fma.f64 a (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 a x))
(fma.f64 a (log.f64 (exp.f64 x)) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x)))
(fma.f64 x a (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x)))
(fma.f64 x (.f64 a (.f64 a (.f64 x #s(literal 1/2 binary64)))) (.f64 a x))
(fma.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x))) a (.f64 a x))
(fma.f64 (.f64 a #s(literal 1/2 binary64)) (.f64 a (.f64 x x)) (.f64 a x))
(fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x))
(fma.f64 (.f64 x x) (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 a x))
(fma.f64 (.f64 a (.f64 x (.f64 a x))) #s(literal 1/2 binary64) (.f64 a x))
(fma.f64 (.f64 a a) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 a x))
(fma.f64 (.f64 a (.f64 a (.f64 x #s(literal 1/2 binary64)))) x (.f64 a x))
(fma.f64 (.f64 (.f64 x x) a) (.f64 a #s(literal 1/2 binary64)) (.f64 a x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 a x) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x))) (.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 a x) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x))) (.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x)))))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))))) (fma.f64 (.f64 a x) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))))) (fma.f64 a (.f64 x (.f64 a x)) (-.f64 (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64)) (.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))))))
(/.f64 (.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x)))) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x)))))) (neg.f64 (fma.f64 (.f64 a x) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x)))))) (neg.f64 (fma.f64 a (.f64 x (.f64 a x)) (-.f64 (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64)) (.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x)))))))
(/.f64 (neg.f64 (.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x))))) (neg.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x)))))
(/.f64 (-.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64))) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))))))) (neg.f64 (neg.f64 (fma.f64 (.f64 a x) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x)))))) (neg.f64 (neg.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x))))))
(/.f64 (neg.f64 (-.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x)))))
(pow.f64 (/.f64 (fma.f64 (.f64 a x) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1/4 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x))) (.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x))))) #s(literal -1 binary64))
(.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))
(.f64 x (+.f64 a (.f64 a (.f64 a (.f64 x #s(literal 1/2 binary64))))))
(.f64 x (fma.f64 a (.f64 a (*.f64 x #s(literal 1/2 binary64))) a))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 a (.f64 a a)) (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 a x) (-.f64 (.f64 a x) (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x))) (.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (*.f64 a x)))) #s(literal 1/4 binary64)))))
(.f64 (.f64 (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x)))) (/.f64 #s(literal 1 binary64) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (neg.f64 x)))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
(.f64 a (.f64 a #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 a a))
(.f64 (.f64 a #s(literal 1/2 binary64)) a)
(.f64 (.f64 a a) #s(literal 1/2 binary64))
(*.f64 a #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) a)
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 a x)))
(+.f64 (.f64 a x) (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(+.f64 (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (*.f64 a x))
(-.f64 (/.f64 (.f64 (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 a x))) (/.f64 (.f64 a (.f64 x (.f64 a x))) (-.f64 (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 a x))))
(fma.f64 a x (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(fma.f64 a (.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 a x))
(fma.f64 a (log.f64 (exp.f64 x)) (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(fma.f64 x a (.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(fma.f64 x (.f64 (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) a) (.f64 a x))
(fma.f64 (.f64 a x) (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 a x))
(fma.f64 (.f64 a (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 a x) (.f64 a x))
(fma.f64 (.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 (.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) a (.f64 a x))
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(pow.f64 (exp.f64 (*.f64 a x)) #s(literal 6 binary64))
(pow.f64 (exp.f64 (*.f64 a x)) #s(literal 9 binary64))
(pow.f64 (exp.f64 (.f64 a x)) (.f64 #s(literal 2 binary64) (+.f64 a a)))
(pow.f64 (exp.f64 a) (+.f64 x x))
(pow.f64 (exp.f64 a) (*.f64 x #s(literal 3 binary64)))
(pow.f64 (exp.f64 a) (+.f64 (+.f64 x x) x))
(pow.f64 (exp.f64 a) (+.f64 x (+.f64 x x)))
(pow.f64 (exp.f64 a) (*.f64 (+.f64 x x) #s(literal 3/2 binary64)))
(pow.f64 (exp.f64 a) (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)))
(pow.f64 (exp.f64 a) (fma.f64 x #s(literal 3 binary64) (*.f64 x #s(literal 3 binary64))))
(pow.f64 (exp.f64 a) (+.f64 (/.f64 (+.f64 x x) #s(literal 2 binary64)) (/.f64 (+.f64 x x) #s(literal 2 binary64))))
(pow.f64 (neg.f64 (exp.f64 (+.f64 x x))) #s(literal 2 binary64))
(pow.f64 (exp.f64 (neg.f64 (+.f64 x x))) #s(literal -1 binary64))
(pow.f64 (exp.f64 (neg.f64 (+.f64 x x))) #s(literal -3 binary64))
(pow.f64 (exp.f64 (neg.f64 (+.f64 x x))) #s(literal -2 binary64))
(pow.f64 (exp.f64 (neg.f64 (+.f64 x x))) #s(literal -3/2 binary64))
(pow.f64 (exp.f64 (+.f64 a a)) x)
(pow.f64 (exp.f64 (+.f64 a a)) (*.f64 a x))
(pow.f64 (exp.f64 (+.f64 a a)) (+.f64 x x))
(pow.f64 (exp.f64 (+.f64 a a)) (*.f64 x #s(literal 3 binary64)))
(pow.f64 (exp.f64 (+.f64 a a)) (/.f64 (+.f64 x x) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (+.f64 a a)) (+.f64 (+.f64 x x) x))
(pow.f64 (exp.f64 (+.f64 a a)) (+.f64 x (+.f64 x x)))
(pow.f64 (exp.f64 (+.f64 a a)) (*.f64 x #s(literal 3/2 binary64)))
(pow.f64 (exp.f64 (+.f64 a a)) (*.f64 (+.f64 x x) #s(literal 3/2 binary64)))
(pow.f64 (exp.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 x) (+.f64 a a))
(pow.f64 (exp.f64 x) #s(literal 4 binary64))
(pow.f64 (exp.f64 x) (*.f64 a #s(literal 2 binary64)))
