Average Error: 12.9 → 1.7
Time: 2.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.20696722601438008 \cdot 10^{57} \lor \neg \left(y \le 1.0892891581621931 \cdot 10^{51}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.20696722601438008 \cdot 10^{57} \lor \neg \left(y \le 1.0892891581621931 \cdot 10^{51}\right):\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r1031581 = x;
        double r1031582 = y;
        double r1031583 = z;
        double r1031584 = r1031582 - r1031583;
        double r1031585 = r1031581 * r1031584;
        double r1031586 = r1031585 / r1031582;
        return r1031586;
}
↓
double f(double x, double y, double z) {
        double r1031587 = y;
        double r1031588 = -1.20696722601438e+57;
        bool r1031589 = r1031587 <= r1031588;
        double r1031590 = 1.0892891581621931e+51;
        bool r1031591 = r1031587 <= r1031590;
        double r1031592 = !r1031591;
        bool r1031593 = r1031589 || r1031592;
        double r1031594 = x;
        double r1031595 = z;
        double r1031596 = r1031587 - r1031595;
        double r1031597 = r1031596 / r1031587;
        double r1031598 = r1031594 * r1031597;
        double r1031599 = r1031594 * r1031595;
        double r1031600 = r1031599 / r1031587;
        double r1031601 = r1031594 - r1031600;
        double r1031602 = r1031593 ? r1031598 : r1031601;
        return r1031602;
}

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

Original12.9
Target3.3
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.20696722601438e+57 or 1.0892891581621931e+51 < y

    1. Initial program 20.1

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

    3. Applied *-un-lft-identity20.1

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -1.20696722601438e+57 < y < 1.0892891581621931e+51

    1. Initial program 6.0

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

    3. Applied associate-/l*5.6

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

    4. Taylor expanded around 0 3.2

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.20696722601438008 \cdot 10^{57} \lor \neg \left(y \le 1.0892891581621931 \cdot 10^{51}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 +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))