Average Error: 3.9 → 0.4
Time: 6.6s
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 r761402 = x;
        double r761403 = y;
        double r761404 = z;
        double r761405 = 3.0;
        double r761406 = r761404 * r761405;
        double r761407 = r761403 / r761406;
        double r761408 = r761402 - r761407;
        double r761409 = t;
        double r761410 = r761406 * r761403;
        double r761411 = r761409 / r761410;
        double r761412 = r761408 + r761411;
        return r761412;
}
↓
double f(double x, double y, double z, double t) {
        double r761413 = t;
        double r761414 = -43648.09610487145;
        bool r761415 = r761413 <= r761414;
        double r761416 = 5.854675196306246e+46;
        bool r761417 = r761413 <= r761416;
        double r761418 = !r761417;
        bool r761419 = r761415 || r761418;
        double r761420 = x;
        double r761421 = 0.3333333333333333;
        double r761422 = y;
        double r761423 = z;
        double r761424 = r761422 / r761423;
        double r761425 = r761421 * r761424;
        double r761426 = r761420 - r761425;
        double r761427 = 3.0;
        double r761428 = r761423 * r761427;
        double r761429 = r761428 * r761422;
        double r761430 = r761413 / r761429;
        double r761431 = r761426 + r761430;
        double r761432 = r761422 / r761428;
        double r761433 = r761420 - r761432;
        double r761434 = 1.0;
        double r761435 = r761434 / r761423;
        double r761436 = r761413 / r761427;
        double r761437 = r761422 / r761436;
        double r761438 = r761435 / r761437;
        double r761439 = r761433 + r761438;
        double r761440 = r761419 ? r761431 : r761439;
        return r761440;
}

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 +o rules:numerics
(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))))