Average Error: 3.1 → 3.1
Time: 3.6s
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 r776541 = x;
        double r776542 = y;
        double r776543 = z;
        double r776544 = t;
        double r776545 = r776543 * r776544;
        double r776546 = r776542 - r776545;
        double r776547 = r776541 / r776546;
        return r776547;
}
↓
double f(double x, double y, double z, double t) {
        double r776548 = x;
        double r776549 = y;
        double r776550 = z;
        double r776551 = t;
        double r776552 = r776550 * r776551;
        double r776553 = r776549 - r776552;
        double r776554 = r776548 / r776553;
        return r776554;
}

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

Original3.1
Target1.8
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 3.1

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

  2. Final simplification3.1

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

Reproduce

herbie shell --seed 2020049 
(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))))