(pow.f64 (exp.f64 x) (*.f64 a #s(literal 3 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 a x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (+.f64 x x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (+.f64 x x) #s(literal 3/2 binary64)))
(pow.f64 (*.f64 (exp.f64 (neg.f64 (+.f64 x x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (exp.f64 (neg.f64 (+.f64 x x))) #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (exp.f64 (neg.f64 (+.f64 x x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (*.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3/2 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (exp.f64 a) a) (+.f64 x x))
(pow.f64 (pow.f64 (exp.f64 a) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(pow.f64 (pow.f64 (exp.f64 a) (+.f64 a a)) (+.f64 x x))
(pow.f64 (pow.f64 (exp.f64 a) (*.f64 a #s(literal 2 binary64))) x)
(pow.f64 (pow.f64 (exp.f64 (+.f64 a a)) a) (+.f64 x x))
(pow.f64 (pow.f64 (exp.f64 (+.f64 a a)) #s(literal 2 binary64)) x)
(pow.f64 (pow.f64 (exp.f64 (+.f64 a a)) #s(literal 2 binary64)) (*.f64 a x))
(pow.f64 (pow.f64 (exp.f64 (+.f64 a a)) #s(literal 2 binary64)) (+.f64 x x))
(pow.f64 (pow.f64 (exp.f64 (+.f64 a a)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(pow.f64 (pow.f64 (exp.f64 (+.f64 a a)) (+.f64 a a)) (+.f64 x x))
(pow.f64 (pow.f64 (exp.f64 (+.f64 a a)) (*.f64 a #s(literal 2 binary64))) x)
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) a) (+.f64 x x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) x)
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 a x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 x x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (+.f64 a a)) (+.f64 x x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 a #s(literal 2 binary64))) x)
(pow.f64 (*.f64 (exp.f64 (+.f64 a a)) (exp.f64 a)) x)
(pow.f64 (*.f64 (exp.f64 (+.f64 a a)) (exp.f64 a)) (+.f64 x x))
(pow.f64 (*.f64 (exp.f64 #s(literal 2 binary64)) (exp.f64 a)) (+.f64 x x))
(pow.f64 (*.f64 (exp.f64 (+.f64 a a)) (exp.f64 (+.f64 a a))) x)
(pow.f64 (*.f64 (exp.f64 (+.f64 a a)) (exp.f64 (+.f64 a a))) (+.f64 x x))
(pow.f64 (*.f64 (exp.f64 a) (exp.f64 (+.f64 a a))) x)
(pow.f64 (*.f64 (exp.f64 a) (exp.f64 (+.f64 a a))) (+.f64 x x))
(pow.f64 (*.f64 (exp.f64 #s(literal 2 binary64)) (exp.f64 (+.f64 a a))) (+.f64 x x))
(pow.f64 (*.f64 (exp.f64 a) (exp.f64 #s(literal 2 binary64))) (+.f64 x x))
(pow.f64 (*.f64 (exp.f64 (+.f64 a a)) (exp.f64 #s(literal 2 binary64))) (+.f64 x x))
(pow.f64 (*.f64 (exp.f64 #s(literal 2 binary64)) (exp.f64 #s(literal 2 binary64))) (+.f64 x x))
(pow.f64 (*.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)) a)
(pow.f64 (*.f64 (exp.f64 x) (exp.f64 (+.f64 x x))) a)
(pow.f64 (exp.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))
(*.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))
(*.f64 (exp.f64 (+.f64 x x)) (exp.f64 (+.f64 x x)))
(*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x)))
(.f64 (exp.f64 (+.f64 x x)) (exp.f64 (.f64 a x)))
(*.f64 (exp.f64 (+.f64 x x)) (pow.f64 (exp.f64 (+.f64 a a)) (fma.f64 a x (+.f64 x x))))
(*.f64 (exp.f64 (+.f64 x x)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (+.f64 x (+.f64 x x))))
(*.f64 (exp.f64 (+.f64 x x)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (fma.f64 a x (+.f64 x x))))
(*.f64 (exp.f64 (+.f64 x x)) (pow.f64 #s(literal 1 binary64) a))
(*.f64 (exp.f64 (+.f64 x x)) (pow.f64 #s(literal 1 binary64) (+.f64 a a)))
(*.f64 (exp.f64 (+.f64 x x)) (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal 3 binary64)))
(.f64 (exp.f64 (.f64 a x)) (exp.f64 (+.f64 x x)))
(.f64 (exp.f64 (.f64 a x)) (exp.f64 (*.f64 a x)))
(*.f64 (neg.f64 (exp.f64 (+.f64 x x))) #s(literal -1 binary64))
(*.f64 (neg.f64 (exp.f64 (+.f64 x x))) (neg.f64 (exp.f64 (+.f64 x x))))
(*.f64 (exp.f64 x) (exp.f64 x))
(*.f64 (exp.f64 x) (exp.f64 (+.f64 x (+.f64 x x))))
(.f64 (exp.f64 (.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) (exp.f64 (*.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))))
(.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3/2 binary64))) (exp.f64 (.f64 (*.f64 a x) #s(literal 3/2 binary64))))
(*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (expm1.f64 (+.f64 x x)))
(.f64 (pow.f64 (exp.f64 a) (.f64 a x)) (pow.f64 (exp.f64 a) (*.f64 a x)))
(.f64 (pow.f64 (exp.f64 a) (.f64 a x)) (pow.f64 (exp.f64 a) (fma.f64 a x (+.f64 x x))))
(.f64 (pow.f64 (exp.f64 a) (.f64 (.f64 a x) #s(literal 2 binary64))) (pow.f64 (exp.f64 a) (.f64 (*.f64 a x) #s(literal 2 binary64))))
(.f64 (pow.f64 (exp.f64 a) (fma.f64 x #s(literal 2 binary64) (.f64 a x))) (pow.f64 (exp.f64 a) (*.f64 a x)))
(.f64 (pow.f64 (exp.f64 (+.f64 a a)) (.f64 (.f64 a x) #s(literal 2 binary64))) (pow.f64 (exp.f64 (+.f64 a a)) (.f64 (*.f64 a x) #s(literal 2 binary64))))
(.f64 (pow.f64 (exp.f64 (+.f64 a a)) (fma.f64 x #s(literal 2 binary64) (.f64 a x))) (exp.f64 (+.f64 x x)))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 a x) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (*.f64 a x) #s(literal 2 binary64))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 2 binary64) (.f64 a x))) (exp.f64 (+.f64 x x)))
(*.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (+.f64 (+.f64 x x) x)) (exp.f64 (+.f64 x x)))
(*.f64 (pow.f64 (neg.f64 (exp.f64 (+.f64 x x))) #s(literal 3/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) a) (exp.f64 (+.f64 x x)))
(.f64 (pow.f64 (exp.f64 (.f64 a x)) a) (pow.f64 (exp.f64 (*.f64 a x)) a))
(.f64 (pow.f64 (exp.f64 (.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) a) (pow.f64 (exp.f64 (*.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) a))
(.f64 (pow.f64 (exp.f64 (.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (exp.f64 (*.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) #s(literal 3 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) (+.f64 a a)) (exp.f64 (+.f64 x x)))
(.f64 (pow.f64 (exp.f64 (.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) (+.f64 a a)) (pow.f64 (exp.f64 (*.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) (+.f64 a a)))
(*.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) #s(literal 3 binary64)) (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal 3 binary64)))
(.f64 (pow.f64 (exp.f64 (.f64 a (/.f64 x #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (exp.f64 (*.f64 a (/.f64 x #s(literal 2 binary64)))) #s(literal 3 binary64)))
(.f64 (pow.f64 (exp.f64 (.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) #s(literal 3/2 binary64)) (pow.f64 (exp.f64 (*.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3/2 binary64))) #s(literal 3 binary64)) (pow.f64 (exp.f64 (.f64 (*.f64 a x) #s(literal 3/2 binary64))) #s(literal 3 binary64)))
(*.f64 (exp.f64 (+.f64 (+.f64 x x) x)) (exp.f64 x))
#s(literal 1 binary64)

