Metrics for expm1 (example 3.7)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample468.0ms (8.9%)

Memory

21.1MiB live, 527.6MiB allocated

Samples

291.0ms

8 256×

valid

Precisions

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

ival-expm1: 76.0ms (48.4% of total)

ival-fabs: 50.0ms (31.8% of total)

ival-<=: 24.0ms (15.3% of total)

exact: 4.0ms (2.5% of total)

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

Bogosity

explain62.0ms (1.2%)

Memory

-26.2MiB live, 91.1MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	253	0

Confusion

	Predicted +	Predicted -
+	253	0
-	0	3

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	253	0	0
-	0	0	3

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	3
1	253

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms

512×

valid

Compiler

Compiled 25 to 16 computations (36% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-exp: 4.0ms (50.2% of total)

ival-expm1: 3.0ms (37.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess14.0ms (0.3%)

Memory

27.1MiB live, 27.1MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`sub-neg`
18×	`+-commutative`
10×	`*-commutative`
10×	`associate--r+`
8×	`--rgt-identity`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	17	11
2	35	10
3	54	10
4	70	10
5	90	10
6	108	10
7	123	10
8	135	10
9	137	10
0	4	4
0	6	4
1	11	4
2	12	4
0	12	2

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.7%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory

-32.8MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

4×	`lower-+.f64`
4×	`lower-+.f32`
2×	`lower-expm1.f64`
2×	`lift-exp.f64`
2×	`lower-expm1.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	11	8
2	12	8
0	12	6

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize14.0ms (0.3%)

Memory

27.5MiB live, 27.5MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(exp.f64 x)
accuracy	58.46224290163754	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

9.0ms

256×

valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-exp: 2.0ms (50.4% of total)

ival-expm1: 2.0ms (50.4% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())

Inputs

#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())

#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify23.0ms (0.4%)

Memory

-3.1MiB live, 36.1MiB allocated

Algorithm

1×	egg-herbie

Rules

1 308×	`lower-fma.f64`
1 308×	`lower-fma.f32`
364×	`lower-*.f64`
364×	`lower-*.f32`
308×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	108
1	77	108
2	168	108
3	371	108
4	587	108
5	718	108
6	723	108
0	723	81

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 23

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)

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

rewrite101.0ms (1.9%)

Memory

-19.4MiB live, 72.0MiB allocated

Rules

594×	`lower-fma.f64`
594×	`lower-fma.f32`
574×	`lower-/.f64`
574×	`lower-/.f32`
536×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
0	6	6
1	24	6
2	130	6
0	1143	4

Stop Event

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

Counts

2 → 84

Calls

Call 1

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

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

eval12.0ms (0.2%)

Memory: 15.2MiB live, 15.2MiB allocated
Compiler: Compiled 1 895 to 241 computations (87.3% saved)

prune45.0ms (0.9%)

Memory

-8.7MiB live, 29.8MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	8	108

Accuracy

100.0%

Counts

108 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.7%	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
	7.5%	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
	7.2%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	5.6%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 x)
▶	99.2%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x))
▶	99.0%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
▶	98.7%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))

Compiler

Compiled 146 to 82 computations (43.8% saved)

simplify23.0ms (0.4%)

Memory

-7.8MiB live, 30.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

1 068×	`lower-fma.f32`
1 056×	`lower-fma.f64`
336×	`lower-*.f32`
332×	`lower-*.f64`
236×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	110
0	36	110
1	65	110
2	106	110
3	194	110
4	405	110
5	480	110
6	617	110
7	618	110
0	618	110

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize73.0ms (1.4%)

Memory

20.8MiB live, 98.6MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.015625	(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
accuracy	0.3678433013091696	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x))
accuracy	0	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
accuracy	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.490784298067508	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
accuracy	0	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.6775490988874917	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
accuracy	1.2204518737994654	#s(approx (exp x) #s(literal 1 binary64))
accuracy	58.45443040163754	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(expm1.f64 x)

Samples

51.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 96 to 23 computations (76% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 13.0ms (37.4% of total)

ival-add: 10.0ms (28.8% of total)

const: 6.0ms (17.3% of total)

ival-exp: 2.0ms (5.8% of total)

ival-expm1: 2.0ms (5.8% 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)

series14.0ms (0.3%)

