Average Error: 14.5 → 0.2
Time: 18.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.3965389460309517 \cdot 10^{+227}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.052978762430741 \cdot 10^{-268}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.7216736802426 \cdot 10^{-312}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.1564349635110415 \cdot 10^{+243}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.3965389460309517 \cdot 10^{+227}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.052978762430741 \cdot 10^{-268}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 1.7216736802426 \cdot 10^{-312}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;\frac{y}{z} \le 1.1564349635110415 \cdot 10^{+243}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3354037 = x;
        double r3354038 = y;
        double r3354039 = z;
        double r3354040 = r3354038 / r3354039;
        double r3354041 = t;
        double r3354042 = r3354040 * r3354041;
        double r3354043 = r3354042 / r3354041;
        double r3354044 = r3354037 * r3354043;
        return r3354044;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3354045 = y;
        double r3354046 = z;
        double r3354047 = r3354045 / r3354046;
        double r3354048 = -1.3965389460309517e+227;
        bool r3354049 = r3354047 <= r3354048;
        double r3354050 = x;
        double r3354051 = r3354050 * r3354045;
        double r3354052 = r3354051 / r3354046;
        double r3354053 = -1.052978762430741e-268;
        bool r3354054 = r3354047 <= r3354053;
        double r3354055 = r3354047 * r3354050;
        double r3354056 = 1.7216736802426e-312;
        bool r3354057 = r3354047 <= r3354056;
        double r3354058 = r3354050 / r3354046;
        double r3354059 = r3354058 * r3354045;
        double r3354060 = 1.1564349635110415e+243;
        bool r3354061 = r3354047 <= r3354060;
        double r3354062 = r3354046 / r3354050;
        double r3354063 = r3354045 / r3354062;
        double r3354064 = r3354061 ? r3354055 : r3354063;
        double r3354065 = r3354057 ? r3354059 : r3354064;
        double r3354066 = r3354054 ? r3354055 : r3354065;
        double r3354067 = r3354049 ? r3354052 : r3354066;
        return r3354067;
}

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 4 regimes

  2. if (/ y z) < -1.3965389460309517e+227

    1. Initial program 43.2

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

    2. Simplified0.3

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

    4. Applied associate-*l/0.9

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

    if -1.3965389460309517e+227 < (/ y z) < -1.052978762430741e-268 or 1.7216736802426e-312 < (/ y z) < 1.1564349635110415e+243

    1. Initial program 9.6

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

    2. Simplified8.1

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

    4. Applied associate-*l/8.0

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

    6. Applied div-inv8.0

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

    8. Applied pow18.0

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

    9. Applied pow18.0

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

    10. Applied pow18.0

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

    11. Applied pow-prod-down8.0

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

    12. Applied pow-prod-down8.0

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

    13. Simplified8.0

      \[\leadsto {\color{blue}{\left(\frac{y}{\frac{z}{x}}\right)}}^{1}\]
    14. Using strategy rm

    15. Applied associate-/r/0.2

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

    if -1.052978762430741e-268 < (/ y z) < 1.7216736802426e-312

    1. Initial program 18.4

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

    2. Simplified0.1

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

    if 1.1564349635110415e+243 < (/ y z)

    1. Initial program 45.2

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

    2. Simplified0.2

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

    4. Applied associate-*l/0.5

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

    6. Applied div-inv0.6

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

    8. Applied pow10.6

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

    9. Applied pow10.6

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

    10. Applied pow10.6

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

    11. Applied pow-prod-down0.6

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

    12. Applied pow-prod-down0.6

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

    13. Simplified0.2

      \[\leadsto {\color{blue}{\left(\frac{y}{\frac{z}{x}}\right)}}^{1}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.3965389460309517 \cdot 10^{+227}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.052978762430741 \cdot 10^{-268}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.7216736802426 \cdot 10^{-312}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.1564349635110415 \cdot 10^{+243}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 +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)))