Metrics for expax (section 3.5)

analyze17.0ms (0.2%)

Memory

18.4MiB live, 18.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75.9%	68.7%	21.9%	0.1%	0%	9.4%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
86%	71.8%	11.7%	0.1%	0%	16.4%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.4%	73.4%	6%	0.1%	0%	20.5%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 12 to 7 computations (41.7% saved)

sample1.2s (14.5%)

Memory

12.1MiB live, 667.2MiB allocated

Samples

702.0ms	8 256×	0	valid
72.0ms	299×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 367.0ms

ival-mult: 170.0ms (46.3% of total)

ival-expm1: 114.0ms (31% of total)

ival->: 73.0ms (19.9% of total)

exact: 7.0ms (1.9% of total)

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

Bogosity

preprocess18.0ms (0.2%)

Memory

13.4MiB live, 13.4MiB 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)

explain110.0ms (1.3%)

Memory

-14.0MiB live, 70.2MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`	cancellation	135	0
`exp.f64`	`(exp.f64 (*.f64 a x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	136	0
-	0	120

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	0	0
-	0	0	120

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	120
1	136

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms

512×

valid

Compiler

Compiled 52 to 28 computations (46.2% saved)

Precisions

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

ival-mult: 4.0ms (35.6% of total)

ival-exp: 3.0ms (26.7% of total)

ival-expm1: 3.0ms (26.7% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.6%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	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)

localize18.0ms (0.2%)

Memory

16.3MiB live, 16.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 a x)
✓	accuracy	100.0%	(exp.f64 (*.f64 a x))
✓	accuracy	50.7%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Samples

12.0ms

256×

valid

Compiler

Compiled 18 to 8 computations (55.6% saved)

Precisions

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

ival-exp: 2.0ms (36.8% of total)

ival-mult: 2.0ms (36.8% of total)

ival-expm1: 1.0ms (18.4% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

3.7MiB live, 3.7MiB 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	@	inf	(* a x)
0.0ms	a	@	0	(- (exp (* a x)) 1)
0.0ms	x	@	0	(- (exp (* a x)) 1)
0.0ms	a	@	0	(* a x)
0.0ms	x	@	inf	(* a x)

simplify361.0ms (4.2%)

Memory

-22.3MiB live, 140.7MiB 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 (*.f64 a 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 (*.f64 a 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)

rewrite140.0ms (1.6%)

Memory

-1.4MiB live, 74.1MiB allocated

Algorithm

1×	batch-egg-rewrite

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))
(fma.f64 (exp.f64 (.f64 a x)) (/.f64 (exp.f64 (.f64 a 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)))))
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(.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)

eval29.0ms (0.3%)

Memory: -1.5MiB live, 35.9MiB allocated
Compiler: Compiled 3 258 to 324 computations (90.1% saved)

prune33.0ms (0.4%)

Memory

-2.5MiB live, 40.2MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

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

Accuracy

100.0%

Counts

184 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
	99.3%	(/.f64 (expm1.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))))))
▶	18.1%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	17.0%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 a x))
▶	61.1%	#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)))
	60.2%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.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)))) x)))
	60.2%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
	67.2%	#s(approx (- (exp (* a x)) 1) (*.f64 a x))

Compiler

Compiled 236 to 140 computations (40.7% saved)

simplify432.0ms (5.1%)

Memory

40.4MiB live, 666.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

18 690×	`lower-fma.f32`
18 684×	`lower-fma.f64`
2 786×	`lower-*.f32`
2 774×	`lower-*.f64`
2 560×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	163
0	49	154
1	93	154
2	203	154
3	539	154
4	905	154
5	1304	154
6	1454	154
7	2072	154
8	5283	154
0	8249	154

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

localize86.0ms (1%)

Memory

1.3MiB live, 158.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(exp.f64 (*.f64 a x))
✓	accuracy	99.9%	(expm1.f64 (*.f64 a (+.f64 x x)))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	98.9%	(.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))
✓	accuracy	87.8%	(.f64 a (.f64 x x))
✓	accuracy	67.1%	#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)))
✓	accuracy	100.0%	(fma.f64 a x #s(literal 1 binary64))
✓	accuracy	66.5%	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	accuracy	50.7%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	accuracy	66.6%	#s(approx (exp (* a x)) #s(literal 1 binary64))
✓	accuracy	50.7%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 a x)
✓	accuracy	100.0%	(expm1.f64 (*.f64 a x))

Samples

46.0ms

256×

valid

Compiler

Compiled 149 to 24 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 13.0ms (44.7% of total)

ival-add: 6.0ms (20.6% of total)

const: 4.0ms (13.8% of total)

ival-expm1: 3.0ms (10.3% of total)

ival-div: 2.0ms (6.9% of total)

ival-exp: 2.0ms (6.9% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.3%)

Memory

-3.5MiB live, 35.0MiB allocated

Counts

18 → 408

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

102 calls:

Time	Variable		Point	Expression
5.0ms	a	@	0	(* a (* x x))
1.0ms	x	@	0	(/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1))
1.0ms	a	@	0	(* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x))
1.0ms	x	@	-inf	(+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)
1.0ms	a	@	0	(/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1))

simplify557.0ms (6.6%)

Memory

-12.7MiB live, 904.9MiB allocated

Algorithm

1×	egg-herbie

Rules

25 396×	`lower-fma.f64`
25 396×	`lower-fma.f32`
6 196×	`lower-*.f64`
6 196×	`lower-*.f32`
4 148×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	281	3540
1	911	3434
2	3008	3340
3	7245	3332
0	8361	2936

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 406

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

rewrite135.0ms (1.6%)

