Metrics for expm1 (example 3.7)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample532.0ms (10.6%)

Memory

22.7MiB live, 631.6MiB allocated

Samples

340.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 196.0ms

ival-fabs: 110.0ms (56% of total)

ival-expm1: 53.0ms (27% of total)

ival-<=: 25.0ms (12.7% of total)

exact: 5.0ms (2.5% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain65.0ms (1.3%)

Memory

-1.5MiB live, 44.1MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	253	0
-	0	3

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	3
1	253

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

34.0ms

512×

valid

Compiler

Compiled 24 to 16 computations (33.3% saved)

Precisions

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

ival-exp: 4.0ms (49.8% of total)

ival-expm1: 3.0ms (37.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess125.0ms (2.5%)

Memory

33.8MiB live, 79.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	16	11
2	33	11
3	111	11
4	482	11
5	6534	11
0	4	4
0	6	4
1	11	4
2	21	4
3	47	4
4	183	4
5	1673	4
6	5180	4
0	8366	2

Stop Event

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

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 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.0%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify167.0ms (3.3%)

Memory

-35.7MiB live, 61.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	11	8
2	21	8
3	47	8
4	183	8
5	1673	8
6	5180	8
0	8366	6

Stop Event

1×	iter limit
1×	node limit
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)

localize13.0ms (0.3%)

Memory

10.3MiB live, 10.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(exp.f64 x)
accuracy	58.90527446441327	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

9.0ms

256×

valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

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

ival-exp: 2.0ms (50.8% of total)

ival-expm1: 2.0ms (50.8% 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

0.5MiB live, 0.5MiB allocated

Counts

2 → 10

Calls

Call 1

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

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

Calls

3 calls:

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

simplify178.0ms (3.5%)

Memory

-8.6MiB live, 81.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	66
1	100	66
2	323	66
3	1033	66
4	2579	66
5	5281	66
0	8149	53

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 9

Calls

Call 1

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

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

rewrite280.0ms (5.6%)

Memory

31.1MiB live, 123.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
0	6	6
1	25	6
2	152	6
3	1559	6
0	8950	4

