Average Error: 3.6 → 1.4
Time: 20.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -465104846371001377193813340330265673728:\\ \;\;\;\;\frac{t}{y \cdot \left(3 \cdot z\right)} + \left(x - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{t}{3}}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -465104846371001377193813340330265673728:\\
\;\;\;\;\frac{t}{y \cdot \left(3 \cdot z\right)} + \left(x - \frac{\frac{y}{z}}{3}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{\frac{t}{3}}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r29239703 = x;
        double r29239704 = y;
        double r29239705 = z;
        double r29239706 = 3.0;
        double r29239707 = r29239705 * r29239706;
        double r29239708 = r29239704 / r29239707;
        double r29239709 = r29239703 - r29239708;
        double r29239710 = t;
        double r29239711 = r29239707 * r29239704;
        double r29239712 = r29239710 / r29239711;
        double r29239713 = r29239709 + r29239712;
        return r29239713;
}
↓
double f(double x, double y, double z, double t) {
        double r29239714 = y;
        double r29239715 = -4.651048463710014e+38;
        bool r29239716 = r29239714 <= r29239715;
        double r29239717 = t;
        double r29239718 = 3.0;
        double r29239719 = z;
        double r29239720 = r29239718 * r29239719;
        double r29239721 = r29239714 * r29239720;
        double r29239722 = r29239717 / r29239721;
        double r29239723 = x;
        double r29239724 = r29239714 / r29239719;
        double r29239725 = r29239724 / r29239718;
        double r29239726 = r29239723 - r29239725;
        double r29239727 = r29239722 + r29239726;
        double r29239728 = r29239717 / r29239718;
        double r29239729 = r29239728 / r29239719;
        double r29239730 = r29239729 / r29239714;
        double r29239731 = 1.0;
        double r29239732 = r29239731 / r29239719;
        double r29239733 = r29239714 / r29239718;
        double r29239734 = r29239732 * r29239733;
        double r29239735 = r29239723 - r29239734;
        double r29239736 = r29239730 + r29239735;
        double r29239737 = r29239716 ? r29239727 : r29239736;
        return r29239737;
}

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
Target1.8
Herbie1.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.651048463710014e+38

    1. Initial program 0.5

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*0.5

      \[\leadsto \left(x - \color{blue}{\frac{\frac{y}{z}}{3}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]

    if -4.651048463710014e+38 < y

    1. Initial program 4.4

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*1.7

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]
    4. Using strategy rm

    5. Applied associate-/r*1.7

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity1.7

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\frac{t}{z}}{3}}{\color{blue}{1 \cdot y}}\]

    8. Applied associate-/r*1.7

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{\frac{\frac{t}{z}}{3}}{1}}{y}}\]

    9. Simplified1.7

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{3}}{z}}}{y}\]
    10. Using strategy rm

    11. Applied *-un-lft-identity1.7

      \[\leadsto \left(x - \frac{\color{blue}{1 \cdot y}}{z \cdot 3}\right) + \frac{\frac{\frac{t}{3}}{z}}{y}\]

    12. Applied times-frac1.7

      \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}}\right) + \frac{\frac{\frac{t}{3}}{z}}{y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -465104846371001377193813340330265673728:\\ \;\;\;\;\frac{t}{y \cdot \left(3 \cdot z\right)} + \left(x - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{t}{3}}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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))))