Metrics for expax (section 3.5)

start0.0ms (0%)

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

analyze17.0ms (0.8%)

Memory

26.5MiB live, 26.5MiB allocated; 0ms 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)

sample712.0ms (31.3%)

Memory

12.4MiB live, 644.1MiB allocated; 241ms collecting garbage

Samples

466.0ms	8 256×	0	valid
12.0ms	288×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 157.0ms

ival-mult: 72.0ms (45.7% of total)

ival-expm1: 51.0ms (32.4% of total)

ival->: 21.0ms (13.3% of total)

exact: 7.0ms (4.4% of total)

ival-assert: 3.0ms (1.9% of total)

adjust: 2.0ms (1.3% of total)

Bogosity

explain66.0ms (2.9%)

Memory

12.2MiB live, 65.7MiB allocated; 7ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`	cancellation	128	0
`exp.f64`	`(exp.f64 (*.f64 a x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	128	0
-	1	127

Precision

0.9922480620155039

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	0
-	1	0	127

Precision?

0.9922480620155039

Recall?

1.0

Freqs

test

number	freq
0	127
1	129

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 42 to 22 computations (47.6% saved)

Precisions

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

ival-exp: 4.0ms (34.9% of total)

ival-mult: 4.0ms (34.9% of total)

ival-expm1: 3.0ms (26.2% 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)

preprocess187.0ms (8.2%)

Memory

17.2MiB live, 149.7MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	39	36
2	76	36
3	214	36
4	966	36
0	6	6
0	9	6
1	17	6
2	35	6
3	84	6
4	297	6
5	2733	6
0	8456	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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.0%	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))

Compiler

Compiled 6 to 6 computations (0% saved)

series4.0ms (0.2%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Counts

6 → 17

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

Calls

6 calls:

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

simplify232.0ms (10.2%)

Memory

-18.5MiB live, 164.2MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	203
1	236	203
2	902	195
3	3264	195
4	6013	195
0	8041	170

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 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)))))))
a
(- (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)))))))
x

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

rewrite36.0ms (1.6%)

Memory

27.7MiB live, 27.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	9	16
1	31	16
0	212	14

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

6 → 32

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

eval5.0ms (0.2%)

Memory: 6.3MiB live, 6.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 578 to 142 computations (75.4% saved)

prune2.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	4	44

Accuracy

100.0%

Counts

44 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	80.5%	(/.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 2 binary64))) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)))
▶	20.3%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 (*.f64 x a))
▶	67.6%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 35 to 30 computations (14.3% saved)

series98.0ms (4.3%)

Memory

-4.7MiB live, 52.5MiB allocated; 74ms collecting garbage

Counts

16 → 43

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	inf	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1 (/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) 2 (- (pow (exp x) a) -1) (pow (exp x) a) (exp x) -1)
20.0ms	x	@	-inf	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1 (/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) 2 (- (pow (exp x) a) -1) (pow (exp x) a) (exp x) -1)
3.0ms	x	@	0	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1 (/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) 2 (- (pow (exp x) a) -1) (pow (exp x) a) (exp x) -1)
2.0ms	a	@	0	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1 (/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) 2 (- (pow (exp x) a) -1) (pow (exp x) a) (exp x) -1)
1.0ms	a	@	-inf	((- (exp (* a x)) 1) (* x a) x a (- (exp (* x a)) 1) (- (exp (* a x)) 1) (exp (* a x)) 1 (/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) 2 (- (pow (exp x) a) -1) (pow (exp x) a) (exp x) -1)

simplify152.0ms (6.7%)

Memory

-20.7MiB live, 111.4MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	194	774
1	722	678
2	2886	658
0	8280	581

Stop Event

1×	iter limit
1×	node limit

Counts

43 → 41

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

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

rewrite53.0ms (2.3%)

Memory

-15.8MiB live, 36.2MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	72
0	30	61
1	121	61
0	783	61

Stop Event

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

Counts

16 → 192

Calls

Call 1

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

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

eval26.0ms (1.2%)

Memory: 32.7MiB live, 32.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 4 089 to 636 computations (84.4% saved)

prune6.0ms (0.3%)

