Average Error: 2.8 → 2.8
Time: 3.5s
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 r755369 = x;
        double r755370 = y;
        double r755371 = z;
        double r755372 = t;
        double r755373 = r755371 * r755372;
        double r755374 = r755370 - r755373;
        double r755375 = r755369 / r755374;
        return r755375;
}
↓
double f(double x, double y, double z, double t) {
        double r755376 = x;
        double r755377 = y;
        double r755378 = z;
        double r755379 = t;
        double r755380 = r755378 * r755379;
        double r755381 = r755377 - r755380;
        double r755382 = r755376 / r755381;
        return r755382;
}

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
Target1.8
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.8

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

  2. Final simplification2.8

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

Reproduce

herbie shell --seed 2020100 
(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))))