Stop Event

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

Counts

2 → 276

Calls

Call 1

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

Outputs
(.f64 (/.f64 (expm1.f64 x) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64))))
(.f64 (/.f64 (expm1.f64 x) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x))))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))))
(.f64 (/.f64 (expm1.f64 x) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (expm1.f64 x))
(*.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (expm1.f64 x))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (/.f64 (expm1.f64 x) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (expm1.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (.f64 #s(literal 1 binary64) (expm1.f64 x)) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (/.f64 (expm1.f64 x) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (expm1.f64 (.f64 #s(literal 3 binary64) x))))) (/.f64 (.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x))))) (/.f64 (expm1.f64 x) (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (.f64 #s(literal 3 binary64) x)))) (/.f64 (.f64 #s(literal 1 binary64) (expm1.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (/.f64 (expm1.f64 x) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64))) (/.f64 (neg.f64 (expm1.f64 x)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (.f64 #s(literal 1 binary64) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1 binary64) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64)) (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (expm1.f64 x))))
(*.f64 (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) x)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))) (-.f64 (*.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) x)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal 6 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (pow.f64 (exp.f64 x) #s(literal 4 binary64))))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (expm1.f64 x))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 (expm1.f64 x) (expm1.f64 x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (expm1.f64 x) (/.f64 (expm1.f64 x) (expm1.f64 x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (expm1.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (expm1.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) (cosh.f64 x)))))
(/.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (-.f64 (cosh.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (.f64 (-.f64 (cosh.f64 x) #s(literal 1 binary64)) (-.f64 (cosh.f64 x) #s(literal 1 binary64))) (.f64 (sinh.f64 x) (-.f64 (cosh.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (pow.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 9 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))) (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (pow.f64 (-.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x))))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))) (.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))) (neg.f64 (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))))
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(/.f64 (sqrt.f64 (.f64 (exp.f64 x) (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))))) (sqrt.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (*.f64 (sinh.f64 x) (cosh.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 (cosh.f64 x) (exp.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sinh.f64 x) (exp.f64 x)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (.f64 (cosh.f64 x) (exp.f64 x)) (.f64 (sinh.f64 x) (exp.f64 x)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (.f64 (cosh.f64 x) (exp.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sinh.f64 x) (exp.f64 x)) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (.f64 (cosh.f64 x) (exp.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sinh.f64 x) (exp.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cosh.f64 x) (exp.f64 x)) (*.f64 (sinh.f64 x) (exp.f64 x)))))))
(/.f64 (sqrt.f64 (.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))))) (sqrt.f64 (.f64 (exp.f64 (neg.f64 x)) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x))))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x))) (exp.f64 (neg.f64 x)))))
(/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x))))
(/.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))))) (exp.f64 (log.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x))))))
(/.f64 (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (pow.f64 (cosh.f64 x) #s(literal 2 binary64))) (-.f64 (sinh.f64 x) (cosh.f64 x)))
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 x) (*.f64 #s(literal 2 binary64) (cosh.f64 x))) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 x) (*.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (sinh.f64 x) (cosh.f64 x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64)))) (neg.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x)))))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64)))) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (*.f64 (sinh.f64 x) (cosh.f64 x))))
(/.f64 (.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (*.f64 (sinh.f64 x) (cosh.f64 x))))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 x)))) #s(literal 4 binary64))
(/.f64 (fabs.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64)))) (fabs.f64 (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (sinh.f64 x) (cosh.f64 x))))))
(/.f64 (fabs.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64)))) (fabs.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (sinh.f64 x) (cosh.f64 x)))))
(/.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 (neg.f64 x)))))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(fma.f64 (sinh.f64 x) #s(literal 1 binary64) (*.f64 (cosh.f64 x) #s(literal 1 binary64)))
(fma.f64 (cosh.f64 x) #s(literal 1 binary64) (*.f64 (sinh.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (sinh.f64 x) (*.f64 #s(literal 1 binary64) (cosh.f64 x)))
(fma.f64 #s(literal 1 binary64) (cosh.f64 x) (*.f64 #s(literal 1 binary64) (sinh.f64 x)))
(sqrt.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (-.f64 (sinh.f64 x) (cosh.f64 x))) (/.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (-.f64 (sinh.f64 x) (cosh.f64 x))))
(-.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))))
(-.f64 (cosh.f64 x) (sinh.f64 (neg.f64 x)))
(fabs.f64 (-.f64 (/.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))) (/.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))))
(fabs.f64 (neg.f64 (neg.f64 (exp.f64 x))))
(fabs.f64 (neg.f64 (exp.f64 x)))
(fabs.f64 (exp.f64 x))
(+.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64)) #s(literal 4 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 x))) #s(literal 4 binary64)))
(+.f64 (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) (cosh.f64 x))))) (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) (cosh.f64 x))))))
(+.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) (cosh.f64 x))))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (.f64 (sinh.f64 x) (cosh.f64 x))))))
(+.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64)) #s(literal 4 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 4 binary64)))
(+.f64 (.f64 (cosh.f64 x) #s(literal 1 binary64)) (.f64 (sinh.f64 x) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (sinh.f64 x)) (.f64 #s(literal 1 binary64) (cosh.f64 x)))
(+.f64 (.f64 #s(literal 1 binary64) (cosh.f64 x)) (.f64 #s(literal 1 binary64) (sinh.f64 x)))
(+.f64 (.f64 (sinh.f64 x) #s(literal 1 binary64)) (.f64 (cosh.f64 x) #s(literal 1 binary64)))
(+.f64 (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x)))) (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x)))))
(+.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x)))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (sinh.f64 x) (cosh.f64 x)))))
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(exp.f64 (/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)))
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(exp.f64 x)

eval81.0ms (1.6%)

Memory: -10.0MiB live, 35.0MiB allocated
Compiler: Compiled 6 736 to 862 computations (87.2% saved)

prune8.0ms (0.2%)

Memory

16.1MiB live, 16.1MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	277	8	285
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	278	8	286

Accuracy

100.0%

Counts

286 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.3%	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
	7.1%	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
	6.8%	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
▶	5.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 x)
▶	99.4%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
▶	99.2%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
▶	98.9%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))

Compiler

Compiled 170 to 128 computations (24.7% saved)

simplify224.0ms (4.5%)

Memory

-16.6MiB live, 123.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	125
0	38	125
1	58	125
2	139	125
3	399	125
4	1311	125
5	4174	125
0	8842	125

Stop Event

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

Calls

Call 1

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

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

localize56.0ms (1.1%)

Memory

32.7MiB live, 78.8MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64))
accuracy	0.01171875	(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
accuracy	0.01171875	(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.38183967706494176	#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
accuracy	0.0	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.0	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	0.01171875	(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.48263501827723454	#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	0.680123107033536	#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
accuracy	1.2499093475086729	#s(approx (exp x) #s(literal 1 binary64))
accuracy	58.90527446441327	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0.0	(expm1.f64 x)

