Average Error: 15.2 → 1.0
Time: 28.0s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.35613759911877656476275151503320492094 \cdot 10^{280}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -8.828782166850766038005620975563547450989 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.939139322974091469623957424428358865557 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.459953299034684076090573649758520228965 \cdot 10^{86}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.35613759911877656476275151503320492094 \cdot 10^{280}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -8.828782166850766038005620975563547450989 \cdot 10^{-175}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 6.939139322974091469623957424428358865557 \cdot 10^{-194}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 2.459953299034684076090573649758520228965 \cdot 10^{86}:\\
\;\;\;\;\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 r344902 = x;
        double r344903 = y;
        double r344904 = z;
        double r344905 = r344903 / r344904;
        double r344906 = t;
        double r344907 = r344905 * r344906;
        double r344908 = r344907 / r344906;
        double r344909 = r344902 * r344908;
        return r344909;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r344910 = y;
        double r344911 = z;
        double r344912 = r344910 / r344911;
        double r344913 = -1.3561375991187766e+280;
        bool r344914 = r344912 <= r344913;
        double r344915 = x;
        double r344916 = r344915 / r344911;
        double r344917 = r344910 * r344916;
        double r344918 = -8.828782166850766e-175;
        bool r344919 = r344912 <= r344918;
        double r344920 = r344912 * r344915;
        double r344921 = 6.939139322974091e-194;
        bool r344922 = r344912 <= r344921;
        double r344923 = r344915 * r344910;
        double r344924 = r344923 / r344911;
        double r344925 = 2.459953299034684e+86;
        bool r344926 = r344912 <= r344925;
        double r344927 = r344926 ? r344920 : r344917;
        double r344928 = r344922 ? r344924 : r344927;
        double r344929 = r344919 ? r344920 : r344928;
        double r344930 = r344914 ? r344917 : r344929;
        return r344930;
}

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

Target

Original15.2
Target1.5
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -1.3561375991187766e+280 or 2.459953299034684e+86 < (/ y z)

    1. Initial program 34.5

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

    2. Simplified20.9

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

    4. Applied div-inv21.0

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

    5. Applied associate-*l*3.9

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

    6. Simplified3.8

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

    if -1.3561375991187766e+280 < (/ y z) < -8.828782166850766e-175 or 6.939139322974091e-194 < (/ y z) < 2.459953299034684e+86

    1. Initial program 8.3

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

    2. Simplified0.2

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

    if -8.828782166850766e-175 < (/ y z) < 6.939139322974091e-194

    1. Initial program 17.1

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

    2. Simplified9.7

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

    4. Applied add-cube-cbrt10.0

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

    5. Applied *-un-lft-identity10.0

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

    6. Applied times-frac10.0

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

    7. Applied associate-*l*2.7

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

    9. Applied associate-*l/1.3

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

    10. Applied frac-times1.3

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

    11. Simplified1.3

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

    12. Simplified0.8

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.35613759911877656476275151503320492094 \cdot 10^{280}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -8.828782166850766038005620975563547450989 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.939139322974091469623957424428358865557 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.459953299034684076090573649758520228965 \cdot 10^{86}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))