eval746.0ms (9.2%)

Memory: -22.1MiB live, 642.7MiB allocated
Compiler: Compiled 92 579 to 7 492 computations (91.9% saved)

prune295.0ms (3.6%)

Memory

21.8MiB live, 531.9MiB allocated

Pruning

11 alts after pruning (4 fresh and 7 done)

	Pruned	Kept	Total
New	2 682	3	2 685
Fresh	2	1	3
Picked	1	4	5
Done	0	3	3
Total	2 685	11	2 696

Accuracy

100.0%

Counts

2 696 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.0%	(/.f64 (-.f64 (/.f64 (exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
▶	53.0%	(-.f64 (pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	20.5%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 a x))
✓	68.9%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))
✓	60.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x)))
✓	68.3%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x)))
▶	69.1%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x)))
▶	68.0%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x)))
✓	20.1%	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64)))))))

Compiler

Compiled 165 to 93 computations (43.6% saved)

simplify302.0ms (3.7%)

Memory

-17.2MiB live, 235.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64)))))
cost-diff	0	(/.f64 (exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (+.f64 x x)))))
cost-diff	0	(-.f64 (/.f64 (exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))))
cost-diff	0	(/.f64 (-.f64 (/.f64 (exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
cost-diff	0	(.f64 a (.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64))))
cost-diff	192	(-.f64 (pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 1 binary64))
cost-diff	6784	(pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(fma.f64 (.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x)
cost-diff	0	(.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x)))
cost-diff	0	(.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))
cost-diff	0	(fma.f64 (.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x)
cost-diff	0	(.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x)))

Rules

15 084×	`lower-fma.f32`
15 078×	`lower-fma.f64`
4 554×	`lower-*.f32`
4 532×	`lower-*.f64`
2 344×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	508
0	82	490
1	164	478
2	335	473
3	663	469
4	891	469
5	1709	469
6	4090	469
7	5500	469
8	6977	469
0	8550	443

Stop Event

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

Calls

Call 1

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

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

localize276.0ms (3.4%)

