Average Error: 0.0 → 0.0
Time: 16.3s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5
double f(double x, double y, double z, double t) {
        double r38937 = x;
        double r38938 = y;
        double r38939 = r38937 + r38938;
        double r38940 = z;
        double r38941 = r38939 - r38940;
        double r38942 = t;
        double r38943 = 2.0;
        double r38944 = r38942 * r38943;
        double r38945 = r38941 / r38944;
        return r38945;
}
↓
double f(double x, double y, double z, double t) {
        double r38946 = y;
        double r38947 = t;
        double r38948 = r38946 / r38947;
        double r38949 = x;
        double r38950 = r38949 / r38947;
        double r38951 = z;
        double r38952 = r38951 / r38947;
        double r38953 = r38950 - r38952;
        double r38954 = r38948 + r38953;
        double r38955 = 0.5;
        double r38956 = r38954 * r38955;
        return r38956;
}

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

Derivation

  1. Initial program 0.0

    \[\frac{\left(x + y\right) - z}{t \cdot 2}\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \frac{y}{t} + 0.5 \cdot \frac{x}{t}\right) - 0.5 \cdot \frac{z}{t}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \left(\left(\frac{x}{t} - \frac{z}{t}\right) + \frac{y}{t}\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))