Memory

11.9MiB live, 11.9MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	200	4	204

Accuracy

100.0%

Counts

204 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.1%	(/.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) #s(literal 2 binary64)))
✓	20.3%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
✓	67.6%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 37 to 31 computations (16.2% saved)

series19.0ms (0.8%)

Memory

-23.6MiB live, 23.0MiB allocated; 3ms collecting garbage

Counts

8 → 25

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	x	@	inf	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) (* x a) x a 2 (- (pow (exp x) a) -1))
7.0ms	x	@	-inf	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) (* x a) x a 2 (- (pow (exp x) a) -1))
2.0ms	x	@	0	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) (* x a) x a 2 (- (pow (exp x) a) -1))
1.0ms	a	@	-inf	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) (* x a) x a 2 (- (pow (exp x) a) -1))
1.0ms	a	@	inf	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* x a) 2) (* x a) x a 2 (- (pow (exp x) a) -1))

simplify142.0ms (6.3%)

Memory

3.3MiB live, 93.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	159	557
1	575	453
2	2301	437
3	7753	437
0	8004	390

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 23

Calls

Call 1

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

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

rewrite62.0ms (2.7%)

Memory

-12.0MiB live, 36.6MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
0	18	40
1	70	40
0	495	40

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

8 → 57

Calls

Call 1

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

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

eval9.0ms (0.4%)

Memory: 12.0MiB live, 12.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 031 to 312 computations (84.6% saved)

prune3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	77	4	81

Accuracy

100.0%

Counts

81 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.4%	(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) x a) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) #s(literal 2 binary64)))
✓	20.3%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
✓	67.6%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 50 to 39 computations (22% saved)

series23.0ms (1%)

Memory

-20.9MiB live, 25.2MiB allocated; 3ms collecting garbage

Counts

10 → 40

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	-inf	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* (+ (* (* a a) x) a) x) 2) (* (+ (* (* a a) x) a) x) (+ (* (* a a) x) a) (* a a) a x 2 (- (pow (exp x) a) -1))
7.0ms	x	@	inf	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* (+ (* (* a a) x) a) x) 2) (* (+ (* (* a a) x) a) x) (+ (* (* a a) x) a) (* a a) a x 2 (- (pow (exp x) a) -1))
1.0ms	a	@	-inf	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* (+ (* (* a a) x) a) x) 2) (* (+ (* (* a a) x) a) x) (+ (* (* a a) x) a) (* a a) a x 2 (- (pow (exp x) a) -1))
1.0ms	a	@	inf	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* (+ (* (* a a) x) a) x) 2) (* (+ (* (* a a) x) a) x) (+ (* (* a a) x) a) (* a a) a x 2 (- (pow (exp x) a) -1))
1.0ms	a	@	0	((/ (- (exp (* (* x a) 2)) 1) (- (pow (exp x) a) -1)) (- (exp (* (* x a) 2)) 1) (* (* (+ (* (* a a) x) a) x) 2) (* (+ (* (* a a) x) a) x) (+ (* (* a a) x) a) (* a a) a x 2 (- (pow (exp x) a) -1))

simplify163.0ms (7.2%)

Memory

43.3MiB live, 131.3MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	189	686
1	709	582
2	2716	566
0	8238	508

Stop Event

1×	iter limit
1×	node limit

Counts

40 → 38

Calls

Call 1

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

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

rewrite52.0ms (2.3%)

Memory

-24.7MiB live, 26.4MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	85
0	25	85
1	98	85
0	684	81

Stop Event

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

Counts

10 → 77

Calls

Call 1

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

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

eval13.0ms (0.6%)

Memory: 16.8MiB live, 16.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 3 832 to 561 computations (85.4% saved)

prune6.0ms (0.3%)

Memory

9.6MiB live, 9.6MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	110	5	115

Accuracy

100.0%

Counts

115 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
	58.7%	(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 (fma.f64 (.f64 a a) x a) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) (fma.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(literal 2 binary64))))
	66.2%	(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 #s(approx (+ (* (* a a) x) a) (*.f64 (fma.f64 a x #s(literal 1 binary64)) a)) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) #s(literal 2 binary64)))
✓	20.3%	(-.f64 #s(approx (exp (* a x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 (*.f64 x a))
✓	67.6%	#s(approx (- (exp (* a x)) 1) (*.f64 x a))

