Average Error: 14.5 → 1.2
Time: 12.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.539793361071769873969043675808442911102 \cdot 10^{214}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.530604856090351627042526853504735687815 \cdot 10^{-166}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.053074699504574675208589942494399087398 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 6.289758256242324172285873340578120865516 \cdot 10^{161}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -4.539793361071769873969043675808442911102 \cdot 10^{214}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -2.530604856090351627042526853504735687815 \cdot 10^{-166}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 6.053074699504574675208589942494399087398 \cdot 10^{-63}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;\frac{y}{z} \le 6.289758256242324172285873340578120865516 \cdot 10^{161}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r89402 = x;
        double r89403 = y;
        double r89404 = z;
        double r89405 = r89403 / r89404;
        double r89406 = t;
        double r89407 = r89405 * r89406;
        double r89408 = r89407 / r89406;
        double r89409 = r89402 * r89408;
        return r89409;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r89410 = y;
        double r89411 = z;
        double r89412 = r89410 / r89411;
        double r89413 = -4.53979336107177e+214;
        bool r89414 = r89412 <= r89413;
        double r89415 = x;
        double r89416 = r89415 / r89411;
        double r89417 = r89410 * r89416;
        double r89418 = -2.5306048560903516e-166;
        bool r89419 = r89412 <= r89418;
        double r89420 = r89412 * r89415;
        double r89421 = 6.053074699504575e-63;
        bool r89422 = r89412 <= r89421;
        double r89423 = r89411 / r89415;
        double r89424 = r89410 / r89423;
        double r89425 = 6.289758256242324e+161;
        bool r89426 = r89412 <= r89425;
        double r89427 = r89410 * r89415;
        double r89428 = r89427 / r89411;
        double r89429 = r89426 ? r89420 : r89428;
        double r89430 = r89422 ? r89424 : r89429;
        double r89431 = r89419 ? r89420 : r89430;
        double r89432 = r89414 ? r89417 : r89431;
        return r89432;
}

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) < -4.53979336107177e+214

    1. Initial program 42.7

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

    2. Simplified0.6

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

    4. Applied *-un-lft-identity0.6

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

    5. Applied times-frac0.4

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

    6. Simplified0.4

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

    if -4.53979336107177e+214 < (/ y z) < -2.5306048560903516e-166 or 6.053074699504575e-63 < (/ y z) < 6.289758256242324e+161

    1. Initial program 7.3

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

    2. Simplified11.4

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

    4. Applied associate-/l*10.3

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

    6. Applied associate-/r/0.2

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

    if -2.5306048560903516e-166 < (/ y z) < 6.053074699504575e-63

    1. Initial program 14.9

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

    2. Simplified2.5

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

    4. Applied associate-/l*2.2

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

    if 6.289758256242324e+161 < (/ y z)

    1. Initial program 34.1

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

    2. Simplified2.3

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.539793361071769873969043675808442911102 \cdot 10^{214}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.530604856090351627042526853504735687815 \cdot 10^{-166}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.053074699504574675208589942494399087398 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 6.289758256242324172285873340578120865516 \cdot 10^{161}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))