Average Error: 2.8 → 2.8
Time: 28.6s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\frac{x}{y - z \cdot t}\]
\frac{x}{y - z \cdot t}
↓
\frac{x}{y - z \cdot t}
double f(double x, double y, double z, double t) {
        double r31956855 = x;
        double r31956856 = y;
        double r31956857 = z;
        double r31956858 = t;
        double r31956859 = r31956857 * r31956858;
        double r31956860 = r31956856 - r31956859;
        double r31956861 = r31956855 / r31956860;
        return r31956861;
}
↓
double f(double x, double y, double z, double t) {
        double r31956862 = x;
        double r31956863 = y;
        double r31956864 = z;
        double r31956865 = t;
        double r31956866 = r31956864 * r31956865;
        double r31956867 = r31956863 - r31956866;
        double r31956868 = r31956862 / r31956867;
        return r31956868;
}

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
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.8

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

  2. Final simplification2.8

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

Reproduce

herbie shell --seed 2019192 +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))))