Average Error: 2.7 → 2.7
Time: 15.6s
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 r33690421 = x;
        double r33690422 = y;
        double r33690423 = z;
        double r33690424 = t;
        double r33690425 = r33690423 * r33690424;
        double r33690426 = r33690422 - r33690425;
        double r33690427 = r33690421 / r33690426;
        return r33690427;
}
↓
double f(double x, double y, double z, double t) {
        double r33690428 = x;
        double r33690429 = y;
        double r33690430 = z;
        double r33690431 = t;
        double r33690432 = r33690430 * r33690431;
        double r33690433 = r33690429 - r33690432;
        double r33690434 = r33690428 / r33690433;
        return r33690434;
}

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
Target1.7
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

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 2019158 +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 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

  (/ x (- y (* z t))))