Memory

4.3MiB live, 313.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (+.f64 x x)))))
accuracy	0.017910009768442016	(exp.f64 (*.f64 a (+.f64 x x)))
accuracy	0.026386279305326048	(exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64)))))
accuracy	29.831834192025507	(-.f64 (/.f64 (exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))))
accuracy	0	(.f64 a (.f64 x #s(literal 1/2 binary64)))
accuracy	0.00390625	(exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64))))
accuracy	0.01953125	(pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy	29.83848831906992	(-.f64 (pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 1 binary64))
accuracy	0.47506980703421264	(fma.f64 (.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x)
accuracy	0.9793933225553222	(.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x))
accuracy	20.294237130866314	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x)))
accuracy	20.520880567391057	#s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
accuracy	0.47506980703421264	(fma.f64 (.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x)
accuracy	0.9793933225553222	(.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x))
accuracy	20.07977214328211	#s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))
accuracy	20.294237130866314	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x)))

Samples

106.0ms	85×	2	valid
76.0ms	84×	1	valid
26.0ms	86×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 394 to 43 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 149.0ms

ival-exp: 54.0ms (36.3% of total)

ival-mult: 28.0ms (18.8% of total)

adjust: 18.0ms (12.1% of total)

ival-add: 15.0ms (10.1% of total)

const: 9.0ms (6% of total)

ival-div: 9.0ms (6% of total)

ival-sub: 7.0ms (4.7% of total)

ival-pow2: 5.0ms (3.4% of total)

ival-expm1: 2.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

29.5MiB live, 29.5MiB allocated

Counts

20 → 480

Calls

Call 1

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

Outputs
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))>
#<alt (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))>
#<alt (* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
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#<alt (* x (+ a (* x (- (+ (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* x (- (+ (* 1/2 (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))) (* x (- (* 1/2 (- (+ (* -1 (* a (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1 (* (pow a 2) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/3 (pow a 4)) (* 16/3 (pow a 4))))) (+ (* 2/3 (* (pow a 3) (- (* 2 a) (* 1/2 a)))) (+ (* a (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a))))))) (* (pow a 2) (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))))))) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 1/2 (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))))))) (* 1/2 (pow a 2))))))>
#<alt (/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))>
#<alt (/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))>
#<alt (/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))>
#<alt (/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))>
#<alt (/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))>
#<alt (/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))>
#<alt (/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))>
#<alt (/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))>
#<alt (* 2 (* a x))>
#<alt (* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x)))))))>
#<alt (* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (+ (* 4 (pow x 2)) (* a (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (* x (- (* 2 x) (* 1/2 x)))))))>
#<alt (* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (+ (* 4 (pow x 2)) (* a (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (+ (* 16/3 (pow x 3)) (* a (- (+ (* -1 (* x (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1 (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/3 (pow x 4)) (* 16/3 (pow x 4))))) (+ (* 2/3 (* (pow x 3) (- (* 2 x) (* 1/2 x)))) (+ (* x (- (* 16/3 (pow x 3)) (+ (* 1/3 (pow x 3)) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x))))))) (* (pow x 2) (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))))))))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (* x (- (* 2 x) (* 1/2 x)))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
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#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
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#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
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#<alt (* x (+ (* 2 a) (* x (- (+ (* -1/2 (pow a 2)) (+ (* 4 (pow a 2)) (* x (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (+ (* 16/3 (pow a 3)) (* x (- (+ (* -1 (* a (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1 (* (pow a 2) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/3 (pow a 4)) (* 16/3 (pow a 4))))) (+ (* 2/3 (* (pow a 3) (- (* 2 a) (* 1/2 a)))) (+ (* a (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a))))))) (* (pow a 2) (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))))))))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))))) (* a (- (* 2 a) (* 1/2 a)))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))>
#<alt 1/2>
#<alt (+ 1/2 (* a (- (* 2 x) (* 1/2 x))))>
#<alt (+ 1/2 (* a (- (+ (* 2 x) (* a (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))) (* 1/2 x))))>
#<alt (+ 1/2 (* a (- (+ (* 2 x) (* a (- (+ (* 4 (pow x 2)) (* a (- (* 16/3 (pow x 3)) (+ (* 1/3 (pow x 3)) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))) (* 1/2 x))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt 1/2>
#<alt (+ 1/2 (* x (- (* 2 a) (* 1/2 a))))>
#<alt (+ 1/2 (* x (- (+ (* 2 a) (* x (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))) (* 1/2 a))))>
#<alt (+ 1/2 (* x (- (+ (* 2 a) (* x (- (+ (* 4 (pow a 2)) (* x (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))))) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))) (* 1/2 a))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))>
#<alt 1>
#<alt (+ 1 (* 4 (* a x)))>
#<alt (+ 1 (* a (+ (* 4 x) (* 8 (* a (pow x 2))))))>
#<alt (+ 1 (* a (+ (* 4 x) (* a (+ (* 8 (pow x 2)) (* 32/3 (* a (pow x 3))))))))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt 1>
#<alt (+ 1 (* 4 (* a x)))>
#<alt (+ 1 (* x (+ (* 4 a) (* 8 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ (* 4 a) (* x (+ (* 8 (pow a 2)) (* 32/3 (* (pow a 3) x)))))))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt (exp (* 4 (* a x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))>
#<alt (+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))>
#<alt (* 1/24 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))>
#<alt (* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))>
#<alt (* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))>
#<alt (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))>
#<alt (* 1/24 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))>
#<alt (+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))>
#<alt (* 1/24 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))>
#<alt (* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))>
#<alt (* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))>
#<alt (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))>
#<alt (* 1/24 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt 1>
#<alt (+ 1 (* 2 (* a x)))>
#<alt (+ 1 (* a (+ (* 2 x) (* 2 (* a (pow x 2))))))>
#<alt (+ 1 (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2)))))))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt 1>
#<alt (+ 1 (* 2 (* a x)))>
#<alt (+ 1 (* x (+ (* 2 a) (* 2 (* (pow a 2) x)))))>
#<alt (+ 1 (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2)))))))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt (exp (* 2 (* a x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/2 (* a x)))>
#<alt (+ 1/2 (* a (- (* -1 (* a (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 1/2 x))))>
#<alt (+ 1/2 (* a (- (* a (- (* -1 (* a (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 1/2 x))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/2 (* a x)))>
#<alt (+ 1/2 (* x (- (* -1 (* x (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (* 1/2 a))))>
#<alt (+ 1/2 (* x (- (* x (- (* -1 (* x (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (* 1/2 a))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>
#<alt (/ 1 (+ 1 (exp (* 2 (* a x)))))>