Memory

-24.5MiB live, 11.8MiB allocated

Counts

14 → 168

Calls

Call 1

Inputs
#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (patch #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (patch (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x)) (patch #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) (patch (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) (taylor 0 x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (expm1.f64 x) (patch (expm1.f64 x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- (exp x) 1) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (patch (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (patch #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (patch #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (patch #s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) (patch (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) (patch (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) (patch (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) (patch (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) (patch (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/6 x)) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (+ 1/6 (* 1/24 x)))) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (+ 1/6 (* 1/24 x)))) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/6 (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/6 (* 1/24 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/6 (* 1/24 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/6 (* 1/24 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())

Calls

42 calls:

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

simplify253.0ms (4.8%)

Memory

26.5MiB live, 255.7MiB allocated

Algorithm

1×	egg-herbie

Rules

20 252×	`lower-fma.f64`
20 252×	`lower-fma.f32`
3 310×	`lower-*.f64`
3 310×	`lower-*.f32`
1 700×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	946
1	236	946
2	617	942
3	1658	942
4	5005	934
0	8389	746

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 160

Calls

Call 1

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

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

rewrite295.0ms (5.6%)

Memory

0.7MiB live, 313.6MiB allocated

Rules

5 760×	`lower-fma.f32`
5 748×	`lower-fma.f64`
4 798×	`lower-*.f32`
4 794×	`lower-*.f64`
4 554×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	96
0	36	96
1	159	96
2	1163	96
0	8221	96

Stop Event

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

Counts

14 → 369

Calls

Call 1

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

Outputs
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) #s(literal -1 binary64))))))
(expm1.f64 x)
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 x) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))) (expm1.f64 (.f64 x #s(literal 3 binary64)))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal -1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (.f64 #s(literal -1 binary64) (exp.f64 x)))))
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(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/144 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 x #s(literal 1/144 binary64))))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal -1/36 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/144 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal -1/36 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)))))
(.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))

eval79.0ms (1.5%)

Memory: 6.1MiB live, 123.1MiB allocated
Compiler: Compiled 14 372 to 1 277 computations (91.1% saved)

prune214.0ms (4.1%)

Memory

-142.6MiB live, 146.6MiB allocated

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	541	6	547
Fresh	0	3	3
Picked	1	4	5
Done	0	0	0
Total	542	13	555

Accuracy

100.0%

Counts

555 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.7%	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
	7.5%	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
▶	7.2%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	5.6%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
✓	99.0%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
▶	99.2%	#s(approx (- (exp x) 1) (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x x))
✓	98.7%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
	46.4%	#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
▶	99.0%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
▶	98.6%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
▶	99.2%	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x))))
	6.2%	#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))

Compiler

Compiled 301 to 149 computations (50.5% saved)

simplify23.0ms (0.4%)

Memory

34.0MiB live, 34.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x x)
cost-diff	0	#s(approx (- (exp x) 1) (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x x))
cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
cost-diff	0	(+.f64 x #s(literal 1 binary64))
cost-diff	0	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	0	(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))
cost-diff	0	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x))))
cost-diff	960	(fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x))

Rules

1 072×	`lower-fma.f32`
1 056×	`lower-fma.f64`
340×	`lower-*.f32`
326×	`lower-*.f64`
240×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	260
0	59	250
1	116	238
2	220	230
3	408	230
4	598	230
5	685	230
6	685	230
0	685	222

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize107.0ms (2%)

Memory

9.5MiB live, 164.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
accuracy	0.015625	(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
accuracy	0.0234375	(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
accuracy	0.3678433013091696	#s(approx (- (exp x) 1) (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x x))
accuracy	0	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
accuracy	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy	0.015625	(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
accuracy	0.490784298067508	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
accuracy	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
accuracy	0.01171875	(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
accuracy	0.6775490988874917	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0.7120049563434541	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
accuracy	58.45443040163754	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.02734375	(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
accuracy	0.04296875	(.f64 (.f64 x (*.f64 x x)) x)
accuracy	0.0625	(.f64 x (.f64 x x))
accuracy	0.3678433013091696	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x))))

Samples

68.0ms	254×	0	valid
1.0ms	1×	5	exit
1.0ms	1×	2	valid

Compiler

Compiled 195 to 34 computations (82.6% saved)

