Average Error: 2.8 → 2.8
Time: 16.8s
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 r30231936 = x;
        double r30231937 = y;
        double r30231938 = z;
        double r30231939 = t;
        double r30231940 = r30231938 * r30231939;
        double r30231941 = r30231937 - r30231940;
        double r30231942 = r30231936 / r30231941;
        return r30231942;
}
↓
double f(double x, double y, double z, double t) {
        double r30231943 = x;
        double r30231944 = y;
        double r30231945 = z;
        double r30231946 = t;
        double r30231947 = r30231945 * r30231946;
        double r30231948 = r30231944 - r30231947;
        double r30231949 = r30231943 / r30231948;
        return r30231949;
}

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
Target1.9
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 2019172 +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))))