Average Error: 12.5 → 2.7
Time: 10.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.164590204538870698162352482223739848451 \cdot 10^{-122} \lor \neg \left(x \le 1.503950824539007656103296067322360995492 \cdot 10^{-300}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.164590204538870698162352482223739848451 \cdot 10^{-122} \lor \neg \left(x \le 1.503950824539007656103296067322360995492 \cdot 10^{-300}\right):\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r531615 = x;
        double r531616 = y;
        double r531617 = z;
        double r531618 = r531616 - r531617;
        double r531619 = r531615 * r531618;
        double r531620 = r531619 / r531616;
        return r531620;
}
↓
double f(double x, double y, double z) {
        double r531621 = x;
        double r531622 = -1.1645902045388707e-122;
        bool r531623 = r531621 <= r531622;
        double r531624 = 1.5039508245390077e-300;
        bool r531625 = r531621 <= r531624;
        double r531626 = !r531625;
        bool r531627 = r531623 || r531626;
        double r531628 = 1.0;
        double r531629 = z;
        double r531630 = y;
        double r531631 = r531629 / r531630;
        double r531632 = r531628 - r531631;
        double r531633 = r531621 * r531632;
        double r531634 = r531621 * r531629;
        double r531635 = r531634 / r531630;
        double r531636 = r531621 - r531635;
        double r531637 = r531627 ? r531633 : r531636;
        return r531637;
}

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

Original12.5
Target3.1
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.1645902045388707e-122 or 1.5039508245390077e-300 < x

    1. Initial program 13.4

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

    3. Applied *-un-lft-identity13.4

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

    4. Applied times-frac2.3

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

    5. Simplified2.3

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

    7. Applied div-sub2.3

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

    8. Simplified2.3

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

    if -1.1645902045388707e-122 < x < 1.5039508245390077e-300

    1. Initial program 8.1

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

    3. Applied associate-/l*6.9

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

    4. Taylor expanded around 0 4.4

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

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.164590204538870698162352482223739848451 \cdot 10^{-122} \lor \neg \left(x \le 1.503950824539007656103296067322360995492 \cdot 10^{-300}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :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))