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

Average Error: 0.0 → 0.0

Time: 4.1s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* x y)) 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 ((x / 2.0) + (x * y)) + 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 = ((x / 2.0d0) + (x * y)) + 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 ((x / 2.0) + (x * y)) + z;
}

Python

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

↓

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

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (x * y)) + 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[(x / 2.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	27.4
Cost	1116

\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-67}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-248}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-212}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 10^{-190}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-164}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-113}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 2
Error	11.4
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-156} \lor \neg \left(z \leq 4.6 \cdot 10^{-101}\right):\\ \;\;\;\;x \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \end{array} \]

Alternative 3
Error	0.9
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 5.1 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} + z\\ \end{array} \]

Alternative 4
Error	16.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5
Error	27.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-156}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-104}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	34.0
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023073 
(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))