Precisions

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

ival-mult: 31.0ms (58.8% of total)

ival-add: 10.0ms (19% of total)

const: 6.0ms (11.4% of total)

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

ival-expm1: 2.0ms (3.8% 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)

series16.0ms (0.3%)

Memory

-18.0MiB live, 20.4MiB allocated

Counts

21 → 252

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 4)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x)))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) (patch (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) (patch #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x)))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (.f64 (.f64 x (.f64 x x)) x) (patch (.f64 (.f64 x (.f64 x x)) x) #<representation binary64>) () ())) ())
#s(alt 1/6 (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/6 (* 1/24 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/6 (* 1/24 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/6 (* 1/24 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (patch (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())

Calls

63 calls:

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

simplify211.0ms (4%)

Memory

5.2MiB live, 206.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 634×	`lower-fma.f64`
12 634×	`lower-fma.f32`
3 598×	`lower-*.f64`
3 598×	`lower-*.f32`
1 250×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	1524
1	297	1520
2	775	1520
3	2673	1508
4	6622	1508
0	8425	1234

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 240

Calls

Call 1

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

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

rewrite286.0ms (5.4%)

Memory

-6.5MiB live, 306.6MiB allocated

Rules

5 900×	`lower-fma.f32`
5 884×	`lower-fma.f64`
4 194×	`lower-/.f64`
4 194×	`lower-/.f32`
3 926×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	226
0	59	214
1	251	206
2	1786	206
0	8193	198

Stop Event

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

Counts

21 → 570

Calls

Call 1

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

Outputs
(+.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))))
(+.f64 (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
(+.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x))) x))
(+.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
(+.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) x)
(-.f64 (/.f64 (.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (-.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x))) (/.f64 (.f64 (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x)) (-.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x))))
(-.f64 (/.f64 (.f64 (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x)) (-.f64 (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)))) (/.f64 (.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (-.f64 (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)))))
(-.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))) (-.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) x)))
(fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x))
(fma.f64 x #s(literal 1 binary64) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))) x)
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x))
(fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x))
(fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x))
(fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/24 binary64)) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x))
(fma.f64 #s(literal 1 binary64) x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))))
(fma.f64 #s(literal 1 binary64) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)))
(fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) (neg.f64 x))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x))
(fma.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) (neg.f64 x)))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/24 binary64) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x))
(fma.f64 (fma.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))))) x)
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))) x)
(fma.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64)) x (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)))
(fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x))) x))
(fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) x))
(fma.f64 (.f64 x (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) x) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
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(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 x #s(literal 1/144 binary64))))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal -1/36 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (*.f64 x #s(literal 1/144 binary64)))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal -1/36 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)))))
(.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))

eval150.0ms (2.8%)

Memory: 27.1MiB live, 181.1MiB allocated
Compiler: Compiled 24 472 to 1 922 computations (92.1% saved)

prune167.0ms (3.2%)

Memory

-26.1MiB live, 210.3MiB allocated

Pruning

14 alts after pruning (5 fresh and 9 done)

	Pruned	Kept	Total
New	850	3	853
Fresh	2	2	4
Picked	0	5	5
Done	0	4	4
Total	852	14	866

Accuracy

100.0%

Counts

866 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.7%	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
▶	7.5%	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	7.2%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	5.6%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
✓	99.0%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	99.2%	#s(approx (- (exp x) 1) (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x x))
✓	98.7%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
▶	46.4%	#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
✓	99.0%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
✓	98.6%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
▶	97.8%	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64)) x))
▶	99.2%	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))))
✓	99.2%	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x))))

Compiler

Compiled 312 to 146 computations (53.2% saved)

simplify214.0ms (4.1%)

Memory

21.1MiB live, 255.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
cost-diff	128	(-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
cost-diff	448	(-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
cost-diff	3904	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64)) x))
cost-diff	0	(.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -1 binary64)) x)
cost-diff	0	#s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x))))))
cost-diff	0	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))))
cost-diff	3776	(fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))

Rules

12 316×	`lower-fma.f32`
12 296×	`lower-fma.f64`
4 564×	`lower-*.f32`
4 542×	`lower-*.f64`
2 582×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	554
0	86	526
1	183	518
2	463	501
3	2000	501
4	4654	413
0	8244	398

Stop Event

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

Calls

Call 1

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

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

localize177.0ms (3.4%)

