Average Error: 3.3 → 1.3
Time: 49.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -353705408395.80334:\\ \;\;\;\;\frac{t}{z \cdot \left(3.0 \cdot y\right)} + \left(x - \frac{y}{z \cdot 3.0}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{y}{z \cdot 3.0} - \frac{\frac{\frac{t}{z}}{3.0}}{y}\right)\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -353705408395.80334:\\
\;\;\;\;\frac{t}{z \cdot \left(3.0 \cdot y\right)} + \left(x - \frac{y}{z \cdot 3.0}\right)\\

\mathbf{else}:\\
\;\;\;\;x - \left(\frac{y}{z \cdot 3.0} - \frac{\frac{\frac{t}{z}}{3.0}}{y}\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r35485978 = x;
        double r35485979 = y;
        double r35485980 = z;
        double r35485981 = 3.0;
        double r35485982 = r35485980 * r35485981;
        double r35485983 = r35485979 / r35485982;
        double r35485984 = r35485978 - r35485983;
        double r35485985 = t;
        double r35485986 = r35485982 * r35485979;
        double r35485987 = r35485985 / r35485986;
        double r35485988 = r35485984 + r35485987;
        return r35485988;
}
↓
double f(double x, double y, double z, double t) {
        double r35485989 = y;
        double r35485990 = -353705408395.80334;
        bool r35485991 = r35485989 <= r35485990;
        double r35485992 = t;
        double r35485993 = z;
        double r35485994 = 3.0;
        double r35485995 = r35485994 * r35485989;
        double r35485996 = r35485993 * r35485995;
        double r35485997 = r35485992 / r35485996;
        double r35485998 = x;
        double r35485999 = r35485993 * r35485994;
        double r35486000 = r35485989 / r35485999;
        double r35486001 = r35485998 - r35486000;
        double r35486002 = r35485997 + r35486001;
        double r35486003 = r35485992 / r35485993;
        double r35486004 = r35486003 / r35485994;
        double r35486005 = r35486004 / r35485989;
        double r35486006 = r35486000 - r35486005;
        double r35486007 = r35485998 - r35486006;
        double r35486008 = r35485991 ? r35486002 : r35486007;
        return r35486008;
}

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

Original3.3
Target1.7
Herbie1.3
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -353705408395.80334

    1. Initial program 0.5

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

    3. Applied associate-/r*2.1

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

    5. Applied div-inv2.1

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

    6. Applied associate-/l*0.5

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

    7. Simplified0.5

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

    if -353705408395.80334 < y

    1. Initial program 4.2

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

    3. Applied associate-/r*1.5

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

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

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

    6. Applied associate-/r*1.5

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

    7. Simplified1.5

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

    9. Applied associate-+l-1.5

      \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3.0} - \frac{\frac{\frac{t}{z}}{3.0}}{y}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -353705408395.80334:\\ \;\;\;\;\frac{t}{z \cdot \left(3.0 \cdot y\right)} + \left(x - \frac{y}{z \cdot 3.0}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{y}{z \cdot 3.0} - \frac{\frac{\frac{t}{z}}{3.0}}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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))))