Memory

26.9MiB live, 184.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

886×	`lower-fma.f32`
880×	`lower-fma.f64`
726×	`lower-*.f32`
714×	`lower-*.f64`
516×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	138
0	49	129
1	188	129
0	1414	129

Stop Event

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

Counts

18 → 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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
(fma.f64 a x #s(literal 1 binary64))
#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)))
(.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))
(fma.f64 (.f64 a (.f64 x x)) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(.f64 a (.f64 x x))
(/.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 1/6 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))) (+.f64 #s(literal -1 binary64) (neg.f64 (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 (+.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 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))) #s(literal 1 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)))) (+.f64 #s(literal -1 binary64) (neg.f64 (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 (.f64 (expm1.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x))) (exp.f64 (.f64 a (+.f64 x x))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (.f64 a (+.f64 x x))))) (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 a x))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x)))) (/.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.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 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 (.f64 (/.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x)))) (/.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x))))) (.f64 (/.f64 #s(literal 1 binary64) (+.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 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 (expm1.f64 (.f64 a (+.f64 x x))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x))))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 a (+.f64 x x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.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 (.f64 (expm1.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x))))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a x)))
(.f64 (expm1.f64 (.f64 a (+.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)))))
(.f64 (neg.f64 (expm1.f64 (.f64 a (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (*.f64 a x))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x)))) (expm1.f64 (*.f64 a (+.f64 x x))))
(.f64 (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) (/.f64 #s(literal 1 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)))) (expm1.f64 (.f64 a x)))
(.f64 (/.f64 (expm1.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)))))
(+.f64 (exp.f64 (*.f64 a (+.f64 x x))) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 (*.f64 a (+.f64 x x))))
(-.f64 (exp.f64 (*.f64 a (+.f64 x x))) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 a (+.f64 x x)) #s(literal 3 binary64))) (+.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 (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 (/.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))))))
(expm1.f64 (*.f64 a (+.f64 x x)))
(expm1.f64 (*.f64 (log.f64 (exp.f64 a)) (+.f64 x x)))
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (+.f64 x x))) #s(literal -1 binary64))
(fma.f64 (exp.f64 (.f64 a x)) (exp.f64 (.f64 a x)) #s(literal -1 binary64))
(fma.f64 (exp.f64 (*.f64 a (+.f64 x x))) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (pow.f64 (exp.f64 a) (/.f64 (+.f64 x x) #s(literal 2 binary64))) (pow.f64 (exp.f64 a) (/.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 #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))))) (expm1.f64 (.f64 (.f64 a (+.f64 x x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x)))) (expm1.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x))))))
(/.f64 (expm1.f64 (.f64 (.f64 a (+.f64 x x)) #s(literal 3 binary64))) (+.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 (+.f64 x x)) #s(literal 3 binary64))) (+.f64 (exp.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 (*.f64 a (+.f64 x x))) #s(literal -1 binary64)))))
(/.f64 (expm1.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 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (-.f64 (exp.f64 (.f64 a (+.f64 x x))) #s(literal -1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 a (+.f64 x x)) #s(literal 3 binary64)))) (neg.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 (neg.f64 (expm1.f64 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))))
(.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x))) (expm1.f64 (*.f64 a x)))
(.f64 (expm1.f64 (.f64 (.f64 a (+.f64 x x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.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 (fma.f64 a (+.f64 x x) (.f64 a (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a (+.f64 x x))))))
(+.f64 (.f64 a x) (.f64 a x))
(fma.f64 a x (*.f64 a x))
(fma.f64 a (.f64 x #s(literal 1 binary64)) (.f64 a x))
(fma.f64 x a (*.f64 a x))
(fma.f64 x (.f64 a #s(literal 1 binary64)) (.f64 a x))
(fma.f64 (.f64 a x) #s(literal 1 binary64) (.f64 a x))
(fma.f64 #s(literal 1 binary64) (.f64 a x) (.f64 a x))
(/.f64 (fma.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))))) (fma.f64 a (.f64 x (.f64 a x)) (-.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (*.f64 a x))))))
(/.f64 (-.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) (-.f64 (.f64 a x) (.f64 a x)))
(/.f64 (.f64 a (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 a #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) a) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 #s(literal 0 binary64) a) #s(literal 0 binary64))
(*.f64 a (+.f64 x x))
(*.f64 x (+.f64 a a))
(*.f64 (+.f64 x x) a)
(.f64 #s(literal 2 binary64) (.f64 a x))
(.f64 (.f64 a #s(literal 2 binary64)) x)
(+.f64 x x)
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))))
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(.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 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(exp.f64 (*.f64 a x))
(exp.f64 (*.f64 (log.f64 (exp.f64 a)) x))
(pow.f64 (exp.f64 a) x)
(pow.f64 (exp.f64 x) a)
(.f64 #s(literal 1 binary64) (exp.f64 (.f64 a x)))
(.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))
(*.f64 (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64))))
(+.f64 #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))) (expm1.f64 (.f64 a x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.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 (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))
(/.f64 #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) (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a (+.f64 x x)))))
(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (expm1.f64 (.f64 a x)))
(/.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 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)))))

eval84.0ms (1%)

Memory: -6.9MiB live, 218.7MiB allocated
Compiler: Compiled 12 188 to 867 computations (92.9% saved)

prune56.0ms (0.7%)

Memory

12.3MiB live, 175.3MiB allocated

Pruning

18 alts after pruning (14 fresh and 4 done)

	Pruned	Kept	Total
New	722	13	735
Fresh	3	1	4
Picked	1	4	5
Done	0	0	0
Total	726	18	744

