Average Error: 12.2 → 3.0
Time: 15.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.129631320517597363958139490268193814357 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;y \le 3.156569997277614025814580562307745592284 \cdot 10^{-264}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.129631320517597363958139490268193814357 \cdot 10^{-30}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;y \le 3.156569997277614025814580562307745592284 \cdot 10^{-264}:\\
\;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r30055496 = x;
        double r30055497 = y;
        double r30055498 = z;
        double r30055499 = r30055497 - r30055498;
        double r30055500 = r30055496 * r30055499;
        double r30055501 = r30055500 / r30055497;
        return r30055501;
}
↓
double f(double x, double y, double z) {
        double r30055502 = y;
        double r30055503 = -5.1296313205175974e-30;
        bool r30055504 = r30055502 <= r30055503;
        double r30055505 = x;
        double r30055506 = z;
        double r30055507 = r30055502 - r30055506;
        double r30055508 = r30055502 / r30055507;
        double r30055509 = r30055505 / r30055508;
        double r30055510 = 3.156569997277614e-264;
        bool r30055511 = r30055502 <= r30055510;
        double r30055512 = 1.0;
        double r30055513 = r30055505 * r30055507;
        double r30055514 = r30055502 / r30055513;
        double r30055515 = r30055512 / r30055514;
        double r30055516 = r30055506 / r30055502;
        double r30055517 = r30055512 - r30055516;
        double r30055518 = r30055517 * r30055505;
        double r30055519 = r30055511 ? r30055515 : r30055518;
        double r30055520 = r30055504 ? r30055509 : r30055519;
        return r30055520;
}

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

Original12.2
Target2.9
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -5.1296313205175974e-30

    1. Initial program 15.7

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

    3. Applied associate-/l*0.1

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

    if -5.1296313205175974e-30 < y < 3.156569997277614e-264

    1. Initial program 7.9

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

    3. Applied clear-num8.0

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

    if 3.156569997277614e-264 < y

    1. Initial program 11.7

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

    3. Applied *-un-lft-identity11.7

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

    4. Applied times-frac2.8

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

    5. Simplified2.8

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

    7. Applied div-sub2.7

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

    8. Simplified2.7

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.129631320517597363958139490268193814357 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;y \le 3.156569997277614025814580562307745592284 \cdot 10^{-264}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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))