Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

Average Error: 0.0 → 0.0

Time: 13.0s

Precision: binary64

Cost: 448

Math

\[\left(\frac{x}{2} + y \cdot x\right) + z \]

↓

\[\left(y - -0.5\right) \cdot x + z \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

↓

(FPCore (x y z) :precision binary64 (+ (* (- y -0.5) x) z))

C

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

↓

double code(double x, double y, double z) {
	return ((y - -0.5) * x) + z;
}

Fortran

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

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((y - (-0.5d0)) * x) + z
end function

Java

public static double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

↓

public static double code(double x, double y, double z) {
	return ((y - -0.5) * x) + z;
}

Python

def code(x, y, z):
	return ((x / 2.0) + (y * x)) + z

↓

def code(x, y, z):
	return ((y - -0.5) * x) + z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

↓

function code(x, y, z)
	return Float64(Float64(Float64(y - -0.5) * x) + z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (y * x)) + z;
end

↓

function tmp = code(x, y, z)
	tmp = ((y - -0.5) * x) + z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / 2.0), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(N[(y - -0.5), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\left(\frac{x}{2} + y \cdot x\right) + z \]

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{\left(0.5 + y\right) \cdot x} + z \]

3. Simplified 0.0

   \[\leadsto \color{blue}{\left(y - -0.5\right) \cdot x} + z \]
   Proof

Alternatives

Alternative 1
Error	1.6
Cost	584

\[\begin{array}{l} t_0 := y \cdot x + z\\ \mathbf{if}\;y \leq -8.4 \cdot 10^{+27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-19}:\\ \;\;\;\;0.5 \cdot x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.7
Cost	320

\[0.5 \cdot x + z \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))