Memory

-0.5MiB live, 228.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.04296875	(.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
accuracy	0.078125	(.f64 (.f64 x x) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
accuracy	0.3678433013091696	#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
accuracy	33.76262862183539	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
accuracy	0	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
accuracy	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy	0.4048551315065115	#s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	58.45443040163754	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
accuracy	0.5227846303097173	#s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	58.45443040163754	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.015625	(.f64 #s(approx (+ ( x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64)) x)
accuracy	0.490784298067508	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64)) x))
accuracy	1.1818083351453241	#s(approx (+ (* x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64))
accuracy	0.05078125	(.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))
accuracy	0.0625	(.f64 x (.f64 x x))
accuracy	0.109375	(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
accuracy	0.3678433013091696	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))))

Samples

100.0ms	254×	0	valid
2.0ms	1×	5	exit
1.0ms	1×	2	valid

Compiler

Compiled 432 to 46 computations (89.4% saved)

Precisions

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

ival-mult: 40.0ms (55.2% of total)

ival-add: 12.0ms (16.6% of total)

ival-div: 7.0ms (9.7% of total)

const: 6.0ms (8.3% of total)

ival-exp: 2.0ms (2.8% of total)

ival-sub: 2.0ms (2.8% of total)

ival-expm1: 2.0ms (2.8% of total)

adjust: 1.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series22.0ms (0.4%)

Memory

-0.2MiB live, 38.1MiB allocated

Counts

25 → 300

Calls

Call 1

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

Outputs
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#s(alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) (patch (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))))))) (patch #s(approx (- (exp x) 1) #s(approx (+ ( (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x))))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x))))) (taylor inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (patch (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (patch (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 1/576 (pow x 8)) (taylor -inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (patch (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x)))) (taylor -inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (patch (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x))))) (taylor -inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (patch (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x)))) (taylor -inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (patch (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())

Calls

75 calls:

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

simplify209.0ms (4%)

Memory

25.4MiB live, 261.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 662×	`lower-fma.f64`
11 662×	`lower-fma.f32`
4 310×	`lower-*.f64`
4 310×	`lower-*.f32`
2 684×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	247	2242
1	780	2226
2	2080	2181
3	5791	2173
0	8310	1917

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 290

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(* -1 x)
(* x (- (* 1/4 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/4 (* 1/6 x))) 1))
(* x (- (* (pow x 2) (+ 1/4 (* x (+ 1/6 (* 1/36 x))))) 1))
(* 1/36 (pow x 5))
(* (pow x 5) (+ 1/36 (* 1/6 (/ 1 x))))
(* (pow x 5) (+ 1/36 (+ (/ 1/4 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 5) (- (+ 1/36 (+ (/ 1/4 (pow x 2)) (* 1/6 (/ 1 x)))) (/ 1 (pow x 4))))
(* 1/36 (pow x 5))
(* (pow x 5) (+ 1/36 (* 1/6 (/ 1 x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/4 (/ 1 x))) x)) 1/36)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/6 (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x))) x)) 1/36)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* -1/6 x) 1/4))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* x (- (* -5/72 x) 1/6)) 1/4))))
(* -1/576 (pow x 8))
(* -1 (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x)))))
(* (pow x 8) (- (* -1 (/ (+ 1/72 (* 5/72 (/ 1 x))) x)) 1/576))
(* (pow x 8) (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) (pow x 2))) (+ 1/576 (* 1/72 (/ 1 x)))))
(* -1/576 (pow x 8))
(* -1 (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x)))))
(* (pow x 8) (- (* -1 (/ (+ 1/72 (* 5/72 (/ 1 x))) x)) 1/576))
(* (pow x 8) (- (* -1 (/ (+ 1/72 (+ (/ 1/6 (pow x 2)) (* 5/72 (/ 1 x)))) x)) 1/576))
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* -1/6 x) 1/2))))
(* x (+ 1 (* x (- (* x (- (* -1/24 x) 1/6)) 1/2))))
(* -1/24 (pow x 4))
(* -1 (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x)))))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))
(* (pow x 4) (- (/ 1 (pow x 3)) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(* -1/24 (pow x 4))
(* -1 (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x)))))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* -1 (/ (- (/ 1 x) 1/2) x))) x)) 1/24))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(* 1/24 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
(* 1/24 (pow x 4))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* 1/6 x)))
(* (pow x 3) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* (pow x 3) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* 1/24 (pow x 5))
(* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 5))
(* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* 1/6 x)))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* 5/72 x)))))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* x (+ 5/72 (* 1/72 x)))))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3)))))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x))))

