Metrics for expax (section 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze28.0ms (0.3%)

Memory

-24.3MiB live, 14.5MiB 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)

sample602.0ms (6.4%)

Memory

15.7MiB live, 879.1MiB allocated

Samples

375.0ms	8 256×	0	valid
11.0ms	279×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 202.0ms

ival-mult: 89.0ms (44.1% of total)

ival-expm1: 57.0ms (28.3% of total)

ival->: 46.0ms (22.8% of total)

exact: 6.0ms (3% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain64.0ms (0.7%)

Memory

16.3MiB live, 93.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
143	39	(3.4619349306228356e-121 1.3729867894015478e-276)	-	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
1	0	-	-	`(exp.f64 (*.f64 a x))`
0	0	-	-	`a`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 a x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`	cancellation	182	0
`exp.f64`	`(exp.f64 (*.f64 a x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	144	0
-	39	73

Precision

0.7868852459016393

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	144	0	0
-	39	0	73

Precision?

0.7868852459016393

Recall?

1.0

Freqs

test

number	freq
0	73
1	183

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 62 to 29 computations (53.2% saved)

Precisions

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

ival-exp: 5.0ms (38.8% of total)

ival-mult: 4.0ms (31.1% of total)

ival-expm1: 3.0ms (23.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess17.0ms (0.2%)

Memory

24.8MiB live, 24.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort a x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval4.0ms (0%)

Memory: -37.4MiB live, 0.9MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.9%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.2%)

Memory

25.7MiB live, 25.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a x)
accuracy	0.023166942724855026	(exp.f64 (*.f64 a x))
accuracy	32.65152196063494	(-.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: 6.0ms

ival-exp: 2.0ms (36.3% of total)

ival-mult: 2.0ms (36.3% of total)

ival-expm1: 2.0ms (36.3% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

5.2MiB live, 5.2MiB 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	x	@	inf	(* a x)
0.0ms	a	@	0	(* a x)

simplify362.0ms (3.9%)

Memory

-34.6MiB live, 202.9MiB 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)

rewrite89.0ms (0.9%)

Memory

29.8MiB live, 67.4MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 111

Calls

Call 1

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

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

eval49.0ms (0.5%)

Memory: -7.7MiB live, 30.4MiB allocated
Compiler: Compiled 3 258 to 324 computations (90.1% saved)

prune97.0ms (1%)

Memory

-9.8MiB live, 36.6MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	173	10	183
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	173	11	184

Accuracy

100.0%

Counts

184 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))
✓	48.9%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
▶	20.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) #s(literal 1 binary64))) #s(literal 1 binary64))
▶	21.4%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	19.9%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
	99.9%	(.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)))))
▶	100.0%	(expm1.f64 (*.f64 a x))
	67.4%	#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)))
▶	66.7%	#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)))
	66.6%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
	71.9%	#s(approx (- (exp (* a x)) 1) (*.f64 a x))

Compiler

Compiled 256 to 148 computations (42.2% saved)

simplify587.0ms (6.3%)

Memory

19.4MiB live, 249.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

14 824×	`lower-fma.f32`
14 812×	`lower-fma.f64`
4 364×	`lower-+.f64`
4 364×	`lower-+.f32`
2 582×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	232
0	50	232
1	107	232
2	272	232
3	788	232
4	2029	232
5	3495	232
6	5749	232
7	5768	232
8	5778	232
9	5778	232
10	5778	232
0	8399	232

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

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

localize120.0ms (1.3%)

Memory

15.1MiB live, 93.2MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.2586489501747718	(.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)))
accuracy	0.7166689466768138	(.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))
accuracy	5.210631111022899	(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)
accuracy	18.147943079271165	#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)))
accuracy	1.4583429547907447	(fma.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) #s(literal 1 binary64))
accuracy	6.428562972218733	(fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
accuracy	18.038364258188704	#s(approx (exp (* a x)) (fma.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) #s(literal 1 binary64)))
accuracy	32.65152196063494	(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0	(fma.f64 a x #s(literal 1 binary64))
accuracy	18.14489256349713	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
accuracy	32.65152196063494	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	18.31198596421146	#s(approx (exp (* a x)) #s(literal 1 binary64))
accuracy	32.65152196063494	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(*.f64 a x)
accuracy	0.030979442724855026	(expm1.f64 (*.f64 a x))

Samples

90.0ms

256×

valid

Compiler

Compiled 196 to 27 computations (86.2% saved)

Precisions

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

ival-mult: 32.0ms (43% of total)

const: 32.0ms (43% of total)

ival-add: 7.0ms (9.4% of total)

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

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

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

exact: 0.0ms (0% of total)

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

series45.0ms (0.5%)

Memory

-14.2MiB live, 23.6MiB allocated

Counts

16 → 384

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

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

Calls

96 calls:

Time	Variable		Point	Expression
28.0ms	x	@	0	(- (exp (* a x)) 1)
1.0ms	a	@	-inf	(* a (+ (* a (* x (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)))) x))
1.0ms	a	@	inf	(+ (* a (+ (* a (* 1/2 (* x x))) x)) 1)
1.0ms	x	@	-inf	(* a (+ (* a (* x (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)))) x))
0.0ms	x	@	inf	(* a (+ (* a (* x (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)))) x))

simplify853.0ms (9.1%)

Memory

1.2MiB live, 587.0MiB allocated

Algorithm

1×	egg-herbie

Rules

19 260×	`lower-fma.f64`
19 260×	`lower-fma.f32`
5 680×	`lower-*.f64`
5 680×	`lower-*.f32`
3 252×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	315	3809
1	1060	3766
2	3248	3724
0	8226	3290

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 380

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

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

rewrite391.0ms (4.2%)

