Average Error: 15.3 → 0.7
Time: 12.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.548240730790440881436662006949490760264 \cdot 10^{219}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.442433262831919710603838797359517016977 \cdot 10^{-140}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.548240730790440881436662006949490760264 \cdot 10^{219}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.442433262831919710603838797359517016977 \cdot 10^{-140}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le -0.0:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3824039 = x;
        double r3824040 = y;
        double r3824041 = z;
        double r3824042 = r3824040 / r3824041;
        double r3824043 = t;
        double r3824044 = r3824042 * r3824043;
        double r3824045 = r3824044 / r3824043;
        double r3824046 = r3824039 * r3824045;
        return r3824046;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3824047 = y;
        double r3824048 = z;
        double r3824049 = r3824047 / r3824048;
        double r3824050 = -1.548240730790441e+219;
        bool r3824051 = r3824049 <= r3824050;
        double r3824052 = x;
        double r3824053 = r3824052 / r3824048;
        double r3824054 = r3824047 * r3824053;
        double r3824055 = -1.4424332628319197e-140;
        bool r3824056 = r3824049 <= r3824055;
        double r3824057 = r3824049 * r3824052;
        double r3824058 = -0.0;
        bool r3824059 = r3824049 <= r3824058;
        double r3824060 = 9.19341618785794e+231;
        bool r3824061 = r3824049 <= r3824060;
        double r3824062 = r3824048 / r3824047;
        double r3824063 = r3824052 / r3824062;
        double r3824064 = r3824052 * r3824047;
        double r3824065 = r3824064 / r3824048;
        double r3824066 = r3824061 ? r3824063 : r3824065;
        double r3824067 = r3824059 ? r3824054 : r3824066;
        double r3824068 = r3824056 ? r3824057 : r3824067;
        double r3824069 = r3824051 ? r3824054 : r3824068;
        return r3824069;
}

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) < -1.548240730790441e+219 or -1.4424332628319197e-140 < (/ y z) < -0.0

    1. Initial program 22.6

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

    2. Simplified1.1

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

    4. Applied div-inv1.2

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

    6. Applied pow11.2

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

    7. Applied pow11.2

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

    8. Applied pow11.2

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

    9. Applied pow-prod-down1.2

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

    10. Applied pow-prod-down1.2

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

    11. Simplified1.0

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

    if -1.548240730790441e+219 < (/ y z) < -1.4424332628319197e-140

    1. Initial program 8.5

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

    2. Simplified10.5

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

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

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

    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 -0.0 < (/ y z) < 9.19341618785794e+231

    1. Initial program 10.8

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

    2. Simplified7.4

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

    4. Applied associate-/l*0.7

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

    if 9.19341618785794e+231 < (/ y z)

    1. Initial program 45.4

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

    2. Simplified0.6

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.548240730790440881436662006949490760264 \cdot 10^{219}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.442433262831919710603838797359517016977 \cdot 10^{-140}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 +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)))