Outputs
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))) x)
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
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(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* -1/6 x) 1/4))))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) (fma.f64 x #s(literal -1/6 binary64) #s(literal -1/4 binary64)) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* x (- (* -5/72 x) 1/6)) 1/4))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal -5/72 binary64) #s(literal -1/6 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(* -1/576 (pow x 8))
(*.f64 #s(literal -1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* -1 (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x)))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/576 binary64) (/.f64 #s(literal -1/72 binary64) x)))
(* (pow x 8) (- (* -1 (/ (+ 1/72 (* 5/72 (/ 1 x))) x)) 1/576))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/576 binary64) (/.f64 (-.f64 #s(literal -1/72 binary64) (/.f64 #s(literal 5/72 binary64) x)) x)))
(* (pow x 8) (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) (pow x 2))) (+ 1/576 (* 1/72 (/ 1 x)))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/576 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -5/72 binary64) (/.f64 #s(literal -1/6 binary64) x)) x) #s(literal -1/72 binary64)) x)))
(* -1/576 (pow x 8))
(*.f64 #s(literal -1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* -1 (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x)))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/576 binary64) (/.f64 #s(literal -1/72 binary64) x)))
(* (pow x 8) (- (* -1 (/ (+ 1/72 (* 5/72 (/ 1 x))) x)) 1/576))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/576 binary64) (/.f64 (-.f64 #s(literal -1/72 binary64) (/.f64 #s(literal 5/72 binary64) x)) x)))
(* (pow x 8) (- (* -1 (/ (+ 1/72 (+ (/ 1/6 (pow x 2)) (* 5/72 (/ 1 x)))) x)) 1/576))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/576 binary64) (/.f64 (+.f64 (-.f64 #s(literal -1/72 binary64) (/.f64 #s(literal 5/72 binary64) x)) (/.f64 #s(literal -1/6 binary64) (.f64 x x))) x)))
x
(* x (+ 1 (* -1/2 x)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
(* x (+ 1 (* x (- (* -1/6 x) 1/2))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal -1/6 binary64) #s(literal -1/2 binary64)) x)
(* x (+ 1 (* x (- (* x (- (* -1/24 x) 1/6)) 1/2))))
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal -1/24 binary64) #s(literal -1/6 binary64)) #s(literal -1/2 binary64)) x)
(* -1/24 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/24 binary64))
(* -1 (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (- (/ 1 (pow x 3)) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) x)
(* -1/24 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/24 binary64))
(* -1 (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* -1 (/ (- (/ 1 x) 1/2) x))) x)) 1/24))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) x)))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/2 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(* (pow x 3) (+ 1/2 (* 1/6 x)))
(.f64 x (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(* (pow x 3) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 x (.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(* (pow x 3) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 x (.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(* 1/24 (pow x 5))
(.f64 #s(literal 1/24 binary64) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))) (.f64 x (.f64 (.f64 x x) (.f64 x x))))
(* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))) (.f64 x (.f64 (.f64 x x) (.f64 x x))))
(* 1/24 (pow x 5))
(.f64 #s(literal 1/24 binary64) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* 1/4 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64))
(* (pow x 4) (+ 1/4 (* 1/6 x)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* 5/72 x)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 x (fma.f64 x #s(literal 5/72 binary64) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* x (+ 5/72 (* 1/72 x)))))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/72 binary64) #s(literal 5/72 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(* 1/576 (pow x 8))
(*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/576 binary64))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3)))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (+.f64 (/.f64 #s(literal 5/72 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (/.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x)))))))
(* 1/576 (pow x 8))
(*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/576 binary64))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 (+.f64 #s(literal 1/72 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) x) #s(literal 5/72 binary64)) x)) x)))

rewrite287.0ms (5.4%)

Memory

-14.7MiB live, 380.8MiB allocated

Rules

4 454×	`lower-fma.f32`
4 434×	`lower-fma.f64`
4 012×	`lower-/.f32`
4 008×	`lower-/.f64`
3 990×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	456
0	86	431
1	377	306
2	3058	306
0	8334	293

