Metrics for expm1 (example 3.7)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample450.0ms (10.7%)

Memory

36.9MiB live, 490.1MiB allocated

Samples

267.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 134.0ms

ival-expm1: 53.0ms (39.7% of total)

ival-fabs: 48.0ms (35.9% of total)

ival-<=: 25.0ms (18.7% of total)

exact: 4.0ms (3% of total)

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

Bogosity

explain53.0ms (1.3%)

Memory

-10.5MiB live, 67.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.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	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms

512×

valid

Compiler

Compiled 34 to 21 computations (38.2% saved)

Precisions

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

ival-exp: 4.0ms (48.9% of total)

ival-expm1: 3.0ms (36.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess14.0ms (0.3%)

Memory

14.7MiB live, 14.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.6%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB 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)

localize28.0ms (0.7%)

Memory

-44.1MiB live, 16.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(exp.f64 x)
accuracy	59.79861407423911	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

22.0ms

256×

valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-expm1: 15.0ms (86.5% of total)

ival-exp: 2.0ms (11.5% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.0MiB live, 1.0MiB 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)

simplify29.0ms (0.7%)

Memory

29.2MiB live, 29.2MiB 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)

rewrite127.0ms (3%)

Memory

-1.7MiB live, 74.0MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 84

Calls

Call 1

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

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

eval13.0ms (0.3%)

Memory: -16.4MiB live, 21.4MiB allocated
Compiler: Compiled 1 895 to 241 computations (87.3% saved)

prune11.0ms (0.3%)

Memory

23.7MiB live, 23.7MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	4	108

Accuracy

100.0%

Counts

108 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.4%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	5.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
▶	99.9%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))

Compiler

Compiled 31 to 17 computations (45.2% saved)

simplify17.0ms (0.4%)

Memory

-28.8MiB live, 12.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

212×	`lower-fma.f32`
206×	`lower-fma.f64`
138×	`lower-*.f32`
134×	`lower-*.f64`
68×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	85
0	29	85
1	47	85
2	66	85
3	98	85
4	153	85
5	162	85
6	216	85
7	218	85
0	218	81

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#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)
(-.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)
(-.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)

Outputs
#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)
(-.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)
(-.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)

localize50.0ms (1.2%)

Memory

35.1MiB live, 73.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0.09532981926421238	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
accuracy	59.79861407423911	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.5376698350766833	#s(approx (exp x) #s(literal 1 binary64))
accuracy	59.79861407423911	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
accuracy	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy	0	(*.f64 x x)
accuracy	0	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
accuracy	0	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.08181171191451778	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))

Samples

33.0ms

256×

valid

Compiler

Compiled 62 to 17 computations (72.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 8.0ms (39.8% of total)

ival-add: 4.0ms (19.9% of total)

const: 3.0ms (14.9% of total)

ival-exp: 2.0ms (9.9% of total)

ival-expm1: 2.0ms (9.9% 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

-30.3MiB live, 8.5MiB allocated

Counts

12 → 144

Calls

Call 1

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

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 (* 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 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 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)))>

Calls

36 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(* x 1/2)
1.0ms	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 1/2)

simplify387.0ms (9.2%)

Memory

44.6MiB live, 473.0MiB allocated

Algorithm

1×	egg-herbie

Rules

17 462×	`lower-fma.f64`
17 462×	`lower-fma.f32`
3 964×	`lower-*.f64`
3 964×	`lower-*.f32`
2 308×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	678
1	156	678
2	381	678
3	1416	678
4	4870	678
5	7957	678
0	8142	547

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 136

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 (* 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)
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)
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)))

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

rewrite343.0ms (8.2%)

Memory

10.8MiB live, 438.3MiB allocated

Rules

8 900×	`lower-fma.f32`
8 894×	`lower-fma.f64`
5 626×	`lower-*.f32`
5 622×	`lower-*.f64`
4 228×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	77
0	29	77
1	125	77
2	897	77
0	8447	73

Stop Event

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

Counts

12 → 393

Calls

Call 1

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

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

eval65.0ms (1.6%)

Memory: -1.7MiB live, 111.9MiB allocated
Compiler: Compiled 12 756 to 1 107 computations (91.3% saved)

prune96.0ms (2.3%)

