Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A

Average Error: 0.1 → 0.0

Time: 2.5s

Precision: binary64

Cost: 448

\[ \begin{array}{c}[y, z] = \mathsf{sort}([y, z])\\ \end{array} \]

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y, double z) {
	return 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 - ((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 + (y * (z * (-4.0d0)))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Simplified 0.0

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

   [Start] 0.1	\[ x - \left(y \cdot 4\right) \cdot z \]
   associate-*l* [=>] 0.0	\[ x - \color{blue}{y \cdot \left(4 \cdot z\right)} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.8
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+32} \lor \neg \left(x \leq -350\right) \land x \leq 3.3 \cdot 10^{-72}:\\ \;\;\;\;-4 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	27.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023073 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))