Stop Event

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

Counts

25 → 557

Calls

Call 1

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

Outputs
(+.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
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(.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))
(.f64 (.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))) (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (*.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x x) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(fma.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(pow.f64 (.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 x)) #s(literal 2 binary64))
(.f64 x (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 x x) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 x x) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 x x) (.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 (.f64 x x) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 x)) (.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 x)))
(.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 x x) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) x)
(.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (*.f64 x x))
(.f64 (.f64 (.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 x x)) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 (.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))
(.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 x (*.f64 x x))) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 (.f64 (.f64 x x) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 x (.f64 x (*.f64 x x))))

eval197.0ms (3.7%)

Memory: 11.1MiB live, 245.4MiB allocated
Compiler: Compiled 39 574 to 2 302 computations (94.2% saved)

prune315.0ms (6%)

Memory

12.9MiB live, 175.4MiB allocated

Pruning

16 alts after pruning (4 fresh and 12 done)

	Pruned	Kept	Total
New	954	4	958
Fresh	0	0	0
Picked	2	3	5
Done	0	9	9
Total	956	16	972

Accuracy

100.0%

Counts

972 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.7%	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	7.5%	(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
✓	7.2%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	5.6%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
✓	99.0%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	99.2%	#s(approx (- (exp x) 1) (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x x))
✓	98.7%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
	46.4%	#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) #s(approx ( (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/72 binary64) #s(literal 5/72 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
	46.4%	#s(approx (- (exp x) 1) (/.f64 #s(approx (- (* x x) (* (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal -5/72 binary64) #s(literal -1/6 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)))) (-.f64 x (.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
✓	99.0%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
✓	98.6%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
✓	97.8%	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64)) x))
	20.5%	#s(approx (- (exp x) 1) #s(approx (/ (- (* x x) (* (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (- x (* x (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))))
	99.2%	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (fma.f64 x (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))))
✓	99.2%	#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x))))

Compiler

Compiled 632 to 223 computations (64.7% saved)

regimes95.0ms (1.8%)

Memory

-18.5MiB live, 20.0MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64)) x))
(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x x))
#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x))
#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x))))
#s(approx (- (exp x) 1) #s(approx (/ (- (* x x) (* (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (- x (* x (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))))
#s(approx (- (exp x) 1) (/.f64 #s(approx (- (* x x) (* (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal -5/72 binary64) #s(literal -1/6 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)))) (-.f64 x (.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (fma.f64 x (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))))
#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))))
#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) #s(approx ( (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/72 binary64) #s(literal 5/72 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
(expm1.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))

Outputs
(expm1.f64 x)

Calls

3 calls:

84.0ms	x
5.0ms	(exp.f64 x)
5.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes16.0ms (0.3%)

Memory

18.0MiB live, 18.0MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x (+ (* x 1/6) 1/2)) 1) #s(literal 1 binary64)) x))
(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
(-.f64 #s(approx (exp x) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x x))
#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x))
#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x) x))))
#s(approx (- (exp x) 1) #s(approx (/ (- (* x x) (* (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (- x (* x (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))))
#s(approx (- (exp x) 1) (/.f64 #s(approx (- (* x x) (* (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2))))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal -5/72 binary64) #s(literal -1/6 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)))) (-.f64 x (.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (fma.f64 x (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))))
#s(approx (- (exp x) 1) #s(approx (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x) (fma.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))))
#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) #s(approx ( (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)) (* (* x x) (* x (+ (* x (+ (* x 1/24) 1/6)) 1/2)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/72 binary64) #s(literal 5/72 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
#s(approx (- (exp x) 1) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 x (.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))

Outputs

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

Calls

3 calls:

6.0ms	x
4.0ms	(exp.f64 x)
4.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.2%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes11.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.2%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes38.0ms (0.7%)

Memory

-28.0MiB live, 10.8MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

31.0ms	(exp.f64 x)
3.0ms	x
3.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.0%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes8.0ms (0.2%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.0%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
98.7%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
98.6%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes23.0ms (0.4%)

Memory

-41.4MiB live, 6.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	x
2.0ms	(exp.f64 x)
2.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
97.8%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
5.6%	1	`x`
5.6%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
5.6%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	132
1	62	132
2	66	132
3	69	132
4	72	132
5	75	132

