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

Average Error: 0.1 → 0.1

Time: 3.7s

Precision: binary64

Cost: 320

Math

\[x - \frac{3}{8} \cdot y \]

↓

\[x - 0.375 \cdot y \]

FPCore

(FPCore (x y) :precision binary64 (- x (* (/ 3.0 8.0) y)))

↓

(FPCore (x y) :precision binary64 (- x (* 0.375 y)))

C

double code(double x, double y) {
	return x - ((3.0 / 8.0) * y);
}

↓

double code(double x, double y) {
	return x - (0.375 * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - ((3.0d0 / 8.0d0) * y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (0.375d0 * y)
end function

Java

public static double code(double x, double y) {
	return x - ((3.0 / 8.0) * y);
}

↓

public static double code(double x, double y) {
	return x - (0.375 * y);
}

Python

def code(x, y):
	return x - ((3.0 / 8.0) * y)

↓

def code(x, y):
	return x - (0.375 * y)

Julia

function code(x, y)
	return Float64(x - Float64(Float64(3.0 / 8.0) * y))
end

↓

function code(x, y)
	return Float64(x - Float64(0.375 * y))
end

MATLAB

function tmp = code(x, y)
	tmp = x - ((3.0 / 8.0) * y);
end

↓

function tmp = code(x, y)
	tmp = x - (0.375 * y);
end

Wolfram

code[x_, y_] := N[(x - N[(N[(3.0 / 8.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(x - N[(0.375 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[x - \frac{3}{8} \cdot y \]

2. Simplified 0.1

   \[\leadsto \color{blue}{x - 0.375 \cdot y} \]
   Proof

   [Start] 0.1	\[ x - \frac{3}{8} \cdot y \]
   metadata-eval [=>] 0.1	\[ x - \color{blue}{0.375} \cdot y \]

3. Final simplification 0.1

   \[\leadsto x - 0.375 \cdot y \]

Alternatives

Alternative 1
Error	16.9
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-21}:\\ \;\;\;\;-0.375 \cdot y\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.55 \cdot 10^{+76}:\\ \;\;\;\;-0.375 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	31.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023068 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (/ 3.0 8.0) y)))