Average Error: 3.6 → 2.0
Time: 11.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4304353906633112215992288673792:\\ \;\;\;\;\left(x - y \cdot \frac{1}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -4304353906633112215992288673792:\\
\;\;\;\;\left(x - y \cdot \frac{1}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r832456 = x;
        double r832457 = y;
        double r832458 = z;
        double r832459 = 3.0;
        double r832460 = r832458 * r832459;
        double r832461 = r832457 / r832460;
        double r832462 = r832456 - r832461;
        double r832463 = t;
        double r832464 = r832460 * r832457;
        double r832465 = r832463 / r832464;
        double r832466 = r832462 + r832465;
        return r832466;
}
↓
double f(double x, double y, double z, double t) {
        double r832467 = t;
        double r832468 = -4.304353906633112e+30;
        bool r832469 = r832467 <= r832468;
        double r832470 = x;
        double r832471 = y;
        double r832472 = 1.0;
        double r832473 = z;
        double r832474 = 3.0;
        double r832475 = r832473 * r832474;
        double r832476 = r832472 / r832475;
        double r832477 = r832471 * r832476;
        double r832478 = r832470 - r832477;
        double r832479 = r832475 * r832471;
        double r832480 = r832467 / r832479;
        double r832481 = r832478 + r832480;
        double r832482 = r832475 / r832471;
        double r832483 = r832472 / r832482;
        double r832484 = r832470 - r832483;
        double r832485 = r832472 / r832473;
        double r832486 = r832467 / r832474;
        double r832487 = r832471 / r832486;
        double r832488 = r832485 / r832487;
        double r832489 = r832484 + r832488;
        double r832490 = r832469 ? r832481 : r832489;
        return r832490;
}

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
Herbie2.0
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4.304353906633112e+30

    1. Initial program 0.6

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

    3. Applied div-inv0.7

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

    if -4.304353906633112e+30 < t

    1. Initial program 4.2

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

    3. Applied associate-/r*1.5

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

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

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

    6. Applied times-frac1.5

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

    7. Applied associate-/l*2.3

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

    9. Applied clear-num2.3

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4304353906633112215992288673792:\\ \;\;\;\;\left(x - y \cdot \frac{1}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 
(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))))