Metrics for expax (section 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze17.0ms (0.3%)

Memory

13.6MiB live, 13.6MiB 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)

sample741.0ms (14.4%)

Memory

-1.6MiB live, 534.9MiB allocated

Samples

405.0ms	8 256×	0	valid
57.0ms	309×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 221.0ms

ival-mult: 134.0ms (60.6% of total)

ival-expm1: 55.0ms (24.9% of total)

ival->: 22.0ms (9.9% of total)

exact: 8.0ms (3.6% of total)

ival-assert: 4.0ms (1.8% of total)

Bogosity

explain65.0ms (1.3%)

Memory

12.2MiB live, 95.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	1	(2.7199303465696236e-212 5.3700283560748185e+209)	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
0	-	0	-	`a`
0	-	0	-	`(exp.f64 (*.f64 a x))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(*.f64 a x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`	cancellation	124	1

Confusion

	Predicted +	Predicted -
+	124	1
-	0	131

Precision

1.0

Recall

0.992

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

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

ival-exp: 4.0ms (34.3% of total)

ival-mult: 4.0ms (34.3% of total)

ival-expm1: 3.0ms (25.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess18.0ms (0.3%)

Memory

-16.0MiB live, 22.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	42	36
2	73	34
3	108	34
4	141	34
5	165	34
6	205	34
7	227	34
8	241	34
9	252	34
10	253	34
0	6	6
0	9	6
1	17	6
2	20	6
0	20	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort a x)

Compiler

Compiled 6 to 6 computations (0% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.0%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 6 to 6 computations (0% saved)

simplify3.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.3%)

Memory

25.7MiB live, 25.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 a x)
accuracy	0.00390625	(exp.f64 (*.f64 a x))
accuracy	28.14340552309742	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Samples

12.0ms

256×

valid

Compiler

Compiled 34 to 14 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-exp: 2.0ms (35.8% of total)

ival-mult: 2.0ms (35.8% of total)

ival-expm1: 2.0ms (35.8% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

3 → 15

Calls

Call 1

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

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

Calls

6 calls:

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

simplify211.0ms (4.1%)

Memory

-3.4MiB live, 75.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	201
1	195	201
2	526	193
3	1045	193
4	1672	193
5	1873	193
6	1900	193
7	1920	193
8	1934	193
9	1937	193
10	1937	193
11	2619	189
12	3094	189
13	4061	189
14	4062	189
15	4062	189
16	4190	189
17	4190	189
18	6071	185
19	6279	185
20	6321	185
21	6335	185
22	6335	185
23	6511	185
24	6849	185
25	6849	185
26	7408	185
0	7408	160

Stop Event

1×	iter limit
1×	saturated

Counts

15 → 15

Calls

Call 1

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

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

rewrite63.0ms (1.2%)

Memory

0.9MiB live, 78.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
0	9	13
1	30	13
2	152	13
0	1348	11

Stop Event

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

Counts

3 → 111

Calls

Call 1

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

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

eval16.0ms (0.3%)

Memory: -10.2MiB live, 28.3MiB allocated
Compiler: Compiled 2 806 to 340 computations (87.9% saved)

prune7.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	9	122

Accuracy

100.0%

Counts

122 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.0%	(/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) (.f64 x a))) (+.f64 (+.f64 (pow.f64 (exp.f64 x) (*.f64 #s(literal 2 binary64) a)) (pow.f64 (exp.f64 x) a)) #s(literal 1 binary64)))
	22.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
	20.9%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	20.9%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 x a))
▶	65.1%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
▶	66.0%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
▶	61.4%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
	65.9%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 298 to 214 computations (28.2% saved)

simplify299.0ms (5.8%)

Memory

13.2MiB live, 280.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	248
0	56	242
1	102	242
2	206	242
3	497	242
4	1445	242
5	3031	242
6	3079	242
7	3108	242
8	3136	242
9	3136	242
10	5004	242
11	5004	242
12	5017	242
13	5017	242
14	5408	242
15	5533	242
16	5533	242
0	9053	242

Stop Event

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

Calls

Call 1

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

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

localize97.0ms (1.9%)

Memory

-2.3MiB live, 118.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.2435586276740939	(fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (*.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64))
accuracy	0.3359375	(*.f64 #s(literal 1/24 binary64) x)
accuracy	0.48138101839787306	(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (*.f64 x a) #s(literal 1/2 binary64)) x)
accuracy	22.289855895024164	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) (*.f64 x a)))
accuracy	0.0625	(fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64))
accuracy	0.3359375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.9747690527834922	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
accuracy	21.724667889633707	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (.f64 x a)))
accuracy	0.0078125	(fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a)
accuracy	0.970725972427479	(.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)
accuracy	7.329199051931495	(.f64 (.f64 a a) x)
accuracy	22.451765332868227	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
accuracy	22.15539202614122	#s(approx (exp (* a x)) #s(literal 1 binary64))
accuracy	28.14340552309742	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x a)
accuracy	0.015625	(expm1.f64 (*.f64 x a))

Samples

69.0ms

256×

valid

Compiler

Compiled 467 to 66 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-mult: 25.0ms (46.7% of total)

ival-add: 15.0ms (28% of total)

const: 9.0ms (16.8% of total)

ival-expm1: 3.0ms (5.6% of total)

ival-exp: 2.0ms (3.7% of total)

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

exact: 0.0ms (0% of total)

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

series30.0ms (0.6%)

Memory

-3.0MiB live, 34.4MiB allocated

Counts

19 → 100

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (+ (* (* 1/6 x) a) 1/2) (* 1/24 x))
4.0ms	x	@	-inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (+ (* (* 1/6 x) a) 1/2) (* 1/24 x))
4.0ms	a	@	inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (+ (* (* 1/6 x) a) 1/2) (* 1/24 x))
3.0ms	a	@	-inf	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (+ (* (* 1/6 x) a) 1/2) (* 1/24 x))
3.0ms	a	@	0	((- (exp (* x a)) 1) (* x a) (- (exp (* a x)) 1) (exp (* a x)) (- (exp (* a x)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* x a)) (+ (* (* (+ (* (* 1/6 x) a) 1/2) a) x) 1) (* (+ (* (* 1/6 x) a) 1/2) a) (- (exp (* a x)) 1) (* (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* x a)) (+ (* (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) a) 1) (* (+ (* (+ (* (* 1/24 x) a) 1/6) (* x a)) 1/2) x) (* 1/6 x) (+ (* (* 1/6 x) a) 1/2) (* 1/24 x))

simplify186.0ms (3.6%)

Memory

-12.2MiB live, 182.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	344	1573
1	1178	1539
2	4037	1453
0	8530	1333

Stop Event

1×	iter limit
1×	node limit

Counts

100 → 99

Calls

Call 1

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

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

rewrite184.0ms (3.6%)

Memory

-0.2MiB live, 154.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	205
0	56	199
1	209	199
2	1346	199
0	8264	199

