Average Error: 14.7 → 0.3
Time: 9.0s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -6.29544524415545219149038523268139908958 \cdot 10^{285}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.575588880456927846517204610144689059531 \cdot 10^{-286}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.757059281014894097749857788400547545613 \cdot 10^{-220}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.409130514825537046443418609777720419861 \cdot 10^{217}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -6.29544524415545219149038523268139908958 \cdot 10^{285}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.575588880456927846517204610144689059531 \cdot 10^{-286}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 3.757059281014894097749857788400547545613 \cdot 10^{-220}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.409130514825537046443418609777720419861 \cdot 10^{217}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r71401 = x;
        double r71402 = y;
        double r71403 = z;
        double r71404 = r71402 / r71403;
        double r71405 = t;
        double r71406 = r71404 * r71405;
        double r71407 = r71406 / r71405;
        double r71408 = r71401 * r71407;
        return r71408;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r71409 = y;
        double r71410 = z;
        double r71411 = r71409 / r71410;
        double r71412 = -6.295445244155452e+285;
        bool r71413 = r71411 <= r71412;
        double r71414 = x;
        double r71415 = r71414 * r71409;
        double r71416 = 1.0;
        double r71417 = r71416 / r71410;
        double r71418 = r71415 * r71417;
        double r71419 = -1.5755888804569278e-286;
        bool r71420 = r71411 <= r71419;
        double r71421 = r71410 / r71409;
        double r71422 = r71414 / r71421;
        double r71423 = 3.757059281014894e-220;
        bool r71424 = r71411 <= r71423;
        double r71425 = r71415 / r71410;
        double r71426 = 1.409130514825537e+217;
        bool r71427 = r71411 <= r71426;
        double r71428 = r71411 * r71414;
        double r71429 = r71414 / r71410;
        double r71430 = r71409 * r71429;
        double r71431 = r71427 ? r71428 : r71430;
        double r71432 = r71424 ? r71425 : r71431;
        double r71433 = r71420 ? r71422 : r71432;
        double r71434 = r71413 ? r71418 : r71433;
        return r71434;
}

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 5 regimes

  2. if (/ y z) < -6.295445244155452e+285

    1. Initial program 58.1

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

    2. Simplified0.2

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

    4. Applied div-inv0.3

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

    if -6.295445244155452e+285 < (/ y z) < -1.5755888804569278e-286

    1. Initial program 10.7

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

    2. Simplified7.7

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

    4. Applied associate-/l*0.2

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

    if -1.5755888804569278e-286 < (/ y z) < 3.757059281014894e-220

    1. Initial program 18.8

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

    2. Simplified0.3

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

    4. Applied associate-/l*15.6

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

    5. Taylor expanded around 0 0.3

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

    if 3.757059281014894e-220 < (/ y z) < 1.409130514825537e+217

    1. Initial program 8.1

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

    2. Simplified9.2

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

    4. Applied associate-/l*0.2

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

    6. Applied div-inv0.3

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

    7. Simplified0.2

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

    if 1.409130514825537e+217 < (/ y z)

    1. Initial program 44.0

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

    2. Simplified1.0

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

    3. Taylor expanded around 0 1.0

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

    4. Simplified0.4

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -6.29544524415545219149038523268139908958 \cdot 10^{285}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.575588880456927846517204610144689059531 \cdot 10^{-286}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.757059281014894097749857788400547545613 \cdot 10^{-220}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.409130514825537046443418609777720419861 \cdot 10^{217}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))