Metrics for expm1 (example 3.7)

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample544.0ms (15.1%)

Memory

-22.1MiB live, 607.8MiB allocated

Samples

364.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 137.0ms

ival-fabs: 58.0ms (42.5% of total)

ival-expm1: 51.0ms (37.3% of total)

ival-<=: 20.0ms (14.6% of total)

exact: 5.0ms (3.7% of total)

ival-assert: 3.0ms (2.2% of total)

Bogosity

preprocess15.0ms (0.4%)

Memory

17.5MiB live, 17.5MiB 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)

explain56.0ms (1.6%)

Memory

-4.7MiB live, 72.3MiB 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

24.0ms

512×

valid

Compiler

Compiled 30 to 20 computations (33.3% saved)

Precisions

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

ival-exp: 7.0ms (61.3% of total)

ival-expm1: 3.0ms (26.3% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.3%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB 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 (0.4%)

Memory

18.1MiB live, 18.1MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	8.3%	(-.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 (52.1% of total)

ival-expm1: 2.0ms (52.1% 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

0.9MiB live, 0.9MiB allocated

Counts

2 → 24

Calls

Call 1

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

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>

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)

simplify32.0ms (0.9%)

Memory

0.6MiB live, 38.8MiB 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)

rewrite103.0ms (2.9%)

Memory

-6.0MiB live, 73.6MiB allocated

Algorithm

1×	batch-egg-rewrite

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))

eval23.0ms (0.7%)

Memory: -23.0MiB live, 15.4MiB allocated
Compiler: Compiled 1 895 to 241 computations (87.3% saved)

prune15.0ms (0.4%)

Memory

30.9MiB live, 30.9MiB 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))
	7.6%	(-.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))
	7.3%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	5.5%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 x)
▶	99.4%	#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))
▶	99.3%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
▶	99.1%	#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)

simplify29.0ms (0.8%)

Memory

1.6MiB live, 39.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

localize79.0ms (2.2%)

Memory

-12.6MiB live, 102.2MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
✓	accuracy	99.4%	#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	100.0%	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.3%	#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	100.0%	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	99.1%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
✓	accuracy	98.1%	#s(approx (exp x) #s(literal 1 binary64))
✓	accuracy	8.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(expm1.f64 x)

Samples

49.0ms

256×

valid

Compiler

Compiled 96 to 23 computations (76% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 14.0ms (37.8% of total)

ival-add: 11.0ms (29.7% of total)

const: 6.0ms (16.2% of total)

ival-exp: 4.0ms (10.8% of total)

ival-expm1: 2.0ms (5.4% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

14 → 168

Calls

Call 1

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

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

Calls

42 calls:

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

simplify396.0ms (11%)

Memory

11.9MiB live, 448.1MiB 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))

rewrite580.0ms (16.1%)

Memory

-86.3MiB live, 491.8MiB allocated

Algorithm

1×	batch-egg-rewrite

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)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.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 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal 3 binary64))) (fma.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 (exp.f64 (.f64 x #s(literal 3 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 (+.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 #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 (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 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.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 #s(literal 1 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 #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 (.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)))))
(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 (exp.f64 (+.f64 x x)) (+.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 #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 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
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(.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/4 binary64)) (.f64 x (*.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) (.f64 x (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
(.f64 (fma.f64 (.f64 x x) (*.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal 1/4 binary64)) (.f64 x (*.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (*.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64))
(+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (neg.f64 (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))))
(-.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (neg.f64 (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (/.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) (/.f64 (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 x #s(literal 1/144 binary64)))) (fma.f64 (.f64 x (*.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 x x) #s(literal 1/576 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 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 1/36 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (*.f64 x #s(literal 1/144 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/576 binary64) #s(literal -1/36 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))) (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 (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 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))) (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 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)) #s(literal 1/36 binary64))) (*.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/2641807540224 binary64) #s(literal 1/10077696 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/191102976 binary64) (-.f64 #s(literal 1/46656 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/2985984 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 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/191102976 binary64) #s(literal -1/46656 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal -1/216 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 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/191102976 binary64) #s(literal -1/46656 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/331776 binary64) (+.f64 #s(literal 1/1296 binary64) (.f64 (.f64 x x) #s(literal 1/20736 binary64)))) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/331776 binary64) #s(literal -1/1296 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64)))) (neg.f64 (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 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/576 binary64) #s(literal -1/36 binary64)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (neg.f64 (-.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (fma.f64 (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)))) (.f64 (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)))))
(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)))))

eval82.0ms (2.3%)

Memory: 21.1MiB live, 97.8MiB allocated
Compiler: Compiled 14 372 to 1 277 computations (91.1% saved)

prune69.0ms (1.9%)

Memory

-18.6MiB live, 96.0MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	545	2	547
Fresh	0	3	3
Picked	0	5	5
Done	0	0	0
Total	545	10	555

Accuracy

100.0%

Counts

555 → 10

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))
▶	7.6%	(-.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))
▶	7.3%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	5.5%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
✓	99.4%	#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))
✓	99.3%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	99.1%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
▶	99.4%	#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))))
▶	6.0%	#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))

Compiler

Compiled 163 to 89 computations (45.4% saved)

simplify39.0ms (1.1%)