Memory

20.7MiB live, 613.4MiB allocated

Rules

5 352×	`lower-*.f32`
5 340×	`lower-*.f64`
4 720×	`lower-fma.f32`
4 708×	`lower-fma.f64`
3 992×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	189
0	50	189
1	221	189
2	1687	189
0	8297	189

Stop Event

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

Counts

16 → 424

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

Outputs
(+.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 x)) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) (+.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 (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))))
(-.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 (.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) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 (.f64 a x)) #s(literal -1 binary64))))))
(-.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))))
(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 #s(literal 1 binary64) (exp.f64 (*.f64 a x)) #s(literal -1 binary64))
(fma.f64 (exp.f64 (.f64 a (/.f64 x #s(literal 2 binary64)))) (exp.f64 (.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 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (expm1.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 (exp.f64 (.f64 a x)) #s(literal 1 binary64))))
(/.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 (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (expm1.f64 (.f64 a (+.f64 x x))))))
(/.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 x))) (-.f64 (exp.f64 (.f64 a x)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 (*.f64 a x)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (expm1.f64 (.f64 a (+.f64 x x)))) (neg.f64 (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (.f64 a (+.f64 x x)))) (neg.f64 (-.f64 (exp.f64 (.f64 a x)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))) (.f64 (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) #s(literal 1 binary64))) (.f64 (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (pow.f64 (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 (fma.f64 a x (.f64 a x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))))) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 (fma.f64 a x (.f64 a x)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 (fma.f64 a x (.f64 a x)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (+.f64 (fma.f64 a x (.f64 a x)) (fma.f64 a x (.f64 a x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a (+.f64 x x))))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))))
(/.f64 (.f64 (expm1.f64 (+.f64 (fma.f64 a x (.f64 a x)) (fma.f64 a x (.f64 a x)))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 a (+.f64 x x))) #s(literal 1 binary64)) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (.f64 a (+.f64 x x))))) (neg.f64 (neg.f64 (+.f64 (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 (pow.f64 (/.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))) (/.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.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 (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))) (.f64 (/.f64 (exp.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) (+.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 (+.f64 x x))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (/.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (fma.f64 (/.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 x)) #s(literal 1 binary64))) (.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)))))))
(pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (expm1.f64 (.f64 a (+.f64 x x)))) #s(literal -1 binary64))
(.f64 (expm1.f64 (.f64 (.f64 a x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a (+.f64 x x))) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))))
(.f64 (expm1.f64 (.f64 a (+.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64))) (/.f64 (expm1.f64 (.f64 a x)) #s(literal 1 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 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 (*.f64 a x) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 a x) #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)
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eval121.0ms (1.3%)

Memory: 3.5MiB live, 232.3MiB allocated
Compiler: Compiled 25 939 to 1 946 computations (92.5% saved)

prune118.0ms (1.3%)

Memory

5.5MiB live, 222.7MiB allocated

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	872	16	888
Fresh	2	3	5
Picked	2	3	5
Done	0	1	1
Total	876	23	899

Accuracy

100.0%

Counts

899 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	21.1%	(/.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)))
	20.5%	(/.f64 (.f64 (-.f64 (.f64 (.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)))) (.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(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)) (fma.f64 a x #s(literal 1 binary64))))))
	21.1%	(/.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))))
▶	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))
✓	48.9%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
	20.5%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 (.f64 (.f64 a #s(literal 1/2 binary64)) x) x x) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	21.4%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
	19.7%	(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 (.f64 x x) (.f64 a a) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
	20.5%	(-.f64 #s(approx (exp (* a x)) (/.f64 (.f64 (-.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 a x) (*.f64 a x) #s(literal 1 binary64)) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
	19.7%	(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 (.f64 x x) (*.f64 a a) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
	6.2%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64))
✓	19.9%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
	20.7%	(.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))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))) #s(literal -1 binary64)) (/.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))) (+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))))))
▶	21.1%	(.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))
	62.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 a a) (.f64 a x)))
	71.6%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a x) x)))
▶	67.4%	#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)))
	66.6%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (*.f64 x #s(literal 1/2 binary64))) x)))
	66.4%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/24 binary64)) x #s(literal 1/6 binary64)))))) x)))
▶	62.9%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)))
	68.2%	#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* x (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)))) x) (fma.f64 x (.f64 x (fma.f64 x (.f64 a (.f64 a #s(literal 1/6 binary64))) (.f64 a #s(literal 1/2 binary64)))) x))))
▶	71.9%	#s(approx (- (exp (* a x)) 1) (*.f64 a x))

Compiler

Compiled 887 to 397 computations (55.2% saved)

simplify290.0ms (3.1%)

Memory

-2.4MiB live, 551.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
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	(.f64 x #s(approx ( x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64))))))
cost-diff	0	(fma.f64 a (.f64 x #s(approx ( x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)
cost-diff	0	(.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)))
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	(*.f64 a x)
cost-diff	0	#s(approx (- (exp (* a x)) 1) (*.f64 a x))
cost-diff	0	(*.f64 a x)
cost-diff	0	(expm1.f64 (*.f64 a x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))

Rules

11 566×	`lower-fma.f32`
11 556×	`lower-fma.f64`
3 526×	`lower-*.f32`
3 502×	`lower-*.f64`
1 448×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	400
0	70	378
1	153	376
2	381	355
3	944	355
4	1512	355
5	3347	355
6	6520	355
0	8128	345

Stop Event

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

Calls

Call 1

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

localize224.0ms (2.4%)

