Average Error: 14.7 → 0.4
Time: 13.9s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.4488390756029045 \cdot 10^{+223}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.897283238983837 \cdot 10^{-237}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.4488390756029045 \cdot 10^{+223}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;\frac{y}{z} \le -1.897283238983837 \cdot 10^{-237}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3208688 = x;
        double r3208689 = y;
        double r3208690 = z;
        double r3208691 = r3208689 / r3208690;
        double r3208692 = t;
        double r3208693 = r3208691 * r3208692;
        double r3208694 = r3208693 / r3208692;
        double r3208695 = r3208688 * r3208694;
        return r3208695;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3208696 = y;
        double r3208697 = z;
        double r3208698 = r3208696 / r3208697;
        double r3208699 = -1.4488390756029045e+223;
        bool r3208700 = r3208698 <= r3208699;
        double r3208701 = x;
        double r3208702 = r3208697 / r3208701;
        double r3208703 = r3208696 / r3208702;
        double r3208704 = -1.897283238983837e-237;
        bool r3208705 = r3208698 <= r3208704;
        double r3208706 = r3208698 * r3208701;
        double r3208707 = 0.0;
        bool r3208708 = r3208698 <= r3208707;
        double r3208709 = 1.1115659814397386e+232;
        bool r3208710 = r3208698 <= r3208709;
        double r3208711 = r3208701 / r3208697;
        double r3208712 = r3208711 * r3208696;
        double r3208713 = r3208710 ? r3208706 : r3208712;
        double r3208714 = r3208708 ? r3208703 : r3208713;
        double r3208715 = r3208705 ? r3208706 : r3208714;
        double r3208716 = r3208700 ? r3208703 : r3208715;
        return r3208716;
}

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) < -1.4488390756029045e+223 or -1.897283238983837e-237 < (/ y z) < 0.0

    1. Initial program 25.5

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

    2. Simplified0.4

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

    4. Applied associate-*r/0.3

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

    6. Applied associate-/l*0.3

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

    if -1.4488390756029045e+223 < (/ y z) < -1.897283238983837e-237 or 0.0 < (/ y z) < 1.1115659814397386e+232

    1. Initial program 9.2

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

    2. Simplified8.9

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

    4. Applied associate-*r/7.8

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

    6. Applied associate-/l*8.8

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

    8. Applied associate-/r/0.3

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

    if 1.1115659814397386e+232 < (/ y z)

    1. Initial program 42.8

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

    2. Simplified0.8

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.4488390756029045 \cdot 10^{+223}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.897283238983837 \cdot 10^{-237}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +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)))