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

Average Error: 0.0 → 0.0

Time: 7.5s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

def code(x, y, z):
	return ((x / 2.0) + (y * 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(x / 2.0) + Float64(y * 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 = ((x / 2.0) + (y * 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[(x / 2.0), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	29.4
Cost	984

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-129}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-230}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-226}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-36}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	17.2
Cost	848

\[\begin{array}{l} t_0 := \left(0.5 + y\right) \cdot x\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+143}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -23000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 3
Error	11.1
Cost	584

\[\begin{array}{l} t_0 := \left(0.5 + y\right) \cdot x\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-14}:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.7
Cost	584

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

Alternative 5
Error	27.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+34}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-12}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	34.8
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023077 
(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))