Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

Average Error: 0.0 → 12.6

Time: 3.5s

Precision: binary64

Cost: 584

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -8.825758568846344 \cdot 10^{+58}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 123168817.04912652:\\ \;\;\;\;z \cdot \left(-4 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.825758568846344e+58)
   (* x x)
   (if (<= x 123168817.04912652) (* z (* -4.0 y)) (* x x))))

C

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

↓

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.825758568846344e+58) {
		tmp = x * x;
	} else if (x <= 123168817.04912652) {
		tmp = z * (-4.0 * y);
	} else {
		tmp = x * x;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (x <= (-8.825758568846344d+58)) then
        tmp = x * x
    else if (x <= 123168817.04912652d0) then
        tmp = z * ((-4.0d0) * y)
    else
        tmp = x * x
    end if
    code = tmp
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) {
	double tmp;
	if (x <= -8.825758568846344e+58) {
		tmp = x * x;
	} else if (x <= 123168817.04912652) {
		tmp = z * (-4.0 * y);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	tmp = 0
	if x <= -8.825758568846344e+58:
		tmp = x * x
	elif x <= 123168817.04912652:
		tmp = z * (-4.0 * y)
	else:
		tmp = x * x
	return tmp

Julia

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

↓

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.825758568846344e+58)
		tmp = Float64(x * x);
	elseif (x <= 123168817.04912652)
		tmp = Float64(z * Float64(-4.0 * y));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.825758568846344e+58)
		tmp = x * x;
	elseif (x <= 123168817.04912652)
		tmp = z * (-4.0 * y);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := If[LessEqual[x, -8.825758568846344e+58], N[(x * x), $MachinePrecision], If[LessEqual[x, 123168817.04912652], N[(z * N[(-4.0 * y), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.82575856884634358e58 or 123168817.049126521 < x

   1. Initial program 0.0

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

   2. Taylor expanded in x around inf 10.0

      \[\leadsto \color{blue}{{x}^{2}} \]

   3. Simplified 10.0

      \[\leadsto \color{blue}{x \cdot x} \]

   if -8.82575856884634358e58 < x < 123168817.049126521

   1. Initial program 0.0

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

   2. Taylor expanded in x around 0 13.5

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

   3. Simplified 13.5

      \[\leadsto \color{blue}{z \cdot \left(-4 \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 12.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.825758568846344 \cdot 10^{+58}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 123168817.04912652:\\ \;\;\;\;z \cdot \left(-4 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternatives

Alternative 1
Error	35.9
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4.0) z)))