Average Error: 15.2 → 1.0
Time: 28.5s
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 r68599 = x;
        double r68600 = y;
        double r68601 = z;
        double r68602 = r68600 / r68601;
        double r68603 = t;
        double r68604 = r68602 * r68603;
        double r68605 = r68604 / r68603;
        double r68606 = r68599 * r68605;
        return r68606;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r68607 = y;
        double r68608 = z;
        double r68609 = r68607 / r68608;
        double r68610 = -1.3561375991187766e+280;
        bool r68611 = r68609 <= r68610;
        double r68612 = x;
        double r68613 = r68612 / r68608;
        double r68614 = r68607 * r68613;
        double r68615 = -8.828782166850766e-175;
        bool r68616 = r68609 <= r68615;
        double r68617 = r68609 * r68612;
        double r68618 = 6.939139322974091e-194;
        bool r68619 = r68609 <= r68618;
        double r68620 = r68612 * r68607;
        double r68621 = r68620 / r68608;
        double r68622 = 2.459953299034684e+86;
        bool r68623 = r68609 <= r68622;
        double r68624 = r68623 ? r68617 : r68614;
        double r68625 = r68619 ? r68621 : r68624;
        double r68626 = r68616 ? r68617 : r68625;
        double r68627 = r68611 ? r68614 : r68626;
        return r68627;
}

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) < -1.3561375991187766e+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 pow12.7

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

    10. Applied pow12.7

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

    11. Applied pow-prod-down2.7

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

    12. Applied pow12.7

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

    13. Applied pow-prod-down2.7

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

    14. Simplified0.8

      \[\leadsto {\color{blue}{\left(\frac{x \cdot y}{z}\right)}}^{1}\]
  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"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))