Average Error: 2.9 → 2.9
Time: 13.7s
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 r33083064 = x;
        double r33083065 = y;
        double r33083066 = z;
        double r33083067 = t;
        double r33083068 = r33083066 * r33083067;
        double r33083069 = r33083065 - r33083068;
        double r33083070 = r33083064 / r33083069;
        return r33083070;
}
↓
double f(double x, double y, double z, double t) {
        double r33083071 = x;
        double r33083072 = y;
        double r33083073 = z;
        double r33083074 = t;
        double r33083075 = r33083073 * r33083074;
        double r33083076 = r33083072 - r33083075;
        double r33083077 = r33083071 / r33083076;
        return r33083077;
}

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
Target1.8
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.9

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

  2. Final simplification2.9

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

Reproduce

herbie shell --seed 2019163 +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))))