Average Error: 2.7 → 2.7
Time: 11.6s
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 r30758656 = x;
        double r30758657 = y;
        double r30758658 = z;
        double r30758659 = t;
        double r30758660 = r30758658 * r30758659;
        double r30758661 = r30758657 - r30758660;
        double r30758662 = r30758656 / r30758661;
        return r30758662;
}
↓
double f(double x, double y, double z, double t) {
        double r30758663 = x;
        double r30758664 = y;
        double r30758665 = z;
        double r30758666 = t;
        double r30758667 = r30758665 * r30758666;
        double r30758668 = r30758664 - r30758667;
        double r30758669 = r30758663 / r30758668;
        return r30758669;
}

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 2019171 +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) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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