Average Error: 2.9 → 2.9
Time: 18.8s
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 r453284 = x;
        double r453285 = y;
        double r453286 = z;
        double r453287 = t;
        double r453288 = r453286 * r453287;
        double r453289 = r453285 - r453288;
        double r453290 = r453284 / r453289;
        return r453290;
}
↓
double f(double x, double y, double z, double t) {
        double r453291 = x;
        double r453292 = y;
        double r453293 = z;
        double r453294 = t;
        double r453295 = r453293 * r453294;
        double r453296 = r453292 - r453295;
        double r453297 = r453291 / r453296;
        return r453297;
}

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

Original2.9
Target1.8
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.9

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

  2. Final simplification2.9

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

Reproduce

herbie shell --seed 2019326 +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))))