Average Error: 0.0 → 0.1
Time: 2.6s
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 r31411 = x;
        double r31412 = y;
        double r31413 = r31411 + r31412;
        double r31414 = z;
        double r31415 = r31413 - r31414;
        double r31416 = t;
        double r31417 = 2.0;
        double r31418 = r31416 * r31417;
        double r31419 = r31415 / r31418;
        return r31419;
}
↓
double f(double x, double y, double z, double t) {
        double r31420 = 0.5;
        double r31421 = y;
        double r31422 = t;
        double r31423 = r31421 / r31422;
        double r31424 = x;
        double r31425 = r31424 / r31422;
        double r31426 = r31423 + r31425;
        double r31427 = z;
        double r31428 = r31427 / r31422;
        double r31429 = r31426 - r31428;
        double r31430 = r31420 * r31429;
        return r31430;
}

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 2020036 +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)))