Average Error: 2.9 → 2.9
Time: 2.3s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\frac{x}{y + \left(-z \cdot t\right)}\]
\frac{x}{y - z \cdot t}
↓
\frac{x}{y + \left(-z \cdot t\right)}
double f(double x, double y, double z, double t) {
        double r880455 = x;
        double r880456 = y;
        double r880457 = z;
        double r880458 = t;
        double r880459 = r880457 * r880458;
        double r880460 = r880456 - r880459;
        double r880461 = r880455 / r880460;
        return r880461;
}
↓
double f(double x, double y, double z, double t) {
        double r880462 = x;
        double r880463 = y;
        double r880464 = z;
        double r880465 = t;
        double r880466 = r880464 * r880465;
        double r880467 = -r880466;
        double r880468 = r880463 + r880467;
        double r880469 = r880462 / r880468;
        return r880469;
}

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
Target1.7
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.9

    \[\frac{x}{y - z \cdot t}\]
  2. Using strategy rm

  3. Applied sub-neg2.9

    \[\leadsto \frac{x}{\color{blue}{y + \left(-z \cdot t\right)}}\]

  4. Final simplification2.9

    \[\leadsto \frac{x}{y + \left(-z \cdot t\right)}\]

Reproduce

herbie shell --seed 2020057 
(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))))