Average Error: 15.1 → 0.7
Time: 30.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.167382686214397895425941397509630236779 \cdot 10^{231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.827587823355642407973457381841440310715 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.053250369059781787110723173910298691639 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.111565981439738552177075156972483526402 \cdot 10^{232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.167382686214397895425941397509630236779 \cdot 10^{231}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.827587823355642407973457381841440310715 \cdot 10^{-156}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 1.053250369059781787110723173910298691639 \cdot 10^{-123}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;\frac{y}{z} \le 1.111565981439738552177075156972483526402 \cdot 10^{232}:\\
\;\;\;\;\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 r3629923 = x;
        double r3629924 = y;
        double r3629925 = z;
        double r3629926 = r3629924 / r3629925;
        double r3629927 = t;
        double r3629928 = r3629926 * r3629927;
        double r3629929 = r3629928 / r3629927;
        double r3629930 = r3629923 * r3629929;
        return r3629930;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3629931 = y;
        double r3629932 = z;
        double r3629933 = r3629931 / r3629932;
        double r3629934 = -1.1673826862143979e+231;
        bool r3629935 = r3629933 <= r3629934;
        double r3629936 = x;
        double r3629937 = r3629936 * r3629931;
        double r3629938 = r3629937 / r3629932;
        double r3629939 = -1.8275878233556424e-156;
        bool r3629940 = r3629933 <= r3629939;
        double r3629941 = r3629933 * r3629936;
        double r3629942 = 1.0532503690597818e-123;
        bool r3629943 = r3629933 <= r3629942;
        double r3629944 = r3629936 / r3629932;
        double r3629945 = r3629944 * r3629931;
        double r3629946 = 1.1115659814397386e+232;
        bool r3629947 = r3629933 <= r3629946;
        double r3629948 = r3629947 ? r3629941 : r3629945;
        double r3629949 = r3629943 ? r3629945 : r3629948;
        double r3629950 = r3629940 ? r3629941 : r3629949;
        double r3629951 = r3629935 ? r3629938 : r3629950;
        return r3629951;
}

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) < -1.1673826862143979e+231

    1. Initial program 50.5

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

    2. Simplified0.8

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

    3. Taylor expanded around 0 0.7

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

    if -1.1673826862143979e+231 < (/ y z) < -1.8275878233556424e-156 or 1.0532503690597818e-123 < (/ y z) < 1.1115659814397386e+232

    1. Initial program 8.2

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

    2. Simplified11.2

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

    3. Taylor expanded around 0 9.7

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

    5. Applied *-un-lft-identity9.7

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

    6. Applied times-frac0.3

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

    7. Simplified0.3

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

    if -1.8275878233556424e-156 < (/ y z) < 1.0532503690597818e-123 or 1.1115659814397386e+232 < (/ y z)

    1. Initial program 20.2

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

    2. Simplified1.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.167382686214397895425941397509630236779 \cdot 10^{231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.827587823355642407973457381841440310715 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.053250369059781787110723173910298691639 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.111565981439738552177075156972483526402 \cdot 10^{232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +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)))