Memory

-11.1MiB live, 297.9MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(+.f64 #s(literal 1 binary64) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))))
accuracy	0.0078125	(.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	18.14489256349713	#s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))
accuracy	32.43455940447869	(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	5.210631111022899	(fma.f64 a (.f64 x #s(approx ( x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)
accuracy	6.007478273315029	(.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64))))
accuracy	18.147943079271165	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)))
accuracy	43.33495513983646	#s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))
accuracy	0.31640625	(*.f64 x #s(literal 1/6 binary64))
accuracy	1.2081983799893141	(.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	8.634907086963173	(.f64 a (.f64 x x))
accuracy	17.690953701233664	#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	0	(*.f64 a x)
accuracy	17.963810042025823	#s(approx (- (exp (* a x)) 1) (*.f64 a x))
accuracy	0	(*.f64 a x)
accuracy	0.030979442724855026	(expm1.f64 (*.f64 a x))
accuracy	0.15625	(/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))
accuracy	0.4953469523775331	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))

Samples

82.0ms	85×	2	valid
57.0ms	92×	1	valid
31.0ms	78×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 281 to 41 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 134.0ms

ival-mult: 57.0ms (42.5% of total)

adjust: 23.0ms (17.1% of total)

ival-add: 19.0ms (14.2% of total)

ival-exp: 16.0ms (11.9% of total)

const: 9.0ms (6.7% of total)

ival-div: 7.0ms (5.2% of total)

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

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.3%)

Memory

22.3MiB live, 60.8MiB allocated

Counts

21 → 492

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))>
#<alt (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))>
#<alt (expm1.f64 (*.f64 a x))>
#<alt (*.f64 a x)>
#<alt #s(approx (- (exp (* a x)) 1) (*.f64 a x))>
#<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 #s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)))>
#<alt (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x))>
#<alt (fma.f64 a (.f64 x #s(approx ( x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)>
#<alt (.f64 x #s(approx ( x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 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 (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 x #s(literal 1/6 binary64))>
#<alt #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))>
#<alt (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 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 (* 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 (* a x))>
#<alt (/ (+ (* -1/2 a) (/ 1 x)) a)>
#<alt (/ (+ (* a (- (* -1 (* a (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)>
#<alt (/ (+ (* a (- (* a (- (* -1 (* a (+ (* -1/2 (* x (+ (* -1/4 x) (* 1/6 x)))) (+ (* -1/12 (pow x 2)) (* 1/24 (pow x 2)))))) (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (* a x))>
#<alt (/ (+ (* -1/2 x) (/ 1 a)) x)>
#<alt (/ (+ (* x (- (* -1 (* x (+ (* -1/4 a) (* 1/6 a)))) 1/2)) (/ 1 a)) x)>
#<alt (/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (* a (+ (* -1/4 a) (* 1/6 a)))) (+ (* -1/12 (pow a 2)) (* 1/24 (pow a 2)))))) (+ (* -1/4 a) (* 1/6 a)))) 1/2)) (/ 1 a)) x)>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (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 (* 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 (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))>
#<alt (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))>
#<alt (* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 (* a x))))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt (* (pow x 4) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))>
#<alt (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))>
#<alt (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* 1/24 (* (pow a 2) (pow x 4)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* a (+ x (* a (- (pow x 2) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (- (+ (* a (- (* 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))))))>
#<alt (* 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))))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 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 (- (* 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))))))>
#<alt (* 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))))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (/ (- (pow (exp (* a x)) 2) 1) (+ 1 (exp (* a x))))>
#<alt (* 2 (* a x))>
#<alt (* a (+ (* 2 x) (* 2 (* a (pow x 2)))))>
#<alt (* a (+ (* 2 x) (* a (+ (* 2 (pow x 2)) (* a (+ (* 1/3 (pow x 3)) (pow x 3)))))))>
#<alt (* 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))))))))>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (* 2 (* a x))>
#<alt (* x (+ (* 2 a) (* 2 (* (pow a 2) x))))>
#<alt (* x (+ (* 2 a) (* x (+ (* 2 (pow a 2)) (* x (+ (* 1/3 (pow a 3)) (pow a 3)))))))>
#<alt (* 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))))))))>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 1)>
#<alt (- (pow (exp (* a x)) 2) 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 (* 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 (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 (* a x))))>
#<alt (* x (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* x (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 3) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 3) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ a x)) (* -1/24 (pow a 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 a) (* 1/2 (/ 1 x))) x)) (* -1/24 (pow a 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 a) (* 1/2 (/ 1 x))) x)) (* -1/24 (pow a 2)))))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))>
#<alt (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))>
#<alt (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ x a)) (* -1/6 (pow x 2))) a)) (* 1/24 (pow x 3))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ x a)) (* -1/6 (pow x 2))) a)) (* 1/24 (pow x 3))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<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

123 calls:

Time	Variable		Point	Expression
2.0ms	a	@	0	(+ (* (exp (* a x)) (exp (* a x))) -1)
2.0ms	a	@	0	(* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x))
1.0ms	x	@	-inf	(* (+ (* (exp (* a x)) (exp (* a x))) -1) (/ 1 (+ 1 (exp (* a x)))))
1.0ms	x	@	0	(* (+ (* (exp (* a x)) (exp (* a x))) -1) (/ 1 (+ 1 (exp (* a x)))))
1.0ms	a	@	0	(* (+ (* (exp (* a x)) (exp (* a x))) -1) (/ 1 (+ 1 (exp (* a x)))))

simplify376.0ms (4%)

Memory

6.5MiB live, 521.6MiB allocated

Algorithm

1×	egg-herbie

Rules

13 886×	`lower-fma.f64`
13 886×	`lower-fma.f32`
6 868×	`lower-*.f64`
6 868×	`lower-*.f32`
2 816×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	509	5493
1	1731	5300
2	5919	5298
0	8135	4748

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 488

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

rewrite371.0ms (4%)

Memory

2.1MiB live, 392.7MiB allocated

Rules

5 762×	`lower-fma.f32`
5 752×	`lower-fma.f64`
4 038×	`lower-*.f32`
4 014×	`lower-*.f64`
3 806×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	335
0	70	303
1	276	303
2	1925	289
0	8139	279

Stop Event

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

Counts

21 → 708

Calls

Call 1

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

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

eval194.0ms (2.1%)

