Metrics for expax (section 3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze119.0ms (2.2%)

Memory

-15.3MiB live, 52.7MiB allocated; 120ms collecting garbage

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)

sample831.0ms (15.4%)

Memory

60.9MiB live, 595.2MiB allocated; 137ms collecting garbage

Samples

463.0ms	8 256×	0	valid
14.0ms	336×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 262.0ms

ival-expm1: 155.0ms (59.2% of total)

ival-mult: 71.0ms (27.1% of total)

ival->: 22.0ms (8.4% of total)

exact: 7.0ms (2.7% of total)

ival-assert: 4.0ms (1.5% of total)

adjust: 3.0ms (1.1% of total)

Bogosity

explain102.0ms (1.9%)

Memory

-21.3MiB live, 69.4MiB allocated; 12ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
119	-	2	(-4.4627864674736766e-66 -2.866765319731832e+63)	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
1	-	0	-	`(exp.f64 (*.f64 a x))`
0	-	0	-	`a`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(*.f64 a x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`	cancellation	117	3
`exp.f64`	`(exp.f64 (*.f64 a x))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	117	2
-	1	136

Precision

0.9915254237288136

Recall

0.9831932773109243

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	2	0
-	1	2	134

Precision?

0.9754098360655737

Recall?

1.0

Freqs

test

number	freq
0	138
1	118

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

63.0ms

512×

valid

Compiler

Compiled 42 to 22 computations (47.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-expm1: 35.0ms (69.7% of total)

ival-exp: 10.0ms (19.9% of total)

ival-mult: 4.0ms (8% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess193.0ms (3.6%)

Memory

4.9MiB live, 147.1MiB allocated; 114ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	39	36
2	73	36
3	193	36
4	778	36
5	6198	36
0	6	6
0	9	6
1	17	6
2	32	6
3	73	6
4	241	6
5	1878	6
6	5696	6
0	8242	4

Stop Event

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

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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	58.5%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 6 to 6 computations (0% saved)

simplify470.0ms (8.7%)

Memory

-9.8MiB live, 109.7MiB allocated; 888ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 a x)
cost-diff	0	(exp.f64 (*.f64 a x))
cost-diff	2	(-.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	32	16
3	73	16
4	241	16
5	1878	16
6	5696	16
0	8242	14

Stop Event

1×	iter limit
1×	node limit
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)

localize25.0ms (0.5%)

Memory

-37.2MiB live, 31.7MiB allocated; 14ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 a x)
accuracy	0.034276511951567085	(exp.f64 (*.f64 a x))
accuracy	26.541764005404655	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Samples

20.0ms

256×

valid

Compiler

Compiled 18 to 8 computations (55.6% saved)

Precisions

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

ival-mult: 9.0ms (68.8% of total)

ival-exp: 2.0ms (15.3% of total)

ival-expm1: 2.0ms (15.3% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Counts

3 → 15

Calls

Call 1

Inputs
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(exp.f64 (*.f64 a x))
(*.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) (exp (* a x)) (* a x))
1.0ms	a	@	0	((- (exp (* a x)) 1) (exp (* a x)) (* a x))
1.0ms	a	@	inf	((- (exp (* a x)) 1) (exp (* a x)) (* a x))
1.0ms	x	@	-inf	((- (exp (* a x)) 1) (exp (* a x)) (* a x))
0.0ms	a	@	-inf	((- (exp (* a x)) 1) (exp (* a x)) (* a x))

simplify247.0ms (4.6%)

Memory

15.7MiB live, 198.9MiB allocated; 29ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	201
1	236	201
2	889	193
3	3196	193
4	5768	193
0	8321	168

