Average Error: 15.2 → 1.0
Time: 23.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.35613759911877656476275151503320492094 \cdot 10^{280}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -8.828782166850766038005620975563547450989 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.939139322974091469623957424428358865557 \cdot 10^{-194}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.459953299034684076090573649758520228965 \cdot 10^{86}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
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{y \cdot x}{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 r466928 = x;
        double r466929 = y;
        double r466930 = z;
        double r466931 = r466929 / r466930;
        double r466932 = t;
        double r466933 = r466931 * r466932;
        double r466934 = r466933 / r466932;
        double r466935 = r466928 * r466934;
        return r466935;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r466936 = y;
        double r466937 = z;
        double r466938 = r466936 / r466937;
        double r466939 = -1.3561375991187766e+280;
        bool r466940 = r466938 <= r466939;
        double r466941 = x;
        double r466942 = r466941 / r466937;
        double r466943 = r466936 * r466942;
        double r466944 = -8.828782166850766e-175;
        bool r466945 = r466938 <= r466944;
        double r466946 = r466938 * r466941;
        double r466947 = 6.939139322974091e-194;
        bool r466948 = r466938 <= r466947;
        double r466949 = r466936 * r466941;
        double r466950 = r466949 / r466937;
        double r466951 = 2.459953299034684e+86;
        bool r466952 = r466938 <= r466951;
        double r466953 = r466952 ? r466946 : r466943;
        double r466954 = r466948 ? r466950 : r466953;
        double r466955 = r466945 ? r466946 : r466954;
        double r466956 = r466940 ? r466943 : r466955;
        return r466956;
}

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

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

    12. Simplified0.8

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

  4. Final simplification1.0

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

Reproduce

herbie shell --seed 2019326 
(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)))