Memory: 30.9MiB live, 290.8MiB allocated
Compiler: Compiled 43 047 to 2 573 computations (94% saved)

prune156.0ms (1.7%)

Memory

-1.8MiB live, 275.6MiB allocated

Pruning

22 alts after pruning (16 fresh and 6 done)

	Pruned	Kept	Total
New	1 411	9	1 420
Fresh	7	7	14
Picked	3	2	5
Done	0	4	4
Total	1 421	22	1 443

Accuracy

100.0%

Counts

1 443 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	21.1%	(/.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)))
✓	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))
	71.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 a x))))
	71.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x (fma.f64 a (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x)))
▶	75.5%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x)))
✓	48.9%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
	20.5%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 (.f64 (.f64 a #s(literal 1/2 binary64)) x) x x) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	21.4%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
	19.7%	(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 (.f64 x x) (.f64 a a) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
	6.2%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64))
✓	19.9%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 a x))
▶	66.6%	#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
▶	72.3%	#s(approx (- (exp (* a x)) 1) (fma.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 a (.f64 a x))) (*.f64 a x)))
	62.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 a a) (.f64 a x)))
	63.0%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 a a) (.f64 (.f64 x x) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
▶	71.6%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a x) x)))
	72.3%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 a x) (.f64 x (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)))
	66.3%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 (.f64 (.f64 a x) (.f64 x x)) (*.f64 #s(literal 1/24 binary64) a)))) x)))
	66.4%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/24 binary64)) x #s(literal 1/6 binary64)))))) x)))
✓	71.9%	#s(approx (- (exp (* a x)) 1) (*.f64 a x))
▶	20.1%	#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x)))

Compiler

Compiled 631 to 341 computations (46% saved)

simplify827.0ms (8.8%)

Memory

3.6MiB live, 839.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

48 522×	`lower-fma.f32`
48 508×	`lower-fma.f64`
5 678×	`lower-+.f64`
5 678×	`lower-+.f32`
3 198×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	400
0	85	381
1	186	380
2	478	374
3	1191	368
4	1905	368
5	3353	368
6	4751	368
7	4762	368
8	4762	368
9	4762	368
10	7529	368
0	8136	352

Stop Event

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

Calls

Call 1

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

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

localize140.0ms (1.5%)

Memory

14.0MiB live, 209.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2586489501747718	(.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
accuracy	0.31640625	(*.f64 x #s(literal 1/24 binary64))
accuracy	0.7166689466768138	(.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a x) x))
accuracy	18.147943079271165	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a x) x)))
accuracy	0.140625	(.f64 a (.f64 a x))
accuracy	0.31640625	(*.f64 x #s(literal 1/6 binary64))
accuracy	3.8989537171719797	(.f64 x (.f64 a (*.f64 a x)))
accuracy	17.690953701233664	#s(approx (- (exp (* a x)) 1) (fma.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 a (.f64 a x))) (*.f64 a x)))
accuracy	5.201960401853239	(.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x)
accuracy	5.237660150565978	(.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (*.f64 a a)))))
accuracy	17.690953701233664	#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x)))
accuracy	33.36384603699993	#s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x))
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (.f64 x x))
accuracy	1.4661554547907447	(.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))
accuracy	6.428562972218733	(fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
accuracy	18.347368023978483	#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
accuracy	0.00390625	(fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a))
accuracy	0.15234375	(/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x)
accuracy	0.4953469523775331	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x)))
accuracy	15.15827550828243	#s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x))

Samples

91.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 308 to 48 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-mult: 43.0ms (60% of total)

ival-add: 10.0ms (14% of total)

const: 7.0ms (9.8% of total)

ival-div: 7.0ms (9.8% of total)

ival-expm1: 5.0ms (7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series45.0ms (0.5%)

