Average Error: 12.2 → 2.6
Time: 2.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 5.8561005025320592 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;x \le 7.80513442966517965 \cdot 10^{-43}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le 5.8561005025320592 \cdot 10^{-177}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;x \le 7.80513442966517965 \cdot 10^{-43}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r803997 = x;
        double r803998 = y;
        double r803999 = z;
        double r804000 = r803998 - r803999;
        double r804001 = r803997 * r804000;
        double r804002 = r804001 / r803998;
        return r804002;
}
↓
double f(double x, double y, double z) {
        double r804003 = x;
        double r804004 = 5.856100502532059e-177;
        bool r804005 = r804003 <= r804004;
        double r804006 = y;
        double r804007 = z;
        double r804008 = r804006 - r804007;
        double r804009 = r804006 / r804008;
        double r804010 = r804003 / r804009;
        double r804011 = 7.80513442966518e-43;
        bool r804012 = r804003 <= r804011;
        double r804013 = r804003 * r804007;
        double r804014 = r804013 / r804006;
        double r804015 = r804003 - r804014;
        double r804016 = r804008 / r804006;
        double r804017 = r804003 * r804016;
        double r804018 = r804012 ? r804015 : r804017;
        double r804019 = r804005 ? r804010 : r804018;
        return r804019;
}

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
Target3.0
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < 5.856100502532059e-177

    1. Initial program 11.4

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

    3. Applied associate-/l*3.8

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

    if 5.856100502532059e-177 < x < 7.80513442966518e-43

    1. Initial program 1.9

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

    3. Applied associate-/l*4.9

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

    4. Taylor expanded around 0 1.0

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

    if 7.80513442966518e-43 < x

    1. Initial program 19.0

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

    3. Applied *-un-lft-identity19.0

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 5.8561005025320592 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;x \le 7.80513442966517965 \cdot 10^{-43}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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))