Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1

Average Error: 0.0 → 0.0

Time: 1.5s

Precision: binary64

Cost: 320

Math

\[x \cdot y - x \]

↓

\[\left(y + -1\right) \cdot x \]

FPCore

(FPCore (x y) :precision binary64 (- (* x y) x))

↓

(FPCore (x y) :precision binary64 (* (+ y -1.0) x))

C

double code(double x, double y) {
	return (x * y) - x;
}

↓

double code(double x, double y) {
	return (y + -1.0) * x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) - x
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + (-1.0d0)) * x
end function

Java

public static double code(double x, double y) {
	return (x * y) - x;
}

↓

public static double code(double x, double y) {
	return (y + -1.0) * x;
}

Python

def code(x, y):
	return (x * y) - x

↓

def code(x, y):
	return (y + -1.0) * x

Julia

function code(x, y)
	return Float64(Float64(x * y) - x)
end

↓

function code(x, y)
	return Float64(Float64(y + -1.0) * x)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * y) - x;
end

↓

function tmp = code(x, y)
	tmp = (y + -1.0) * x;
end

Wolfram

code[x_, y_] := N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]

↓

code[x_, y_] := N[(N[(y + -1.0), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[x \cdot y - x \]

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{\left(y - 1\right) \cdot x} \]

3. Final simplification 0.0

   \[\leadsto \left(y + -1\right) \cdot x \]

Alternatives

Alternative 1
Error	1.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	27.4
Cost	128

\[-x \]

Reproduce

herbie shell --seed 2022338 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))