Memory

-11.7MiB live, 26.1MiB allocated

Counts

23 → 516

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x)))>
#<alt #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x))>
#<alt (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x)>
#<alt (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a))>
#<alt #s(approx (/ 1 (/ 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) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x)))>
#<alt #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x))>
#<alt (.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x)>
#<alt (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (*.f64 a a)))))>
#<alt (fma.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 a (.f64 a x))) (*.f64 a x))>
#<alt #s(approx (- (exp (* a x)) 1) (fma.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 a (.f64 a x))) (*.f64 a x)))>
#<alt (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x #s(literal 1/6 binary64))>
#<alt #s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a x) x)))>
#<alt (.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a x) x))>
#<alt (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 a x) x)>
#<alt (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))>
#<alt (.f64 x (.f64 a (*.f64 a x)))>
#<alt (.f64 a (.f64 a x))>
#<alt (*.f64 x #s(literal 1/24 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 (/ 1 (* a x))>
#<alt (/ (+ (* -1/2 a) (/ 1 x)) a)>
#<alt (/ (+ (* a (- (* -1 (* a (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)>
#<alt (/ (+ (* a (- (* a (- (* -1 (* a (+ (* -1/2 (* x (+ (* -1/4 x) (* 1/6 x)))) (+ (* -1/12 (pow x 2)) (* 1/24 (pow x 2)))))) (+ (* -1/4 x) (* 1/6 x)))) 1/2)) (/ 1 x)) a)>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (* a x))>
#<alt (/ (+ (* -1/2 x) (/ 1 a)) x)>
#<alt (/ (+ (* x (- (* -1 (* x (+ (* -1/4 a) (* 1/6 a)))) 1/2)) (/ 1 a)) x)>
#<alt (/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (* a (+ (* -1/4 a) (* 1/6 a)))) (+ (* -1/12 (pow a 2)) (* 1/24 (pow a 2)))))) (+ (* -1/4 a) (* 1/6 a)))) 1/2)) (/ 1 a)) x)>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (- (exp (* a x)) 1))>
#<alt (/ 1 (* a x))>
#<alt (/ (+ (* -1/2 x) (/ 1 a)) x)>
#<alt (/ (+ (* -1/2 x) (/ 1 a)) x)>
#<alt (/ (+ (* -1/2 x) (/ 1 a)) x)>
#<alt -1/2>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt -1/2>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (/ 1 (* a x))>
#<alt (/ (+ (* -1/2 a) (/ 1 x)) a)>
#<alt (/ (+ (* -1/2 a) (/ 1 x)) a)>
#<alt (/ (+ (* -1/2 a) (/ 1 x)) a)>
#<alt -1/2>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt -1/2>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (- (/ 1 (* a x)) 1/2)>
#<alt (/ 1 a)>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (* -1/2 x)>
#<alt (* x (- (/ 1 (* a x)) 1/2))>
#<alt (* x (- (/ 1 (* a x)) 1/2))>
#<alt (* x (- (/ 1 (* a x)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (- 1/2 (/ 1 (* a x)))))>
#<alt (* -1 (* x (- 1/2 (/ 1 (* a x)))))>
#<alt (* -1 (* x (- 1/2 (/ 1 (* a x)))))>
#<alt (/ 1 a)>
#<alt (/ (+ 1 (* -1/2 (* a x))) a)>
#<alt (/ (+ 1 (* -1/2 (* a x))) a)>
#<alt (/ (+ 1 (* -1/2 (* a x))) a)>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (+ (* -1/2 x) (/ 1 a))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* 1/2 (* (pow a 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt (* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* a (+ (* 1/2 (pow x 2)) (/ x a)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt (* -1 (* a (+ (* -1 (/ x a)) (* -1/2 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* 1/2 (* a (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/2 a) (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* 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 (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 3)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* 1/6 (* (pow a 3) (pow x 2)))>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* 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 (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (* 1/6 (* a x))>
#<alt (* a (+ (* 1/6 x) (* 1/2 (/ 1 a))))>
#<alt (* a (+ (* 1/6 x) (* 1/2 (/ 1 a))))>
#<alt (* a (+ (* 1/6 x) (* 1/2 (/ 1 a))))>
#<alt (* 1/6 (* a x))>
#<alt (* -1 (* a (- (* -1/6 x) (* 1/2 (/ 1 a)))))>
#<alt (* -1 (* a (- (* -1/6 x) (* 1/2 (/ 1 a)))))>
#<alt (* -1 (* a (- (* -1/6 x) (* 1/2 (/ 1 a)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (+ 1/2 (* 1/6 (* a x)))>
#<alt (* 1/6 (* a x))>
#<alt (* x (+ (* 1/6 a) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/6 a) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/6 a) (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (* a x))>
#<alt (* -1 (* x (- (* -1/6 a) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* -1/6 a) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* -1/6 a) (* 1/2 (/ 1 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 (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (- (exp (* a x)) 1)>
#<alt (* a x)>
#<alt (* a (+ x (* 1/2 (* a (pow x 2)))))>
#<alt (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))>
#<alt (* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))>
#<alt (* a x)>
#<alt (* x (+ a (* 1/2 (* (pow a 2) x))))>
#<alt (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))>
#<alt (* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (* 1/2 (/ (pow a 2) (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (+ (* 1/6 (/ (pow a 3) x)) (+ (* 1/2 (/ (pow a 2) (pow x 2))) (/ a (pow x 3))))))>
#<alt (* 1/24 (* (pow a 4) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 4)) (* 1/6 (/ (pow a 3) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (* a x))))>
#<alt (* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))>
#<alt (* x (+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2))))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow x 4) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt (* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2))) x)) (* 1/24 (pow a 3))))>
#<alt x>
#<alt (+ x (* 1/2 (* a (pow x 2))))>
#<alt (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))>
#<alt (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3)))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))>
#<alt (* (pow a 3) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))>
#<alt (* 1/24 (* (pow a 3) (pow x 4)))>
#<alt (* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 3) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))) a)) (* -1/24 (pow x 4)))))>
#<alt (* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))) a)) (* -1/24 (pow x 4)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 (* a x))))>
#<alt (* x (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* x (+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))>
#<alt (* (pow x 3) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 3) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ a x)) (* -1/24 (pow a 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 a) (* 1/2 (/ 1 x))) x)) (* -1/24 (pow a 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 a) (* 1/2 (/ 1 x))) x)) (* -1/24 (pow a 2)))))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))>
#<alt (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))>
#<alt (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))>
#<alt (* 1/24 (* (pow a 2) (pow x 3)))>
#<alt (* (pow a 2) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ x a)) (* -1/6 (pow x 2))) a)) (* 1/24 (pow x 3))))>
#<alt (* (pow a 2) (+ (* -1 (/ (+ (* -1/2 (/ x a)) (* -1/6 (pow x 2))) a)) (* 1/24 (pow x 3))))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) (pow x 2))>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* (pow a 2) x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>

Calls

129 calls:

Time	Variable		Point	Expression
20.0ms	x	@	inf	(* 1/2 (* x x))
6.0ms	a	@	0	(* (* x (* x (* 1/6 (* a (* a a))))) x)
1.0ms	x	@	0	(* (* x (* x (* 1/6 (* a (* a a))))) x)
1.0ms	x	@	0	(/ (+ (* x -1/2) (/ 1 a)) x)
0.0ms	x	@	inf	(* (* x (* x (* 1/6 (* a (* a a))))) x)

simplify638.0ms (6.8%)

Memory

25.3MiB live, 610.3MiB allocated

Algorithm

1×	egg-herbie

Rules

23 810×	`lower-fma.f64`
23 810×	`lower-fma.f32`
6 418×	`lower-*.f64`
6 418×	`lower-*.f32`
5 674×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	364	5188
1	1196	5161
2	3999	5035
0	8217	4560

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 512

Calls

Call 1

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

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

rewrite691.0ms (7.4%)