Samples

44.0ms

256×

valid

Compiler

Compiled 117 to 24 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 13.0ms (41.2% of total)

const: 8.0ms (25.4% of total)

ival-add: 6.0ms (19% of total)

ival-exp: 2.0ms (6.3% of total)

ival-expm1: 2.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

-37.0MiB live, 9.2MiB allocated

Counts

15 → 47

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((- (exp x) 1) (- (exp x) 1) (exp x) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (+ (* 1/2 x) 1) (- (exp x) 1) (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2) (- (exp x) 1) (* (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) x) (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) (+ (* (+ (* 1/24 x) 1/6) x) 1/2) (+ (* 1/24 x) 1/6))
2.0ms	x	@	inf	((- (exp x) 1) (- (exp x) 1) (exp x) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (+ (* 1/2 x) 1) (- (exp x) 1) (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2) (- (exp x) 1) (* (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) x) (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) (+ (* (+ (* 1/24 x) 1/6) x) 1/2) (+ (* 1/24 x) 1/6))
2.0ms	x	@	-inf	((- (exp x) 1) (- (exp x) 1) (exp x) (- (exp x) 1) (* (+ (* 1/2 x) 1) x) (+ (* 1/2 x) 1) (- (exp x) 1) (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2) (- (exp x) 1) (* (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) x) (+ (* (+ (* (+ (* 1/24 x) 1/6) x) 1/2) x) 1) (+ (* (+ (* 1/24 x) 1/6) x) 1/2) (+ (* 1/24 x) 1/6))

Time

Variable

Point

Expression

4.0ms

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

2.0ms

inf

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

2.0ms

-inf

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

simplify157.0ms (3.1%)

Memory

9.8MiB live, 154.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	369
1	347	359
2	1151	355
3	5300	355
0	8393	302

Stop Event

1×	iter limit
1×	node limit

Counts

47 → 46

Calls

Call 1

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

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

rewrite193.0ms (3.9%)

Memory

35.9MiB live, 217.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	111
0	38	111
1	150	111
2	1101	111
0	8264	111

Stop Event

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

Counts

15 → 346

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (expm1.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) (.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))))
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(+.f64 (/.f64 #s(literal 1/8 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64)))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64)))))
(+.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 (neg.f64 x)) (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64)))) (.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))))) (+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (-.f64 (*.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64)))))) (.f64 (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))))) (-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (*.f64 x #s(literal 1/144 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (fma.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (-.f64 (*.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64)))))))
(/.f64 (-.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 #s(literal -1/24 binary64) x) #s(literal 3 binary64))) (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/24 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (-.f64 (.f64 (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64)))))) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) #s(literal 1/36 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/216 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64)) #s(literal 1/36 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64)))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64)))) #s(literal 1/216 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (*.f64 x #s(literal 1/144 binary64))))))
(/.f64 (-.f64 #s(literal 1/36 binary64) (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) #s(literal 1/36 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/216 binary64))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (.f64 (neg.f64 x) #s(literal 1/144 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/216 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64)))
(/.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/216 binary64)) (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (.f64 (neg.f64 x) #s(literal 1/144 binary64)))))
(/.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/216 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64)))))
(neg.f64 (fma.f64 #s(literal -1/24 binary64) x #s(literal -1/6 binary64)))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(-.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) x))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (-.f64 (*.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))))
(-.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/24 binary64) x))
(+.f64 (/.f64 #s(literal 1/216 binary64) (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (.f64 (neg.f64 x) #s(literal 1/144 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (*.f64 (neg.f64 x) #s(literal 1/144 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (.f64 (neg.f64 x) #s(literal 1/144 binary64))))) (/.f64 #s(literal 1/216 binary64) (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (*.f64 (neg.f64 x) #s(literal 1/144 binary64))))))
(+.f64 (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (*.f64 x #s(literal 1/144 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 x #s(literal 1/144 binary64))))) (/.f64 #s(literal 1/216 binary64) (fma.f64 (.f64 x x) #s(literal 1/576 binary64) (-.f64 #s(literal 1/36 binary64) (*.f64 x #s(literal 1/144 binary64))))))
(+.f64 (*.f64 #s(literal 1/24 binary64) x) #s(literal 1/6 binary64))
(+.f64 #s(literal 1/6 binary64) (*.f64 (neg.f64 (neg.f64 x)) #s(literal 1/24 binary64)))
(+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) x))

eval72.0ms (1.4%)

