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

Average Error: 0.0 → 0.0

Time: 13.5s

Precision: binary64

Cost: 320

Math

\[x \cdot y - x \]

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = x * ((-1.0d0) + y)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

   \[x \cdot y - x \]

2. Simplified 0.0

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

Alternatives

Alternative 1
Error	1.4
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	27.0
Cost	128

\[-x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))