Calls

120 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(pow (exp (* a (* x 1/2))) 2)
0.0ms	a	@	0	(pow (exp (* a (* x 1/2))) 2)
0.0ms	x	@	0	(- (pow (exp (* a (* x 1/2))) 2) 1)
0.0ms	a	@	inf	(pow (exp (* a (* x 1/2))) 2)
0.0ms	a	@	0	(- (pow (exp (* a (* x 1/2))) 2) 1)

simplify397.0ms (4.9%)

Memory

7.3MiB live, 287.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 584×	`lower-fma.f64`
13 584×	`lower-fma.f32`
6 294×	`lower-*.f64`
6 294×	`lower-*.f32`
4 558×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	687	8016
1	2295	7588
2	7972	7524
0	8005	7042

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 476

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))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 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))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* 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))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))
x
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
(* 1/2 (* a x))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2))))))
(* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 2) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* 1/2 (* a x))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))
(* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 (/ (pow a 2) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(- (exp (* a x)) 1)
(* 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))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* 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))))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))
x
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))
(* 1/24 (* (pow a 3) (pow x 4)))
(* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))
(* 1/2 (* a x))
(* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x)))
(* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2))))))
(* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 2) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* 1/2 (* a x))
(* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))
(* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 (/ (pow a 2) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (pow x 3)) (* 1/8 (pow x 3)))))))))
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
1
(+ 1 (* a x))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (pow a 3)) (* 1/8 (pow a 3)))))))))
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(pow (exp (* 1/2 (* a x))) 2)
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (pow x 3)) (* 1/8 (pow x 3))))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (pow x 3)) (+ (* 1/8 (pow x 3)) (* a (+ (* 1/192 (pow x 4)) (+ (* 1/64 (pow x 4)) (* 1/48 (pow x 4))))))))))))
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (pow a 3)) (* 1/8 (pow a 3))))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (pow a 3)) (+ (* 1/8 (pow a 3)) (* x (+ (* 1/192 (pow a 4)) (+ (* 1/64 (pow a 4)) (* 1/48 (pow a 4))))))))))))
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
(- (pow (exp (* 1/2 (* a x))) 2) 1)
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/8 (* a (pow x 2))) (* 1/2 x))))
(+ 1 (* a (+ (* 1/2 x) (* a (+ (* 1/48 (* a (pow x 3))) (* 1/8 (pow x 2)))))))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* x (+ (* 1/8 (* (pow a 2) x)) (* 1/2 a))))
(+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/48 (* (pow a 3) x)) (* 1/8 (pow a 2)))))))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(exp (* 1/2 (* a x)))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* 1/2 (* a x))
(* a x)
(* a (+ x (* a (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* a (- (* 1/2 (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2))))))))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* a (- (+ (* 1/2 (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))) (* a (- (* 1/2 (- (+ (* -1 (* x (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1 (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/3 (pow x 4)) (* 16/3 (pow x 4))))) (+ (* 2/3 (* (pow x 3) (- (* 2 x) (* 1/2 x)))) (+ (* x (- (* 16/3 (pow x 3)) (+ (* 1/3 (pow x 3)) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x))))))) (* (pow x 2) (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))))))) (+ (* 1/12 (pow x 4)) (+ (* 1/4 (* (pow x 2) (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2))))) (* 1/2 (* x (- (* 1/2 (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2)))))))))))))) (+ (* 1/4 (pow x 3)) (* 1/2 (* x (- (* 1/2 (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x))))) (* 1/2 (pow x 2))))))))) (* 1/2 (pow x 2))))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(* a x)
(* x (+ a (* x (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* x (- (* 1/2 (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))))))) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* x (- (+ (* 1/2 (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))) (* x (- (* 1/2 (- (+ (* -1 (* a (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1 (* (pow a 2) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/3 (pow a 4)) (* 16/3 (pow a 4))))) (+ (* 2/3 (* (pow a 3) (- (* 2 a) (* 1/2 a)))) (+ (* a (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a))))))) (* (pow a 2) (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))))))) (+ (* 1/12 (pow a 4)) (+ (* 1/4 (* (pow a 2) (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))) (* 1/2 (* a (- (* 1/2 (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2)))))))))))))) (+ (* 1/4 (pow a 3)) (* 1/2 (* a (- (* 1/2 (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a))))) (* 1/2 (pow a 2))))))))) (* 1/2 (pow a 2))))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(/ (- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x)))))) (+ 1 (exp (* a x))))