Stop Event

1×	iter limit
1×	node limit

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 (.f64 x x) (fma.f64 (.f64 x a) #s(literal 1/6 binary64) #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 x a #s(literal 1 binary64))
(+ 1 (* a (+ x (* 1/2 (* a (pow x 2))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #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 a a) (fma.f64 (*.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x a) x #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 (.f64 x x) (fma.f64 (.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) a 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)
(+ 1 (* x (+ a (* 1/2 (* (pow a 2) x)))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #s(literal 1 binary64))
(+ 1 (* x (+ a (* x (+ (* 1/6 (* (pow a 3) x)) (* 1/2 (pow a 2)))))))
(fma.f64 (fma.f64 (.f64 (.f64 a a) (fma.f64 (*.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x a) x #s(literal 1 binary64))

rewrite143.0ms (2.6%)

Memory

1.1MiB live, 132.7MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
0	9	13
1	31	13
2	177	13
3	1792	13
0	8079	11

Stop Event

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

Counts

3 → 384

Calls

Call 1

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

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

eval59.0ms (1.1%)

Memory: 8.6MiB live, 67.5MiB allocated; 9ms collecting garbage
Compiler: Compiled 12 018 to 1 184 computations (90.1% saved)

prune11.0ms (0.2%)

Memory

-23.6MiB live, 22.6MiB allocated; 2ms collecting garbage

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	387	8	395
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	387	9	396

Accuracy

100.0%

Counts

396 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	58.5%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
▶	22.4%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) (fma.f64 (*.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x a) x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	21.8%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
▶	22.9%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
▶	21.1%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 x a))
	61.7%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) a x) a))
	57.8%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
	63.9%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 232 to 168 computations (27.6% saved)

simplify152.0ms (2.8%)

Memory

9.1MiB live, 99.1MiB allocated; 9ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	212
0	47	212
1	94	212
2	285	212
3	1142	212
4	3344	212
5	7164	212
0	8261	212

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

localize128.0ms (2.4%)

Memory

25.2MiB live, 118.8MiB allocated; 26ms collecting garbage

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	1.1953545887324541	(fma.f64 (fma.f64 (.f64 (.f64 a a) (fma.f64 (*.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x a) x #s(literal 1 binary64))
accuracy	5.482916335163541	(fma.f64 (.f64 (.f64 a a) (fma.f64 (*.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x a)
accuracy	23.079718002186183	#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) (fma.f64 (*.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x a) x #s(literal 1 binary64)))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 (.f64 a a) (fma.f64 (*.f64 x a) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x a) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) a)
accuracy	0.1015625	(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #s(literal 1 binary64))
accuracy	23.19020892581679	#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #s(literal 1 binary64)))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.0	(fma.f64 x a #s(literal 1 binary64))
accuracy	23.411521866628295	#s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64)))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	23.471526540697493	#s(approx (exp (* a x)) #s(literal 1 binary64))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x a)
accuracy	0.01171875	(expm1.f64 (*.f64 x a))

Samples

112.0ms

256×

valid

Compiler

Compiled 155 to 26 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-mult: 70.0ms (78.9% of total)

ival-add: 7.0ms (7.9% of total)

ival-expm1: 6.0ms (6.8% of total)

const: 3.0ms (3.4% of total)

ival-exp: 2.0ms (2.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Counts

16 → 59

Calls

Call 1

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

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

Calls

6 calls:

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

simplify179.0ms (3.3%)

Memory

-11.9MiB live, 177.4MiB allocated; 23ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	212	869
1	774	849
2	3243	801
0	8633	731

Stop Event

1×	iter limit
1×	node limit

Counts

59 → 58

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

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

rewrite182.0ms (3.4%)

Memory

12.7MiB live, 154.6MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	172
0	47	172
1	218	172
2	1668	172
0	8438	172

Stop Event

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

Counts

16 → 291

Calls

Call 1

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

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

eval56.0ms (1%)

Memory: -17.6MiB live, 71.7MiB allocated; 10ms collecting garbage
Compiler: Compiled 17 440 to 1 799 computations (89.7% saved)

prune12.0ms (0.2%)

Memory

25.9MiB live, 25.9MiB allocated; 0ms collecting garbage

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	362	7	369
Fresh	2	1	3
Picked	1	4	5
Done	0	1	1
Total	365	13	378

