Average Error: 14.5 → 6.0
Time: 10.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 1.6218775689393483 \cdot 10^{-99} \lor \neg \left(z \le 1.32166055357661369 \cdot 10^{217}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le 1.6218775689393483 \cdot 10^{-99} \lor \neg \left(z \le 1.32166055357661369 \cdot 10^{217}\right):\\
\;\;\;\;\frac{y \cdot x}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r399309 = x;
        double r399310 = y;
        double r399311 = z;
        double r399312 = r399310 / r399311;
        double r399313 = t;
        double r399314 = r399312 * r399313;
        double r399315 = r399314 / r399313;
        double r399316 = r399309 * r399315;
        return r399316;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r399317 = z;
        double r399318 = 1.6218775689393483e-99;
        bool r399319 = r399317 <= r399318;
        double r399320 = 1.3216605535766137e+217;
        bool r399321 = r399317 <= r399320;
        double r399322 = !r399321;
        bool r399323 = r399319 || r399322;
        double r399324 = y;
        double r399325 = x;
        double r399326 = r399324 * r399325;
        double r399327 = r399326 / r399317;
        double r399328 = r399317 / r399324;
        double r399329 = r399325 / r399328;
        double r399330 = r399323 ? r399327 : r399329;
        return r399330;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
Target1.5
Herbie6.0
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < 1.6218775689393483e-99 or 1.3216605535766137e+217 < z

    1. Initial program 15.2

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified6.7

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

    if 1.6218775689393483e-99 < z < 1.3216605535766137e+217

    1. Initial program 12.7

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified4.3

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

    4. Applied clear-num4.8

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

    5. Simplified4.8

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{x \cdot y}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity4.8

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

    8. Applied times-frac4.7

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

    9. Applied associate-/r*4.4

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

    10. Simplified4.3

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

  4. Final simplification6.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 1.6218775689393483 \cdot 10^{-99} \lor \neg \left(z \le 1.32166055357661369 \cdot 10^{217}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))