Average Error: 0.0 → 0.1
Time: 16.1s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)
double f(double x, double y, double z, double t) {
        double r81195 = x;
        double r81196 = y;
        double r81197 = r81195 + r81196;
        double r81198 = z;
        double r81199 = r81197 - r81198;
        double r81200 = t;
        double r81201 = 2.0;
        double r81202 = r81200 * r81201;
        double r81203 = r81199 / r81202;
        return r81203;
}
↓
double f(double x, double y, double z, double t) {
        double r81204 = 0.5;
        double r81205 = y;
        double r81206 = t;
        double r81207 = r81205 / r81206;
        double r81208 = x;
        double r81209 = r81208 / r81206;
        double r81210 = r81207 + r81209;
        double r81211 = z;
        double r81212 = r81211 / r81206;
        double r81213 = r81210 - r81212;
        double r81214 = r81204 * r81213;
        return r81214;
}

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 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))