Average Error: 2.9 → 1.8
Time: 10.5s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t \le 1.543751143088452374202847261662502060674 \cdot 10^{293}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{\frac{x}{t}}}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t \le 1.543751143088452374202847261662502060674 \cdot 10^{293}:\\
\;\;\;\;\frac{x}{y - z \cdot t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r447742 = x;
        double r447743 = y;
        double r447744 = z;
        double r447745 = t;
        double r447746 = r447744 * r447745;
        double r447747 = r447743 - r447746;
        double r447748 = r447742 / r447747;
        return r447748;
}
↓
double f(double x, double y, double z, double t) {
        double r447749 = z;
        double r447750 = t;
        double r447751 = r447749 * r447750;
        double r447752 = 1.5437511430884524e+293;
        bool r447753 = r447751 <= r447752;
        double r447754 = x;
        double r447755 = y;
        double r447756 = r447755 - r447751;
        double r447757 = r447754 / r447756;
        double r447758 = 1.0;
        double r447759 = r447755 / r447754;
        double r447760 = r447754 / r447750;
        double r447761 = r447749 / r447760;
        double r447762 = r447759 - r447761;
        double r447763 = r447758 / r447762;
        double r447764 = r447753 ? r447757 : r447763;
        return r447764;
}

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

Original2.9
Target1.8
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < 1.5437511430884524e+293

    1. Initial program 1.6

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

    if 1.5437511430884524e+293 < (* z t)

    1. Initial program 19.8

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

    3. Applied clear-num19.8

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

    4. Simplified19.8

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

    6. Applied div-sub23.9

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

    7. Simplified4.9

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \le 1.543751143088452374202847261662502060674 \cdot 10^{293}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{\frac{x}{t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(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))))