Accuracy

100.0%

Counts

378 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	58.5%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
▶	23.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 a x) (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 a x) #s(literal 1/2 binary64)) a) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	21.8%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	22.9%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
	3.9%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) x) x))) #s(literal 1 binary64))
▶	4.2%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
▶	20.5%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) (-.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) a))))) #s(literal 1 binary64))
✓	21.1%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
	61.7%	#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a))
	63.1%	#s(approx (- (exp (* x a)) 1) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 a x) #s(literal 1 binary64)) a) x))
▶	63.9%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
▶	57.8%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))

Compiler

Compiled 401 to 281 computations (29.9% saved)

simplify152.0ms (2.8%)

Memory

-26.9MiB live, 113.4MiB allocated; 18ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	368
0	73	366
1	134	366
2	334	363
3	1130	363
4	3346	356
5	7531	356
0	8094	345

Stop Event

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

Calls

Call 1

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

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

localize95.0ms (1.8%)

Memory

10.9MiB live, 101.6MiB allocated; 8ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(fma.f64 #s(literal 1/6 binary64) (*.f64 a x) #s(literal 1/2 binary64))
accuracy	1.1953545887324541	(fma.f64 (fma.f64 (.f64 a x) (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 a x) #s(literal 1/2 binary64)) a) a) x #s(literal 1 binary64))
accuracy	23.079718002186183	#s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 a x) (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 a x) #s(literal 1/2 binary64)) a) a) x #s(literal 1 binary64)))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 a x) (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 a x) #s(literal 1/2 binary64)) a) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	11.442431750223802	(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a)
accuracy	23.19020892581679	#s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a)))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
accuracy	39.995278467378576	#s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))
accuracy	0.0078125	(-.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) a))
accuracy	0.09765625	(*.f64 (neg.f64 a) (-.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) a)))
accuracy	23.411521866628295	#s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) (-.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) a)))))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) (-.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) a))))) #s(literal 1 binary64))
accuracy	0.0078125	(fma.f64 (.f64 (.f64 a a) x) #s(literal 1/2 binary64) a)
accuracy	0.9626661389975781	(.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x)
accuracy	7.350069367926369	(.f64 (.f64 a a) x)
accuracy	23.60858416368618	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a a) x) #s(literal 1/2 binary64) a) x))
accuracy	0.0	(*.f64 a x)
accuracy	23.08035066065367	#s(approx (- (exp (* x a)) 1) (*.f64 a x))

Samples

72.0ms

256×

valid

Compiler

Compiled 224 to 41 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 28.0ms (53.2% of total)

ival-add: 9.0ms (17.1% of total)

ival-div: 4.0ms (7.6% of total)

ival-expm1: 3.0ms (5.7% of total)

const: 3.0ms (5.7% of total)

ival-exp: 2.0ms (3.8% of total)

ival-neg: 2.0ms (3.8% of total)

ival-sub: 1.0ms (1.9% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series17.0ms (0.3%)

Memory

20.5MiB live, 20.6MiB allocated; 0ms collecting garbage

Counts

20 → 77

Calls

Call 1

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

Calls

6 calls:

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

simplify251.0ms (4.6%)

Memory

6.3MiB live, 191.7MiB allocated; 45ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	241	998
1	909	978
2	3651	966
0	8619	883

Stop Event

1×	iter limit
1×	node limit

Counts

77 → 75

Calls

Call 1

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

rewrite192.0ms (3.5%)

Memory

-27.7MiB live, 158.4MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	304
0	73	304
1	300	304
2	2093	304
0	8216	291

