Average Error: 0.1 → 0.1
Time: 2.9s
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 r40689 = x;
        double r40690 = y;
        double r40691 = r40689 + r40690;
        double r40692 = z;
        double r40693 = r40691 - r40692;
        double r40694 = t;
        double r40695 = 2.0;
        double r40696 = r40694 * r40695;
        double r40697 = r40693 / r40696;
        return r40697;
}
↓
double f(double x, double y, double z, double t) {
        double r40698 = 0.5;
        double r40699 = y;
        double r40700 = t;
        double r40701 = r40699 / r40700;
        double r40702 = x;
        double r40703 = r40702 / r40700;
        double r40704 = r40701 + r40703;
        double r40705 = z;
        double r40706 = r40705 / r40700;
        double r40707 = r40704 - r40706;
        double r40708 = r40698 * r40707;
        return r40708;
}

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 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))