Average Error: 7.2 → 0.3
Time: 15.8s
Precision: 64
\[\frac{x + y}{1 - \frac{y}{z}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.071871468207686476603092703114047700488 \cdot 10^{70} \lor \neg \left(y \le 1.355210724208745242774185963715620540714 \cdot 10^{44}\right):\\ \;\;\;\;\frac{1}{\frac{1}{x + y} - \frac{\frac{y}{x + y}}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array}\]
\frac{x + y}{1 - \frac{y}{z}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.071871468207686476603092703114047700488 \cdot 10^{70} \lor \neg \left(y \le 1.355210724208745242774185963715620540714 \cdot 10^{44}\right):\\
\;\;\;\;\frac{1}{\frac{1}{x + y} - \frac{\frac{y}{x + y}}{z}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\

\end{array}
double f(double x, double y, double z) {
        double r1116556 = x;
        double r1116557 = y;
        double r1116558 = r1116556 + r1116557;
        double r1116559 = 1.0;
        double r1116560 = z;
        double r1116561 = r1116557 / r1116560;
        double r1116562 = r1116559 - r1116561;
        double r1116563 = r1116558 / r1116562;
        return r1116563;
}
↓
double f(double x, double y, double z) {
        double r1116564 = y;
        double r1116565 = -1.0718714682076865e+70;
        bool r1116566 = r1116564 <= r1116565;
        double r1116567 = 1.3552107242087452e+44;
        bool r1116568 = r1116564 <= r1116567;
        double r1116569 = !r1116568;
        bool r1116570 = r1116566 || r1116569;
        double r1116571 = 1.0;
        double r1116572 = 1.0;
        double r1116573 = x;
        double r1116574 = r1116573 + r1116564;
        double r1116575 = r1116572 / r1116574;
        double r1116576 = r1116564 / r1116574;
        double r1116577 = z;
        double r1116578 = r1116576 / r1116577;
        double r1116579 = r1116575 - r1116578;
        double r1116580 = r1116571 / r1116579;
        double r1116581 = r1116564 / r1116577;
        double r1116582 = r1116572 - r1116581;
        double r1116583 = r1116574 / r1116582;
        double r1116584 = r1116570 ? r1116580 : r1116583;
        return r1116584;
}

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

Original7.2
Target4.1
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -3.742931076268985646434612946949172132145 \cdot 10^{171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y \lt 3.553466245608673435460441960303815115662 \cdot 10^{168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.0718714682076865e+70 or 1.3552107242087452e+44 < y

    1. Initial program 17.4

      \[\frac{x + y}{1 - \frac{y}{z}}\]
    2. Using strategy rm

    3. Applied clear-num17.5

      \[\leadsto \color{blue}{\frac{1}{\frac{1 - \frac{y}{z}}{x + y}}}\]
    4. Using strategy rm

    5. Applied div-sub17.5

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

    6. Simplified0.2

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

    if -1.0718714682076865e+70 < y < 1.3552107242087452e+44

    1. Initial program 0.4

      \[\frac{x + y}{1 - \frac{y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.071871468207686476603092703114047700488 \cdot 10^{70} \lor \neg \left(y \le 1.355210724208745242774185963715620540714 \cdot 10^{44}\right):\\ \;\;\;\;\frac{1}{\frac{1}{x + y} - \frac{\frac{y}{x + y}}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.74293107626898565e171) (* (/ (+ y x) (- y)) z) (if (< y 3.55346624560867344e168) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1 (/ y z))))