Average Error: 3.0 → 3.0
Time: 4.3s
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 r667597 = x;
        double r667598 = y;
        double r667599 = z;
        double r667600 = t;
        double r667601 = r667599 * r667600;
        double r667602 = r667598 - r667601;
        double r667603 = r667597 / r667602;
        return r667603;
}
↓
double f(double x, double y, double z, double t) {
        double r667604 = x;
        double r667605 = y;
        double r667606 = z;
        double r667607 = t;
        double r667608 = r667606 * r667607;
        double r667609 = r667605 - r667608;
        double r667610 = r667604 / r667609;
        return r667610;
}

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

Original3.0
Target1.8
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 3.0

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

  2. Final simplification3.0

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

Reproduce

herbie shell --seed 2020081 +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))))