Average Error: 12.7 → 2.8
Time: 11.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.490642558059576896453221775138123235637 \cdot 10^{-108} \lor \neg \left(z \le 1.856430226021134379054288393664915709911 \cdot 10^{-163}\right) \land z \le 1.195496640822689062730349933551884171007 \cdot 10^{233}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.490642558059576896453221775138123235637 \cdot 10^{-108} \lor \neg \left(z \le 1.856430226021134379054288393664915709911 \cdot 10^{-163}\right) \land z \le 1.195496640822689062730349933551884171007 \cdot 10^{233}:\\
\;\;\;\;x - \frac{z}{\frac{y}{x}}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\

\end{array}
double f(double x, double y, double z) {
        double r627492 = x;
        double r627493 = y;
        double r627494 = z;
        double r627495 = r627493 - r627494;
        double r627496 = r627492 * r627495;
        double r627497 = r627496 / r627493;
        return r627497;
}
↓
double f(double x, double y, double z) {
        double r627498 = z;
        double r627499 = -1.4906425580595769e-108;
        bool r627500 = r627498 <= r627499;
        double r627501 = 1.8564302260211344e-163;
        bool r627502 = r627498 <= r627501;
        double r627503 = !r627502;
        double r627504 = 1.195496640822689e+233;
        bool r627505 = r627498 <= r627504;
        bool r627506 = r627503 && r627505;
        bool r627507 = r627500 || r627506;
        double r627508 = x;
        double r627509 = y;
        double r627510 = r627509 / r627508;
        double r627511 = r627498 / r627510;
        double r627512 = r627508 - r627511;
        double r627513 = 1.0;
        double r627514 = r627509 - r627498;
        double r627515 = r627509 / r627514;
        double r627516 = r627515 / r627508;
        double r627517 = r627513 / r627516;
        double r627518 = r627507 ? r627512 : r627517;
        return r627518;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.7
Target3.0
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.4906425580595769e-108 or 1.8564302260211344e-163 < z < 1.195496640822689e+233

    1. Initial program 11.6

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

    2. Simplified11.3

      \[\leadsto \color{blue}{\frac{y - z}{\frac{y}{x}}}\]
    3. Using strategy rm

    4. Applied div-sub11.3

      \[\leadsto \color{blue}{\frac{y}{\frac{y}{x}} - \frac{z}{\frac{y}{x}}}\]

    5. Simplified3.5

      \[\leadsto \color{blue}{1 \cdot x} - \frac{z}{\frac{y}{x}}\]

    if -1.4906425580595769e-108 < z < 1.8564302260211344e-163 or 1.195496640822689e+233 < z

    1. Initial program 14.4

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

    2. Simplified14.2

      \[\leadsto \color{blue}{\frac{y - z}{\frac{y}{x}}}\]
    3. Using strategy rm

    4. Applied clear-num14.3

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y}{x}}{y - z}}}\]

    5. Simplified1.7

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{y}{y - z}}{x}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.490642558059576896453221775138123235637 \cdot 10^{-108} \lor \neg \left(z \le 1.856430226021134379054288393664915709911 \cdot 10^{-163}\right) \land z \le 1.195496640822689062730349933551884171007 \cdot 10^{233}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))