Average Error: 0.1 → 0.1
Time: 3.1s
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 r30032 = x;
        double r30033 = y;
        double r30034 = r30032 + r30033;
        double r30035 = z;
        double r30036 = r30034 - r30035;
        double r30037 = t;
        double r30038 = 2.0;
        double r30039 = r30037 * r30038;
        double r30040 = r30036 / r30039;
        return r30040;
}
↓
double f(double x, double y, double z, double t) {
        double r30041 = 0.5;
        double r30042 = y;
        double r30043 = t;
        double r30044 = r30042 / r30043;
        double r30045 = x;
        double r30046 = r30045 / r30043;
        double r30047 = r30044 + r30046;
        double r30048 = z;
        double r30049 = r30048 / r30043;
        double r30050 = r30047 - r30049;
        double r30051 = r30041 * r30050;
        return r30051;
}

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 0.1

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

  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 2020021 +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)))