Stop Event

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

Counts

19 → 508

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (/.f64 (expm1.f64 (.f64 a x)) #s(literal 1 binary64)))
(.f64 (neg.f64 (expm1.f64 (.f64 x (*.f64 #s(literal 2 binary64) a)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)))))
(.f64 (neg.f64 (expm1.f64 (.f64 x (*.f64 a #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)))))
(.f64 (expm1.f64 (.f64 x (*.f64 #s(literal 2 binary64) a))) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))))))
(.f64 (expm1.f64 (.f64 x (*.f64 a #s(literal 3 binary64)))) (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)))) (.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) (/.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)))) (.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (exp.f64 x) (*.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (fma.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) (/.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) (fma.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64)) (.f64 (/.f64 (pow.f64 (exp.f64 x) (*.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64))))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (.f64 #s(literal -1 binary64) (pow.f64 (exp.f64 x) a)))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (.f64 x (.f64 #s(literal 2 binary64) a))))) (neg.f64 (neg.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 3 binary64)))))) (neg.f64 (neg.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)))))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 x) a) #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 x) a) #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) a) #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a))) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 x) a) #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (exp.f64 x) (*.f64 a #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) a) #s(literal 6 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64))))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))))
(/.f64 (-.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) (.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal 1 binary64))) (.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a)) (-.f64 #s(literal -1 binary64) (pow.f64 (exp.f64 x) a)))
(/.f64 (neg.f64 (expm1.f64 (.f64 x (.f64 #s(literal 2 binary64) a)))) (neg.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 3 binary64))))) (neg.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))))
(/.f64 (expm1.f64 (.f64 x (.f64 #s(literal 2 binary64) a))) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x)))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 3 binary64)))) (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (.f64 x (.f64 a #s(literal 3 binary64)))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)))) (expm1.f64 (.f64 x (*.f64 a #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 x) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (/.f64 (pow.f64 (exp.f64 x) a) #s(literal 1 binary64)) (neg.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 1/2 binary64))) (pow.f64 (exp.f64 x) (.f64 a #s(literal 1/2 binary64))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (exp.f64 a) (.f64 #s(literal 1/2 binary64) x)) (pow.f64 (exp.f64 a) (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (pow.f64 (exp.f64 x) (*.f64 a #s(literal 3 binary64))) (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))
(fma.f64 (pow.f64 (exp.f64 x) a) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 3 binary64))) (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))))))
(-.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) (*.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64)))
(-.f64 (pow.f64 (exp.f64 x) a) #s(literal 1 binary64))
(+.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))) (neg.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) (*.f64 a #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a))) (neg.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) a) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) a)) #s(literal -1 binary64))))
(+.f64 #s(literal -1 binary64) (pow.f64 (exp.f64 x) a))
(+.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 a x))
(.f64 (.f64 a x) #s(literal 1 binary64))
(*.f64 a x)
(*.f64 x a)
(fma.f64 #s(literal 1 binary64) (*.f64 a x) #s(literal 0 binary64))
(fma.f64 (*.f64 a x) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 a x #s(literal 0 binary64))
(fma.f64 x a #s(literal 0 binary64))
(+.f64 (log.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 1/2 binary64)))) (log.f64 (pow.f64 (exp.f64 x) (.f64 a #s(literal 1/2 binary64)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 a) (.f64 #s(literal 1/2 binary64) x))) (log.f64 (pow.f64 (exp.f64 a) (.f64 #s(literal 1/2 binary64) x))))
(+.f64 #s(literal 0 binary64) (*.f64 a x))
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(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) a) #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (.f64 a x) #s(literal 2 binary64)) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) a) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/6 binary64) x) a)) (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 1/2 binary64)))) (fma.f64 (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 a #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 2 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal -1/2 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 a x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 a x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 a (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/6 binary64) a) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/6 binary64) x) a))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/6 binary64) x) a))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal -1/2 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal -1/2 binary64)))))
(+.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) a) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/6 binary64) x) a))
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 x #s(literal 1/24 binary64))

eval164.0ms (3.2%)

Memory: 3.7MiB live, 141.6MiB allocated
Compiler: Compiled 24 505 to 2 659 computations (89.1% saved)

prune19.0ms (0.4%)

Memory

2.1MiB live, 40.3MiB allocated

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	615	9	624
Fresh	3	1	4
Picked	3	2	5
Done	0	0	0
Total	621	12	633

Accuracy

100.0%

Counts

633 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	22.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
	21.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 a x) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	20.9%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
▶	65.9%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
▶	61.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x)))
▶	61.3%	#s(approx (- (exp (* a x)) 1) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a))))
	65.1%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 a x) #s(literal 1/2 binary64)) (.f64 a x) #s(literal 1 binary64)) (*.f64 x a)))
▶	64.9%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(approx (+ (* (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a)))
	64.9%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (*.f64 a x) a) x))
	65.1%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (*.f64 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) x) a))
▶	66.0%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x) a))

Compiler

Compiled 426 to 303 computations (28.9% saved)

simplify93.0ms (1.8%)

Memory

-12.9MiB live, 30.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a)
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a))))
cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) x))
cost-diff	0	(.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x)
cost-diff	0	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x)))
cost-diff	320	(fma.f64 x a (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x))
cost-diff	0	(.f64 #s(approx (+ ( (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a)
cost-diff	0	(fma.f64 (.f64 #s(approx (+ ( (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 #s(approx (+ (* (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a))
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(approx (+ (* (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a)))
cost-diff	0	(*.f64 a x)
cost-diff	0	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
cost-diff	0	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x)
cost-diff	0	(.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x) a)
cost-diff	0	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x) a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	296
0	61	296
1	105	288
2	187	288
3	420	288
4	1034	288
5	1462	288
6	2117	288
7	2692	288
8	2969	288
9	3117	288
10	3379	288
11	3615	288
12	3687	288
13	3706	288
14	3709	288
15	3710	288
16	3710	288
17	3714	288
18	3714	288
19	3714	288
0	3714	278

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize76.0ms (1.5%)

Memory

-2.5MiB live, 73.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.12957820068645803	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a))
accuracy	1.091819722427479	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a)))
accuracy	7.329199051931495	(.f64 (.f64 a a) x)
accuracy	22.451765332868227	#s(approx (- (exp (* a x)) 1) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x) a))))
accuracy	0.0078125	(fma.f64 x a (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x))
accuracy	2.7997882374326086	(.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x)
accuracy	7.329199051931495	(.f64 (.f64 a a) x)
accuracy	22.451765332868227	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x)))
accuracy	0.05859375	(.f64 (fma.f64 (.f64 #s(approx (+ (* (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a))
accuracy	0.9747690527834922	(fma.f64 (.f64 #s(approx (+ ( (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
accuracy	21.724667889633707	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(approx (+ (* (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a)))
accuracy	22.599969526064196	#s(approx (+ (* (* 1/6 x) a) 1/2) #s(literal 1/2 binary64))
accuracy	0.0	(*.f64 a x)
accuracy	21.79622366038182	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
accuracy	0.3359375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.4968816483001438	(.f64 (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x)
accuracy	0.9747690527834922	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
accuracy	21.724667889633707	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x) a))

Samples

54.0ms

256×

valid

Compiler

Compiled 545 to 70 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 21.0ms (55.7% of total)

ival-add: 7.0ms (18.6% of total)

ival-div: 3.0ms (8% of total)

const: 3.0ms (8% of total)

ival-expm1: 3.0ms (8% of total)

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

exact: 0.0ms (0% of total)

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

series16.0ms (0.3%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

21 → 86

Calls

Call 1

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

Outputs
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(* 1/2 a)
(* a (+ 1/2 (* 1/6 (* a x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) x))
(/ 1 a)
(/ (+ 1 (* -1/2 (* a x))) a)
(/ (+ 1 (* a (- (* 1/4 (* a (pow x 2))) (* 1/2 x)))) a)
(/ (+ 1 (* a (- (* a (- (* -1/8 (* a (pow x 3))) (* -1/4 (pow x 2)))) (* 1/2 x)))) a)
a
(* a (+ 1 (* 1/2 (* a x))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(* (pow a 2) x)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* 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)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* 1/6 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(/ 2 (* (pow a 2) x))
(/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* a (pow x 2))))) (pow a 2))
(/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow a 2) (pow x 3)))) (/ 4 (* a (pow x 2)))) (pow a 2))
(/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow a 2) (pow x 3))))) (+ (* 16 (/ 1 (* (pow a 3) (pow x 4)))) (/ 4 (* a (pow x 2))))) (pow a 2))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* 1/6 (* a x))
(* a (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* -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)))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(/ (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* a (pow x 3))))) a)) (* 2 (/ 1 x))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* a (pow x 4))))) a)) (* 4 (/ 1 (pow x 2)))) a)) (* 2 (/ 1 x))) (pow a 2))
(* -1 (* a (- (* -1/6 x) (* 1/2 (/ 1 a)))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))
(+ (* -1/2 x) (/ 1 a))
(+ (* x (- (* 1/4 (* a x)) 1/2)) (/ 1 a))
(+ (* x (- (* x (- (* -1/8 (* (pow a 2) x)) (* -1/4 a))) 1/2)) (/ 1 a))
(+ a (* 1/2 (* (pow a 2) x)))
(* 1/6 x)
(* (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 2)) (* 1/2 (/ a x))))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* x (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(/ (- (* 2 (/ 1 (pow a 2))) (* 4 (/ 1 (* (pow a 3) x)))) x)
(/ (- (+ (* 2 (/ 1 (pow a 2))) (/ 8 (* (pow a 4) (pow x 2)))) (/ 4 (* (pow a 3) x))) x)
(/ (- (+ (* 8 (/ 1 (* (pow a 4) (pow x 2)))) (* 2 (/ 1 (pow a 2)))) (+ (* 16 (/ 1 (* (pow a 5) (pow x 3)))) (/ 4 (* (pow a 3) x)))) x)
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/6 a) (* 1/2 (/ 1 x))))
(* -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) (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* -1 (* x (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (/ (- (* 4 (/ 1 (* (pow a 3) x))) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* (pow a 4) x))) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow a 5) x))) (* 8 (/ 1 (pow a 4)))) x)) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (- (* -1/6 a) (* 1/2 (/ 1 x)))))

