Numeric.Log:$cexpm1 from log-domain-0.10.2.1, A

Average Accuracy: 100.0% → 100.0%

Time: 614.0ms

Precision: binary64

Cost: 320

Math

\[\left(x \cdot 2\right) \cdot x \]

↓

\[x \cdot \left(x \cdot 2\right) \]

FPCore

(FPCore (x) :precision binary64 (* (* x 2.0) x))

↓

(FPCore (x) :precision binary64 (* x (* x 2.0)))

C

double code(double x) {
	return (x * 2.0) * x;
}

↓

double code(double x) {
	return x * (x * 2.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 2.0d0) * x
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (x * 2.0d0)
end function

Java

public static double code(double x) {
	return (x * 2.0) * x;
}

↓

public static double code(double x) {
	return x * (x * 2.0);
}

Python

def code(x):
	return (x * 2.0) * x

↓

def code(x):
	return x * (x * 2.0)

Julia

function code(x)
	return Float64(Float64(x * 2.0) * x)
end

↓

function code(x)
	return Float64(x * Float64(x * 2.0))
end

MATLAB

function tmp = code(x)
	tmp = (x * 2.0) * x;
end

↓

function tmp = code(x)
	tmp = x * (x * 2.0);
end

Wolfram

code[x_] := N[(N[(x * 2.0), $MachinePrecision] * x), $MachinePrecision]

↓

code[x_] := N[(x * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

\[\left(2 \cdot x\right) \cdot x \]

Derivation

1. Initial program 100.0%

   \[\left(x \cdot 2\right) \cdot x \]

2. Final simplification 100.0%

   \[\leadsto x \cdot \left(x \cdot 2\right) \]

Reproduce

herbie shell --seed 2023122 
(FPCore (x)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (* (* 2.0 x) x)

  (* (* x 2.0) x))