Average Error: 15.2 → 3.5
Time: 13.2s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 1.33272593359145646097923062849387621848 \cdot 10^{-315}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;\frac{y}{z} \le 5.677676213585449009539499455320000877411 \cdot 10^{146}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le 1.33272593359145646097923062849387621848 \cdot 10^{-315}:\\
\;\;\;\;y \cdot \left(x \cdot \frac{1}{z}\right)\\

\mathbf{elif}\;\frac{y}{z} \le 5.677676213585449009539499455320000877411 \cdot 10^{146}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r121964 = x;
        double r121965 = y;
        double r121966 = z;
        double r121967 = r121965 / r121966;
        double r121968 = t;
        double r121969 = r121967 * r121968;
        double r121970 = r121969 / r121968;
        double r121971 = r121964 * r121970;
        return r121971;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r121972 = y;
        double r121973 = z;
        double r121974 = r121972 / r121973;
        double r121975 = 1.3327259335915e-315;
        bool r121976 = r121974 <= r121975;
        double r121977 = x;
        double r121978 = 1.0;
        double r121979 = r121978 / r121973;
        double r121980 = r121977 * r121979;
        double r121981 = r121972 * r121980;
        double r121982 = 5.677676213585449e+146;
        bool r121983 = r121974 <= r121982;
        double r121984 = r121977 * r121974;
        double r121985 = r121977 * r121972;
        double r121986 = r121985 / r121973;
        double r121987 = r121983 ? r121984 : r121986;
        double r121988 = r121976 ? r121981 : r121987;
        return r121988;
}

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) < 1.3327259335915e-315

    1. Initial program 15.7

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

    2. Simplified5.3

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

    4. Applied clear-num5.7

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

    5. Simplified5.9

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

    7. Applied div-inv6.0

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

    8. Applied add-cube-cbrt6.0

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{z}{x} \cdot \frac{1}{y}}\]

    9. Applied times-frac5.9

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{z}{x}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{y}}}\]

    10. Simplified5.7

      \[\leadsto \color{blue}{\left(\frac{1}{z} \cdot x\right)} \cdot \frac{\sqrt[3]{1}}{\frac{1}{y}}\]

    11. Simplified5.6

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

    if 1.3327259335915e-315 < (/ y z) < 5.677676213585449e+146

    1. Initial program 8.8

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

    2. Simplified9.1

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

    4. Applied *-un-lft-identity9.1

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

    5. Applied times-frac0.3

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

    6. Simplified0.3

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

    if 5.677676213585449e+146 < (/ y z)

    1. Initial program 35.9

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

    2. Simplified2.3

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 1.33272593359145646097923062849387621848 \cdot 10^{-315}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;\frac{y}{z} \le 5.677676213585449009539499455320000877411 \cdot 10^{146}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 +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)))