Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

Average Error: 0.0 → 0.0

Time: 2.4s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

def code(x, y, z):
	return (x * x) + (z * (y * -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(z * Float64(y * -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) + (z * (y * -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[(z * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	12.4
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-64} \lor \neg \left(x \leq 0.0082\right) \land x \leq 1.6 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(z \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	36.2
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2023039 
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4.0) z)))