Accuracy

100.0%

Counts

744 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	17.8%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	100.0%	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
	17.8%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))))
✓	18.1%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
	17.6%	(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
	17.6%	(-.f64 #s(approx (exp (* a x)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 a x #s(literal -1 binary64)) (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64))))) #s(literal 1 binary64))
	17.3%	(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a (.f64 x (.f64 a x)) (-.f64 #s(literal 1 binary64) (.f64 a x)))))) #s(literal 1 binary64))
	17.6%	(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 a (.f64 x (*.f64 a x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
✓	17.0%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	17.8%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))))
✓	100.0%	(expm1.f64 (*.f64 a x))
▶	60.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
▶	67.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))
	67.1%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
▶	67.1%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x x)))
	60.2%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.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)))) x)))
	17.1%	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))))
	16.6%	#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a)))))))

Compiler

Compiled 586 to 287 computations (51% saved)

simplify295.0ms (3.5%)

Memory

13.7MiB live, 486.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 a x #s(literal 1 binary64))
✓	cost-diff	0	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	cost-diff	0	(fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	cost-diff	2176	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))))
✓	cost-diff	0	(fma.f64 a x #s(literal 1 binary64))
✓	cost-diff	0	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	cost-diff	0	(fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	cost-diff	1856	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	cost-diff	0	(.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 a x))
✓	cost-diff	0	(fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 a x)) x x)
✓	cost-diff	0	(.f64 a (fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x x))
✓	cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x 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 x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
✓	cost-diff	0	(*.f64 a x)
✓	cost-diff	0	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))

Rules

13 586×	`lower-fma.f32`
13 576×	`lower-fma.f64`
3 186×	`lower-*.f32`
3 170×	`lower-*.f64`
1 724×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	330
0	57	328
1	119	328
2	223	286
3	553	286
4	1254	286
5	2950	268
6	6172	268
0	8109	262

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

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

localize186.0ms (2.2%)

Memory

-19.7MiB live, 223.8MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))
✓	accuracy	100.0%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))))
✓	accuracy	66.5%	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	accuracy	50.7%	(fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	accuracy	100.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	accuracy	100.0%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	accuracy	66.5%	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	accuracy	50.7%	(fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	99.2%	(fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 a x)) x x)
✓	accuracy	98.9%	(.f64 a (fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x x))
✓	accuracy	67.1%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x x)))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	97.4%	(.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))
✓	accuracy	90.5%	(fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
✓	accuracy	66.1%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
✓	accuracy	100.0%	(*.f64 a x)
✓	accuracy	67.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))

Samples

56.0ms	76×	2	valid
43.0ms	90×	1	valid
21.0ms	90×	0	valid

Compiler

Compiled 240 to 36 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-mult: 25.0ms (27.4% of total)

ival-exp: 16.0ms (17.6% of total)

adjust: 15.0ms (16.5% of total)

ival-add: 13.0ms (14.3% of total)

ival-div: 10.0ms (11% of total)

ival-sub: 4.0ms (4.4% of total)

const: 4.0ms (4.4% of total)

ival-expm1: 4.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.2%)

Memory

19.2MiB live, 19.2MiB allocated

Counts

18 → 408

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

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 (* 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))))>
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#<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

102 calls:

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

simplify443.0ms (5.2%)

Memory

-12.4MiB live, 526.4MiB allocated

Algorithm

1×	egg-herbie

Rules

19 472×	`lower-fma.f64`
19 472×	`lower-fma.f32`
5 796×	`lower-*.f64`
5 796×	`lower-*.f32`
4 924×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	357	5104
1	1215	4554
2	4009	4406
0	8563	3944

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 404

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

rewrite516.0ms (6.1%)

Memory

6.9MiB live, 486.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 678×	`lower-fma.f32`
5 668×	`lower-fma.f64`
3 754×	`lower-*.f32`
3 738×	`lower-*.f64`
3 546×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	255
0	57	232
1	249	186
2	1811	186
0	8907	180

