Average Error: 2.7 → 3.3
Time: 9.2s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5441052365728334568188037948243968 \lor \neg \left(y \le -8.518426596525933669450559259262448611475 \cdot 10^{-213}\right):\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5441052365728334568188037948243968 \lor \neg \left(y \le -8.518426596525933669450559259262448611475 \cdot 10^{-213}\right):\\
\;\;\;\;\frac{x}{y - z \cdot t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r717929 = x;
        double r717930 = y;
        double r717931 = z;
        double r717932 = t;
        double r717933 = r717931 * r717932;
        double r717934 = r717930 - r717933;
        double r717935 = r717929 / r717934;
        return r717935;
}
↓
double f(double x, double y, double z, double t) {
        double r717936 = y;
        double r717937 = -5.441052365728335e+33;
        bool r717938 = r717936 <= r717937;
        double r717939 = -8.518426596525934e-213;
        bool r717940 = r717936 <= r717939;
        double r717941 = !r717940;
        bool r717942 = r717938 || r717941;
        double r717943 = x;
        double r717944 = z;
        double r717945 = t;
        double r717946 = r717944 * r717945;
        double r717947 = r717936 - r717946;
        double r717948 = r717943 / r717947;
        double r717949 = 1.0;
        double r717950 = r717936 / r717943;
        double r717951 = r717944 / r717943;
        double r717952 = r717951 * r717945;
        double r717953 = r717950 - r717952;
        double r717954 = r717949 / r717953;
        double r717955 = r717942 ? r717948 : r717954;
        return r717955;
}

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

Original2.7
Target1.9
Herbie3.3
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.441052365728335e+33 or -8.518426596525934e-213 < y

    1. Initial program 2.7

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

    if -5.441052365728335e+33 < y < -8.518426596525934e-213

    1. Initial program 2.6

      \[\frac{x}{y - z \cdot t}\]
    2. Using strategy rm

    3. Applied clear-num3.0

      \[\leadsto \color{blue}{\frac{1}{\frac{y - z \cdot t}{x}}}\]
    4. Using strategy rm

    5. Applied div-sub3.0

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

    6. Simplified5.6

      \[\leadsto \frac{1}{\frac{y}{x} - \color{blue}{\frac{z}{x} \cdot t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5441052365728334568188037948243968 \lor \neg \left(y \le -8.518426596525933669450559259262448611475 \cdot 10^{-213}\right):\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

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