Average Error: 0.0 → 0.1
Time: 13.0s
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 r41658 = x;
        double r41659 = y;
        double r41660 = r41658 + r41659;
        double r41661 = z;
        double r41662 = r41660 - r41661;
        double r41663 = t;
        double r41664 = 2.0;
        double r41665 = r41663 * r41664;
        double r41666 = r41662 / r41665;
        return r41666;
}
↓
double f(double x, double y, double z, double t) {
        double r41667 = y;
        double r41668 = t;
        double r41669 = r41667 / r41668;
        double r41670 = x;
        double r41671 = r41670 / r41668;
        double r41672 = z;
        double r41673 = r41672 / r41668;
        double r41674 = r41671 - r41673;
        double r41675 = r41669 + r41674;
        double r41676 = 0.5;
        double r41677 = r41675 * r41676;
        return r41677;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +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)))