Calls

6 calls:

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

simplify154.0ms (3%)

Memory

17.3MiB live, 130.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	330	1210
1	1112	1173
2	3356	1124
0	8114	1042

Stop Event

1×	iter limit
1×	node limit

Counts

86 → 84

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))))))))
x
(+ x (* 1/2 (* a (pow x 2))))
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
1
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(* 1/2 a)
(* a (+ 1/2 (* 1/6 (* a x))))
(* 1/2 (* (pow a 2) (pow x 2)))
(* 1/2 (* (pow a 2) x))
(/ 1 a)
(/ (+ 1 (* -1/2 (* a x))) a)
(/ (+ 1 (* a (- (* 1/4 (* a (pow x 2))) (* 1/2 x)))) a)
(/ (+ 1 (* a (- (* a (- (* -1/8 (* a (pow x 3))) (* -1/4 (pow x 2)))) (* 1/2 x)))) a)
a
(* a (+ 1 (* 1/2 (* a x))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(* (pow a 2) x)
(- (exp (* a x)) 1)
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* 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)))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* 1/6 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(/ 2 (* (pow a 2) x))
(/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* a (pow x 2))))) (pow a 2))
(/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow a 2) (pow x 3)))) (/ 4 (* a (pow x 2)))) (pow a 2))
(/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow a 2) (pow x 3))))) (+ (* 16 (/ 1 (* (pow a 3) (pow x 4)))) (/ 4 (* a (pow x 2))))) (pow a 2))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(* 1/6 (* a x))
(* a (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(* -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)))))
(* (pow a 2) (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(/ (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* a (pow x 3))))) a)) (* 2 (/ 1 x))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* a (pow x 4))))) a)) (* 4 (/ 1 (pow x 2)))) a)) (* 2 (/ 1 x))) (pow a 2))
(* -1 (* a (- (* -1/6 x) (* 1/2 (/ 1 a)))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(* x (+ 1 (* 1/2 (* a x))))
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))
(+ (* -1/2 x) (/ 1 a))
(+ (* x (- (* 1/4 (* a x)) 1/2)) (/ 1 a))
(+ (* x (- (* x (- (* -1/8 (* (pow a 2) x)) (* -1/4 a))) 1/2)) (/ 1 a))
(+ a (* 1/2 (* (pow a 2) x)))
(* 1/6 x)
(* (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 2)) (* 1/2 (/ a x))))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* x (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(/ (- (* 2 (/ 1 (pow a 2))) (* 4 (/ 1 (* (pow a 3) x)))) x)
(/ (- (+ (* 2 (/ 1 (pow a 2))) (/ 8 (* (pow a 4) (pow x 2)))) (/ 4 (* (pow a 3) x))) x)
(/ (- (+ (* 8 (/ 1 (* (pow a 4) (pow x 2)))) (* 2 (/ 1 (pow a 2)))) (+ (* 16 (/ 1 (* (pow a 5) (pow x 3)))) (/ 4 (* (pow a 3) x)))) x)
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* x (+ (* 1/6 a) (* 1/2 (/ 1 x))))
(* -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) (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* -1 (* x (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(* -1 (/ (- (* 4 (/ 1 (* (pow a 3) x))) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* (pow a 4) x))) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow a 5) x))) (* 8 (/ 1 (pow a 4)))) x)) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* -1 (* x (- (* -1/6 a) (* 1/2 (/ 1 x)))))