Memory

-48.6MiB live, 465.6MiB allocated

Rules

6 628×	`lower-fma.f32`
6 614×	`lower-fma.f64`
4 310×	`lower-*.f32`
4 278×	`lower-*.f64`
3 778×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	328
0	85	315
1	326	302
2	2247	302
0	8433	290

Stop Event

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

Counts

23 → 398

Calls

Call 1

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

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

eval106.0ms (1.1%)

Memory: 29.3MiB live, 220.1MiB allocated
Compiler: Compiled 23 129 to 1 493 computations (93.5% saved)

prune105.0ms (1.1%)

Memory

-19.0MiB live, 173.6MiB allocated

Pruning

26 alts after pruning (18 fresh and 8 done)

	Pruned	Kept	Total
New	898	12	910
Fresh	5	6	11
Picked	3	2	5
Done	0	6	6
Total	906	26	932

Accuracy

100.0%

Counts

932 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))
	71.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x (fma.f64 a (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x)))
	49.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) a) (.f64 x #s(literal -1/2 binary64)))) x)))
	75.5%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)))) x)))
	46.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 a a))) (.f64 x (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a))))))
	49.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 a a))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)))) x)))
	74.3%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 #s(approx (+ (* x -1/2) (/ 1 a)) (/.f64 (fma.f64 x (*.f64 a #s(literal -1/2 binary64)) #s(literal 1 binary64)) a)) x)))
	75.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 a x)) #s(literal -1/2 binary64)))))
	8.0%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64))))
✓	48.9%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
	20.5%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 (.f64 (.f64 a #s(literal 1/2 binary64)) x) x x) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	21.4%	(-.f64 #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64))) #s(literal 1 binary64))
	6.2%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64))
✓	19.9%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 a x))
	71.3%	#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
	19.4%	#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x))))))
	19.3%	#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 a (.f64 (.f64 a a) #s(literal 1/6 binary64))))))
✓	72.3%	#s(approx (- (exp (* a x)) 1) (fma.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 a (.f64 a x))) (*.f64 a x)))
	62.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 a a) (.f64 a x)))
	67.2%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 a (.f64 x x)) (.f64 (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) a))))
✓	71.6%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a x) x)))
	72.3%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 a x) (.f64 x (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)))
	62.0%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 #s(approx ( x (+ (* (* a x) (+ (* a (* x 1/24)) 1/6)) 1/2)) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 a a))))) (.f64 a x) x)))
	66.4%	#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/24 binary64)) x #s(literal 1/6 binary64)))))) x)))
✓	71.9%	#s(approx (- (exp (* a x)) 1) (*.f64 a x))

Compiler

Compiled 1 223 to 432 computations (64.7% saved)

regimes84.0ms (0.9%)

Memory

1.2MiB live, 127.6MiB allocated

Counts

48 → 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))
(-.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)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64))))
#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x))))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (*.f64 x #s(literal 1/2 binary64))) x)))
#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 (.f64 (.f64 a #s(literal 1/2 binary64)) x) x x) #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 a x))))
#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x)))
#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 a (.f64 (.f64 a a) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 a x)) #s(literal -1/2 binary64)))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 a x) (.f64 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 a (.f64 x x)) (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)))
(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 (.f64 x x) (.f64 a a) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* x (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)))) x) (fma.f64 x (.f64 x (fma.f64 x (.f64 a (.f64 a #s(literal 1/6 binary64))) (.f64 a #s(literal 1/2 binary64)))) x))))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 a a) (.f64 (.f64 x x) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 a (.f64 x x)) (.f64 (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) a))))
#s(approx (- (exp (* a x)) 1) (fma.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 a (.f64 a x))) (*.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(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 (.f64 (.f64 a x) (.f64 x x)) (*.f64 #s(literal 1/24 binary64) a)))) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 #s(approx ( x (+ (* (* a x) (+ (* a (* x 1/24)) 1/6)) 1/2)) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 a a))))) (.f64 a x) x)))
(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 (.f64 x x) (*.f64 a a) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/24 binary64)) x #s(literal 1/6 binary64)))))) x)))
#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)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a 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)) (/.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 (/ 1 (- (exp (* a x)) 1)) (/.f64 #s(approx (+ (* x -1/2) (/ 1 a)) (/.f64 (fma.f64 x (*.f64 a #s(literal -1/2 binary64)) #s(literal 1 binary64)) a)) x)))
#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 a a) (.f64 a x)))
(/.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 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x (fma.f64 a (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)))) x)))
(.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))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))) #s(literal -1 binary64)) (/.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))) (+.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 (/ 1 (- (exp (* a x)) 1)) (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 a a))) (.f64 x (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a))))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) a) (.f64 x #s(literal -1/2 binary64)))) x)))
(-.f64 #s(approx (exp (* a x)) (/.f64 (.f64 (-.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 a x) (*.f64 a x) #s(literal 1 binary64)) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 a a))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)))) x)))
(/.f64 (.f64 (-.f64 (.f64 (.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)))) (.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(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)) (fma.f64 a x #s(literal 1 binary64))))))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #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)))))

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

Calls

5 calls:

24.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
17.0ms	a
15.0ms	(exp.f64 (*.f64 a x))
13.0ms	x
13.0ms	(*.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)

regimes69.0ms (0.7%)