Compiler

Compiled 264 to 132 computations (50% saved)

regimes16.0ms (0.7%)

Memory

-27.9MiB live, 18.1MiB allocated; 3ms collecting garbage

Counts

9 → 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))
(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 #s(approx (+ (* (* a a) x) a) (*.f64 (fma.f64 a x #s(literal 1 binary64)) a)) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) #s(literal 2 binary64)))
(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) x a) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) #s(literal 2 binary64)))
(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 (fma.f64 (.f64 a a) x a) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) (fma.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(literal 2 binary64))))
(expm1.f64 (*.f64 x a))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(/.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) #s(literal 2 binary64)))
(/.f64 (expm1.f64 (.f64 (.f64 x a) #s(literal 2 binary64))) (-.f64 (pow.f64 (exp.f64 x) a) #s(literal -1 binary64)))

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

Calls

5 calls:

5.0ms	a
3.0ms	x
3.0ms	(*.f64 a x)
2.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
2.0ms	(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)

regimes9.0ms (0.4%)

Memory

13.1MiB live, 13.1MiB allocated; 0ms collecting garbage

Counts

5 → 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))
(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 #s(approx (+ (* (* a a) x) a) (*.f64 (fma.f64 a x #s(literal 1 binary64)) a)) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) #s(literal 2 binary64)))
(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 (fma.f64 (*.f64 a a) x a) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) #s(literal 2 binary64)))
(/.f64 #s(approx (- (exp (* (* x a) 2)) 1) (.f64 (.f64 (fma.f64 (.f64 a a) x a) x) #s(literal 2 binary64))) #s(approx (- (pow (exp x) a) -1) (fma.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(literal 2 binary64))))

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
67.6%	1	`(*.f64 a x)`
67.6%	1	`(exp.f64 (*.f64 a x))`
67.6%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
67.6%	1	`a`
67.6%	1	`x`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes5.0ms (0.2%)

Memory

8.8MiB live, 8.8MiB 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	a
1.0ms	x
1.0ms	(*.f64 a x)
1.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
1.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
20.3%	1	`(exp.f64 (*.f64 a x))`
20.3%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
20.3%	1	`x`
20.3%	1	`(*.f64 a x)`
20.3%	1	`a`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

simplify35.0ms (1.5%)

Memory

-20.9MiB live, 25.5MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	21	22
2	43	22
3	100	22
4	329	22
5	2668	22

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations101.0ms (4.4%)

Memory

-5.9MiB live, 39.3MiB allocated; 4ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 22 to 12 computations (45.5% saved)

preprocess18.0ms (0.8%)

Memory: 25.0MiB live, 25.0MiB allocated; 0ms collecting garbage
Remove: (sort a x)
Compiler: Compiled 72 to 52 computations (27.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze17.0ms (0.8%)

sample712.0ms (31.3%)

explain66.0ms (2.9%)

preprocess187.0ms (8.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.2%)

simplify232.0ms (10.2%)

rewrite36.0ms (1.6%)

eval5.0ms (0.2%)

prune2.0ms (0.1%)

series98.0ms (4.3%)

simplify152.0ms (6.7%)

rewrite53.0ms (2.3%)

eval26.0ms (1.2%)

prune6.0ms (0.3%)

series19.0ms (0.8%)

simplify142.0ms (6.3%)

rewrite62.0ms (2.7%)

eval9.0ms (0.4%)

prune3.0ms (0.1%)

series23.0ms (1%)

simplify163.0ms (7.2%)

rewrite52.0ms (2.3%)

eval13.0ms (0.6%)

prune6.0ms (0.3%)

regimes16.0ms (0.7%)

regimes9.0ms (0.4%)

regimes5.0ms (0.2%)

simplify35.0ms (1.5%)

derivations101.0ms (4.4%)

preprocess18.0ms (0.8%)

end0.0ms (0%)

Profiling