Average Error: 3.9 → 0.4
Time: 4.6s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -43648.09610487145255319774150848388671875 \lor \neg \left(t \le 5.854675196306246238384814072270733670477 \cdot 10^{46}\right):\\ \;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -43648.09610487145255319774150848388671875 \lor \neg \left(t \le 5.854675196306246238384814072270733670477 \cdot 10^{46}\right):\\
\;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r656255 = x;
        double r656256 = y;
        double r656257 = z;
        double r656258 = 3.0;
        double r656259 = r656257 * r656258;
        double r656260 = r656256 / r656259;
        double r656261 = r656255 - r656260;
        double r656262 = t;
        double r656263 = r656259 * r656256;
        double r656264 = r656262 / r656263;
        double r656265 = r656261 + r656264;
        return r656265;
}
↓
double f(double x, double y, double z, double t) {
        double r656266 = t;
        double r656267 = -43648.09610487145;
        bool r656268 = r656266 <= r656267;
        double r656269 = 5.854675196306246e+46;
        bool r656270 = r656266 <= r656269;
        double r656271 = !r656270;
        bool r656272 = r656268 || r656271;
        double r656273 = x;
        double r656274 = 0.3333333333333333;
        double r656275 = y;
        double r656276 = z;
        double r656277 = r656275 / r656276;
        double r656278 = r656274 * r656277;
        double r656279 = r656273 - r656278;
        double r656280 = 3.0;
        double r656281 = r656276 * r656280;
        double r656282 = r656281 * r656275;
        double r656283 = r656266 / r656282;
        double r656284 = r656279 + r656283;
        double r656285 = r656275 / r656281;
        double r656286 = r656273 - r656285;
        double r656287 = 1.0;
        double r656288 = r656287 / r656276;
        double r656289 = r656266 / r656280;
        double r656290 = r656275 / r656289;
        double r656291 = r656288 / r656290;
        double r656292 = r656286 + r656291;
        double r656293 = r656272 ? r656284 : r656292;
        return r656293;
}

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

Original3.9
Target1.6
Herbie0.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -43648.09610487145 or 5.854675196306246e+46 < t

    1. Initial program 0.6

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

    2. Taylor expanded around 0 0.7

      \[\leadsto \left(x - \color{blue}{0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]

    if -43648.09610487145 < t < 5.854675196306246e+46

    1. Initial program 5.8

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

    3. Applied associate-/r*1.0

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

    5. Applied *-un-lft-identity1.0

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

    6. Applied times-frac1.0

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

    7. Applied associate-/l*0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -43648.09610487145255319774150848388671875 \lor \neg \left(t \le 5.854675196306246238384814072270733670477 \cdot 10^{46}\right):\\ \;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))