Outputs
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) x) a)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (.f64 x x) x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
x
(+ x (* 1/2 (* a (pow x 2))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) x)
(+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (*.f64 x x) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* a x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
(* a (+ 1/2 (* 1/6 (* a x))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
(* 1/2 (* (pow a 2) (pow x 2)))
(.f64 (.f64 (.f64 (.f64 a a) #s(literal 1/2 binary64)) x) x)
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) #s(literal 1/2 binary64)) x)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ (+ 1 (* -1/2 (* a x))) a)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a)
(/ (+ 1 (* a (- (* 1/4 (* a (pow x 2))) (* 1/2 x)))) a)
(/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x a) #s(literal -1/2 binary64)) x) a #s(literal 1 binary64)) a)
(/ (+ 1 (* a (- (* a (- (* -1/8 (* a (pow x 3))) (* -1/4 (pow x 2)))) (* 1/2 x)))) a)
(/.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal -1/8 binary64) a) x #s(literal 1/4 binary64))) a (.f64 #s(literal -1/2 binary64) x)) a #s(literal 1 binary64)) a)
a
(* a (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 (* a x)))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64))
(* (pow a 2) x)
(.f64 (.f64 a a) x)
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 x a))
(* 1/6 (* (pow a 3) (pow x 3)))
(.f64 (.f64 (pow.f64 a #s(literal 3 binary64)) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(.f64 (.f64 (*.f64 x x) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal 1/2 binary64) a))) (pow.f64 a #s(literal 3 binary64)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (.f64 x x) x) a)
(* 1/6 (* (pow a 2) (pow x 3)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64)) a) a)
(* (pow a 2) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (.f64 x x))
(* (pow a 2) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (.f64 x x) (.f64 (/.f64 x a) a))
(* 1/6 (* (pow a 2) (pow x 2)))
(.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/6 binary64)) x)
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x)
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
(* 1/6 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/6 binary64))
(* (pow a 2) (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) x) a)
(/ 2 (* (pow a 2) x))
(/.f64 (/.f64 #s(literal 2 binary64) (*.f64 a a)) x)
(/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* a (pow x 2))))) (pow a 2))
(/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 a a)) (/.f64 #s(literal 4 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) x))) x)
(/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow a 2) (pow x 3)))) (/ 4 (* a (pow x 2)))) (pow a 2))
(/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) a))) a)) (*.f64 a a))
(/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow a 2) (pow x 3))))) (+ (* 16 (/ 1 (* (pow a 3) (pow x 4)))) (/ 4 (* a (pow x 2))))) (pow a 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) a))) a)) (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 a #s(literal 3 binary64)))) (*.f64 a a))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
(* 1/6 (* a x))
(.f64 (.f64 #s(literal 1/6 binary64) x) a)
(* a (+ (* 1/6 x) (* 1/2 (/ 1 a))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(.f64 (.f64 (*.f64 x x) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal 1/2 binary64) a))) (pow.f64 a #s(literal 3 binary64)))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(.f64 (neg.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a))) (pow.f64 a #s(literal 3 binary64)))
(* (pow a 2) (+ (* -1 (/ (+ (* -1 (/ x a)) (* -1/2 (pow x 2))) a)) (* 1/6 (pow x 3))))
(.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a))) (neg.f64 a))) a) a)
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -1 binary64) a)) (neg.f64 a))) a) a)
(/ (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* a (pow x 3))))) a)) (* 2 (/ 1 x))) (pow a 2))
(/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) a))) a)) (*.f64 a a))
(/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* a (pow x 4))))) a)) (* 4 (/ 1 (pow x 2)))) a)) (* 2 (/ 1 x))) (pow a 2))
(/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 16 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) a))) a)) a)) (*.f64 a a))
(* -1 (* a (- (* -1/6 x) (* 1/2 (/ 1 a)))))
(neg.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) a #s(literal -1/2 binary64)))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) x) a)
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (.f64 x x) x) a)
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 a #s(literal 4 binary64)) x) #s(literal 1/24 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) #s(literal 1/6 binary64))) x (.f64 (*.f64 a a) #s(literal 1/2 binary64))) x a) x)
(* x (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a)))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (*.f64 x x) x)
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
(+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
(+ (* -1/2 x) (/ 1 a))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a))
(+ (* x (- (* 1/4 (* a x)) 1/2)) (/ 1 a))
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x a) #s(literal -1/2 binary64)) x (/.f64 #s(literal 1 binary64) a))
(+ (* x (- (* x (- (* -1/8 (* (pow a 2) x)) (* -1/4 a))) 1/2)) (/ 1 a))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) a (.f64 #s(literal -1/8 binary64) (.f64 (*.f64 a a) x))) x #s(literal -1/2 binary64)) x (/.f64 #s(literal 1 binary64) a))
(+ a (* 1/2 (* (pow a 2) x)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(.f64 (.f64 (*.f64 a a) (fma.f64 #s(literal 1/6 binary64) a (/.f64 #s(literal 1/2 binary64) x))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(.f64 (fma.f64 (.f64 a a) (fma.f64 #s(literal 1/6 binary64) a (/.f64 #s(literal 1/2 binary64) x)) (/.f64 a (*.f64 x x))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (.f64 x x))
(* (pow x 3) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (*.f64 x x) x)
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x)
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
(* x (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) x) a)
(/ (- (* 2 (/ 1 (pow a 2))) (* 4 (/ 1 (* (pow a 3) x)))) x)
(/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 a a)) (/.f64 #s(literal 4 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) x))) x)
(/ (- (+ (* 2 (/ 1 (pow a 2))) (/ 8 (* (pow a 4) (pow x 2)))) (/ 4 (* (pow a 3) x))) x)
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 a #s(literal 4 binary64)) x)) (/.f64 #s(literal 4 binary64) (pow.f64 a #s(literal 3 binary64)))) x) (/.f64 #s(literal 2 binary64) (.f64 a a))) x)
(/ (- (+ (* 8 (/ 1 (* (pow a 4) (pow x 2)))) (* 2 (/ 1 (pow a 2)))) (+ (* 16 (/ 1 (* (pow a 5) (pow x 3)))) (/ 4 (* (pow a 3) x)))) x)
(/.f64 (-.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 a #s(literal 4 binary64)) x)) (/.f64 #s(literal 4 binary64) (pow.f64 a #s(literal 3 binary64)))) x) (/.f64 #s(literal 2 binary64) (.f64 a a))) (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 a #s(literal 5 binary64)))) x)
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
(* x (+ (* 1/6 a) (* 1/2 (/ 1 x))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(.f64 (.f64 (*.f64 a a) (fma.f64 #s(literal 1/6 binary64) a (/.f64 #s(literal 1/2 binary64) x))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 a #s(literal 3 binary64)) (/.f64 (fma.f64 (.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) (neg.f64 x)))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) (.f64 x x))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 a) (/ 1 x)) x)) (* -1/6 (pow a 2)))))
(.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1/6 binary64) a) a (/.f64 (fma.f64 #s(literal -1/2 binary64) a (/.f64 #s(literal -1 binary64) x)) x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) a) a (/.f64 (fma.f64 #s(literal 1/2 binary64) a (/.f64 #s(literal 1 binary64) x)) x)) x) x)
(* -1 (* x (+ (* -1/2 (/ a x)) (* -1/6 (pow a 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a)
(* -1 (/ (- (* 4 (/ 1 (* (pow a 3) x))) (* 2 (/ 1 (pow a 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 a a)) (/.f64 #s(literal 4 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) x))) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* (pow a 4) x))) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 a #s(literal 4 binary64)) x)) (/.f64 #s(literal 4 binary64) (pow.f64 a #s(literal 3 binary64)))) x) (/.f64 #s(literal 2 binary64) (.f64 a a))) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow a 5) x))) (* 8 (/ 1 (pow a 4)))) x)) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (pow.f64 a #s(literal 3 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (pow.f64 a #s(literal 5 binary64)) x)) (/.f64 #s(literal 8 binary64) (pow.f64 a #s(literal 4 binary64)))) x)) x) (/.f64 #s(literal 2 binary64) (.f64 a a))) x)
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x a) #s(literal 1 binary64)) a)
(* -1 (* x (- (* -1/6 a) (* 1/2 (/ 1 x)))))
(neg.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) a) x #s(literal -1/2 binary64)))

rewrite200.0ms (3.9%)

Memory

5.5MiB live, 195.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	250
0	61	250
1	203	240
2	1191	240
0	8480	230

Stop Event

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

Counts

21 → 660

Calls

Call 1

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

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

eval132.0ms (2.6%)

Memory: -27.0MiB live, 132.3MiB allocated
Compiler: Compiled 22 135 to 2 516 computations (88.6% saved)

prune19.0ms (0.4%)

Memory

-1.5MiB live, 37.6MiB allocated

Pruning

14 alts after pruning (8 fresh and 6 done)

	Pruned	Kept	Total
New	580	3	583
Fresh	0	5	5
Picked	1	4	5
Done	0	2	2
Total	581	14	595

Accuracy

100.0%

Counts

595 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	22.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
▶	21.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 a x) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	20.9%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
✓	65.9%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
✓	61.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x)))
▶	70.9%	#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)))))
	69.6%	#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a))))
	65.8%	#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (/.f64 #s(literal 1 binary64) a))))
▶	65.1%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 a x) #s(literal 1/2 binary64)) (.f64 a x) #s(literal 1 binary64)) (*.f64 x a)))
✓	64.9%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(approx (+ (* (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a)))
▶	64.9%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (*.f64 a x) a) x))
	65.1%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (*.f64 a x) #s(literal 1/2 binary64)) x) a #s(literal 1 binary64)) x) a))
✓	66.0%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x) a))

Compiler

Compiled 472 to 331 computations (29.9% saved)

simplify326.0ms (6.3%)

Memory

36.6MiB live, 233.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	379
0	77	376
1	141	376
2	264	376
3	565	376
4	1636	376
5	3374	376
6	3445	376
7	3481	376
8	3509	376
9	3509	376
10	5330	376
11	5330	376
12	5338	376
13	5338	376
14	5820	376
15	5957	376
16	5957	376
0	9220	370

Stop Event

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

Calls

Call 1

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

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

localize135.0ms (2.6%)

Memory

-23.4MiB live, 133.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0390625	(fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 a x) #s(literal 1/2 binary64))
accuracy	0.0859375	(fma.f64 (*.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64))
accuracy	0.3359375	(*.f64 #s(literal 1/24 binary64) x)
accuracy	22.289855895024164	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 a x) #s(literal 1/2 binary64)) (.f64 a x) #s(literal 1 binary64)) (*.f64 x a)))
accuracy	0.3359375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.9747690527834922	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64))
accuracy	22.09107619764099	#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a) #s(literal 1 binary64)))
accuracy	28.14340552309742	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.03515625	(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 a x) #s(literal 1 binary64)) a)
accuracy	0.970725972427479	(fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 a x) #s(literal 1 binary64)) a) x #s(literal 1 binary64))
accuracy	22.123139568813244	#s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 a x) #s(literal 1 binary64)) a) x #s(literal 1 binary64)))
accuracy	28.14340552309742	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 a x) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) a)
accuracy	0.03125	(fma.f64 (.f64 #s(literal 1/2 binary64) a) (.f64 a x) a)
accuracy	0.970725972427479	(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (*.f64 a x) a) x)
accuracy	22.451765332868227	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (*.f64 a x) a) x))
accuracy	0.00390625	(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a))
accuracy	1.091819722427479	(/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a))))
accuracy	22.161430812471004	#s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)))
accuracy	22.451765332868227	#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)))))