Stop Event

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

Counts

20 → 279

Calls

Call 1

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

Outputs
#s(approx (- (exp (* x a)) 1) (*.f64 a x))
(.f64 (.f64 a x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 a x))
(.f64 a (.f64 x #s(literal 1 binary64)))
(*.f64 a x)
(.f64 x (.f64 a #s(literal 1 binary64)))
(*.f64 x a)
(fma.f64 (*.f64 a x) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 a x) #s(literal 0 binary64))
(fma.f64 a (*.f64 x #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 a x #s(literal 0 binary64))
(fma.f64 x (*.f64 a #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 x a #s(literal 0 binary64))
(-.f64 (log.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 a x)) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 a x)) #s(literal 3 binary64)))) (log.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 a x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 a x)) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 a x)) (sinh.f64 (*.f64 a x)))))))
(-.f64 #s(literal 0 binary64) (log.f64 (exp.f64 (neg.f64 (*.f64 a x)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 x) (/.f64 a #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 x) (/.f64 a #s(literal 2 binary64)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 a) (/.f64 x #s(literal 2 binary64)))))
(+.f64 #s(literal 0 binary64) (*.f64 a x))
(+.f64 (*.f64 a x) #s(literal 0 binary64))
(log.f64 (pow.f64 (exp.f64 x) a))
#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) x) a) x))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) x) a) x)
(.f64 x (fma.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) x) a))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (.f64 (.f64 a a) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 a) a)) x)) (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) x)) a)))
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(+.f64 a (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 a x) #s(literal 1/2 binary64)) a) a) x))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 a #s(literal -2 binary64))))) (neg.f64 (neg.f64 (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x))) (.f64 (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x)) (pow.f64 a #s(literal -2 binary64)))) (.f64 (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x)) (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x))))
(/.f64 (-.f64 (.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64))))) (.f64 (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64)))) (pow.f64 a #s(literal -3 binary64)))) (*.f64 (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64)))) (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 a #s(literal -2 binary64)))) (neg.f64 (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64))))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 a #s(literal -2 binary64))) (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (pow.f64 a #s(literal -3 binary64))) (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x))) (/.f64 (pow.f64 a #s(literal -2 binary64)) (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x))))
(-.f64 (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64))))) (/.f64 (pow.f64 a #s(literal -3 binary64)) (fma.f64 x x (fma.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x) (pow.f64 a #s(literal -2 binary64))))))
(-.f64 (neg.f64 x) (pow.f64 a #s(literal -1 binary64)))
(+.f64 (/.f64 (.f64 x x) (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x))) (/.f64 (.f64 (neg.f64 (pow.f64 a #s(literal -1 binary64))) (pow.f64 a #s(literal -1 binary64))) (+.f64 (pow.f64 a #s(literal -1 binary64)) (neg.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (.f64 a x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) (*.f64 a x)) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64)))) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64)))) #s(literal 1/8 binary64))) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64)))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (.f64 a x))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (.f64 (*.f64 a x) #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (.f64 (*.f64 a x) #s(literal 1/12 binary64)))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 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 #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 x #s(literal 1/6 binary64)) #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 #s(literal 1/6 binary64) (.f64 a x)))) (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (.f64 a x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 #s(literal 1/6 binary64) a)) x))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 a x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 a x)) #s(literal 1/6 binary64)))
(+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (.f64 (.f64 a x) #s(literal 1/12 binary64))))) (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (.f64 (.f64 a x) #s(literal 1/12 binary64))))))
(+.f64 (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (.f64 (.f64 a x) #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64))) (.f64 (.f64 a x) #s(literal 1/12 binary64))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64))))) (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64))))))
(+.f64 (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 a x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 a x) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 a x) #s(literal 1/12 binary64))))))
(+.f64 (.f64 #s(literal 1/6 binary64) (.f64 a x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (.f64 a x)))

eval66.0ms (1.2%)

Memory: 2.3MiB live, 99.3MiB allocated; 15ms collecting garbage
Compiler: Compiled 14 934 to 1 786 computations (88% saved)

prune11.0ms (0.2%)

Memory

30.6MiB live, 30.6MiB allocated; 0ms collecting garbage

Pruning

13 alts after pruning (4 fresh and 9 done)

