Average Error: 2.8 → 0.8
Time: 10.5s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 1.343488166531035091051466743529265739987 \cdot 10^{303}\right):\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 1.343488166531035091051466743529265739987 \cdot 10^{303}\right):\\
\;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r663088 = x;
        double r663089 = y;
        double r663090 = z;
        double r663091 = t;
        double r663092 = r663090 * r663091;
        double r663093 = r663089 - r663092;
        double r663094 = r663088 / r663093;
        return r663094;
}
↓
double f(double x, double y, double z, double t) {
        double r663095 = z;
        double r663096 = t;
        double r663097 = r663095 * r663096;
        double r663098 = -inf.0;
        bool r663099 = r663097 <= r663098;
        double r663100 = 1.3434881665310351e+303;
        bool r663101 = r663097 <= r663100;
        double r663102 = !r663101;
        bool r663103 = r663099 || r663102;
        double r663104 = 1.0;
        double r663105 = y;
        double r663106 = x;
        double r663107 = r663105 / r663106;
        double r663108 = r663106 / r663095;
        double r663109 = r663096 / r663108;
        double r663110 = r663107 - r663109;
        double r663111 = r663104 / r663110;
        double r663112 = r663105 - r663097;
        double r663113 = r663106 / r663112;
        double r663114 = r663103 ? r663111 : r663113;
        return r663114;
}

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

Original2.8
Target1.7
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < -inf.0 or 1.3434881665310351e+303 < (* z t)

    1. Initial program 20.4

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

    3. Applied clear-num20.4

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

    4. Simplified20.4

      \[\leadsto \frac{1}{\color{blue}{\frac{\mathsf{fma}\left(-t, z, y\right)}{x}}}\]
    5. Using strategy rm

    6. Applied div-inv20.4

      \[\leadsto \frac{1}{\color{blue}{\mathsf{fma}\left(-t, z, y\right) \cdot \frac{1}{x}}}\]

    7. Taylor expanded around 0 24.8

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

    8. Simplified5.0

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

    if -inf.0 < (* z t) < 1.3434881665310351e+303

    1. Initial program 0.1

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 1.343488166531035091051466743529265739987 \cdot 10^{303}\right):\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(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))))