Average Error: 3.6 → 1.4
Time: 24.1s
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 r29239529 = x;
        double r29239530 = y;
        double r29239531 = z;
        double r29239532 = 3.0;
        double r29239533 = r29239531 * r29239532;
        double r29239534 = r29239530 / r29239533;
        double r29239535 = r29239529 - r29239534;
        double r29239536 = t;
        double r29239537 = r29239533 * r29239530;
        double r29239538 = r29239536 / r29239537;
        double r29239539 = r29239535 + r29239538;
        return r29239539;
}
↓
double f(double x, double y, double z, double t) {
        double r29239540 = y;
        double r29239541 = -4.651048463710014e+38;
        bool r29239542 = r29239540 <= r29239541;
        double r29239543 = t;
        double r29239544 = 3.0;
        double r29239545 = z;
        double r29239546 = r29239544 * r29239545;
        double r29239547 = r29239540 * r29239546;
        double r29239548 = r29239543 / r29239547;
        double r29239549 = x;
        double r29239550 = r29239540 / r29239545;
        double r29239551 = r29239550 / r29239544;
        double r29239552 = r29239549 - r29239551;
        double r29239553 = r29239548 + r29239552;
        double r29239554 = r29239543 / r29239544;
        double r29239555 = r29239554 / r29239545;
        double r29239556 = r29239555 / r29239540;
        double r29239557 = 1.0;
        double r29239558 = r29239557 / r29239545;
        double r29239559 = r29239540 / r29239544;
        double r29239560 = r29239558 * r29239559;
        double r29239561 = r29239549 - r29239560;
        double r29239562 = r29239556 + r29239561;
        double r29239563 = r29239542 ? r29239553 : r29239562;
        return r29239563;
}

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))))