(* 2 (* a x))
(* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (* 4 (pow x 2))) (* x (- (* 2 x) (* 1/2 x)))))))
(* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (+ (* 4 (pow x 2)) (* a (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 16/3 (pow x 3)))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (* x (- (* 2 x) (* 1/2 x)))))))
(* a (+ (* 2 x) (* a (- (+ (* -1/2 (pow x 2)) (+ (* 4 (pow x 2)) (* a (- (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (+ (* 16/3 (pow x 3)) (* a (- (+ (* -1 (* x (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1 (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/3 (pow x 4)) (* 16/3 (pow x 4))))) (+ (* 2/3 (* (pow x 3) (- (* 2 x) (* 1/2 x)))) (+ (* x (- (* 16/3 (pow x 3)) (+ (* 1/3 (pow x 3)) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x))))))) (* (pow x 2) (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))))))))) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (* x (- (* 2 x) (* 1/2 x)))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(* 2 (* a x))
(* x (+ (* 2 a) (* x (- (+ (* -1/2 (pow a 2)) (* 4 (pow a 2))) (* a (- (* 2 a) (* 1/2 a)))))))
(* x (+ (* 2 a) (* x (- (+ (* -1/2 (pow a 2)) (+ (* 4 (pow a 2)) (* x (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 16/3 (pow a 3)))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))))) (* a (- (* 2 a) (* 1/2 a)))))))
(* x (+ (* 2 a) (* x (- (+ (* -1/2 (pow a 2)) (+ (* 4 (pow a 2)) (* x (- (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (+ (* 16/3 (pow a 3)) (* x (- (+ (* -1 (* a (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1 (* (pow a 2) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/3 (pow a 4)) (* 16/3 (pow a 4))))) (+ (* 2/3 (* (pow a 3) (- (* 2 a) (* 1/2 a)))) (+ (* a (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a))))))) (* (pow a 2) (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))))))))) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))))) (* a (- (* 2 a) (* 1/2 a)))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
(- (/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x))))) (/ 1 (+ 1 (exp (* 2 (* a x))))))
1/2
(+ 1/2 (* a (- (* 2 x) (* 1/2 x))))
(+ 1/2 (* a (- (+ (* 2 x) (* a (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))) (* 1/2 x))))
(+ 1/2 (* a (- (+ (* 2 x) (* a (- (+ (* 4 (pow x 2)) (* a (- (* 16/3 (pow x 3)) (+ (* 1/3 (pow x 3)) (+ (* x (- (* 4 (pow x 2)) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x)))))) (* (pow x 2) (- (* 2 x) (* 1/2 x)))))))) (+ (* 1/2 (pow x 2)) (* x (- (* 2 x) (* 1/2 x))))))) (* 1/2 x))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
1/2
(+ 1/2 (* x (- (* 2 a) (* 1/2 a))))
(+ 1/2 (* x (- (+ (* 2 a) (* x (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))) (* 1/2 a))))
(+ 1/2 (* x (- (+ (* 2 a) (* x (- (+ (* 4 (pow a 2)) (* x (- (* 16/3 (pow a 3)) (+ (* 1/3 (pow a 3)) (+ (* a (- (* 4 (pow a 2)) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a)))))) (* (pow a 2) (- (* 2 a) (* 1/2 a)))))))) (+ (* 1/2 (pow a 2)) (* a (- (* 2 a) (* 1/2 a))))))) (* 1/2 a))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
(/ (exp (* 4 (* a x))) (+ 1 (exp (* 2 (* a x)))))
1
(+ 1 (* 4 (* a x)))
(+ 1 (* a (+ (* 4 x) (* 8 (* a (pow x 2))))))
(+ 1 (* a (+ (* 4 x) (* a (+ (* 8 (pow x 2)) (* 32/3 (* a (pow x 3))))))))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
1
(+ 1 (* 4 (* a x)))
(+ 1 (* x (+ (* 4 a) (* 8 (* (pow a 2) x)))))
(+ 1 (* x (+ (* 4 a) (* x (+ (* 8 (pow a 2)) (* 32/3 (* (pow a 3) x)))))))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
(exp (* 4 (* a x)))
1/2
(+ 1/2 (* 1/6 (* a x)))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))
(+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))
(+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
1
(+ 1 (* 2 (* a x)))
(+ 1 (* a (+ (* 2 x) (* 2 (* a (pow x 2))))))
(+ 1 (* a (+ (* 2 x) (* a (+ (* 4/3 (* a (pow x 3))) (* 2 (pow x 2)))))))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
1
(+ 1 (* 2 (* a x)))
(+ 1 (* x (+ (* 2 a) (* 2 (* (pow a 2) x)))))
(+ 1 (* x (+ (* 2 a) (* x (+ (* 4/3 (* (pow a 3) x)) (* 2 (pow a 2)))))))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
(exp (* 2 (* a x)))
1/2
(+ 1/2 (* -1/2 (* a x)))
(+ 1/2 (* a (- (* -1 (* a (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 1/2 x))))
(+ 1/2 (* a (- (* a (- (* -1 (* a (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 3)) (* 1/3 (pow x 3)))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 1/2 x))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
1/2
(+ 1/2 (* -1/2 (* a x)))
(+ 1/2 (* x (- (* -1 (* x (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (* 1/2 a))))
(+ 1/2 (* x (- (* x (- (* -1 (* x (+ (* -1 (* a (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (+ (* -1/2 (pow a 3)) (* 1/3 (pow a 3)))))) (+ (* -1/2 (pow a 2)) (* 1/2 (pow a 2))))) (* 1/2 a))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))
(/ 1 (+ 1 (exp (* 2 (* a x)))))

