Average Error: 0.1 → 0.1
Time: 20.9s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[y \cdot 5 + \left(\left(2 \cdot x\right) \cdot \left(y + z\right) + t \cdot x\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
y \cdot 5 + \left(\left(2 \cdot x\right) \cdot \left(y + z\right) + t \cdot x\right)
double f(double x, double y, double z, double t) {
        double r149076 = x;
        double r149077 = y;
        double r149078 = z;
        double r149079 = r149077 + r149078;
        double r149080 = r149079 + r149078;
        double r149081 = r149080 + r149077;
        double r149082 = t;
        double r149083 = r149081 + r149082;
        double r149084 = r149076 * r149083;
        double r149085 = 5.0;
        double r149086 = r149077 * r149085;
        double r149087 = r149084 + r149086;
        return r149087;
}
↓
double f(double x, double y, double z, double t) {
        double r149088 = y;
        double r149089 = 5.0;
        double r149090 = r149088 * r149089;
        double r149091 = 2.0;
        double r149092 = x;
        double r149093 = r149091 * r149092;
        double r149094 = z;
        double r149095 = r149088 + r149094;
        double r149096 = r149093 * r149095;
        double r149097 = t;
        double r149098 = r149097 * r149092;
        double r149099 = r149096 + r149098;
        double r149100 = r149090 + r149099;
        return r149100;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]

  2. Simplified0.1

    \[\leadsto \color{blue}{y \cdot 5 + \left(2 \cdot \left(y + z\right) + t\right) \cdot x}\]

  3. Taylor expanded around inf 0.1

    \[\leadsto y \cdot 5 + \color{blue}{\left(2 \cdot \left(x \cdot z\right) + \left(2 \cdot \left(x \cdot y\right) + t \cdot x\right)\right)}\]

  4. Simplified0.1

    \[\leadsto y \cdot 5 + \color{blue}{\left(\left(2 \cdot x\right) \cdot \left(y + z\right) + t \cdot x\right)}\]

  5. Final simplification0.1

    \[\leadsto y \cdot 5 + \left(\left(2 \cdot x\right) \cdot \left(y + z\right) + t \cdot x\right)\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))