Samples

83.0ms

256×

valid

Compiler

Compiled 658 to 93 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-mult: 34.0ms (54% of total)

ival-add: 12.0ms (19% of total)

ival-div: 7.0ms (11.1% of total)

const: 6.0ms (9.5% of total)

ival-exp: 2.0ms (3.2% of total)

ival-expm1: 2.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.3%)

Memory

16.3MiB live, 16.3MiB allocated

Counts

23 → 121

Calls

Call 1

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

Outputs
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(/ 1 a)
(/ (+ 1 (* -1/2 (* a x))) a)
(/ (+ 1 (* a (- (* 1/4 (* a (pow x 2))) (* 1/2 x)))) a)
(/ (+ 1 (* a (- (* a (- (* -1/8 (* a (pow x 3))) (* -1/4 (pow x 2)))) (* 1/2 x)))) a)
a
(* a (+ 1 (* 1/2 (* a x))))
(* 1/2 a)
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(+ 1 (* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
1/6
(+ 1/6 (* 1/24 (* a x)))
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(/ 2 (* (pow a 2) x))
(/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* a (pow x 2))))) (pow a 2))
(/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow a 2) (pow x 3)))) (/ 4 (* a (pow x 2)))) (pow a 2))
(/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow a 2) (pow x 3))))) (+ (* 16 (/ 1 (* (pow a 3) (pow x 4)))) (/ 4 (* a (pow x 2))))) (pow a 2))
(* -1/2 x)
(+ (* -1/2 x) (/ 1 a))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(exp (* a x))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow a 2)) (/ x a))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (+ (/ 1 (pow a 3)) (/ x (pow a 2))))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (+ (* 1/2 (/ x (pow a 2))) (/ 1 (pow a 3))))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))
(* 1/24 (* a x))
(* a (+ (* 1/24 x) (* 1/6 (/ 1 a))))
(/ (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* a (pow x 3))))) a)) (* 2 (/ 1 x))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* a (pow x 4))))) a)) (* 4 (/ 1 (pow x 2)))) a)) (* 2 (/ 1 x))) (pow a 2))
(* (pow a 2) (+ (* -1 (/ (- (* -1 x) (/ 1 a)) a)) (* 1/2 (pow x 2))))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1 x) (/ 1 a)) a)) (* 1/2 (pow x 2))) a)) (* -1/6 (pow x 3)))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 2) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))) a)) (* -1/24 (pow x 3)))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))
(* -1 (* a (- (* -1/24 x) (* 1/6 (/ 1 a)))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(+ (* x (- (* 1/4 (* a x)) 1/2)) (/ 1 a))
(+ (* x (- (* x (- (* -1/8 (* (pow a 2) x)) (* -1/4 a))) 1/2)) (/ 1 a))
(+ a (* 1/2 (* (pow a 2) x)))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2)))))))
(+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))
(* 1/6 x)
(* 1/24 x)
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(/ (- (* 2 (/ 1 (pow a 2))) (* 4 (/ 1 (* (pow a 3) x)))) x)
(/ (- (+ (* 2 (/ 1 (pow a 2))) (/ 8 (* (pow a 4) (pow x 2)))) (/ 4 (* (pow a 3) x))) x)
(/ (- (+ (* 8 (/ 1 (* (pow a 4) (pow x 2)))) (* 2 (/ 1 (pow a 2)))) (+ (* 16 (/ 1 (* (pow a 5) (pow x 3)))) (/ 4 (* (pow a 3) x)))) x)
(* x (- (/ 1 (* a x)) 1/2))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (+ (/ 1 (pow x 2)) (/ a x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (+ (/ 1 (pow x 3)) (/ a (pow x 2))))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 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))))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* x (+ (* 1/24 a) (* 1/6 (/ 1 x))))
(* -1 (/ (- (* 4 (/ 1 (* (pow a 3) x))) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* (pow a 4) x))) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow a 5) x))) (* 8 (/ 1 (pow a 4)))) x)) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (* x (- 1/2 (/ 1 (* a x)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 a) (/ 1 x)) x)) (* 1/2 (pow a 2))))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1 a) (/ 1 x)) x)) (* 1/2 (pow a 2))) x)) (* -1/6 (pow a 3)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* -1 (* (pow x 3) (+ (* -1/6 (/ (pow a 2) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))) x)) (* -1/24 (pow a 3)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(* -1 (* x (- (* -1/24 a) (* 1/6 (/ 1 x)))))

Calls

6 calls:

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

simplify172.0ms (3.3%)

Memory

-12.6MiB live, 181.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	506	2055
1	1677	2020
2	5428	1923
0	8114	1786