Memory

3.2MiB live, 45.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

1 308×	`lower-fma.f32`
1 294×	`lower-fma.f64`
364×	`lower-*.f32`
352×	`lower-*.f64`
320×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	279
0	63	266
1	124	256
2	209	253
3	470	253
4	699	253
5	827	253
0	827	239

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

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

localize112.0ms (3.1%)

Memory

10.2MiB live, 166.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	99.4%	#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	8.3%	(-.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	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	99.3%	#s(approx (exp x) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	accuracy	8.3%	(-.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	100.0%	(.f64 x (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	99.1%	#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
✓	accuracy	6.0%	#s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	99.1%	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
✓	accuracy	8.3%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 x (*.f64 x x)) x)
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.4%	#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

62.0ms

256×

valid

Compiler

Compiled 176 to 35 computations (80.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 19.0ms (41.7% of total)

ival-add: 12.0ms (26.3% of total)

const: 6.0ms (13.2% of total)

ival-expm1: 5.0ms (11% of total)

ival-exp: 2.0ms (4.4% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

66 calls:

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

simplify298.0ms (8.3%)

Memory

-5.8MiB live, 347.2MiB allocated

Algorithm

1×	egg-herbie

Rules

14 444×	`lower-fma.f64`
14 444×	`lower-fma.f32`
3 858×	`lower-*.f64`
3 858×	`lower-*.f32`
1 358×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	1444
1	283	1444
2	760	1444
3	2809	1428
4	6518	1428
0	8288	1189

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 254

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)))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 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)
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)))))
(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)
1/2
(+ 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))))

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

rewrite376.0ms (10.5%)

Memory

22.3MiB live, 460.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 250×	`lower-fma.f32`
6 236×	`lower-fma.f64`
3 990×	`lower-*.f32`
3 978×	`lower-*.f64`
3 726×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	247
0	63	237
1	295	227
2	2341	227
0	8533	217

Stop Event

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

Counts

22 → 453

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

eval124.0ms (3.4%)

Memory: -1.2MiB live, 183.3MiB allocated
Compiler: Compiled 21 797 to 1 597 computations (92.7% saved)

prune75.0ms (2.1%)

Memory

13.6MiB live, 174.3MiB allocated

Pruning

10 alts after pruning (0 fresh and 10 done)

	Pruned	Kept	Total
New	744	0	744
Fresh	0	0	0
Picked	0	5	5
Done	0	5	5
Total	744	10	754

Accuracy

100.0%

Counts

754 → 10

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))
✓	7.6%	(-.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))
✓	7.3%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	5.5%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
✓	99.4%	#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))
✓	99.3%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	99.1%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
✓	99.4%	#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))))
✓	6.0%	#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))

Compiler

Compiled 199 to 87 computations (56.3% saved)

regimes12.0ms (0.3%)

Memory

-18.7MiB live, 20.3MiB allocated

Counts

11 → 1

Calls

Call 1

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

Outputs
(expm1.f64 x)

Calls

3 calls:

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

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)

regimes9.0ms (0.2%)

Memory

16.2MiB live, 16.2MiB allocated

Counts

9 → 1

Calls

Call 1

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

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:

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

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.4%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes11.0ms (0.3%)

Memory

-21.1MiB live, 17.5MiB allocated

Counts

8 → 1

Calls

Call 1

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

Calls

3 calls:

6.0ms	x
2.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.4%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.2%)

Memory

15.8MiB live, 15.8MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.3%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.2%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.1%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.2%)

Memory

-32.5MiB live, 10.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

Calls

3 calls:

3.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
2.0ms	x
1.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
7.3%	1	`x`
7.3%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
7.3%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB 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	(exp.f64 x)
1.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
5.5%	1	`x`
5.5%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
5.5%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.2%)

Memory

11.8MiB live, 11.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	97
1	49	97
2	54	97
3	57	97
4	60	97
5	64	97

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

soundness396.0ms (11%)

Memory

20.5MiB live, 250.7MiB allocated

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
0	4	6
0	6	6
1	24	6
2	130	6
0	1143	4
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×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 123 to 61 computations (50.4% saved)

preprocess57.0ms (1.6%)

Memory: 1.8MiB live, 124.8MiB allocated
Compiler: Compiled 142 to 58 computations (59.2% 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	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

analyze0.0ms (0%)

sample544.0ms (15.1%)

preprocess15.0ms (0.4%)

explain56.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize14.0ms (0.4%)

series1.0ms (0%)

simplify32.0ms (0.9%)

rewrite103.0ms (2.9%)

eval23.0ms (0.7%)

prune15.0ms (0.4%)

simplify29.0ms (0.8%)

localize79.0ms (2.2%)

series7.0ms (0.2%)

simplify396.0ms (11%)

rewrite580.0ms (16.1%)

eval82.0ms (2.3%)

prune69.0ms (1.9%)

simplify39.0ms (1.1%)

localize112.0ms (3.1%)

series7.0ms (0.2%)

simplify298.0ms (8.3%)

rewrite376.0ms (10.5%)

eval124.0ms (3.4%)

prune75.0ms (2.1%)

regimes12.0ms (0.3%)

regimes9.0ms (0.2%)

regimes11.0ms (0.3%)

regimes7.0ms (0.2%)

regimes6.0ms (0.2%)

regimes7.0ms (0.2%)

regimes4.0ms (0.1%)

simplify7.0ms (0.2%)

soundness396.0ms (11%)

preprocess57.0ms (1.6%)

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