Average Error: 2.6 → 2.7
Time: 9.5s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.6006653957918148 \cdot 10^{179} \lor \neg \left(z \le -9.05254729579451535 \cdot 10^{115}\right):\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.6006653957918148 \cdot 10^{179} \lor \neg \left(z \le -9.05254729579451535 \cdot 10^{115}\right):\\
\;\;\;\;\frac{x}{y - z \cdot t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r579915 = x;
        double r579916 = y;
        double r579917 = z;
        double r579918 = t;
        double r579919 = r579917 * r579918;
        double r579920 = r579916 - r579919;
        double r579921 = r579915 / r579920;
        return r579921;
}
↓
double f(double x, double y, double z, double t) {
        double r579922 = z;
        double r579923 = -1.6006653957918148e+179;
        bool r579924 = r579922 <= r579923;
        double r579925 = -9.052547295794515e+115;
        bool r579926 = r579922 <= r579925;
        double r579927 = !r579926;
        bool r579928 = r579924 || r579927;
        double r579929 = x;
        double r579930 = y;
        double r579931 = t;
        double r579932 = r579922 * r579931;
        double r579933 = r579930 - r579932;
        double r579934 = r579929 / r579933;
        double r579935 = 1.0;
        double r579936 = r579930 / r579929;
        double r579937 = r579929 / r579922;
        double r579938 = r579931 / r579937;
        double r579939 = r579936 - r579938;
        double r579940 = r579935 / r579939;
        double r579941 = r579928 ? r579934 : r579940;
        return r579941;
}

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

Original2.6
Target1.6
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.6006653957918148e+179 or -9.052547295794515e+115 < z

    1. Initial program 2.5

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

    if -1.6006653957918148e+179 < z < -9.052547295794515e+115

    1. Initial program 5.4

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

    3. Applied clear-num5.7

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

    5. Applied div-sub9.4

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

    6. Simplified7.7

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

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.6006653957918148 \cdot 10^{179} \lor \neg \left(z \le -9.05254729579451535 \cdot 10^{115}\right):\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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