Stop Event

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

Counts

18 → 785

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

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 (*.f64 x #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 a (log.f64 (exp.f64 x)) #s(literal 0 binary64))
(fma.f64 x a #s(literal 0 binary64))
(fma.f64 x (*.f64 a #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 a x) #s(literal 0 binary64))
(fma.f64 (*.f64 a x) #s(literal 1 binary64) #s(literal 0 binary64))
(*.f64 a x)
(.f64 a (.f64 x #s(literal 1 binary64)))
(*.f64 a (log.f64 (exp.f64 x)))
(*.f64 x a)
(.f64 x (.f64 a #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 a x))
(.f64 (.f64 a x) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (*.f64 x #s(literal 1/2 binary64))) x)))
(+.f64 (.f64 a x) (.f64 a (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64))))
(+.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (*.f64 a x))
(-.f64 (/.f64 (.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))) (-.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 a x))) (/.f64 (.f64 a (.f64 x (.f64 a x))) (-.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 a x))))
(fma.f64 a x (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))))
(fma.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)) (.f64 a x))
(fma.f64 a (.f64 x #s(literal 1 binary64)) (.f64 a (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64))))
(fma.f64 a (log.f64 (exp.f64 x)) (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))))
(fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))))
(fma.f64 x (.f64 a #s(literal 1 binary64)) (.f64 a (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 a x) (.f64 a (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64))))
(fma.f64 (.f64 a x) #s(literal 1 binary64) (.f64 a (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 a a) (.f64 a x))
(fma.f64 (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)) a (.f64 a x))
(fma.f64 (.f64 a #s(literal 1/2 binary64)) (.f64 (.f64 x x) a) (.f64 a x))
(fma.f64 (.f64 a a) (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 a x))
(fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 a x))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 a (.f64 a a)) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))))) (fma.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (-.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (*.f64 a x)))))
(/.f64 (-.f64 (.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))) (.f64 a (.f64 x (.f64 a x)))) (-.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (*.f64 a x)))
(/.f64 (.f64 a (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x)))) (fma.f64 x (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64))))
(/.f64 (.f64 a (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x x))) (-.f64 (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)) x))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x))) a) (fma.f64 x (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x x)) a) (-.f64 (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)) x))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 a (.f64 a a)) (.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x)))))) (neg.f64 (fma.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (-.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (*.f64 a x))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))) (.f64 a (.f64 x (.f64 a x))))) (neg.f64 (-.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (*.f64 a x))))
(/.f64 (neg.f64 (.f64 a (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x))))) (neg.f64 (fma.f64 x (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (.f64 a (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x x)))) (neg.f64 (-.f64 (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)) x)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x))) a)) (neg.f64 (fma.f64 x (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x x)) a)) (neg.f64 (-.f64 (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)) x)))
(/.f64 (fma.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 a (.f64 a a)))) (fma.f64 a (.f64 x (.f64 a x)) (-.f64 (.f64 (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))) (.f64 (.f64 a x) (.f64 a (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)))))))
(.f64 a (fma.f64 a (.f64 x (*.f64 x #s(literal 1/2 binary64))) x))
(.f64 (fma.f64 a (.f64 x (*.f64 x #s(literal 1/2 binary64))) x) a)
(+.f64 x (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)) x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))) (/.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (-.f64 x (.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64)))))
(fma.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) a) x)
(fma.f64 (.f64 x x) (.f64 a #s(literal 1/2 binary64)) x)
(fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) a x)
(fma.f64 (.f64 a #s(literal 1/2 binary64)) (.f64 x x) x)
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 a x) x)
(fma.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64) x)
(fma.f64 (.f64 a (.f64 x #s(literal 1/2 binary64))) x x)
(fma.f64 (.f64 (.f64 a #s(literal 1/2 binary64)) x) x x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)) x) (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)) x) (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x x)))))
(/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x))) (fma.f64 x (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (*.f64 a x))) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x))) (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)) x))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x)))) (neg.f64 (fma.f64 x (-.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (*.f64 a x))) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 a (.f64 a a))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x)))) (neg.f64 (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 a x)) (.f64 x (.f64 a x))) #s(literal 1/4 binary64)) (.f64 x x))) (neg.f64 (-.f64 (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)) x)))
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eval381.0ms (4.5%)

Memory: 51.5MiB live, 312.2MiB allocated
Compiler: Compiled 60 371 to 2 534 computations (95.8% saved)

prune167.0ms (2%)

Memory

-5.9MiB live, 392.4MiB allocated

Pruning

27 alts after pruning (20 fresh and 7 done)

	Pruned	Kept	Total
New	1 717	16	1 733
Fresh	5	4	9
Picked	2	3	5
Done	0	4	4
Total	1 724	27	1 751

Accuracy

100.0%

Counts

1 751 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.5%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal -1 binary64)))
▶	17.5%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
	1.7%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))))
	17.3%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) (fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))) x) #s(literal 2 binary64))))
	17.8%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) (fma.f64 a x #s(literal 2 binary64))))
	16.8%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) #s(literal 2 binary64)))
	17.4%	(/.f64 (.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) (.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) (.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	100.0%	(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
	18.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))))
✓	18.1%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
	17.6%	(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
✓	17.0%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
	17.6%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))))
	17.5%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))))))
	17.3%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))) x) #s(literal 2 binary64)))))
	17.8%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a x #s(literal 2 binary64)))))
▶	17.8%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
✓	100.0%	(expm1.f64 (*.f64 a x))
▶	66.1%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))))
	66.0%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
✓	60.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
▶	16.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64))))))
✓	67.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))
✓	67.1%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x x)))
	60.2%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.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)))) x)))
▶	17.1%	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))))
	16.6%	#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a)))))))

Compiler

Compiled 1 051 to 463 computations (55.9% saved)

simplify629.0ms (7.4%)

Memory

-36.0MiB live, 446.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))
✓	cost-diff	320	(.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))))
✓	cost-diff	2176	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
✓	cost-diff	0	(fma.f64 a x #s(literal 1 binary64))
✓	cost-diff	0	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	cost-diff	0	(fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	cost-diff	0	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
✓	cost-diff	0	(.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))))
✓	cost-diff	0	#s(approx (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))
✓	cost-diff	0	(.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))))))
✓	cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))))
✓	cost-diff	0	(.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (+ (* a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
✓	cost-diff	0	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64))))))
✓	cost-diff	0	(.f64 (.f64 x (*.f64 a x)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))))
✓	cost-diff	320	(fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64))))

Rules

19 030×	`lower-fma.f32`
19 022×	`lower-fma.f64`
4 336×	`lower-+.f32`
4 332×	`lower-+.f64`
2 632×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	515
0	85	538
1	179	524
2	364	482
3	780	482
4	1508	482
5	5310	464
0	8948	450

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

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

localize224.0ms (2.6%)

Memory

3.1MiB live, 234.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))))
✓	accuracy	100.0%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
✓	accuracy	66.5%	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	accuracy	50.7%	(+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	accuracy	66.5%	#s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x)))
✓	accuracy	66.5%	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
✓	accuracy	50.7%	(fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	accuracy	35.5%	#s(approx (+ (* a x) 1) (*.f64 a x))
✓	accuracy	98.9%	(.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))))))
✓	accuracy	88.3%	(.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))))
✓	accuracy	67.1%	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))))
✓	accuracy	37.1%	#s(approx (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))
✓	accuracy	97.4%	(.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
✓	accuracy	87.8%	(.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64)))
✓	accuracy	66.1%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64))))))
✓	accuracy	36.7%	#s(approx (+ (* a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(*.f64 a x)
✓	accuracy	99.8%	(.f64 x (.f64 a x))
✓	accuracy	94.1%	(.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))
✓	accuracy	66.1%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))))

