Average Error: 12.4 → 1.8
Time: 27.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.290655561206783908563838071823474030955 \cdot 10^{97}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{elif}\;x \le 2.731727571395544206998641716133386673057 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{-\left(y - z\right)}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.290655561206783908563838071823474030955 \cdot 10^{97}:\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

\mathbf{elif}\;x \le 2.731727571395544206998641716133386673057 \cdot 10^{-15}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r478495 = x;
        double r478496 = y;
        double r478497 = z;
        double r478498 = r478496 - r478497;
        double r478499 = r478495 * r478498;
        double r478500 = r478499 / r478496;
        return r478500;
}
↓
double f(double x, double y, double z) {
        double r478501 = x;
        double r478502 = -1.290655561206784e+97;
        bool r478503 = r478501 <= r478502;
        double r478504 = 1.0;
        double r478505 = z;
        double r478506 = y;
        double r478507 = r478505 / r478506;
        double r478508 = r478504 - r478507;
        double r478509 = r478501 * r478508;
        double r478510 = 2.7317275713955442e-15;
        bool r478511 = r478501 <= r478510;
        double r478512 = r478501 * r478505;
        double r478513 = r478512 / r478506;
        double r478514 = r478501 - r478513;
        double r478515 = -r478506;
        double r478516 = r478506 - r478505;
        double r478517 = -r478516;
        double r478518 = r478515 / r478517;
        double r478519 = r478501 / r478518;
        double r478520 = r478511 ? r478514 : r478519;
        double r478521 = r478503 ? r478509 : r478520;
        return r478521;
}

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

Original12.4
Target3.3
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.290655561206784e+97

    1. Initial program 31.2

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

    3. Applied associate-/l*0.1

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

    5. Applied div-inv0.1

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

    6. Simplified0.1

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

    if -1.290655561206784e+97 < x < 2.7317275713955442e-15

    1. Initial program 5.6

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

    2. Taylor expanded around 0 2.7

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

    if 2.7317275713955442e-15 < x

    1. Initial program 20.8

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

    3. Applied associate-/l*0.1

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

    5. Applied frac-2neg0.1

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.290655561206783908563838071823474030955 \cdot 10^{97}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{elif}\;x \le 2.731727571395544206998641716133386673057 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{-\left(y - z\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 +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 -2.060202331921739e104) (- x (/ (* z x) y)) (if (< z 1.69397660138285259e213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))