Average Error: 14.9 → 6.2
Time: 7.9s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 9.229798147685695329732918179044544221488 \cdot 10^{-158} \lor \neg \left(x \le 5.083972857276357327477703416060128532384 \cdot 10^{179}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le 9.229798147685695329732918179044544221488 \cdot 10^{-158} \lor \neg \left(x \le 5.083972857276357327477703416060128532384 \cdot 10^{179}\right):\\
\;\;\;\;\frac{y \cdot x}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r1675916 = x;
        double r1675917 = y;
        double r1675918 = z;
        double r1675919 = r1675917 / r1675918;
        double r1675920 = t;
        double r1675921 = r1675919 * r1675920;
        double r1675922 = r1675921 / r1675920;
        double r1675923 = r1675916 * r1675922;
        return r1675923;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r1675924 = x;
        double r1675925 = 9.229798147685695e-158;
        bool r1675926 = r1675924 <= r1675925;
        double r1675927 = 5.0839728572763573e+179;
        bool r1675928 = r1675924 <= r1675927;
        double r1675929 = !r1675928;
        bool r1675930 = r1675926 || r1675929;
        double r1675931 = y;
        double r1675932 = r1675931 * r1675924;
        double r1675933 = z;
        double r1675934 = r1675932 / r1675933;
        double r1675935 = r1675933 / r1675924;
        double r1675936 = r1675931 / r1675935;
        double r1675937 = r1675930 ? r1675934 : r1675936;
        return r1675937;
}

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

Original14.9
Target1.6
Herbie6.2
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 9.229798147685695e-158 or 5.0839728572763573e+179 < x

    1. Initial program 15.3

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

    2. Simplified7.0

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

    if 9.229798147685695e-158 < x < 5.0839728572763573e+179

    1. Initial program 13.9

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

    2. Simplified3.7

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

    4. Applied associate-/l*4.0

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

  4. Final simplification6.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 9.229798147685695329732918179044544221488 \cdot 10^{-158} \lor \neg \left(x \le 5.083972857276357327477703416060128532384 \cdot 10^{179}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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)))