Average Error: 0.1 → 0.1
Time: 5.7s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[y \cdot 5 + \left(2 \cdot \left(z + y\right) + t\right) \cdot x\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
y \cdot 5 + \left(2 \cdot \left(z + y\right) + t\right) \cdot x
double f(double x, double y, double z, double t) {
        double r188853 = x;
        double r188854 = y;
        double r188855 = z;
        double r188856 = r188854 + r188855;
        double r188857 = r188856 + r188855;
        double r188858 = r188857 + r188854;
        double r188859 = t;
        double r188860 = r188858 + r188859;
        double r188861 = r188853 * r188860;
        double r188862 = 5.0;
        double r188863 = r188854 * r188862;
        double r188864 = r188861 + r188863;
        return r188864;
}
↓
double f(double x, double y, double z, double t) {
        double r188865 = y;
        double r188866 = 5.0;
        double r188867 = r188865 * r188866;
        double r188868 = 2.0;
        double r188869 = z;
        double r188870 = r188869 + r188865;
        double r188871 = r188868 * r188870;
        double r188872 = t;
        double r188873 = r188871 + r188872;
        double r188874 = x;
        double r188875 = r188873 * r188874;
        double r188876 = r188867 + r188875;
        return r188876;
}

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. Using strategy rm

  3. Applied pow10.1

    \[\leadsto x \cdot \color{blue}{{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}^{1}} + y \cdot 5\]

  4. Applied pow10.1

    \[\leadsto \color{blue}{{x}^{1}} \cdot {\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}^{1} + y \cdot 5\]

  5. Applied pow-prod-down0.1

    \[\leadsto \color{blue}{{\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}^{1}} + y \cdot 5\]

  6. Simplified0.1

    \[\leadsto {\color{blue}{\left(\left(2 \cdot \left(z + y\right) + t\right) \cdot x\right)}}^{1} + y \cdot 5\]

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5)))