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

rewrite395.0ms (4.9%)

Memory

-12.6MiB live, 335.8MiB allocated

Rules

4 276×	`lower-fma.f32`
4 270×	`lower-fma.f64`
4 086×	`lower-*.f32`
4 064×	`lower-*.f64`
3 074×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	420
0	82	390
1	320	343
2	2644	324
0	8548	294

Stop Event

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

Counts

20 → 1 711

Calls

Call 1

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

Outputs
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 a x)))
(+.f64 (.f64 a x) (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))))
(+.f64 (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))) (*.f64 a x))
(fma.f64 a x (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))))
(fma.f64 a (.f64 #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) (.f64 (.f64 a x) x)) (*.f64 a x))
(fma.f64 a (log.f64 (exp.f64 x)) (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))))
(fma.f64 x a (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))))
(fma.f64 x (.f64 (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) a) (*.f64 a x))
(fma.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) (*.f64 a x))
(fma.f64 (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) (.f64 a x) (.f64 a x))
(fma.f64 (.f64 #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) (.f64 (.f64 a x) x)) a (*.f64 a x))
(fma.f64 (.f64 a (.f64 a x)) (.f64 x #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) (*.f64 a x))
(fma.f64 (.f64 a (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))) x (*.f64 a x))
(/.f64 (fma.f64 (.f64 (.f64 #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) (.f64 (.f64 a x) x)) (.f64 (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) (.f64 (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) (.f64 x x)))) (.f64 a (.f64 a a)) (.f64 (.f64 a x) (.f64 (.f64 a x) (.f64 a x)))) (fma.f64 (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))) (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))) (-.f64 (.f64 (.f64 a x) (.f64 a x)) (.f64 (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))) (*.f64 a x)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))) (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))))) (.f64 (.f64 a x) (.f64 a x))) (-.f64 (.f64 (.f64 a x) (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))))) (*.f64 a x)))
(/.f64 (.f64 a (fma.f64 x (.f64 x x) (.f64 (.f64 #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) (.f64 (.f64 a x) x)) (.f64 (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) (.f64 (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) (.f64 x x)))))) (fma.f64 x (-.f64 x (.f64 #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) (.f64 (.f64 a x) x))) (.f64 (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) (.f64 (.f64 x (.f64 a #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)))) (*.f64 x x)))))
(/.f64 (.f64 a (.f64 (fma.f64 #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) (.f64 (.f64 a x) x) x) (fma.f64 #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) (.f64 (.f64 a x) x) (neg.f64 x)))) (fma.f64 #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) (.f64 (.f64 a x) x) (neg.f64 x)))
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(fma.f64 (pow.f64 (exp.f64 (.f64 a (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (.f64 a (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (exp.f64 (+.f64 x x)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (exp.f64 (.f64 a (/.f64 x #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (exp.f64 (.f64 a (/.f64 x #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (exp.f64 (.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) #s(literal 3/2 binary64)) (pow.f64 (exp.f64 (.f64 a (/.f64 (+.f64 x x) #s(literal 2 binary64)))) #s(literal 3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (exp.f64 (+.f64 (+.f64 x x) x)) (exp.f64 x) #s(literal 1 binary64))
(neg.f64 (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)))
(/.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))))
(/.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x)))))
(/.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)))
(/.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)))
(/.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)))
(/.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (neg.f64 (neg.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) (neg.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x)))))
(/.f64 (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) (pow.f64 (neg.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)))
(/.f64 (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 (+.f64 x x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)))
(/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal 3 binary64)) (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal 3 binary64)))
(/.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)))
(/.f64 (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (exp.f64 (+.f64 x x)))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 1 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64))
(pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal -3 binary64))
(pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 9 binary64))
(pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal -9 binary64))
(pow.f64 (/.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (exp.f64 (+.f64 x x))) #s(literal -3 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -3 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal -3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal -3 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal -3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal -3 binary64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal -3 binary64)) (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal -3 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 3/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal 3/2 binary64)) #s(literal 3 binary64)))

eval366.0ms (4.5%)

Memory: 29.4MiB live, 712.1MiB allocated
Compiler: Compiled 66 124 to 6 827 computations (89.7% saved)

prune318.0ms (3.9%)

Memory

7.4MiB live, 496.4MiB allocated

Pruning

13 alts after pruning (3 fresh and 10 done)

	Pruned	Kept	Total
New	2 457	3	2 460
Fresh	0	0	0
Picked	0	4	4
Done	1	6	7
Total	2 458	13	2 471

Accuracy

100.0%

Counts

2 471 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.0%	(/.f64 (-.f64 (/.f64 (exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
✓	53.0%	(-.f64 (pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	20.5%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 a x))
✓	68.9%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))
	69.2%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 a x)))
	68.0%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 a x)))
	68.0%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 a (fma.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) #s(literal 1 binary64))) x))
✓	68.3%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x)))
✓	69.1%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x)))
✓	68.0%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x)))
✓	20.1%	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64)))))))

