Average Error: 2.7 → 1.7
Time: 13.8s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t \le 2.328479595255288586146179238757918271769 \cdot 10^{305}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t \le 2.328479595255288586146179238757918271769 \cdot 10^{305}:\\
\;\;\;\;\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 r438684 = x;
        double r438685 = y;
        double r438686 = z;
        double r438687 = t;
        double r438688 = r438686 * r438687;
        double r438689 = r438685 - r438688;
        double r438690 = r438684 / r438689;
        return r438690;
}
↓
double f(double x, double y, double z, double t) {
        double r438691 = z;
        double r438692 = t;
        double r438693 = r438691 * r438692;
        double r438694 = 2.3284795952552886e+305;
        bool r438695 = r438693 <= r438694;
        double r438696 = x;
        double r438697 = y;
        double r438698 = r438697 - r438693;
        double r438699 = r438696 / r438698;
        double r438700 = 1.0;
        double r438701 = r438697 / r438696;
        double r438702 = r438691 / r438696;
        double r438703 = r438702 * r438692;
        double r438704 = r438701 - r438703;
        double r438705 = r438700 / r438704;
        double r438706 = r438695 ? r438699 : r438705;
        return r438706;
}

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
Target1.8
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < 2.3284795952552886e+305

    1. Initial program 1.5

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

    if 2.3284795952552886e+305 < (* z t)

    1. Initial program 19.8

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

    3. Applied clear-num19.9

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

    5. Applied div-sub24.6

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

    6. Simplified5.5

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \le 2.328479595255288586146179238757918271769 \cdot 10^{305}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e50) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 2.13783064348764444e131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

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