Memory

-0.6MiB live, 90.5MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	527	2	529
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	527	6	533

Accuracy

100.0%

Counts

533 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.4%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	5.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	99.9%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
▶	99.9%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
▶	5.7%	#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify8.0ms (0.2%)

Memory

-30.9MiB live, 7.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

42×	`lower-*.f32`
36×	`lower-*.f64`
24×	`lower-fma.f32`
22×	`lower-fma.f64`
12×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	19	66
1	31	63
2	40	63
3	40	63
4	58	63
5	59	63
0	59	59

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize32.0ms (0.8%)

Memory

5.4MiB live, 43.1MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
accuracy	0.0078125	(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
accuracy	0.08181171191451778	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
accuracy	0	(.f64 x (.f64 x #s(literal 1/2 binary64)))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.08181171191451778	#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
accuracy	60.33042397122574	#s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64))))

Samples

17.0ms

256×

valid

Compiler

Compiled 42 to 11 computations (73.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 5.0ms (51.5% of total)

ival-add: 2.0ms (20.6% of total)

ival-expm1: 2.0ms (20.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

7 → 84

Calls

Call 1

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

Calls

21 calls:

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

simplify400.0ms (9.5%)

Memory

34.0MiB live, 545.4MiB allocated

Algorithm

1×	egg-herbie

Rules

16 416×	`lower-fma.f64`
16 416×	`lower-fma.f32`
4 136×	`lower-*.f64`
4 136×	`lower-*.f32`
3 308×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	428
1	93	428
2	175	428
3	604	428
4	2361	428
5	4408	428
6	5619	428
7	6068	428
8	6725	428
9	7575	428
0	8364	357

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 80

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

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

rewrite474.0ms (11.3%)

Memory

8.6MiB live, 356.1MiB allocated

Rules

7 496×	`lower-fma.f32`
7 494×	`lower-fma.f64`
5 078×	`lower-*.f32`
5 072×	`lower-*.f64`
2 622×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	60
0	19	61
1	65	58
2	418	58
3	4008	58
0	8447	54

Stop Event

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

Counts

7 → 217

Calls

Call 1

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

Outputs
#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))))
(exp.f64 (log.f64 (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(pow.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (.f64 x x))
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) x)
#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x))) #s(literal -1 binary64)))
(+.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64) #s(literal -1 binary64)) (neg.f64 (fma.f64 x (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/512 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 #s(literal 1/8 binary64) x) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64) #s(literal -1 binary64)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/512 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)) (fma.f64 x (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal -1 binary64)) (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64) #s(literal -1 binary64))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (/.f64 #s(literal -1 binary64) (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))))) (/.f64 #s(literal -1 binary64) (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))))) (fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))) (fma.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/512 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) x) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (neg.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -1 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (-.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal 1 binary64)) (.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (+.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (.f64 x #s(literal 1/2 binary64))))) (+.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x))) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/512 binary64) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/8 binary64) x) (*.f64 x x) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/16 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))))

eval33.0ms (0.8%)

Memory: 3.3MiB live, 41.0MiB allocated
Compiler: Compiled 6 564 to 618 computations (90.6% saved)

prune36.0ms (0.9%)

Memory

1.0MiB live, 39.2MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	297	6	303

Accuracy

100.0%

Counts

303 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.4%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	5.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	99.9%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
✓	99.9%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
▶	99.2%	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x 1/2) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify4.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

8×	`lower-+.f64`
8×	`lower-*.f32`
8×	`lower-+.f32`
6×	`lower-*.f64`
4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
0	11	32
1	19	32
2	20	32
0	20	27

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize37.0ms (0.9%)

Memory

-21.7MiB live, 21.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 #s(approx (+ ( x 1/2) 1) #s(literal 1 binary64)) x)
accuracy	0.08181171191451778	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x 1/2) 1) #s(literal 1 binary64)) x))
accuracy	0.5142612227742847	#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))

Samples

30.0ms

256×

valid

Compiler

Compiled 20 to 9 computations (55% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 21.0ms (84.8% of total)

ival-expm1: 2.0ms (8.1% of total)

ival-add: 1.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

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

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

#<alt #s(approx (+ (* x 1/2) 1) #s(literal 1 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 (* 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>
#<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)))>

