Average Error: 13.0 → 2.9
Time: 37.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -9.521607613845950007453395248426574870158 \cdot 10^{-68}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \mathbf{elif}\;y \le 3.555941013430806308389190149371115498978 \cdot 10^{-139}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -9.521607613845950007453395248426574870158 \cdot 10^{-68}:\\
\;\;\;\;\frac{y - z}{y} \cdot x\\

\mathbf{elif}\;y \le 3.555941013430806308389190149371115498978 \cdot 10^{-139}:\\
\;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r35570513 = x;
        double r35570514 = y;
        double r35570515 = z;
        double r35570516 = r35570514 - r35570515;
        double r35570517 = r35570513 * r35570516;
        double r35570518 = r35570517 / r35570514;
        return r35570518;
}
↓
double f(double x, double y, double z) {
        double r35570519 = y;
        double r35570520 = -9.52160761384595e-68;
        bool r35570521 = r35570519 <= r35570520;
        double r35570522 = z;
        double r35570523 = r35570519 - r35570522;
        double r35570524 = r35570523 / r35570519;
        double r35570525 = x;
        double r35570526 = r35570524 * r35570525;
        double r35570527 = 3.555941013430806e-139;
        bool r35570528 = r35570519 <= r35570527;
        double r35570529 = 1.0;
        double r35570530 = r35570525 * r35570523;
        double r35570531 = r35570519 / r35570530;
        double r35570532 = r35570529 / r35570531;
        double r35570533 = r35570528 ? r35570532 : r35570526;
        double r35570534 = r35570521 ? r35570526 : r35570533;
        return r35570534;
}

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

Original13.0
Target3.2
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -9.52160761384595e-68 or 3.555941013430806e-139 < y

    1. Initial program 14.1

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

    3. Applied *-un-lft-identity14.1

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    if -9.52160761384595e-68 < y < 3.555941013430806e-139

    1. Initial program 9.7

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

    3. Applied clear-num9.8

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -9.521607613845950007453395248426574870158 \cdot 10^{-68}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \mathbf{elif}\;y \le 3.555941013430806308389190149371115498978 \cdot 10^{-139}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 +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))