Average Error: 2.8 → 2.8
Time: 3.7s
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 r669239 = x;
        double r669240 = y;
        double r669241 = z;
        double r669242 = t;
        double r669243 = r669241 * r669242;
        double r669244 = r669240 - r669243;
        double r669245 = r669239 / r669244;
        return r669245;
}
↓
double f(double x, double y, double z, double t) {
        double r669246 = x;
        double r669247 = y;
        double r669248 = z;
        double r669249 = t;
        double r669250 = r669248 * r669249;
        double r669251 = r669247 - r669250;
        double r669252 = r669246 / r669251;
        return r669252;
}

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
Target1.6
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 2019354 +o rules:numerics
(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))))