Samples

70.0ms	76×	2	valid
56.0ms	90×	1	valid
30.0ms	90×	0	valid

Compiler

Compiled 319 to 50 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 122.0ms

ival-mult: 46.0ms (37.6% of total)

adjust: 21.0ms (17.2% of total)

ival-add: 17.0ms (13.9% of total)

ival-exp: 16.0ms (13.1% of total)

ival-div: 9.0ms (7.4% of total)

const: 7.0ms (5.7% of total)

ival-expm1: 4.0ms (3.3% of total)

ival-sub: 2.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series21.0ms (0.2%)

Memory

-16.1MiB live, 21.2MiB allocated

Counts

24 → 576

Calls

Call 1

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

Outputs
#<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 (* 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 (* 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 (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* 1/2 (* (pow a 2) (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 (* 1/2 (* a (pow x 2)))>
#<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 (* 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)))>
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#<alt (* x (+ a (/ 1 x)))>
#<alt (* a x)>
#<alt (* -1 (* x (- (* -1 a) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 a) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 a) (/ 1 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 (* 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)>

Calls

144 calls:

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

simplify365.0ms (4.3%)

Memory

11.2MiB live, 400.8MiB allocated

Algorithm

1×	egg-herbie

Rules

15 108×	`lower-fma.f64`
15 108×	`lower-fma.f32`
5 824×	`lower-*.f64`
5 824×	`lower-*.f32`
4 022×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	428	6376
1	1417	5938
2	4742	5818
0	8423	5232

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 572

Calls

Call 1

Inputs
(* 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 (* 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)
(* 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))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* a (pow x 2)))
(* 1/2 (* a (pow x 2)))
(* 1/2 (* a (pow x 2)))
(* 1/2 (* a (pow x 2)))
(* 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 (* 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 (* 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 (* 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 (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* a x)
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))))
x
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2)))))
(* 1/2 (* a (pow x 2)))
(* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* 1/2 (* a (pow x 2)))
(* (pow x 2) (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* (pow x 2) (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* (pow x 2) (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))
(* 1/6 (* (pow a 2) (pow x 3)))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* 1/6 (* (pow a 2) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* a x)
(* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))
(* a (+ x (* a (- (+ (* a (- (* 1/2 (+ (* 1/3 (pow x 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 (- (+ (* 1/2 (+ (* 1/3 (pow x 3)) (pow x 3))) (* a (- (* 1/2 (+ (* 1/12 (pow x 4)) (+ (* 1/4 (pow x 4)) (* 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 (- (* 1/2 (+ (* 1/3 (pow x 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))))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(* a x)
(* x (+ a (* x (- (pow a 2) (* 1/2 (pow a 2))))))
(* x (+ a (* x (- (+ (* x (- (* 1/2 (+ (* 1/3 (pow a 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 (- (+ (* 1/2 (+ (* 1/3 (pow a 3)) (pow a 3))) (* x (- (* 1/2 (+ (* 1/12 (pow a 4)) (+ (* 1/4 (pow a 4)) (* 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 (- (* 1/2 (+ (* 1/3 (pow a 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))))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))
(* 2 (* a x))
(* a (+ (* 2 x) (* 2 (* a (pow x 2)))))
(* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 1/3 (pow x 3)) (pow x 3)))))))
(* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 1/3 (pow x 3)) (+ (* a (+ (* 1/12 (pow x 4)) (+ (* 1/4 (pow x 4)) (* 1/3 (pow x 4))))) (pow x 3))))))))
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(* 2 (* a x))
(* x (+ (* 2 a) (* 2 (* (pow a 2) x))))
(* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 1/3 (pow a 3)) (pow a 3)))))))
(* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 1/3 (pow a 3)) (+ (* x (+ (* 1/12 (pow a 4)) (+ (* 1/4 (pow a 4)) (* 1/3 (pow a 4))))) (pow a 3))))))))
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 1)
(- (pow (exp (* a x)) 2) 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))
1
(+ 1 (* a x))
(+ 1 (* a x))
(+ 1 (* a x))
(* a x)
(* a (+ x (/ 1 a)))
(* a (+ x (/ 1 a)))
(* a (+ x (/ 1 a)))
(* a x)
(* -1 (* a (- (* -1 x) (/ 1 a))))
(* -1 (* a (- (* -1 x) (/ 1 a))))
(* -1 (* a (- (* -1 x) (/ 1 a))))
1
(+ 1 (* a x))
(+ 1 (* a x))
(+ 1 (* a x))
(* a x)
(* x (+ a (/ 1 x)))
(* x (+ a (/ 1 x)))
(* x (+ a (/ 1 x)))
(* a x)
(* -1 (* x (- (* -1 a) (/ 1 x))))
(* -1 (* x (- (* -1 a) (/ 1 x))))
(* -1 (* x (- (* -1 a) (/ 1 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 (* a x))
(* a (+ (* 1/2 x) (* (pow a 2) (- (* 1/12 (pow x 3)) (* 1/8 (pow x 3))))))
(* a (+ (* 1/2 x) (* (pow a 2) (- (+ (* 1/12 (pow x 3)) (* a (- (* 1/48 (pow x 4)) (+ (* 1/24 (pow x 4)) (* 1/2 (* x (- (* 1/12 (pow x 3)) (* 1/8 (pow x 3))))))))) (* 1/8 (pow x 3))))))
(* a (+ (* 1/2 x) (* (pow a 2) (- (+ (* 1/12 (pow x 3)) (* a (- (+ (* 1/48 (pow x 4)) (* a (- (* 1/240 (pow x 5)) (+ (* 1/96 (pow x 5)) (+ (* 1/4 (* (pow x 2) (- (* 1/12 (pow x 3)) (* 1/8 (pow x 3))))) (* 1/2 (* x (- (* 1/48 (pow x 4)) (+ (* 1/24 (pow x 4)) (* 1/2 (* x (- (* 1/12 (pow x 3)) (* 1/8 (pow x 3)))))))))))))) (+ (* 1/24 (pow x 4)) (* 1/2 (* x (- (* 1/12 (pow x 3)) (* 1/8 (pow x 3))))))))) (* 1/8 (pow x 3))))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(* 1/2 (* a x))
(* x (+ (* 1/2 a) (* (pow x 2) (- (* 1/12 (pow a 3)) (* 1/8 (pow a 3))))))
(* x (+ (* 1/2 a) (* (pow x 2) (- (+ (* 1/12 (pow a 3)) (* x (- (* 1/48 (pow a 4)) (+ (* 1/24 (pow a 4)) (* 1/2 (* a (- (* 1/12 (pow a 3)) (* 1/8 (pow a 3))))))))) (* 1/8 (pow a 3))))))
(* x (+ (* 1/2 a) (* (pow x 2) (- (+ (* 1/12 (pow a 3)) (* x (- (+ (* 1/48 (pow a 4)) (* x (- (* 1/240 (pow a 5)) (+ (* 1/96 (pow a 5)) (+ (* 1/4 (* (pow a 2) (- (* 1/12 (pow a 3)) (* 1/8 (pow a 3))))) (* 1/2 (* a (- (* 1/48 (pow a 4)) (+ (* 1/24 (pow a 4)) (* 1/2 (* a (- (* 1/12 (pow a 3)) (* 1/8 (pow a 3)))))))))))))) (+ (* 1/24 (pow a 4)) (* 1/2 (* a (- (* 1/12 (pow a 3)) (* 1/8 (pow a 3))))))))) (* 1/8 (pow a 3))))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (exp (* a x))))
(/ (- (exp (* a x)) 1) (+ 1 (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)))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* a (pow x 2))
(* 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
(+ 1 (* a x))
(+ 1 (* a x))
(+ 1 (* a x))
(* a x)
(* a (+ x (/ 1 a)))
(* a (+ x (/ 1 a)))
(* a (+ x (/ 1 a)))
(* a x)
(* -1 (* a (- (* -1 x) (/ 1 a))))
(* -1 (* a (- (* -1 x) (/ 1 a))))
(* -1 (* a (- (* -1 x) (/ 1 a))))
1
(+ 1 (* a x))
(+ 1 (* a x))
(+ 1 (* a x))
(* a x)
(* x (+ a (/ 1 x)))
(* x (+ a (/ 1 x)))
(* x (+ a (/ 1 x)))
(* a x)
(* -1 (* x (- (* -1 a) (/ 1 x))))
(* -1 (* x (- (* -1 a) (/ 1 x))))
(* -1 (* x (- (* -1 a) (/ 1 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))
(* 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)

