Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B

Average Error: 0.1 → 0.1

Time: 3.8s

Precision: binary64

Math

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

↓

\[0.5 \cdot \frac{x}{t} + 0.5 \cdot \left(\frac{y}{t} - \frac{z}{t}\right) \]

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Taylor expanded in x around inf 0.1

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

3. Final simplification 0.1

   \[\leadsto 0.5 \cdot \frac{x}{t} + 0.5 \cdot \left(\frac{y}{t} - \frac{z}{t}\right) \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))