Average Error: 3.6 → 1.6
Time: 20.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\frac{\frac{\frac{t}{z}}{3.0}}{y} + \left(x - \frac{\frac{y}{z}}{3.0}\right)\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\frac{\frac{\frac{t}{z}}{3.0}}{y} + \left(x - \frac{\frac{y}{z}}{3.0}\right)
double f(double x, double y, double z, double t) {
        double r38586756 = x;
        double r38586757 = y;
        double r38586758 = z;
        double r38586759 = 3.0;
        double r38586760 = r38586758 * r38586759;
        double r38586761 = r38586757 / r38586760;
        double r38586762 = r38586756 - r38586761;
        double r38586763 = t;
        double r38586764 = r38586760 * r38586757;
        double r38586765 = r38586763 / r38586764;
        double r38586766 = r38586762 + r38586765;
        return r38586766;
}
↓
double f(double x, double y, double z, double t) {
        double r38586767 = t;
        double r38586768 = z;
        double r38586769 = r38586767 / r38586768;
        double r38586770 = 3.0;
        double r38586771 = r38586769 / r38586770;
        double r38586772 = y;
        double r38586773 = r38586771 / r38586772;
        double r38586774 = x;
        double r38586775 = r38586772 / r38586768;
        double r38586776 = r38586775 / r38586770;
        double r38586777 = r38586774 - r38586776;
        double r38586778 = r38586773 + r38586777;
        return r38586778;
}

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

Target

Original3.6
Target1.6
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]

Derivation

  1. Initial program 3.6

    \[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r*1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3.0}}{y}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{\color{blue}{1 \cdot y}}\]

  6. Applied associate-/r*1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{\frac{\frac{t}{z \cdot 3.0}}{1}}{y}}\]

  7. Simplified1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3.0}}}{y}\]
  8. Using strategy rm

  9. Applied associate-/r*1.6

    \[\leadsto \left(x - \color{blue}{\frac{\frac{y}{z}}{3.0}}\right) + \frac{\frac{\frac{t}{z}}{3.0}}{y}\]

  10. Final simplification1.6

    \[\leadsto \frac{\frac{\frac{t}{z}}{3.0}}{y} + \left(x - \frac{\frac{y}{z}}{3.0}\right)\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))