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

rewrite455.0ms (5.4%)

Memory

20.4MiB live, 485.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 366×	`lower-fma.f32`
6 358×	`lower-fma.f64`
4 508×	`lower-*.f32`
4 480×	`lower-*.f64`
4 146×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	423
0	85	426
1	352	354
2	2335	354
0	8947	342

Stop Event

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

Counts

24 → 836

Calls

Call 1

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

Outputs
(+.f64 (.f64 x a) (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x)))))
(+.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (*.f64 x a))
(-.f64 (/.f64 (.f64 a (.f64 a (.f64 x x))) (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 a (.f64 a (.f64 x x))) (.f64 a (.f64 a (.f64 x x))))) (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x)))))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 a (.f64 a (.f64 x x))) (.f64 a (.f64 a (.f64 x x))))) (-.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (.f64 x a))) (/.f64 (.f64 a (.f64 a (.f64 x x))) (-.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (*.f64 x a))))
(fma.f64 x a (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))))
(fma.f64 x (.f64 a #s(literal 1 binary64)) (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x)))))
(fma.f64 x (.f64 (.f64 (.f64 x a) #s(literal 1/2 binary64)) a) (.f64 x a))
(fma.f64 a x (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))))
(fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x))) (.f64 x a))
(fma.f64 a (.f64 x #s(literal 1 binary64)) (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x)))))
(fma.f64 a (log.f64 (exp.f64 x)) (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))))
(fma.f64 (.f64 x a) #s(literal 1 binary64) (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x)))))
(fma.f64 (.f64 x a) (.f64 (.f64 x a) #s(literal 1/2 binary64)) (.f64 x a))
(fma.f64 #s(literal 1/2 binary64) (.f64 a (.f64 a (.f64 x x))) (.f64 x a))
(fma.f64 #s(literal 1 binary64) (.f64 x a) (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x))) a (.f64 x a))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 a a) (.f64 x a))
(fma.f64 (.f64 a (.f64 x x)) (.f64 a #s(literal 1/2 binary64)) (.f64 x a))
(fma.f64 (.f64 a (.f64 a (.f64 x x))) #s(literal 1/2 binary64) (.f64 x a))
(fma.f64 (.f64 a #s(literal 1/2 binary64)) (.f64 a (.f64 x x)) (.f64 x a))
(fma.f64 (.f64 a a) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x a))
(fma.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 x x) (.f64 x a))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (-.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (.f64 x a)) (.f64 a (.f64 a (.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x))))) (.f64 (.f64 a (fma.f64 x (.f64 (.f64 x a) #s(literal 1/2 binary64)) x)) (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (-.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (.f64 x a)) (.f64 a (.f64 a (.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x))))) (.f64 (.f64 a (fma.f64 x (.f64 (.f64 x a) #s(literal 1/2 binary64)) x)) (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))) (fma.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (-.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (.f64 x a)) (.f64 a (.f64 a (.f64 x x)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 a (.f64 a (.f64 x x))) (.f64 a (.f64 a (.f64 x x)))) (-.f64 (.f64 a (.f64 a (.f64 x x))) (.f64 x (.f64 a (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))))))))
(/.f64 (.f64 (.f64 a (fma.f64 x (.f64 (.f64 x a) #s(literal 1/2 binary64)) x)) (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))))) (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))))) (neg.f64 (fma.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (-.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (.f64 x a)) (.f64 a (.f64 a (.f64 x x))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))))) (.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x)))))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 a (.f64 a (.f64 x x))) (.f64 a (.f64 a (.f64 x x)))) (-.f64 (.f64 a (.f64 a (.f64 x x))) (.f64 x (.f64 a (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x))))))))))
(/.f64 (neg.f64 (.f64 (.f64 a (fma.f64 x (.f64 (.f64 x a) #s(literal 1/2 binary64)) x)) (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x))))))) (neg.f64 (.f64 a (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 a (.f64 a (.f64 x x))) (.f64 a (.f64 a (.f64 x x))))) (.f64 a (.f64 a (.f64 x x)))) (-.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a (.f64 x x)))) (.f64 x a)))
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eval319.0ms (3.8%)