Stop Event

1×	iter limit
1×	node limit

Counts

121 → 120

Calls

Call 1

Inputs
(* a x)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(/ 1 a)
(/ (+ 1 (* -1/2 (* a x))) a)
(/ (+ 1 (* a (- (* 1/4 (* a (pow x 2))) (* 1/2 x)))) a)
(/ (+ 1 (* a (- (* a (- (* -1/8 (* a (pow x 3))) (* -1/4 (pow x 2)))) (* 1/2 x)))) a)
a
(* a (+ 1 (* 1/2 (* a x))))
(* 1/2 a)
1
(+ 1 (* a x))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(+ 1 (* 1/2 (* a x)))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(+ 1 (* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))))
1/2
(+ 1/2 (* 1/6 (* a x)))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
1/6
(+ 1/6 (* 1/24 (* a x)))
(- (exp (* a x)) 1)
(* 1/2 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(/ 2 (* (pow a 2) x))
(/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* a (pow x 2))))) (pow a 2))
(/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow a 2) (pow x 3)))) (/ 4 (* a (pow x 2)))) (pow a 2))
(/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow a 2) (pow x 3))))) (+ (* 16 (/ 1 (* (pow a 3) (pow x 4)))) (/ 4 (* a (pow x 2))))) (pow a 2))
(* -1/2 x)
(+ (* -1/2 x) (/ 1 a))
(* 1/2 (* (pow a 2) x))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(exp (* a x))
(* (pow a 2) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow a 2)) (/ x a))))
(* 1/6 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (+ (/ 1 (pow a 3)) (/ x (pow a 2))))))
(* 1/6 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))))
(* (pow a 2) (+ (* 1/6 (pow x 2)) (+ (* 1/2 (/ x a)) (/ 1 (pow a 2)))))
(* 1/24 (* (pow a 4) (pow x 4)))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (* 1/6 (/ (pow x 3) a))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (* 1/2 (/ (pow x 2) (pow a 2))))))
(* (pow a 4) (+ (* 1/24 (pow x 4)) (+ (* 1/6 (/ (pow x 3) a)) (+ (* 1/2 (/ (pow x 2) (pow a 2))) (/ x (pow a 3))))))
(* 1/24 (* (pow a 3) (pow x 3)))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (* 1/6 (/ (pow x 2) a))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (* 1/2 (/ x (pow a 2))))))
(* (pow a 3) (+ (* 1/24 (pow x 3)) (+ (* 1/6 (/ (pow x 2) a)) (+ (* 1/2 (/ x (pow a 2))) (/ 1 (pow a 3))))))
(* 1/24 (* (pow a 2) (pow x 2)))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (* 1/6 (/ x a))))
(* (pow a 2) (+ (* 1/24 (pow x 2)) (+ (* 1/6 (/ x a)) (/ 1/2 (pow a 2)))))
(* 1/24 (* a x))
(* a (+ (* 1/24 x) (* 1/6 (/ 1 a))))
(/ (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* a (pow x 3))))) a)) (* 2 (/ 1 x))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* a (pow x 4))))) a)) (* 4 (/ 1 (pow x 2)))) a)) (* 2 (/ 1 x))) (pow a 2))
(* (pow a 2) (+ (* -1 (/ (- (* -1 x) (/ 1 a)) a)) (* 1/2 (pow x 2))))
(* -1 (* (pow a 3) (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1 x) (/ 1 a)) a)) (* 1/2 (pow x 2))) a)) (* -1/6 (pow x 3)))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow x 2) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* (pow a 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow x 2)) (/ x a)) a)) (* -1/6 (pow x 3))) a)) (* 1/24 (pow x 4))))
(* -1 (* (pow a 3) (+ (* -1/6 (/ (pow x 2) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* 1/6 (pow x 2)) (* 1/2 (/ x a))) a)) (* -1/24 (pow x 3)))))
(* -1 (* (pow a 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1/2 x) (/ 1 a)) a)) (* 1/6 (pow x 2))) a)) (* -1/24 (pow x 3)))))
(* (pow a 2) (+ (* -1 (/ (- (* -1/6 x) (* 1/2 (/ 1 a))) a)) (* 1/24 (pow x 2))))
(* -1 (* a (- (* -1/24 x) (* 1/6 (/ 1 a)))))
(* x (+ a (* 1/2 (* (pow a 2) x))))
(* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2))))))
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* x (+ (* 1/24 (* (pow a 4) x)) (* 1/6 (pow a 3))))))))
(+ (* x (- (* 1/4 (* a x)) 1/2)) (/ 1 a))
(+ (* x (- (* x (- (* -1/8 (* (pow a 2) x)) (* -1/4 a))) 1/2)) (/ 1 a))
(+ a (* 1/2 (* (pow a 2) x)))
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(+ 1 (* x (+ (* 1/6 (* (pow a 2) x)) (* 1/2 a))))
(+ 1 (* x (+ (* 1/2 a) (* x (+ (* 1/24 (* (pow a 3) x)) (* 1/6 (pow a 2)))))))
(+ 1/2 (* x (+ (* 1/24 (* (pow a 2) x)) (* 1/6 a))))
(* 1/6 x)
(* 1/24 x)
(* (pow x 2) (+ (* 1/2 (pow a 2)) (/ a x)))
(/ (- (* 2 (/ 1 (pow a 2))) (* 4 (/ 1 (* (pow a 3) x)))) x)
(/ (- (+ (* 2 (/ 1 (pow a 2))) (/ 8 (* (pow a 4) (pow x 2)))) (/ 4 (* (pow a 3) x))) x)
(/ (- (+ (* 8 (/ 1 (* (pow a 4) (pow x 2)))) (* 2 (/ 1 (pow a 2)))) (+ (* 16 (/ 1 (* (pow a 5) (pow x 3)))) (/ 4 (* (pow a 3) x)))) x)
(* x (- (/ 1 (* a x)) 1/2))
(* x (+ (* 1/2 (pow a 2)) (/ a x)))
(* (pow x 2) (+ (* 1/2 (pow a 2)) (+ (/ 1 (pow x 2)) (/ a x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (* 1/2 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (/ a (pow x 2)))))
(* (pow x 3) (+ (* 1/6 (pow a 3)) (+ (* 1/2 (/ (pow a 2) x)) (+ (/ 1 (pow x 3)) (/ a (pow x 2))))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))))
(* (pow x 2) (+ (* 1/6 (pow a 2)) (+ (* 1/2 (/ a x)) (/ 1 (pow x 2)))))
(* (pow x 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))))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (* 1/6 (/ (pow a 2) x))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (* 1/2 (/ a (pow x 2))))))
(* (pow x 3) (+ (* 1/24 (pow a 3)) (+ (* 1/6 (/ (pow a 2) x)) (+ (* 1/2 (/ a (pow x 2))) (/ 1 (pow x 3))))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (* 1/6 (/ a x))))
(* (pow x 2) (+ (* 1/24 (pow a 2)) (+ (* 1/6 (/ a x)) (/ 1/2 (pow x 2)))))
(* x (+ (* 1/24 a) (* 1/6 (/ 1 x))))
(* -1 (/ (- (* 4 (/ 1 (* (pow a 3) x))) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* (pow a 4) x))) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow a 5) x))) (* 8 (/ 1 (pow a 4)))) x)) (* 4 (/ 1 (pow a 3)))) x)) (* 2 (/ 1 (pow a 2)))) x))
(* -1 (* x (- 1/2 (/ 1 (* a x)))))
(* -1 (* x (+ (* -1 (/ a x)) (* -1/2 (pow a 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 a) (/ 1 x)) x)) (* 1/2 (pow a 2))))
(* -1 (* (pow x 3) (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1 a) (/ 1 x)) x)) (* 1/2 (pow a 2))) x)) (* -1/6 (pow a 3)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(* -1 (* (pow x 3) (+ (* -1/6 (/ (pow a 2) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))) x)) (* -1/24 (pow a 3)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(* -1 (* x (- (* -1/24 a) (* 1/6 (/ 1 x)))))

