Average Error: 14.9 → 1.9
Time: 10.5s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.0482842712917167 \cdot 10^{-253}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.3686289682416492 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.2134899625884335 \cdot 10^{+227}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.0482842712917167 \cdot 10^{-253}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 1.3686289682416492 \cdot 10^{-304}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;\frac{y}{z} \le 1.2134899625884335 \cdot 10^{+227}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r2227269 = x;
        double r2227270 = y;
        double r2227271 = z;
        double r2227272 = r2227270 / r2227271;
        double r2227273 = t;
        double r2227274 = r2227272 * r2227273;
        double r2227275 = r2227274 / r2227273;
        double r2227276 = r2227269 * r2227275;
        return r2227276;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r2227277 = y;
        double r2227278 = z;
        double r2227279 = r2227277 / r2227278;
        double r2227280 = -1.0482842712917167e-253;
        bool r2227281 = r2227279 <= r2227280;
        double r2227282 = x;
        double r2227283 = r2227279 * r2227282;
        double r2227284 = 1.3686289682416492e-304;
        bool r2227285 = r2227279 <= r2227284;
        double r2227286 = r2227282 / r2227278;
        double r2227287 = r2227286 * r2227277;
        double r2227288 = 1.2134899625884335e+227;
        bool r2227289 = r2227279 <= r2227288;
        double r2227290 = r2227289 ? r2227283 : r2227287;
        double r2227291 = r2227285 ? r2227287 : r2227290;
        double r2227292 = r2227281 ? r2227283 : r2227291;
        return r2227292;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (/ y z) < -1.0482842712917167e-253 or 1.3686289682416492e-304 < (/ y z) < 1.2134899625884335e+227

    1. Initial program 11.6

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

    2. Simplified7.6

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

    3. Taylor expanded around 0 8.2

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

    5. Applied *-un-lft-identity8.2

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

    6. Applied times-frac2.3

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

    7. Simplified2.3

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

    if -1.0482842712917167e-253 < (/ y z) < 1.3686289682416492e-304 or 1.2134899625884335e+227 < (/ y z)

    1. Initial program 25.7

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

    2. Simplified0.3

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.0482842712917167 \cdot 10^{-253}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.3686289682416492 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.2134899625884335 \cdot 10^{+227}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))