Memory: 61.0MiB live, 480.1MiB allocated
Compiler: Compiled 66 946 to 3 090 computations (95.4% saved)

prune299.0ms (3.5%)

Memory

-16.4MiB live, 441.5MiB allocated

Pruning

40 alts after pruning (29 fresh and 11 done)

	Pruned	Kept	Total
New	1 877	17	1 894
Fresh	3	12	15
Picked	1	4	5
Done	0	7	7
Total	1 881	40	1 921

Accuracy

100.0%

Counts

1 921 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.3%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 a (.f64 (.f64 x x) (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 1 binary64))) #s(literal -1 binary64)))
	17.5%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal -1 binary64)))
✓	17.5%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
	1.7%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))))
	17.3%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) (fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))) x) #s(literal 2 binary64))))
	17.8%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) (fma.f64 a x #s(literal 2 binary64))))
	16.8%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) #s(literal 2 binary64)))
	17.0%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64)))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
	3.8%	(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (.f64 a x))) #s(literal -1 binary64)) (-.f64 #s(approx (exp ( a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
	17.5%	(/.f64 (+.f64 (+.f64 #s(literal -1 binary64) (neg.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))) (.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.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)))
	17.5%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (.f64 x a)))) (fma.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64))))
	18.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))))
✓	18.1%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
	17.6%	(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
✓	17.0%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
	17.5%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 x a))))))
	17.3%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))) x) #s(literal 2 binary64)))))
	17.8%	(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a x #s(literal 2 binary64)))))
	17.5%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64)))) (/.f64 (+.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 x a))))))
	17.6%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))) (/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))))
	1.8%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (/.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))))
	17.4%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64))))))))
	17.4%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (.f64 (fma.f64 a (.f64 a (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x a #s(literal -1 binary64)))))))))
	17.5%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a (fma.f64 a (.f64 (.f64 x x) (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 2 binary64))))))
	19.0%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (/.f64 (fma.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))) #s(literal 1 binary64)) (fma.f64 x (.f64 a (.f64 x a)) (-.f64 #s(literal 1 binary64) (.f64 x a))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))))))
	18.9%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
	17.8%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
	66.9%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 #s(approx (+ (exp ( a x)) -1) (.f64 a x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))))))
	66.0%	(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) #s(approx (* (+ (exp (* a x)) -1) (/ 1 (+ 1 (exp (* a x))))) (.f64 a (.f64 x #s(literal 1/2 binary64)))))
✓	100.0%	(expm1.f64 (*.f64 a x))
✓	66.1%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))))
	66.0%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
✓	60.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
✓	16.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x x) #s(literal 1/2 binary64))))))
✓	67.2%	#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (*.f64 a x))
✓	67.1%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x x)))
	60.2%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.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)))) x)))
✓	17.1%	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))))
	16.6%	#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a)))))))

Compiler

Compiled 2 204 to 642 computations (70.9% saved)

regimes82.0ms (1%)

Memory

-9.2MiB live, 109.2MiB allocated

Counts

56 → 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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x 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 x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) #s(approx (* (+ (exp (* a x)) -1) (/ 1 (+ 1 (exp (* a x))))) (.f64 a (.f64 x #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) #s(literal 2 binary64)))
#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a)))))))
#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))))
#s(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 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x x)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) (fma.f64 a x #s(literal 2 binary64))))
(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (.f64 a x))) #s(literal -1 binary64)) (-.f64 #s(approx (exp ( a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a x #s(literal 2 binary64)))))
(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 a (.f64 x (*.f64 a x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64)))) (/.f64 (+.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 x a))))))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))))))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 x a))))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.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)))) x)))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 #s(approx (+ (exp ( a x)) -1) (.f64 a x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(-.f64 #s(approx (exp (* a x)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 a x #s(literal -1 binary64)) (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (.f64 x a)))) (fma.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))))
(/.f64 (+.f64 (+.f64 #s(literal -1 binary64) (neg.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))) (.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) (fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))) x) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64)))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 a (.f64 (.f64 x x) (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))) x) #s(literal 2 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (/.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))))
(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a (.f64 x (.f64 a x)) (-.f64 #s(literal 1 binary64) (.f64 a x)))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a (fma.f64 a (.f64 (.f64 x x) (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 2 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64))))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (.f64 (fma.f64 a (.f64 a (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x a #s(literal -1 binary64)))))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))) (/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) (.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) (.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (/.f64 (fma.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))) #s(literal 1 binary64)) (fma.f64 x (.f64 a (.f64 x a)) (-.f64 #s(literal 1 binary64) (.f64 x a))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(/.f64 (expm1.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
(/.f64 (expm1.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))))))