Calls

9 calls:

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

simplify419.0ms (10%)

Memory

3.5MiB live, 441.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16 416×	`lower-fma.f64`
16 416×	`lower-fma.f32`
4 136×	`lower-*.f64`
4 136×	`lower-*.f32`
3 308×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	192
1	93	192
2	175	192
3	604	192
4	2361	192
5	4408	192
6	5619	192
7	6068	192
8	6725	192
9	7575	192
0	8364	152

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 34

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

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

rewrite346.0ms (8.2%)

Memory

22.7MiB live, 491.9MiB allocated

Rules

6 762×	`lower-fma.f64`
6 762×	`lower-fma.f32`
4 818×	`lower-/.f64`
4 818×	`lower-/.f32`
3 834×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
0	11	30
1	42	30
2	262	30
3	2337	30
0	8889	25

Stop Event

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

Counts

3 → 4

Calls

Call 1

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

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

eval8.0ms (0.2%)

Memory: -36.8MiB live, 10.0MiB allocated
Compiler: Compiled 252 to 21 computations (91.7% saved)

prune4.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	38	6	44

Accuracy

100.0%

Counts

44 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.4%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	5.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	99.9%	#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
✓	99.9%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
✓	99.2%	#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x 1/2) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 96 to 43 computations (55.2% saved)

regimes8.0ms (0.2%)

Memory

18.6MiB live, 18.6MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (- (exp x) 1) (.f64 #s(approx (+ ( x 1/2) 1) #s(literal 1 binary64)) x))
(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (- (exp x) 1) #s(approx (+ (* x (* x 1/2)) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
#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 (exp.f64 x) #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	(exp.f64 x)
2.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes10.0ms (0.2%)

Memory

-22.2MiB live, 16.1MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.9%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.9%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

-30.8MiB live, 8.4MiB 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:

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

Results

Accuracy	Segments	Branch
5.3%	1	`x`
5.3%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
5.3%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify6.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	56
1	31	56
2	35	56
3	38	56
4	41	56
5	44	56

Stop Event

1×

saturated

Calls

Call 1

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

soundness316.0ms (7.5%)

Memory

-0.3MiB live, 190.1MiB allocated

Rules

16 416×	`lower-fma.f64`
16 416×	`lower-fma.f32`
8 900×	`lower-fma.f32`
8 894×	`lower-fma.f64`
5 626×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	428
1	93	428
2	175	428
3	604	428
4	2361	428
5	4408	428
6	5619	428
7	6068	428
8	6725	428
9	7575	428
0	8364	357
0	18	77
0	29	77
1	125	77
2	897	77
0	8447	73
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×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 90 to 46 computations (48.9% saved)

preprocess347.0ms (8.3%)

Memory: -39.3MiB live, 105.4MiB allocated
Compiler: Compiled 84 to 40 computations (52.4% 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	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

start0.0ms (0%)

analyze0.0ms (0%)

sample450.0ms (10.7%)

explain53.0ms (1.3%)

preprocess14.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize28.0ms (0.7%)

series1.0ms (0%)

simplify29.0ms (0.7%)

rewrite127.0ms (3%)

eval13.0ms (0.3%)

prune11.0ms (0.3%)

simplify17.0ms (0.4%)

localize50.0ms (1.2%)

series7.0ms (0.2%)

simplify387.0ms (9.2%)

rewrite343.0ms (8.2%)

eval65.0ms (1.6%)

prune96.0ms (2.3%)

simplify8.0ms (0.2%)

localize32.0ms (0.8%)

series3.0ms (0.1%)

simplify400.0ms (9.5%)

rewrite474.0ms (11.3%)

eval33.0ms (0.8%)

prune36.0ms (0.9%)

simplify4.0ms (0.1%)

localize37.0ms (0.9%)

series1.0ms (0%)

simplify419.0ms (10%)

rewrite346.0ms (8.2%)

eval8.0ms (0.2%)

prune4.0ms (0.1%)

regimes8.0ms (0.2%)

regimes10.0ms (0.2%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

simplify6.0ms (0.1%)

soundness316.0ms (7.5%)

preprocess347.0ms (8.3%)

end0.0ms (0%)

Profiling

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