Average Error: 2.8 → 2.8
Time: 8.0s
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 r13605925 = x;
        double r13605926 = y;
        double r13605927 = z;
        double r13605928 = t;
        double r13605929 = r13605927 * r13605928;
        double r13605930 = r13605926 - r13605929;
        double r13605931 = r13605925 / r13605930;
        return r13605931;
}
↓
double f(double x, double y, double z, double t) {
        double r13605932 = x;
        double r13605933 = y;
        double r13605934 = z;
        double r13605935 = t;
        double r13605936 = r13605934 * r13605935;
        double r13605937 = r13605933 - r13605936;
        double r13605938 = r13605932 / r13605937;
        return r13605938;
}

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
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

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 2019156 +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 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

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