	Pruned	Kept	Total
New	365	2	367
Fresh	1	2	3
Picked	1	4	5
Done	0	5	5
Total	367	13	380

Accuracy

100.0%

Counts

380 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	58.5%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
✓	23.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 a x) (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 a x) #s(literal 1/2 binary64)) a) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	21.8%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	22.9%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
▶	3.9%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) x) x))) #s(literal 1 binary64))
✓	4.2%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
✓	20.5%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) (-.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) a))))) #s(literal 1 binary64))
▶	19.2%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) #s(approx (- (neg x) (/ 1 a)) (/.f64 #s(literal -1 binary64) a))))) #s(literal 1 binary64))
✓	21.1%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
▶	61.7%	#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a))
✓	63.9%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
▶	63.1%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))

Compiler

Compiled 233 to 165 computations (29.2% saved)

simplify122.0ms (2.2%)

Memory

6.6MiB live, 147.3MiB allocated; 20ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	352
0	72	348
1	139	348
2	394	345
3	1444	345
4	3851	339
0	8350	329

Stop Event

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

Calls

Call 1

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

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

localize134.0ms (2.5%)

Memory

4.2MiB live, 141.2MiB allocated; 10ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	11.488120997192313	(.f64 (fma.f64 (.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) x)
accuracy	23.19020892581679	#s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) x) x)))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) x) x))) #s(literal 1 binary64))
accuracy	39.995278467378576	#s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) x) x))
accuracy	0.09765625	(*.f64 (neg.f64 a) #s(approx (- (neg x) (/ 1 a)) (/.f64 #s(literal -1 binary64) a)))
accuracy	23.411521866628295	#s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) #s(approx (- (neg x) (/ 1 a)) (/.f64 #s(literal -1 binary64) a)))))
accuracy	23.85897640928837	#s(approx (- (neg x) (/ 1 a)) (/.f64 #s(literal -1 binary64) a))
accuracy	26.541764005404655	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) #s(approx (- (neg x) (/ 1 a)) (/.f64 #s(literal -1 binary64) a))))) #s(literal 1 binary64))
accuracy	0.359375	(*.f64 #s(literal 1/6 binary64) a)
accuracy	1.4208937388093605	(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a)
accuracy	3.2279004369893056	(fma.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x)
accuracy	22.73740299911298	#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64))) a x) a))
accuracy	0.0078125	(fma.f64 (.f64 (.f64 a x) a) #s(literal 1/2 binary64) a)
accuracy	0.140625	(.f64 (.f64 a x) a)
accuracy	0.9626661389975781	(.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x)
accuracy	23.60858416368618	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))

Samples

109.0ms

256×

valid

Compiler

Compiled 209 to 43 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-mult: 67.0ms (72.2% of total)

ival-add: 8.0ms (8.6% of total)

ival-div: 5.0ms (5.4% of total)

const: 4.0ms (4.3% of total)

ival-expm1: 3.0ms (3.2% of total)

ival-exp: 2.0ms (2.2% of total)

ival-neg: 2.0ms (2.2% of total)

ival-sub: 1.0ms (1.1% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series57.0ms (1.1%)

