Average Error: 14.5 → 3.4
Time: 25.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 8.413937948676428647326966542545809971377 \cdot 10^{-321} \lor \neg \left(\frac{y}{z} \le 4.894548959283928660268685456970986818461 \cdot 10^{144}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le 8.413937948676428647326966542545809971377 \cdot 10^{-321} \lor \neg \left(\frac{y}{z} \le 4.894548959283928660268685456970986818461 \cdot 10^{144}\right):\\
\;\;\;\;y \cdot \frac{x}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r425990 = x;
        double r425991 = y;
        double r425992 = z;
        double r425993 = r425991 / r425992;
        double r425994 = t;
        double r425995 = r425993 * r425994;
        double r425996 = r425995 / r425994;
        double r425997 = r425990 * r425996;
        return r425997;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r425998 = y;
        double r425999 = z;
        double r426000 = r425998 / r425999;
        double r426001 = 8.4139379486764e-321;
        bool r426002 = r426000 <= r426001;
        double r426003 = 4.894548959283929e+144;
        bool r426004 = r426000 <= r426003;
        double r426005 = !r426004;
        bool r426006 = r426002 || r426005;
        double r426007 = x;
        double r426008 = r426007 / r425999;
        double r426009 = r425998 * r426008;
        double r426010 = r425999 / r425998;
        double r426011 = r426007 / r426010;
        double r426012 = r426006 ? r426009 : r426011;
        return r426012;
}

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

Target

Original14.5
Target1.7
Herbie3.4
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ y z) < 8.4139379486764e-321 or 4.894548959283929e+144 < (/ y z)

    1. Initial program 17.4

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

    2. Simplified9.2

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

    4. Applied div-inv9.3

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

    5. Applied associate-*l*4.9

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

    6. Simplified4.8

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

    if 8.4139379486764e-321 < (/ y z) < 4.894548959283929e+144

    1. Initial program 8.9

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

    2. Simplified0.4

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

    4. Applied associate-*l/8.0

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

    5. Simplified8.0

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

    7. Applied associate-/l*0.6

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 8.413937948676428647326966542545809971377 \cdot 10^{-321} \lor \neg \left(\frac{y}{z} \le 4.894548959283928660268685456970986818461 \cdot 10^{144}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045005e245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.90752223693390633e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.65895442315341522e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))