Outputs
(* a x)
(*.f64 x a)
(* a (+ x (* 1/2 (* a (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x)
(* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64))) a x) a)
(* a (+ x (* a (+ (* 1/2 (pow x 2)) (* a (+ (* 1/24 (* a (pow x 4))) (* 1/6 (pow x 3))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) a) #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))) a (.f64 (*.f64 x x) #s(literal 1/2 binary64))) a x) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ (+ 1 (* -1/2 (* a x))) a)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a)
(/ (+ 1 (* a (- (* 1/4 (* a (pow x 2))) (* 1/2 x)))) a)
(/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x a) #s(literal -1/2 binary64)) x) a #s(literal 1 binary64)) a)
(/ (+ 1 (* a (- (* a (- (* -1/8 (* a (pow x 3))) (* -1/4 (pow x 2)))) (* 1/2 x)))) a)
(/.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal -1/8 binary64) a) x #s(literal 1/4 binary64))) a (.f64 #s(literal -1/2 binary64) x)) a #s(literal 1 binary64)) a)
a
(* a (+ 1 (* 1/2 (* a x))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a)
(* 1/2 a)
(*.f64 #s(literal 1/2 binary64) a)
1
#s(literal 1 binary64)
(+ 1 (* a x))
(fma.f64 x a #s(literal 1 binary64))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a) x #s(literal 1 binary64))
(+ 1 (* a (+ x (* a (+ (* 1/6 (* a (pow x 3))) (* 1/2 (pow x 2)))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x a) #s(literal 1/2 binary64))) a x) a #s(literal 1 binary64))
(+ 1 (* 1/2 (* a x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64))
(+ 1 (* a (+ (* 1/6 (* a (pow x 2))) (* 1/2 x))))
(fma.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x a) #s(literal 1/2 binary64))) a #s(literal 1 binary64))
(+ 1 (* a (+ (* 1/2 x) (* a (+ (* 1/24 (* a (pow x 3))) (* 1/6 (pow x 2)))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x a) #s(literal 1/6 binary64))) a (.f64 #s(literal 1/2 binary64) x)) a #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 (* a x)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x a) #s(literal 1/2 binary64))
(+ 1/2 (* a (+ (* 1/24 (* a (pow x 2))) (* 1/6 x))))
(fma.f64 (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x a) #s(literal 1/6 binary64))) a #s(literal 1/2 binary64))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* 1/24 (* a x)))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x a) #s(literal 1/6 binary64))
(- (exp (* a x)) 1)
(expm1.f64 (*.f64 x a))
(* 1/2 (* (pow a 2) (pow x 2)))
(.f64 (.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64)) x)
(* (pow a 2) (+ (* 1/2 (pow x 2)) (/ x a)))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a)
(/ 2 (* (pow a 2) x))
(/.f64 (/.f64 #s(literal 2 binary64) (*.f64 a a)) x)
(/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* a (pow x 2))))) (pow a 2))
(/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 4 binary64) (.f64 (.f64 x x) a))) (*.f64 a a))
(/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow a 2) (pow x 3)))) (/ 4 (* a (pow x 2)))) (pow a 2))
(/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) a) a)) (-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 4 binary64) (.f64 (.f64 x x) a)))) (*.f64 a a))
(/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow a 2) (pow x 3))))) (+ (* 16 (/ 1 (* (pow a 3) (pow x 4)))) (/ 4 (* a (pow x 2))))) (pow a 2))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) a) a)) (/.f64 #s(literal 2 binary64) x)) (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 a #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 4 binary64) (.f64 (.f64 x x) a)))) (*.f64 a a))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(+ (* -1/2 x) (/ 1 a))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a))
(* 1/2 (* (pow a 2) x))
(.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64))
(* (pow a 2) (+ (* 1/2 x) (/ 1 a)))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) a #s(literal 1 binary64)) a)
(exp (* a x))
(pow.f64 (exp.f64 x) a)
(* (pow a 2) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow a 2)) (/ x a))))
(fma.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) a) x) a (fma.f64 (/.f64 x #s(literal 1 binary64)) a #s(literal 1 binary64)))
(* 1/6 (* (pow a 3) (pow x 3)))
(.f64 (.f64 (pow.f64 a #s(literal 3 binary64)) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (* 1/2 (/ (pow x 2) a))))
(.f64 (.f64 (*.f64 x x) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal 1/2 binary64) a))) (pow.f64 a #s(literal 3 binary64)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (/ x (pow a 2)))))
(.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal 1/2 binary64) a)) (/.f64 (/.f64 x a) a)) (pow.f64 a #s(literal 3 binary64)))
(* (pow a 3) (+ (* 1/6 (pow x 3)) (+ (* 1/2 (/ (pow x 2) a)) (+ (/ 1 (pow a 3)) (/ x (pow a 2))))))
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(.f64 (neg.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 a #s(literal 3 binary64)) (/.f64 (fma.f64 (.f64 a a) #s(literal 1/2 binary64) (/.f64 (+.f64 a (/.f64 #s(literal 1 binary64) x)) x)) (neg.f64 x)))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) a) a (/.f64 (fma.f64 #s(literal -1/2 binary64) a (/.f64 #s(literal -1 binary64) x)) (neg.f64 x))) x) x)
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (/ (pow a 2) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(.f64 (fma.f64 (pow.f64 a #s(literal 4 binary64)) #s(literal 1/24 binary64) (/.f64 (.f64 (*.f64 a a) (fma.f64 #s(literal -1/6 binary64) a (/.f64 #s(literal -1/2 binary64) x))) (neg.f64 x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (pow a 2)) (/ a x)) x)) (* -1/6 (pow a 3))) x)) (* 1/24 (pow a 4))))
(.f64 (fma.f64 (pow.f64 a #s(literal 4 binary64)) #s(literal 1/24 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 a #s(literal 3 binary64)) (/.f64 (fma.f64 (.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) (neg.f64 x))) (neg.f64 x))) (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 3) (+ (* -1/6 (/ (pow a 2) x)) (* -1/24 (pow a 3)))))
(.f64 (.f64 (*.f64 a a) (fma.f64 #s(literal 1/24 binary64) a (/.f64 #s(literal 1/6 binary64) x))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/6 (pow a 2)) (* 1/2 (/ a x))) x)) (* -1/24 (pow a 3)))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (pow.f64 a #s(literal 3 binary64)) (/.f64 (.f64 a (fma.f64 #s(literal 1/6 binary64) a (/.f64 #s(literal 1/2 binary64) x))) (neg.f64 x)))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (- (* -1/2 a) (/ 1 x)) x)) (* 1/6 (pow a 2))) x)) (* -1/24 (pow a 3)))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (pow.f64 a #s(literal 3 binary64)) (/.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) a) a (/.f64 (fma.f64 #s(literal -1/2 binary64) a (/.f64 #s(literal -1 binary64) x)) (neg.f64 x))) (neg.f64 x)))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/6 a) (* 1/2 (/ 1 x))) x)) (* 1/24 (pow a 2))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) a) a (/.f64 (fma.f64 #s(literal -1/6 binary64) a (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 x))) x) x)
(* -1 (* x (- (* -1/24 a) (* 1/6 (/ 1 x)))))
(fma.f64 (*.f64 #s(literal -1/24 binary64) a) (neg.f64 x) #s(literal 1/6 binary64))

rewrite282.0ms (5.5%)

Memory

20.8MiB live, 207.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	319
0	77	316
1	321	316
2	2208	316
0	8566	310

Stop Event

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

Counts

23 → 556

Calls

Call 1

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

Outputs
#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))))
(.f64 (pow.f64 #s(approx (/ 1 (+ ( 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 #s(approx (/ 1 (+ ( 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) #s(literal -1 binary64)) x)
(.f64 (neg.f64 x) (pow.f64 (neg.f64 #s(approx (/ 1 (+ ( 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 x #s(approx (/ 1 (+ ( 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))))
(.f64 x (pow.f64 #s(approx (/ 1 (+ ( 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (/.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) x) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 x #s(literal 1 binary64))) (neg.f64 #s(approx (/ 1 (+ ( 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))))))
(/.f64 (.f64 x #s(literal 1 binary64)) #s(approx (/ 1 (+ ( 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))))))
(/.f64 (neg.f64 x) (neg.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) x) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) x))
(/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))))
(neg.f64 (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))))
(neg.f64 (/.f64 x (neg.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))))) (/.f64 x (neg.f64 #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (/ 1 (+ ( 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))) x)) #s(literal -1 binary64)))
#s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 a #s(literal -2 binary64))) (pow.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64))) (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 (pow.f64 a #s(literal -2 binary64)) (/.f64 (*.f64 #s(literal -1/2 binary64) x) a))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 a #s(literal -2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 (pow.f64 a #s(literal -2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) x) a))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) (fma.f64 (/.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) (/.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) (.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) (/.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal -2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (pow.f64 a #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 a #s(literal -2 binary64))))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 (pow.f64 a #s(literal -2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) x) a))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))) (pow.f64 a #s(literal -2 binary64)))) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal -2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64))) (-.f64 (pow.f64 a #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 a #s(literal -2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) x) a)))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 (pow.f64 a #s(literal -2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) x) a)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 a #s(literal -2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64))) (+.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) x) a))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 (pow.f64 a #s(literal -2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) x) a))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 a #s(literal -2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 (pow.f64 a #s(literal -2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) x) a))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 a #s(literal -2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 (pow.f64 a #s(literal -2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) x) a))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64)))))
(fma.f64 (pow.f64 a #s(literal -1/2 binary64)) (pow.f64 a #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) a) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 (pow.f64 a #s(literal -1 binary64)) #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 a #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 x #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (pow.f64 a #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))) (/.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))))
(+.f64 (*.f64 #s(literal -1/2 binary64) x) (pow.f64 a #s(literal -1 binary64)))
(+.f64 (pow.f64 a #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
(.f64 (.f64 (fma.f64 (*.f64 x a) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) a)
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(fma.f64 (*.f64 #s(literal 1/24 binary64) a) x #s(literal 1/6 binary64))
(fma.f64 (*.f64 a #s(literal 1/24 binary64)) x #s(literal 1/6 binary64))
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x a) #s(literal 1/6 binary64))
(fma.f64 (*.f64 x a) #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) a) #s(literal 1/6 binary64))
(fma.f64 a (*.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))
(-.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 (.f64 #s(literal 1/24 binary64) x) a))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 1/24 binary64) x) a) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (.f64 (.f64 #s(literal 1/24 binary64) x) a))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 1/24 binary64) x) a) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal -1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal -1/6 binary64))))
(+.f64 (.f64 (.f64 #s(literal 1/24 binary64) x) a) #s(literal 1/6 binary64))
(+.f64 #s(literal 1/6 binary64) (.f64 (.f64 #s(literal 1/24 binary64) x) a))

eval78.0ms (1.5%)

Memory: 21.8MiB live, 103.1MiB allocated
Compiler: Compiled 25 702 to 2 695 computations (89.5% saved)

prune26.0ms (0.5%)

Memory

-31.7MiB live, 43.9MiB allocated

Pruning

15 alts after pruning (5 fresh and 10 done)

	Pruned	Kept	Total
New	577	4	581
Fresh	2	1	3
Picked	1	4	5
Done	0	6	6
Total	580	15	595