Memory

-24.5MiB live, 31.7MiB allocated; 54ms collecting garbage

Counts

18 → 71

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	a	@	inf	((- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* x a)) 1) (* (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) a) (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) (* (* x x) (+ (* (* 1/6 a) x) 1/2)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (* (neg a) (- (neg x) (/ 1 a))) (* (+ (* (* a a) 1/2) (/ a x)) x) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (* 1/6 a) (- (neg x) (/ 1 a)))
18.0ms	a	@	-inf	((- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* x a)) 1) (* (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) a) (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) (* (* x x) (+ (* (* 1/6 a) x) 1/2)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (* (neg a) (- (neg x) (/ 1 a))) (* (+ (* (* a a) 1/2) (/ a x)) x) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (* 1/6 a) (- (neg x) (/ 1 a)))
3.0ms	x	@	-inf	((- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* x a)) 1) (* (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) a) (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) (* (* x x) (+ (* (* 1/6 a) x) 1/2)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (* (neg a) (- (neg x) (/ 1 a))) (* (+ (* (* a a) 1/2) (/ a x)) x) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (* 1/6 a) (- (neg x) (/ 1 a)))
2.0ms	a	@	0	((- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* x a)) 1) (* (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) a) (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) (* (* x x) (+ (* (* 1/6 a) x) 1/2)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (* (neg a) (- (neg x) (/ 1 a))) (* (+ (* (* a a) 1/2) (/ a x)) x) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (* 1/6 a) (- (neg x) (/ 1 a)))
2.0ms	x	@	inf	((- (exp (* a x)) 1) (* (+ (* (* (* a x) a) 1/2) a) x) (+ (* (* (* a x) a) 1/2) a) (* (* a x) a) (- (exp (* x a)) 1) (* (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) a) (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) (* (* x x) (+ (* (* 1/6 a) x) 1/2)) (- (exp (* a x)) 1) (exp (* a x)) (+ (* x a) 1) (* (neg a) (- (neg x) (/ 1 a))) (* (+ (* (* a a) 1/2) (/ a x)) x) (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (* 1/6 a) (- (neg x) (/ 1 a)))

simplify201.0ms (3.7%)

Memory

17.3MiB live, 200.8MiB allocated; 27ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	213	867
1	805	835
2	3217	800
0	8657	727

Stop Event

1×	iter limit
1×	node limit

Counts

71 → 69

Calls

Call 1

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

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

rewrite196.0ms (3.6%)

Memory

-24.2MiB live, 209.9MiB allocated; 48ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	295
0	72	295
1	284	295
2	1947	295
0	9003	282

Stop Event

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

Counts

18 → 273

Calls

Call 1

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

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

eval40.0ms (0.7%)

Memory: 15.1MiB live, 60.0MiB allocated; 4ms collecting garbage
Compiler: Compiled 13 305 to 1 403 computations (89.5% saved)

prune15.0ms (0.3%)

Memory

29.7MiB live, 29.7MiB allocated; 0ms collecting garbage

Pruning

15 alts after pruning (4 fresh and 11 done)

	Pruned	Kept	Total
New	314	4	318
Fresh	0	0	0
Picked	1	3	4
Done	1	8	9
Total	316	15	331

Accuracy

100.0%

Counts

331 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	58.5%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
✓	23.2%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 a x) (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 a x) #s(literal 1/2 binary64)) a) a) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	21.8%	(-.f64 #s(approx (exp (* a x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) x #s(literal 1 binary64)) (.f64 x a) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	22.9%	(-.f64 #s(approx (exp (* a x)) (fma.f64 x a #s(literal 1 binary64))) #s(literal 1 binary64))
✓	3.9%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) #s(literal 1/2 binary64) (/.f64 a x)) x) x))) #s(literal 1 binary64))
✓	4.2%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (/.f64 x a)) a) a))) #s(literal 1 binary64))
	20.5%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) (-.f64 (/.f64 #s(literal -1 binary64) a) x)))) #s(literal 1 binary64))
✓	19.2%	(-.f64 #s(approx (exp (* a x)) #s(approx (+ (* x a) 1) (*.f64 (neg.f64 a) #s(approx (- (neg x) (/ 1 a)) (/.f64 #s(literal -1 binary64) a))))) #s(literal 1 binary64))
✓	21.1%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
	64.5%	#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 (.f64 x a) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64)) x) x) a))
	47.2%	#s(approx (- (exp (* x a)) 1) (.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (.f64 a (.f64 x x)) (fma.f64 (*.f64 #s(literal 1/6 binary64) a) x #s(literal 1/2 binary64)))) a))
✓	63.9%	#s(approx (- (exp (* x a)) 1) (*.f64 a x))
	63.0%	#s(approx (- (exp (* a x)) 1) (fma.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) a) x) a) x (.f64 x a)))
✓	63.1%	#s(approx (- (exp (* a x)) 1) (.f64 (fma.f64 (.f64 (*.f64 a x) a) #s(literal 1/2 binary64) a) x))

