Average Error: 14.5 → 0.7
Time: 15.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.0746832567059644 \cdot 10^{+132}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \le -3.2662471639158817 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 6.625650070508862 \cdot 10^{-168}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.643944490104231 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.0746832567059644 \cdot 10^{+132}:\\
\;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\

\mathbf{elif}\;\frac{y}{z} \le -3.2662471639158817 \cdot 10^{-215}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 6.625650070508862 \cdot 10^{-168}:\\
\;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 5.643944490104231 \cdot 10^{+261}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r25860490 = x;
        double r25860491 = y;
        double r25860492 = z;
        double r25860493 = r25860491 / r25860492;
        double r25860494 = t;
        double r25860495 = r25860493 * r25860494;
        double r25860496 = r25860495 / r25860494;
        double r25860497 = r25860490 * r25860496;
        return r25860497;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r25860498 = y;
        double r25860499 = z;
        double r25860500 = r25860498 / r25860499;
        double r25860501 = -5.0746832567059644e+132;
        bool r25860502 = r25860500 <= r25860501;
        double r25860503 = 1.0;
        double r25860504 = x;
        double r25860505 = r25860498 * r25860504;
        double r25860506 = r25860499 / r25860505;
        double r25860507 = r25860503 / r25860506;
        double r25860508 = -3.2662471639158817e-215;
        bool r25860509 = r25860500 <= r25860508;
        double r25860510 = r25860499 / r25860498;
        double r25860511 = r25860504 / r25860510;
        double r25860512 = 6.625650070508862e-168;
        bool r25860513 = r25860500 <= r25860512;
        double r25860514 = r25860503 / r25860499;
        double r25860515 = r25860505 * r25860514;
        double r25860516 = 5.643944490104231e+261;
        bool r25860517 = r25860500 <= r25860516;
        double r25860518 = r25860504 * r25860500;
        double r25860519 = r25860517 ? r25860518 : r25860507;
        double r25860520 = r25860513 ? r25860515 : r25860519;
        double r25860521 = r25860509 ? r25860511 : r25860520;
        double r25860522 = r25860502 ? r25860507 : r25860521;
        return r25860522;
}

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) < -5.0746832567059644e+132 or 5.643944490104231e+261 < (/ y z)

    1. Initial program 34.4

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

    2. Simplified21.9

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

    3. Taylor expanded around 0 2.7

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

    5. Applied clear-num2.8

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

    if -5.0746832567059644e+132 < (/ y z) < -3.2662471639158817e-215

    1. Initial program 7.1

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

    2. Simplified0.2

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

    3. Taylor expanded around 0 10.0

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

    5. Applied associate-/l*0.2

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

    if -3.2662471639158817e-215 < (/ y z) < 6.625650070508862e-168

    1. Initial program 17.5

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

    2. Simplified10.2

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

    3. Taylor expanded around 0 0.7

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

    5. Applied div-inv0.7

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

    if 6.625650070508862e-168 < (/ y z) < 5.643944490104231e+261

    1. Initial program 9.2

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

    2. Simplified0.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.0746832567059644 \cdot 10^{+132}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \le -3.2662471639158817 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 6.625650070508862 \cdot 10^{-168}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.643944490104231 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019121 +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)))