Memory: -21.7MiB live, 74.4MiB allocated
Compiler: Compiled 14 044 to 1 768 computations (87.4% saved)

prune11.0ms (0.2%)

Memory

25.3MiB live, 25.3MiB allocated

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	377	3	380
Fresh	0	3	3
Picked	0	5	5
Done	0	0	0
Total	377	11	388

Accuracy

100.0%

Counts

388 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.3%	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	7.1%	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	6.8%	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
✓	5.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
▶	99.2%	#s(approx (- (exp x) 1) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x (.f64 #s(literal 1 binary64) x)))
▶	98.9%	#s(approx (- (exp x) 1) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal 1 binary64) x)))
✓	99.4%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
✓	99.2%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
✓	98.9%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
▶	5.7%	#s(approx (- (exp x) 1) #s(approx (* (+ (* 1/2 x) 1) x) (.f64 (.f64 x x) #s(literal 1/2 binary64))))

Compiler

Compiled 214 to 158 computations (26.2% saved)

simplify92.0ms (1.8%)

Memory

-8.5MiB live, 84.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	168
0	45	156
1	83	156
2	223	156
3	668	156
4	1556	156
5	3531	156
0	8132	150

Stop Event

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

Calls

Call 1

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

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

localize70.0ms (1.4%)

Memory

-27.2MiB live, 67.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal 1 binary64) x))
accuracy	0.0	(*.f64 #s(literal 1 binary64) x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.680123107033536	#s(approx (- (exp x) 1) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal 1 binary64) x)))
accuracy	0.0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.5158233535518089	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy	58.90527446441327	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.680123107033536	#s(approx (- (exp x) 1) #s(approx (* (+ (* 1/2 x) 1) x) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	60.32130193339038	#s(approx (* (+ (* 1/2 x) 1) x) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.7162114193206022	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
accuracy	58.90527446441327	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
accuracy	0.0	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	0.0	(*.f64 #s(literal 1 binary64) x)
accuracy	0.01171875	(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
accuracy	0.48263501827723454	#s(approx (- (exp x) 1) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x (.f64 #s(literal 1 binary64) x)))

Samples

44.0ms

256×

valid

Compiler

Compiled 115 to 23 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 13.0ms (41.8% of total)

ival-add: 7.0ms (22.5% of total)

ival-expm1: 6.0ms (19.3% of total)

const: 4.0ms (12.9% of total)

ival-exp: 2.0ms (6.4% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

7.3MiB live, 7.3MiB allocated

Counts

19 → 29

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify158.0ms (3.2%)

Memory

-0.4MiB live, 131.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	179
1	209	179
2	655	178
3	2873	178
0	8488	153

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

Calls

Call 1

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

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

rewrite234.0ms (4.7%)

Memory

38.8MiB live, 223.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	151
0	45	141
1	193	141
2	1354	141
0	8290	135

Stop Event

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

Counts

19 → 547

Calls

Call 1

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

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

eval108.0ms (2.2%)

Memory: 5.9MiB live, 108.3MiB allocated
Compiler: Compiled 19 119 to 2 366 computations (87.6% saved)

prune16.0ms (0.3%)

Memory

-6.3MiB live, 37.7MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	597	2	599
Fresh	0	1	1
Picked	2	3	5
Done	2	3	5
Total	601	9	610

Accuracy

100.0%

Counts

610 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.3%	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	7.1%	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	6.8%	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
✓	5.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
▶	99.2%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))
▶	98.9%	#s(approx (- (exp x) 1) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x x))
✓	99.4%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
✓	5.7%	#s(approx (- (exp x) 1) #s(approx (* (+ (* 1/2 x) 1) x) (.f64 (.f64 x x) #s(literal 1/2 binary64))))

Compiler

Compiled 103 to 75 computations (27.2% saved)

simplify112.0ms (2.2%)

Memory

-26.9MiB live, 72.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	108
0	30	108
1	54	108
2	147	108
3	488	108
4	1272	108
5	3696	108
6	7982	108
0	8027	104

Stop Event

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

Calls

Call 1

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

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

localize49.0ms (1%)

Memory

18.6MiB live, 63.1MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.0	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	0.41172765561355273	#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy	58.90527446441327	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0.0	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)
accuracy	0.0	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.48263501827723454	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))
accuracy	0.0	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.680123107033536	#s(approx (- (exp x) 1) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x x))