Memory

-12.4MiB live, 108.0MiB allocated

Counts

44 → 2

Calls

Call 1

Inputs
(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (*.f64 a x))
(-.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)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64))))
#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a #s(approx (+ ( a (* 1/2 (* x x))) x) (.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 x x))))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x (*.f64 x #s(literal 1/2 binary64))) x)))
#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))
(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 #s(approx (exp (* a x)) (fma.f64 a (fma.f64 (.f64 (.f64 a #s(literal 1/2 binary64)) x) x x) #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (exp (* a x)) 1) (*.f64 a x))))
#s(approx (- (exp (* a x)) 1) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 a (.f64 a a))))) x)))
#s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) #s(approx (* a (+ (* (* a (* x x)) (+ (* a (* x 1/6)) 1/2)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 a (.f64 (.f64 a a) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 a x)) #s(literal -1/2 binary64)))))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 a x) (.f64 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 a (.f64 x x)) (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)))
(-.f64 #s(approx (exp (* a x)) (/.f64 (fma.f64 (.f64 x x) (.f64 a a) #s(literal -1 binary64)) (fma.f64 a x #s(literal -1 binary64)))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 a #s(approx (+ ( a (* x (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)))) x) (fma.f64 x (.f64 x (fma.f64 x (.f64 a (.f64 a #s(literal 1/6 binary64))) (.f64 a #s(literal 1/2 binary64)))) x))))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 a a) (.f64 (.f64 x x) (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 a (.f64 x x)) (.f64 (fma.f64 a (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) a))))
#s(approx (- (exp (* a x)) 1) (fma.f64 (fma.f64 a (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 a (.f64 a x))) (*.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(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 a (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64)))))) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 (.f64 (.f64 a x) (.f64 x x)) (*.f64 #s(literal 1/24 binary64) a)))) x)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 #s(approx ( x (+ (* (* a x) (+ (* a (* x 1/24)) 1/6)) 1/2)) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 a a))))) (.f64 a x) x)))
(-.f64 #s(approx (exp (* a x)) (.f64 (fma.f64 (.f64 x x) (*.f64 a a) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 a (.f64 x #s(approx (* x (+ (* (* a x) (+ (* (* a x) 1/24) 1/6)) 1/2)) (.f64 a (.f64 (.f64 x x) (fma.f64 (.f64 a #s(literal 1/24 binary64)) x #s(literal 1/6 binary64)))))) x)))
#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)))
#s(approx (- (exp (* a x)) 1) (.f64 a (fma.f64 (.f64 x (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 a 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)) (/.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 (/ 1 (- (exp (* a x)) 1)) (/.f64 #s(approx (+ (* x -1/2) (/ 1 a)) (/.f64 (fma.f64 x (*.f64 a #s(literal -1/2 binary64)) #s(literal 1 binary64)) a)) x)))
#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 a x) (fma.f64 a (.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 a a) (.f64 a x)))
(/.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 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (fma.f64 x (fma.f64 a (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) a)))) x)))
(.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))) #s(approx (exp (* a x)) (fma.f64 a x #s(literal 1 binary64)))) #s(literal -1 binary64)) (/.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))) (+.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 (/ 1 (- (exp (* a x)) 1)) (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 a a))) (.f64 x (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a))))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) a) (.f64 x #s(literal -1/2 binary64)))) x)))
(-.f64 #s(approx (exp (* a x)) (/.f64 (.f64 (-.f64 (.f64 (.f64 a (.f64 x (.f64 a x))) (.f64 a (.f64 x (.f64 a x)))) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 a x) (*.f64 a x) #s(literal 1 binary64)) (fma.f64 a x #s(literal -1 binary64))))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) (/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 a a))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)))) x)))
(/.f64 (.f64 (-.f64 (.f64 (.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)))) (.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(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)) (fma.f64 a x #s(literal 1 binary64))))))

Outputs

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

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

Calls

5 calls:

16.0ms	x
14.0ms	(*.f64 a x)
12.0ms	a
10.0ms	(exp.f64 (*.f64 a x))
10.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
77.4%	2	`a`
75.7%	1	`x`
75.7%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
75.7%	1	`(exp.f64 (*.f64 a x))`
75.7%	1	`(*.f64 a x)`

Compiler

Compiled 25 to 17 computations (32% saved)

regimes23.0ms (0.2%)

Memory

36.4MiB live, 36.4MiB allocated

Counts

15 → 3

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

Outputs

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

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
71.9%	1	`x`
76.3%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
76.3%	2	`(exp.f64 (*.f64 a x))`
78.3%	3	`(*.f64 a x)`
74.7%	2	`a`

Compiler

Compiled 25 to 17 computations (32% saved)

regimes11.0ms (0.1%)

Memory

-25.2MiB live, 13.9MiB allocated

Counts

9 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
76.3%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
76.3%	2	`(exp.f64 (*.f64 a x))`
76.3%	2	`(*.f64 a x)`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes8.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	(*.f64 a x)
3.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
2.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
75.8%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
75.8%	2	`(exp.f64 (*.f64 a x))`
75.8%	2	`(*.f64 a x)`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes7.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

3 → 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))

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

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

Calls

4 calls:

2.0ms	a
2.0ms	(*.f64 a x)
1.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
1.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
71.9%	1	`a`
71.9%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
71.9%	1	`(exp.f64 (*.f64 a x))`
71.9%	1	`(*.f64 a x)`

Compiler

Compiled 22 to 15 computations (31.8% saved)

regimes7.0ms (0.1%)

Memory

-26.7MiB live, 11.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	a
1.0ms	x
1.0ms	(*.f64 a x)
1.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
1.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
19.9%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
19.9%	1	`(exp.f64 (*.f64 a x))`
19.9%	1	`(*.f64 a x)`
19.9%	1	`x`
19.9%	1	`a`

Compiler

Compiled 25 to 17 computations (32% saved)

bsearch6.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	-2.8270840669581056e+237	-1.0242172470218014e+237

Samples

3.0ms

80×

valid

Compiler

Compiled 161 to 104 computations (35.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-mult: 1.0ms (82.5% of total)

ival-expm1: 1.0ms (82.5% of total)

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

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

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	-4.11990027618442e+18	-0.3176043839416204
0.0ms	-2.7709183722588282e+101	-2.693867247459102e+99

Compiler

Compiled 11 to 9 computations (18.2% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.11990027618442e+18	-0.3176043839416204

