Average Error: 12.8 → 3.0
Time: 2.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.5365340962361011 \cdot 10^{-241} \lor \neg \left(y \le 1.66582439427973057 \cdot 10^{-242}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.5365340962361011 \cdot 10^{-241} \lor \neg \left(y \le 1.66582439427973057 \cdot 10^{-242}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r905000 = x;
        double r905001 = y;
        double r905002 = z;
        double r905003 = r905001 - r905002;
        double r905004 = r905000 * r905003;
        double r905005 = r905004 / r905001;
        return r905005;
}
↓
double f(double x, double y, double z) {
        double r905006 = y;
        double r905007 = -2.536534096236101e-241;
        bool r905008 = r905006 <= r905007;
        double r905009 = 1.6658243942797306e-242;
        bool r905010 = r905006 <= r905009;
        double r905011 = !r905010;
        bool r905012 = r905008 || r905011;
        double r905013 = x;
        double r905014 = z;
        double r905015 = r905006 - r905014;
        double r905016 = r905006 / r905015;
        double r905017 = r905013 / r905016;
        double r905018 = r905013 / r905006;
        double r905019 = r905018 * r905015;
        double r905020 = r905012 ? r905017 : r905019;
        return r905020;
}

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

Original12.8
Target3.3
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.536534096236101e-241 or 1.6658243942797306e-242 < y

    1. Initial program 12.8

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

    3. Applied associate-/l*2.2

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

    if -2.536534096236101e-241 < y < 1.6658243942797306e-242

    1. Initial program 13.2

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

    3. Applied associate-/l*13.4

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

    5. Applied associate-/r/13.7

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.5365340962361011 \cdot 10^{-241} \lor \neg \left(y \le 1.66582439427973057 \cdot 10^{-242}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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))