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

Calls

5 calls:

19.0ms	a
17.0ms	(*.f64 a x)
15.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
14.0ms	x
12.0ms	(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)

regimes76.0ms (0.9%)

Memory

28.6MiB live, 103.9MiB allocated

Counts

52 → 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))
(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 a (.f64 (*.f64 x 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 x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) #s(approx (* (+ (exp (* a x)) -1) (/ 1 (+ 1 (exp (* a x))))) (.f64 a (.f64 x #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* a (+ x x))) 1) (+ (exp (* a x)) 1)) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) #s(literal 2 binary64)))
#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a)))))))
#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))))
#s(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 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 a x)) x x)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) (fma.f64 a x #s(literal 2 binary64))))
(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (.f64 a x))) #s(literal -1 binary64)) (-.f64 #s(approx (exp ( a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 a (.f64 (.f64 x (.f64 a x)) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a x #s(literal 2 binary64)))))
(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 a (.f64 x (*.f64 a x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64)))) (/.f64 (+.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 x a))))))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))))))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 x a))))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.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)))) x)))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 #s(approx (+ (exp ( a x)) -1) (.f64 a x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(-.f64 #s(approx (exp (* a x)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 a x #s(literal -1 binary64)) (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (.f64 x a)))) (fma.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64))))
(/.f64 (+.f64 (+.f64 #s(literal -1 binary64) (neg.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))) (.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(approx (- (exp (* a x)) -1) (fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))) x) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64)))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a x) 1) (*.f64 a x))) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 x (.f64 a x)) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 a (.f64 (.f64 x x) (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a (fma.f64 a (.f64 x (.f64 x (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)))) x) #s(literal 2 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (/.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))))
(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 (.f64 a x) (.f64 a (.f64 x (.f64 a x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a (.f64 x (.f64 a x)) (-.f64 #s(literal 1 binary64) (.f64 a x)))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp (* a x))) (fma.f64 a (fma.f64 a (.f64 (.f64 x x) (fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 2 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (/.f64 (fma.f64 a (.f64 a (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x a #s(literal -1 binary64))))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (.f64 (fma.f64 a (.f64 a (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x a #s(literal -1 binary64)))))))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
(.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 x a #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))))) (/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) (.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) (.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))) (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 (+.f64 #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal -1 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))) (.f64 (+.f64 #s(approx (exp ( a x)) (/.f64 (fma.f64 (.f64 x a) (.f64 a (.f64 a (.f64 x x))) #s(literal 1 binary64)) (fma.f64 x (.f64 a (.f64 x a)) (-.f64 #s(literal 1 binary64) (.f64 x a))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (exp ( a x)) (fma.f64 a x #s(literal 1 binary64)))))))

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

Calls

5 calls:

18.0ms	x
17.0ms	(exp.f64 (*.f64 a x))
13.0ms	a
13.0ms	(*.f64 a x)
11.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
67.2%	1	`a`
67.2%	1	`x`
67.2%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
67.2%	1	`(exp.f64 (*.f64 a x))`
67.2%	1	`(*.f64 a x)`

Compiler

Compiled 25 to 17 computations (32% saved)

regimes10.0ms (0.1%)

Memory

-25.7MiB live, 12.4MiB 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:

5.0ms	(exp.f64 (*.f64 a x))
1.0ms	x
1.0ms	a
1.0ms	(*.f64 a x)
1.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
17.0%	1	`x`
17.0%	1	`a`
17.0%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
17.0%	1	`(exp.f64 (*.f64 a x))`
17.0%	1	`(*.f64 a x)`

Compiler

Compiled 25 to 17 computations (32% saved)

simplify6.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-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	11	22
1	17	22
2	21	22
3	24	22
4	27	22
5	30	22

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness607.0ms (7.1%)

Memory

-14.6MiB live, 147.4MiB allocated

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	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

Compiler

Compiled 36 to 21 computations (41.7% saved)

preprocess62.0ms (0.7%)

Memory: -4.8MiB live, 120.9MiB allocated
Remove: (sort a x)
Compiler: Compiled 80 to 50 computations (37.5% 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

analyze17.0ms (0.2%)

sample1.2s (14.5%)

preprocess18.0ms (0.2%)

explain110.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize18.0ms (0.2%)

series3.0ms (0%)

simplify361.0ms (4.2%)

rewrite140.0ms (1.6%)

eval29.0ms (0.3%)

prune33.0ms (0.4%)

simplify432.0ms (5.1%)

localize86.0ms (1%)

series23.0ms (0.3%)

simplify557.0ms (6.6%)

rewrite135.0ms (1.6%)

eval84.0ms (1%)

prune56.0ms (0.7%)

simplify295.0ms (3.5%)

localize186.0ms (2.2%)

series19.0ms (0.2%)

simplify443.0ms (5.2%)

rewrite516.0ms (6.1%)

eval381.0ms (4.5%)

prune167.0ms (2%)

simplify629.0ms (7.4%)

localize224.0ms (2.6%)

series21.0ms (0.2%)

simplify365.0ms (4.3%)

rewrite455.0ms (5.4%)

eval319.0ms (3.8%)

prune299.0ms (3.5%)

regimes82.0ms (1%)

regimes76.0ms (0.9%)

regimes10.0ms (0.1%)

simplify6.0ms (0.1%)

soundness607.0ms (7.1%)

preprocess62.0ms (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