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

Average Error: 0.0 → 0.0

Time: 3.5s

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	11.8
Cost	1115

\[\begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+118} \lor \neg \left(x \leq -5.35 \cdot 10^{+89}\right) \land \left(x \leq -7.6 \cdot 10^{+52} \lor \neg \left(x \leq 4.1 \cdot 10^{-75}\right) \land \left(x \leq 1.05 \cdot 10^{-22} \lor \neg \left(x \leq 8.5 \cdot 10^{+50}\right)\right)\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z\\ \end{array} \]

Alternative 2
Error	27.1
Cost	984

\[\begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+121}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -5.35 \cdot 10^{+89}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+59}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \]

Alternative 3
Error	29.3
Cost	984

\[\begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-111}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-275}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-192}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4
Error	0.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -31 \lor \neg \left(y \leq 0.5\right):\\ \;\;\;\;x \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} + z\\ \end{array} \]

Alternative 5
Error	15.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+98}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	33.9
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023031 
(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))