Average Error: 2.7 → 2.7
Time: 15.5s
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 r459939 = x;
        double r459940 = y;
        double r459941 = z;
        double r459942 = t;
        double r459943 = r459941 * r459942;
        double r459944 = r459940 - r459943;
        double r459945 = r459939 / r459944;
        return r459945;
}
↓
double f(double x, double y, double z, double t) {
        double r459946 = x;
        double r459947 = y;
        double r459948 = z;
        double r459949 = t;
        double r459950 = r459948 * r459949;
        double r459951 = r459947 - r459950;
        double r459952 = r459946 / r459951;
        return r459952;
}

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
Target1.8
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.7

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

  2. Final simplification2.7

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

Reproduce

herbie shell --seed 2019347 +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))))