Average Error: 14.8 → 1.9
Time: 9.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.1216973775124759 \cdot 10^{253}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.58981900482305871 \cdot 10^{-298} \lor \neg \left(\frac{y}{z} \le 1.0873747502010816 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(y \cdot x\right)\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.1216973775124759 \cdot 10^{253}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;\frac{y}{z} \le -1.58981900482305871 \cdot 10^{-298} \lor \neg \left(\frac{y}{z} \le 1.0873747502010816 \cdot 10^{-201}\right):\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{z} \cdot \left(y \cdot x\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r71458 = x;
        double r71459 = y;
        double r71460 = z;
        double r71461 = r71459 / r71460;
        double r71462 = t;
        double r71463 = r71461 * r71462;
        double r71464 = r71463 / r71462;
        double r71465 = r71458 * r71464;
        return r71465;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r71466 = y;
        double r71467 = z;
        double r71468 = r71466 / r71467;
        double r71469 = -2.121697377512476e+253;
        bool r71470 = r71468 <= r71469;
        double r71471 = x;
        double r71472 = r71467 / r71471;
        double r71473 = r71466 / r71472;
        double r71474 = -1.5898190048230587e-298;
        bool r71475 = r71468 <= r71474;
        double r71476 = 1.0873747502010816e-201;
        bool r71477 = r71468 <= r71476;
        double r71478 = !r71477;
        bool r71479 = r71475 || r71478;
        double r71480 = r71468 * r71471;
        double r71481 = 1.0;
        double r71482 = r71481 / r71467;
        double r71483 = r71466 * r71471;
        double r71484 = r71482 * r71483;
        double r71485 = r71479 ? r71480 : r71484;
        double r71486 = r71470 ? r71473 : r71485;
        return r71486;
}

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) < -2.121697377512476e+253

    1. Initial program 50.4

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

    2. Simplified0.6

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

    4. Applied associate-/l*0.3

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

    if -2.121697377512476e+253 < (/ y z) < -1.5898190048230587e-298 or 1.0873747502010816e-201 < (/ y z)

    1. Initial program 12.1

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

    2. Simplified8.4

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

    4. Applied associate-/l*8.0

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

    6. Applied associate-/r/2.5

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

    if -1.5898190048230587e-298 < (/ y z) < 1.0873747502010816e-201

    1. Initial program 17.8

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

    2. Simplified0.3

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

    4. Applied associate-/l*0.3

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

    6. Applied div-inv0.4

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

    7. Applied *-un-lft-identity0.4

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

    8. Applied times-frac0.4

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

    9. Simplified0.4

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.1216973775124759 \cdot 10^{253}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.58981900482305871 \cdot 10^{-298} \lor \neg \left(\frac{y}{z} \le 1.0873747502010816 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(y \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 +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)))