Compiler

Compiled 11 to 9 computations (18.2% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.11990027618442e+18	-0.3176043839416204

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify8.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
8×	`+-commutative_binary64`
6×	`unsub-neg_binary64`
6×	`sub-neg_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	256
1	71	256
2	76	256
3	79	256
4	82	256
5	86	256

Stop Event

1×

saturated

Calls

Call 1

Inputs
(expm1.f64 (*.f64 a x))
(if (<=.f64 a #s(literal -2500000000000000121618993321816252601212038274992763789933827599354662781839433675197975751392532227632934736472208035607146149291377427155799116613741537178668580245385771452639253305009843825518337655911472905907779794727251663076196352 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 a x)) #s(literal -1/2 binary64))))))
(if (<=.f64 (.f64 a x) #s(literal -199999999999999995409902653049067325689368543984830001225999194946398690436157982260652258896302309376 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64)))) (if (<=.f64 (.f64 a x) #s(literal -4000000000000000000 binary64)) (-.f64 #s(approx (exp ( a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64)) #s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))))
(if (<=.f64 (.f64 a x) #s(literal -4000000000000000000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x))))
(if (<=.f64 (.f64 a x) #s(literal -4000000000000000000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (*.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))
(if (<=.f64 a #s(literal -2500000000000000121618993321816252601212038274992763789933827599354662781839433675197975751392532227632934736472208035607146149291377427155799116613741537178668580245385771452639253305009843825518337655911472905907779794727251663076196352 binary64)) (-.f64 #s(approx (exp (* a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 a x)) #s(literal -1/2 binary64))))))
(if (<=.f64 a #s(literal -2500000000000000121618993321816252601212038274992763789933827599354662781839433675197975751392532227632934736472208035607146149291377427155799116613741537178668580245385771452639253305009843825518337655911472905907779794727251663076196352 binary64)) (+.f64 #s(approx (exp (* a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp (* a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 a x)))))))
(if (<=.f64 (.f64 a x) #s(literal -199999999999999995409902653049067325689368543984830001225999194946398690436157982260652258896302309376 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64)))) (if (<=.f64 (.f64 a x) #s(literal -4000000000000000000 binary64)) (-.f64 #s(approx (exp ( a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal 1 binary64)) #s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x)))))
(if (<=.f64 (.f64 a x) #s(literal -199999999999999995409902653049067325689368543984830001225999194946398690436157982260652258896302309376 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64)))) (if (<=.f64 (.f64 a x) #s(literal -4000000000000000000 binary64)) (+.f64 #s(approx (exp ( a x)) #s(approx (+ (* a (+ (* a (* 1/2 (* x x))) x)) 1) (.f64 a (.f64 a (.f64 x (.f64 x #s(literal 1/2 binary64))))))) #s(literal -1 binary64)) #s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 x (*.f64 a #s(literal 1/2 binary64))) x x)))))
(if (<=.f64 (.f64 a x) #s(literal -4000000000000000000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 (*.f64 a #s(literal 1/2 binary64)) x) x x))))
(if (<=.f64 (.f64 a x) #s(literal -4000000000000000000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (/ 1 (/ 1 (- (exp (* a x)) 1))) (.f64 a (fma.f64 (.f64 x (*.f64 a #s(literal 1/2 binary64))) x x))))
(if (<=.f64 (.f64 a x) #s(literal -4000000000000000000 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (exp ( a x)) 1)) #s(approx (/ (+ (* x -1/2) (/ 1 a)) x) #s(literal -1/2 binary64)))) #s(approx (- (exp (* a x)) 1) (*.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))

soundness1.3s (14.1%)

Memory

-1.6MiB live, 609.5MiB allocated

Rules

23 810×	`lower-fma.f64`
23 810×	`lower-fma.f32`
19 260×	`lower-fma.f64`
19 260×	`lower-fma.f32`
13 886×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	328
0	85	315
1	326	302
2	2247	302
0	8433	290
0	509	5493
1	1731	5300
2	5919	5298
0	8135	4748
0	364	5188
1	1196	5161
2	3999	5035
0	8217	4560
0	6	13
0	9	13
1	30	13
2	152	13
0	1346	11
0	315	3809
1	1060	3766
2	3248	3724
0	8226	3290
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×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 455 to 215 computations (52.7% saved)

preprocess52.0ms (0.6%)

Memory: 16.6MiB live, 93.8MiB allocated
Remove: (sort a x)
Compiler: Compiled 292 to 102 computations (65.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

start0.0ms (0%)

analyze28.0ms (0.3%)

sample602.0ms (6.4%)

explain64.0ms (0.7%)

preprocess17.0ms (0.2%)

eval4.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize18.0ms (0.2%)

series4.0ms (0%)

simplify362.0ms (3.9%)

rewrite89.0ms (0.9%)

eval49.0ms (0.5%)

prune97.0ms (1%)

simplify587.0ms (6.3%)

localize120.0ms (1.3%)

series45.0ms (0.5%)

simplify853.0ms (9.1%)

rewrite391.0ms (4.2%)

eval121.0ms (1.3%)

prune118.0ms (1.3%)

simplify290.0ms (3.1%)

localize224.0ms (2.4%)

series28.0ms (0.3%)

simplify376.0ms (4%)

rewrite371.0ms (4%)

eval194.0ms (2.1%)

prune156.0ms (1.7%)

simplify827.0ms (8.8%)

localize140.0ms (1.5%)

series45.0ms (0.5%)

simplify638.0ms (6.8%)

rewrite691.0ms (7.4%)

eval106.0ms (1.1%)

prune105.0ms (1.1%)

regimes84.0ms (0.9%)

regimes69.0ms (0.7%)

regimes23.0ms (0.2%)

regimes11.0ms (0.1%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

bsearch6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness1.3s (14.1%)

preprocess52.0ms (0.6%)

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