Samples

38.0ms

256×

valid

Compiler

Compiled 81 to 20 computations (75.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 10.0ms (35.5% of total)

const: 8.0ms (28.4% of total)

ival-add: 5.0ms (17.8% of total)

ival-exp: 2.0ms (7.1% of total)

ival-expm1: 2.0ms (7.1% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

11 → 29

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify139.0ms (2.8%)

Memory

5.8MiB live, 95.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	209
1	228	209
2	773	204
3	3065	203
0	8508	175

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

Calls

Call 1

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

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

rewrite189.0ms (3.8%)

Memory

-8.4MiB live, 173.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	95
0	30	95
1	135	95
2	1033	95
0	8280	91

Stop Event

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

Counts

11 → 281

Calls

Call 1

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

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

eval69.0ms (1.4%)

Memory: 7.6MiB live, 66.9MiB allocated
Compiler: Compiled 12 829 to 1 370 computations (89.3% saved)

prune15.0ms (0.3%)

Memory

-14.3MiB live, 30.7MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	0	0
Picked	0	3	3
Done	0	6	6
Total	337	9	346

Accuracy

100.0%

Counts

346 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.3%	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	7.1%	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	6.8%	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
✓	5.3%	(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	100.0%	(expm1.f64 x)
✓	99.2%	#s(approx (- (exp x) 1) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	98.9%	#s(approx (- (exp x) 1) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x x))
✓	99.4%	#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
✓	5.7%	#s(approx (- (exp x) 1) #s(approx (* (+ (* 1/2 x) 1) x) (.f64 (.f64 x x) #s(literal 1/2 binary64))))

Compiler

Compiled 264 to 128 computations (51.5% saved)

regimes11.0ms (0.2%)

Memory

22.7MiB live, 22.7MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs
(expm1.f64 x)

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes11.0ms (0.2%)

Memory

-29.3MiB live, 17.0MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes9.0ms (0.2%)

Memory

16.0MiB live, 16.0MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes7.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) 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
99.2%	1	`(exp.f64 x)`
99.2%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.2%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes6.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.9%	1	`(exp.f64 x)`
98.9%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
98.9%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes9.0ms (0.2%)

Memory

-35.9MiB live, 9.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	x
1.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
1.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
98.9%	1	`(exp.f64 x)`
98.9%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
98.9%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes4.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
6.8%	1	`(exp.f64 x)`
6.8%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
6.8%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes3.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

simplify45.0ms (0.9%)

Memory

-4.9MiB live, 47.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	83
1	39	83
2	53	83
3	81	83
4	219	83
5	1788	83
6	6052	83

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness1.4s (27.8%)

Memory

-29.7MiB live, 515.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	151
0	45	141
1	193	141
2	1354	141
0	8290	135
0	22	111
0	38	111
1	150	111
2	1101	111
0	8264	111
0	4	6
0	6	6
1	25	6
2	152	6
3	1559	6
0	8950	4
0	25	66
1	100	66
2	323	66
3	1033	66
4	2579	66
5	5281	66
0	8149	53

Stop Event

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

Compiler

Compiled 193 to 119 computations (38.3% saved)

preprocess74.0ms (1.5%)

Memory: 1.9MiB live, 98.1MiB allocated
Compiler: Compiled 178 to 76 computations (57.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample532.0ms (10.6%)

explain65.0ms (1.3%)

preprocess125.0ms (2.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify167.0ms (3.3%)

localize13.0ms (0.3%)

series1.0ms (0%)

simplify178.0ms (3.5%)

rewrite280.0ms (5.6%)

eval81.0ms (1.6%)

prune8.0ms (0.2%)

simplify224.0ms (4.5%)

localize56.0ms (1.1%)

series8.0ms (0.2%)

simplify157.0ms (3.1%)

rewrite193.0ms (3.9%)

eval72.0ms (1.4%)

prune11.0ms (0.2%)

simplify92.0ms (1.8%)

localize70.0ms (1.4%)

series6.0ms (0.1%)

simplify158.0ms (3.2%)

rewrite234.0ms (4.7%)

eval108.0ms (2.2%)

prune16.0ms (0.3%)

simplify112.0ms (2.2%)

localize49.0ms (1%)

series4.0ms (0.1%)

simplify139.0ms (2.8%)

rewrite189.0ms (3.8%)

eval69.0ms (1.4%)

prune15.0ms (0.3%)

regimes11.0ms (0.2%)

regimes11.0ms (0.2%)

regimes9.0ms (0.2%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes9.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify45.0ms (0.9%)

soundness1.4s (27.8%)

preprocess74.0ms (1.5%)

end0.0ms (0%)

Profiling