Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

Average Error: 0.0 → 0.0

Time: 3.5s

Precision: binary64

Cost: 576

Math

\[x \cdot x - \left(y \cdot 4\right) \cdot z \]

↓

\[x \cdot x + \left(y \cdot z\right) \cdot -4 \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x x) (* (* y 4.0) z)))

↓

(FPCore (x y z) :precision binary64 (+ (* x x) (* (* y z) -4.0)))

C

double code(double x, double y, double z) {
	return (x * x) - ((y * 4.0) * z);
}

↓

double code(double x, double y, double z) {
	return (x * x) + ((y * z) * -4.0);
}

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 * x) - ((y * 4.0d0) * 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 * x) + ((y * z) * (-4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return (x * x) - ((y * 4.0) * z);
}

↓

public static double code(double x, double y, double z) {
	return (x * x) + ((y * z) * -4.0);
}

Python

def code(x, y, z):
	return (x * x) - ((y * 4.0) * z)

↓

def code(x, y, z):
	return (x * x) + ((y * z) * -4.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * x) - Float64(Float64(y * 4.0) * z))
end

↓

function code(x, y, z)
	return Float64(Float64(x * x) + Float64(Float64(y * z) * -4.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * x) - ((y * 4.0) * z);
end

↓

function tmp = code(x, y, z)
	tmp = (x * x) + ((y * z) * -4.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * x), $MachinePrecision] - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(x * x), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[x \cdot x - \left(y \cdot 4\right) \cdot z \]

2. Taylor expanded in y around 0 0.0

   \[\leadsto x \cdot x - \color{blue}{4 \cdot \left(y \cdot z\right)} \]

3. Final simplification 0.0

   \[\leadsto x \cdot x + \left(y \cdot z\right) \cdot -4 \]

Alternatives

Alternative 1
Error	11.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3938974253818427 \cdot 10^{+27}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1.607963984789733 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	36.4
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4.0) z)))