Average Error: 3.6 → 2.5
Time: 18.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 3.472080681334310435565607809050836361326 \cdot 10^{-277} \lor \neg \left(y \le 1.630497026224573899168920625461559533427 \cdot 10^{76}\right):\\ \;\;\;\;\left(x - y \cdot \frac{\frac{1}{z}}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le 3.472080681334310435565607809050836361326 \cdot 10^{-277} \lor \neg \left(y \le 1.630497026224573899168920625461559533427 \cdot 10^{76}\right):\\
\;\;\;\;\left(x - y \cdot \frac{\frac{1}{z}}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r542470 = x;
        double r542471 = y;
        double r542472 = z;
        double r542473 = 3.0;
        double r542474 = r542472 * r542473;
        double r542475 = r542471 / r542474;
        double r542476 = r542470 - r542475;
        double r542477 = t;
        double r542478 = r542474 * r542471;
        double r542479 = r542477 / r542478;
        double r542480 = r542476 + r542479;
        return r542480;
}
↓
double f(double x, double y, double z, double t) {
        double r542481 = y;
        double r542482 = 3.4720806813343104e-277;
        bool r542483 = r542481 <= r542482;
        double r542484 = 1.630497026224574e+76;
        bool r542485 = r542481 <= r542484;
        double r542486 = !r542485;
        bool r542487 = r542483 || r542486;
        double r542488 = x;
        double r542489 = 1.0;
        double r542490 = z;
        double r542491 = r542489 / r542490;
        double r542492 = 3.0;
        double r542493 = r542491 / r542492;
        double r542494 = r542481 * r542493;
        double r542495 = r542488 - r542494;
        double r542496 = t;
        double r542497 = r542496 / r542492;
        double r542498 = r542481 / r542497;
        double r542499 = r542491 / r542498;
        double r542500 = r542495 + r542499;
        double r542501 = r542490 * r542492;
        double r542502 = r542501 / r542481;
        double r542503 = r542489 / r542502;
        double r542504 = r542488 - r542503;
        double r542505 = r542496 / r542501;
        double r542506 = r542505 / r542481;
        double r542507 = r542504 + r542506;
        double r542508 = r542487 ? r542500 : r542507;
        return r542508;
}

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
Target1.7
Herbie2.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < 3.4720806813343104e-277 or 1.630497026224574e+76 < y

    1. Initial program 3.3

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

    3. Applied associate-/r*1.9

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

    5. Applied *-un-lft-identity1.9

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

    6. Applied times-frac1.9

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

    7. Applied associate-/l*3.0

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

    9. Applied div-inv3.0

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

    10. Simplified3.0

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

    if 3.4720806813343104e-277 < y < 1.630497026224574e+76

    1. Initial program 4.3

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

    3. Applied associate-/r*1.3

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

    5. Applied clear-num1.4

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 3.472080681334310435565607809050836361326 \cdot 10^{-277} \lor \neg \left(y \le 1.630497026224573899168920625461559533427 \cdot 10^{76}\right):\\ \;\;\;\;\left(x - y \cdot \frac{\frac{1}{z}}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(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))))