Compiler

Compiled 490 to 189 computations (61.4% saved)

regimes47.0ms (0.6%)

Memory

-3.9MiB live, 36.2MiB 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 a x))
#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))
#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 x (.f64 a (*.f64 x #s(literal 1/2 binary64)))))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64))) x x)))
#s(approx (- (exp (* a x)) 1) (.f64 (.f64 a (fma.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) #s(literal 1 binary64))) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 a x)))
#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 a (.f64 x x)) (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) #s(approx (+ ( a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x x)))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 a x) #s(approx (+ (* a (* x (+ (* (* a x) 1/24) 1/6))) 1/2) (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 a x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (.f64 a x) (fma.f64 a (.f64 x (fma.f64 (*.f64 a x) #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/2 binary64))) x x)))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (pow.f64 (exp.f64 (.f64 a (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 (exp.f64 #s(approx (+ (* a (+ x x)) (* a (+ x x))) (.f64 x (.f64 a #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 (exp.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))

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

Calls

5 calls:

21.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
7.0ms	a
7.0ms	x
6.0ms	(*.f64 a x)
5.0ms	(exp.f64 (*.f64 a x))

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 25 to 17 computations (32% saved)

regimes25.0ms (0.3%)

Memory

2.0MiB live, 39.9MiB allocated

Counts

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

Outputs

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 25 to 17 computations (32% saved)

regimes21.0ms (0.3%)

Memory

-3.6MiB live, 34.5MiB allocated

Counts

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

Outputs

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
69.1%	1	`a`
69.1%	1	`x`
69.1%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
69.1%	1	`(exp.f64 (*.f64 a x))`
69.1%	1	`(*.f64 a x)`

Compiler

Compiled 25 to 17 computations (32% saved)

regimes20.0ms (0.2%)

Memory

-5.4MiB live, 32.7MiB allocated

Counts

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

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

Calls

5 calls:

5.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
4.0ms	x
4.0ms	a
4.0ms	(*.f64 a x)
3.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
68.9%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
68.9%	1	`(exp.f64 (*.f64 a x))`
68.9%	1	`a`
68.9%	1	`(*.f64 a x)`
68.9%	1	`x`

Compiler

Compiled 25 to 17 computations (32% saved)

regimes6.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB 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	a
1.0ms	x
1.0ms	(*.f64 a x)
1.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
1.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
20.5%	1	`x`
20.5%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
20.5%	1	`(exp.f64 (*.f64 a x))`
20.5%	1	`(*.f64 a x)`
20.5%	1	`a`

Compiler

Compiled 25 to 17 computations (32% saved)

simplify7.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
4×	`unsub-neg_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	94
1	39	94
2	43	94
3	46	94
4	49	94
5	52	94

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (13.6%)

Memory

-37.9MiB live, 454.9MiB allocated

Rules

13 656×	`lower-fma.f64`
13 656×	`lower-fma.f32`
8 560×	`lower-fma.f64`
8 560×	`lower-fma.f32`
6 690×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	686	7632
1	2271	7022
2	7838	7006
0	8148	6524
0	51	420
0	82	390
1	320	343
2	2644	324
0	8548	294
0	32	177
0	57	168
1	220	168
0	1607	168
0	6	13
0	9	13
1	30	13
2	152	13
0	1346	11
0	63	432
1	195	432
2	526	424
3	1050	424
4	1650	424
5	1848	424
6	1875	424
7	1895	424
8	1909	424
9	1912	424
10	1912	424
11	2607	420
12	3082	420
13	4049	420
14	4050	420
15	4050	420
16	4178	420
17	4178	420
18	6095	416
19	6319	416
20	6361	416
21	6375	416
22	6375	416
23	6551	416
24	6889	416
25	6889	416
26	7463	416
0	7463	360

Stop Event

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

Compiler

Compiled 139 to 70 computations (49.6% saved)

preprocess58.0ms (0.7%)

Memory: 23.8MiB live, 101.6MiB allocated
Remove: (sort a x)
Compiler: Compiled 160 to 76 computations (52.5% 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%)

analyze21.0ms (0.3%)

sample593.0ms (7.3%)

explain108.0ms (1.3%)

preprocess21.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize23.0ms (0.3%)

series4.0ms (0%)

simplify287.0ms (3.5%)

rewrite86.0ms (1.1%)

eval19.0ms (0.2%)

prune25.0ms (0.3%)

simplify486.0ms (6%)

localize93.0ms (1.1%)

series27.0ms (0.3%)

simplify343.0ms (4.2%)

rewrite122.0ms (1.5%)

eval133.0ms (1.6%)

prune72.0ms (0.9%)

simplify183.0ms (2.2%)

localize474.0ms (5.8%)

series41.0ms (0.5%)

simplify290.0ms (3.6%)

rewrite269.0ms (3.3%)

eval746.0ms (9.2%)

prune295.0ms (3.6%)

simplify302.0ms (3.7%)

localize276.0ms (3.4%)

series15.0ms (0.2%)

simplify397.0ms (4.9%)

rewrite395.0ms (4.9%)

eval366.0ms (4.5%)

prune318.0ms (3.9%)

regimes47.0ms (0.6%)

regimes25.0ms (0.3%)

regimes21.0ms (0.3%)

regimes20.0ms (0.2%)

regimes6.0ms (0.1%)

simplify7.0ms (0.1%)

soundness1.1s (13.6%)

preprocess58.0ms (0.7%)

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