Average Error: 2.7 → 2.7
Time: 3.1s
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 r763872 = x;
        double r763873 = y;
        double r763874 = z;
        double r763875 = t;
        double r763876 = r763874 * r763875;
        double r763877 = r763873 - r763876;
        double r763878 = r763872 / r763877;
        return r763878;
}
↓
double f(double x, double y, double z, double t) {
        double r763879 = x;
        double r763880 = y;
        double r763881 = z;
        double r763882 = t;
        double r763883 = r763881 * r763882;
        double r763884 = r763880 - r763883;
        double r763885 = r763879 / r763884;
        return r763885;
}

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
Target1.9
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.7

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

  2. Final simplification2.7

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :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))))