Compiler

Compiled 687 to 319 computations (53.6% saved)

regimes29.0ms (0.5%)

Memory

2.5MiB live, 49.0MiB allocated; 3ms collecting garbage

Counts

22 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes29.0ms (0.5%)

Memory

-12.7MiB live, 41.0MiB allocated; 8ms collecting garbage

Counts

20 → 1

Calls

Call 1

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

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

Calls

5 calls:

10.0ms	x
5.0ms	a
5.0ms	(*.f64 a x)
4.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
4.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
64.5%	1	`(*.f64 a x)`
64.5%	1	`(exp.f64 (*.f64 a x))`
64.5%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
64.5%	1	`a`
64.5%	1	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes28.0ms (0.5%)

Memory

-26.2MiB live, 20.6MiB allocated; 2ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

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

Calls

5 calls:

14.0ms	x
4.0ms	a
3.0ms	(*.f64 a x)
3.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
3.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
63.9%	1	`(*.f64 a x)`
63.9%	1	`a`
63.9%	1	`x`
63.9%	1	`(exp.f64 (*.f64 a x))`
63.9%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes5.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
21.1%	1	`(*.f64 a x)`
21.1%	1	`(exp.f64 (*.f64 a x))`
21.1%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
21.1%	1	`a`
21.1%	1	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

simplify46.0ms (0.9%)

Memory

3.6MiB live, 48.4MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	38	44
2	58	44
3	104	44
4	290	44
5	2120	44
6	5431	44

Stop Event

1×	node limit

Calls

Call 1

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

derivations683.0ms (12.6%)

Memory

29.4MiB live, 409.9MiB allocated; 52ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	295
0	72	295
1	284	295
2	1947	295
0	9003	282
0	212	869
1	774	849
2	3243	801
0	8633	731
0	63	201
1	236	201
2	889	193
3	3196	193
4	5768	193
0	8321	168
0	6	13
0	9	13
1	31	13
2	177	13
3	1792	13
0	8079	11

Stop Event

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

Compiler

Compiled 44 to 22 computations (50% saved)

preprocess113.0ms (2.1%)

Memory: 2.5MiB live, 93.3MiB allocated; 17ms collecting garbage
Remove: (sort a x)
Compiler: Compiled 124 to 80 computations (35.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze119.0ms (2.2%)

sample831.0ms (15.4%)

explain102.0ms (1.9%)

preprocess193.0ms (3.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify470.0ms (8.7%)

localize25.0ms (0.5%)

series4.0ms (0.1%)

simplify247.0ms (4.6%)

rewrite143.0ms (2.6%)

eval59.0ms (1.1%)

prune11.0ms (0.2%)

simplify152.0ms (2.8%)

localize128.0ms (2.4%)

series12.0ms (0.2%)

simplify179.0ms (3.3%)

rewrite182.0ms (3.4%)

eval56.0ms (1%)

prune12.0ms (0.2%)

simplify152.0ms (2.8%)

localize95.0ms (1.8%)

series17.0ms (0.3%)

simplify251.0ms (4.6%)

rewrite192.0ms (3.5%)

eval66.0ms (1.2%)

prune11.0ms (0.2%)

simplify122.0ms (2.2%)

localize134.0ms (2.5%)

series57.0ms (1.1%)

simplify201.0ms (3.7%)

rewrite196.0ms (3.6%)

eval40.0ms (0.7%)

prune15.0ms (0.3%)

regimes29.0ms (0.5%)

regimes29.0ms (0.5%)

regimes28.0ms (0.5%)

regimes5.0ms (0.1%)

simplify46.0ms (0.9%)

derivations683.0ms (12.6%)

preprocess113.0ms (2.1%)

end0.0ms (0%)

Profiling