Accuracy

100.0%

Counts

595 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	22.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	21.0%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 a x) #s(literal 1 binary64)) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
	5.8%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* a x)) 1) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) #s(literal 1/2 binary64) (/.f64 (+.f64 a (/.f64 #s(literal 1 binary64) x)) x)) x) x))) #s(literal 1 binary64))
	7.7%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (* (+ (* 1/2 (* a x)) 1) a) x) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) a)) a)) a) a))) #s(literal 1 binary64))
✓	20.9%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
✓	65.9%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
✓	61.4%	#s(approx (- (exp (* a x)) 1) (fma.f64 x a (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) x)) x)))
✓	70.9%	#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)))))
	69.6%	#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x a) #s(literal 1 binary64)) a))))
	8.8%	#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) #s(approx (+ (* -1/2 x) (/ 1 a)) (*.f64 #s(literal -1/2 binary64) x)))))
✓	64.9%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(approx (+ (* (* 1/6 x) a) 1/2) #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) (*.f64 x a)))
✓	64.9%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (*.f64 a x) a) x))
	65.1%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) a #s(literal 1/6 binary64)) (.f64 x a) #s(literal 1/2 binary64)) (*.f64 x a) #s(literal 1 binary64)) x) a))
✓	66.0%	#s(approx (- (exp (* a x)) 1) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) a #s(literal 1/2 binary64)) a) x #s(literal 1 binary64)) x) a))

Compiler

Compiled 887 to 382 computations (56.9% saved)

regimes34.0ms (0.7%)

Memory

1.8MiB live, 40.0MiB allocated

Counts

26 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`x`
100.0%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
100.0%	1	`(exp.f64 (*.f64 a x))`
100.0%	1	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes29.0ms (0.6%)

Memory

35.9MiB live, 35.9MiB allocated

Counts

23 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes19.0ms (0.4%)

Memory

-23.0MiB live, 20.8MiB allocated

Counts

11 → 2

Calls

Call 1

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

Outputs

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
65.9%	1	`a`
65.9%	1	`x`
71.1%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
71.1%	2	`(exp.f64 (*.f64 a x))`
71.1%	2	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes5.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

3 calls:

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
70.7%	2	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
70.7%	2	`(exp.f64 (*.f64 a x))`
70.7%	2	`(*.f64 a x)`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes8.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB 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 x a))
#s(approx (- (exp (* x a)) 1) (*.f64 a x))

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

Calls

5 calls:

2.0ms	a
2.0ms	x
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
65.9%	1	`a`
65.9%	1	`x`
65.9%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
65.9%	1	`(exp.f64 (*.f64 a x))`
65.9%	1	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes7.0ms (0.1%)

Memory

-28.3MiB live, 10.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
20.9%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
20.9%	1	`(exp.f64 (*.f64 a x))`
20.9%	1	`a`
20.9%	1	`x`
20.9%	1	`(*.f64 a x)`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-13.549835252170034	-7.92021522835445e-14

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-13.549835252170034	-7.92021522835445e-14

Compiler

Compiled 9 to 9 computations (0% saved)

simplify76.0ms (1.5%)

Memory

4.2MiB live, 42.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	152
1	59	152
2	80	152
3	109	152
4	136	152
5	171	152
6	256	152
7	712	152
8	1244	152
9	3374	152
10	5330	152
11	7992	152

Stop Event

1×	node limit

Calls

Call 1

Inputs
(expm1.f64 (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)))))
(if (<=.f64 (.f64 a x) #s(literal -10 binary64)) #s(approx (- (exp ( a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) #s(approx (+ (* -1/2 x) (/ 1 a)) (.f64 #s(literal -1/2 binary64) x))))) #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (*.f64 a x) a) x)))
(if (<=.f64 (.f64 a x) #s(literal -10 binary64)) #s(approx (- (exp ( a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) #s(approx (+ (* -1/2 x) (/ 1 a)) (.f64 #s(literal -1/2 binary64) x))))) #s(approx (- (exp ( a x)) 1) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))

Outputs
(expm1.f64 (*.f64 x a))
#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) a)))))
#s(approx (- (exp (* a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) (fma.f64 #s(literal -1/2 binary64) x (pow.f64 a #s(literal -1 binary64))))))
(if (<=.f64 (.f64 a x) #s(literal -10 binary64)) #s(approx (- (exp ( a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) #s(approx (+ (* -1/2 x) (/ 1 a)) (.f64 #s(literal -1/2 binary64) x))))) #s(approx (- (exp ( a x)) 1) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (*.f64 a x) a) x)))
(if (<=.f64 (.f64 a x) #s(literal -10 binary64)) #s(approx (- (exp ( a x)) 1) (/.f64 x #s(approx (/ 1 (+ (* 1/2 (* (* a a) x)) a)) #s(approx (+ (* -1/2 x) (/ 1 a)) (.f64 #s(literal -1/2 binary64) x))))) #s(approx (- (exp ( a x)) 1) (*.f64 x a)))
#s(approx (- (exp (* a x)) 1) (*.f64 x a))
(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))

soundness1.1s (20.8%)

Memory

2.3MiB live, 435.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	506	2055
1	1677	2020
2	5428	1923
0	8114	1786
0	6	13
0	9	13
1	30	13
2	152	13
0	1348	11
0	31	205
0	56	199
1	209	199
2	1346	199
0	8264	199
0	63	201
1	195	201
2	526	193
3	1045	193
4	1672	193
5	1873	193
6	1900	193
7	1920	193
8	1934	193
9	1937	193
10	1937	193
11	2619	189
12	3094	189
13	4061	189
14	4062	189
15	4062	189
16	4190	189
17	4190	189
18	6071	185
19	6279	185
20	6321	185
21	6335	185
22	6335	185
23	6511	185
24	6849	185
25	6849	185
26	7408	185
0	7408	160
0	330	1210
1	1112	1173
2	3356	1124
0	8114	1042

Stop Event

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

Compiler

Compiled 243 to 129 computations (46.9% saved)

preprocess39.0ms (0.8%)

Memory: 13.6MiB live, 51.3MiB allocated
Remove: (sort a x)
Compiler: Compiled 340 to 124 computations (63.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	36
1	42	36
2	73	34
3	108	34
4	141	34
5	165	34
6	205	34
7	227	34
8	241	34
9	252	34
10	253	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	205	34
7	227	34
8	241	34
9	252	34
10	253	34
0	6	6
0	9	6
1	17	6
2	20	6
0	20	4

start0.0ms (0%)

analyze17.0ms (0.3%)

sample741.0ms (14.4%)

explain65.0ms (1.3%)

preprocess18.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize17.0ms (0.3%)

series4.0ms (0.1%)

simplify211.0ms (4.1%)

rewrite63.0ms (1.2%)

eval16.0ms (0.3%)

prune7.0ms (0.1%)

simplify299.0ms (5.8%)

localize97.0ms (1.9%)

series30.0ms (0.6%)

simplify186.0ms (3.6%)

rewrite184.0ms (3.6%)

eval164.0ms (3.2%)

prune19.0ms (0.4%)

simplify93.0ms (1.8%)

localize76.0ms (1.5%)

series16.0ms (0.3%)

simplify154.0ms (3%)

rewrite200.0ms (3.9%)

eval132.0ms (2.6%)

prune19.0ms (0.4%)

simplify326.0ms (6.3%)

localize135.0ms (2.6%)

series16.0ms (0.3%)

simplify172.0ms (3.3%)

rewrite282.0ms (5.5%)

eval78.0ms (1.5%)

prune26.0ms (0.5%)

regimes34.0ms (0.7%)

regimes29.0ms (0.6%)

regimes19.0ms (0.4%)

regimes5.0ms (0.1%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify76.0ms (1.5%)

soundness1.1s (20.8%)

preprocess39.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	36
1	42	36
2	73	34
3	108	34
4	141	34
5	165	34
6	205	34
7	227	34
8	241	34
9	252	34
10	253	34
0	6	6
0	9	6
1	17	6
2	20	6
0	20	4