Average Error: 14.1 → 0.5
Time: 16.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.866510888004296 \cdot 10^{+182}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -3.378460893183651 \cdot 10^{-220}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.3295321152449 \cdot 10^{-313}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 7.69896986350915 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -3.866510888004296 \cdot 10^{+182}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -3.378460893183651 \cdot 10^{-220}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 1.3295321152449 \cdot 10^{-313}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;\frac{y}{z} \le 7.69896986350915 \cdot 10^{+178}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r22683476 = x;
        double r22683477 = y;
        double r22683478 = z;
        double r22683479 = r22683477 / r22683478;
        double r22683480 = t;
        double r22683481 = r22683479 * r22683480;
        double r22683482 = r22683481 / r22683480;
        double r22683483 = r22683476 * r22683482;
        return r22683483;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r22683484 = y;
        double r22683485 = z;
        double r22683486 = r22683484 / r22683485;
        double r22683487 = -3.866510888004296e+182;
        bool r22683488 = r22683486 <= r22683487;
        double r22683489 = x;
        double r22683490 = r22683489 * r22683484;
        double r22683491 = r22683490 / r22683485;
        double r22683492 = -3.378460893183651e-220;
        bool r22683493 = r22683486 <= r22683492;
        double r22683494 = r22683486 * r22683489;
        double r22683495 = 1.3295321152449e-313;
        bool r22683496 = r22683486 <= r22683495;
        double r22683497 = 1.0;
        double r22683498 = r22683485 / r22683490;
        double r22683499 = r22683497 / r22683498;
        double r22683500 = 7.69896986350915e+178;
        bool r22683501 = r22683486 <= r22683500;
        double r22683502 = r22683501 ? r22683494 : r22683491;
        double r22683503 = r22683496 ? r22683499 : r22683502;
        double r22683504 = r22683493 ? r22683494 : r22683503;
        double r22683505 = r22683488 ? r22683491 : r22683504;
        return r22683505;
}

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 3 regimes

  2. if (/ y z) < -3.866510888004296e+182 or 7.69896986350915e+178 < (/ y z)

    1. Initial program 36.4

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

    2. Simplified1.3

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

    if -3.866510888004296e+182 < (/ y z) < -3.378460893183651e-220 or 1.3295321152449e-313 < (/ y z) < 7.69896986350915e+178

    1. Initial program 8.4

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

    2. Simplified8.3

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

    4. Applied *-un-lft-identity8.3

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

    5. Applied times-frac0.2

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

    6. Simplified0.2

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

    if -3.378460893183651e-220 < (/ y z) < 1.3295321152449e-313

    1. Initial program 16.9

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

    2. Simplified0.3

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

    4. Applied clear-num0.8

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.866510888004296 \cdot 10^{+182}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -3.378460893183651 \cdot 10^{-220}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.3295321152449 \cdot 10^{-313}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 7.69896986350915 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019124 +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)))