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness823.0ms (15.6%)

Memory

14.2MiB live, 279.4MiB allocated

Rules

20 252×	`lower-fma.f64`
20 252×	`lower-fma.f32`
12 634×	`lower-fma.f64`
12 634×	`lower-fma.f32`
5 760×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	946
1	236	946
2	617	942
3	1658	942
4	5005	934
0	8389	746
0	21	96
0	36	96
1	159	96
2	1163	96
0	8221	96
0	25	108
1	77	108
2	168	108
3	371	108
4	587	108
5	718	108
6	723	108
0	723	81
0	4	6
0	6	6
1	24	6
2	130	6
0	1143	4
0	85	1524
1	297	1520
2	775	1520
3	2673	1508
4	6622	1508
0	8425	1234

Stop Event

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

Compiler

Compiled 209 to 104 computations (50.2% saved)

preprocess156.0ms (3%)

Memory: 11.3MiB live, 126.6MiB allocated
Compiler: Compiled 174 to 66 computations (62.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	11
1	17	11
2	35	10
3	54	10
4	70	10
5	90	10
6	108	10
7	123	10
8	135	10
9	137	10
0	4	4
0	6	4
1	11	4
2	12	4
0	12	2

Iter	Nodes	Cost
0	21	110
0	36	110
1	65	110
2	106	110
3	194	110
4	405	110
5	480	110
6	617	110
7	618	110
0	618	110

Iter	Nodes	Cost
0	37	260
0	59	250
1	116	238
2	220	230
3	408	230
4	598	230
5	685	230
6	685	230
0	685	222

Iter	Nodes	Cost
0	6	11
1	17	11
2	35	10
3	54	10
4	70	10
5	90	10
6	108	10
7	123	10
8	135	10
9	137	10
0	4	4
0	6	4
1	11	4
2	12	4
0	12	2

Iter	Nodes	Cost
0	21	110
0	36	110
1	65	110
2	106	110
3	194	110
4	405	110
5	480	110
6	617	110
7	618	110
0	618	110

Iter	Nodes	Cost
0	37	260
0	59	250
1	116	238
2	220	230
3	408	230
4	598	230
5	685	230
6	685	230
0	685	222

start0.0ms (0%)

analyze0.0ms (0%)

sample468.0ms (8.9%)

explain62.0ms (1.2%)

preprocess14.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize14.0ms (0.3%)

series1.0ms (0%)

simplify23.0ms (0.4%)

rewrite101.0ms (1.9%)

eval12.0ms (0.2%)

prune45.0ms (0.9%)

simplify23.0ms (0.4%)

localize73.0ms (1.4%)

series14.0ms (0.3%)

simplify253.0ms (4.8%)

rewrite295.0ms (5.6%)

eval79.0ms (1.5%)

prune214.0ms (4.1%)

simplify23.0ms (0.4%)

localize107.0ms (2%)

series16.0ms (0.3%)

simplify211.0ms (4%)

rewrite286.0ms (5.4%)

eval150.0ms (2.8%)

prune167.0ms (3.2%)

simplify214.0ms (4.1%)

localize177.0ms (3.4%)

series22.0ms (0.4%)

simplify209.0ms (4%)

rewrite287.0ms (5.4%)

eval197.0ms (3.7%)

prune315.0ms (6%)

regimes95.0ms (1.8%)

regimes16.0ms (0.3%)

regimes11.0ms (0.2%)

regimes38.0ms (0.7%)

regimes8.0ms (0.2%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes23.0ms (0.4%)

regimes4.0ms (0.1%)

simplify7.0ms (0.1%)

soundness823.0ms (15.6%)

preprocess156.0ms (3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	11
1	17	11
2	35	10
3	54	10
4	70	10
5	90	10
6	108	10
7	123	10
8	135	10
9	137	10
0	4	4
0	6	4
1	11	4
2	12	4
0	12	2

Iter	Nodes	Cost
0	21	110
0	36	110
1	65	110
2	106	110
3	194	110
4	405	110
5	480	110
6	617	110
7	618	110
0	618	110

Iter	Nodes	Cost
0	37	260
0	59	250
1	116	238
2	220	230
3	408	230
4	598	230
5	685	230
6	685	230
0	685	222