Average Error: 0.0 → 0.0
Time: 12.1s
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 r41279 = x;
        double r41280 = y;
        double r41281 = r41279 + r41280;
        double r41282 = z;
        double r41283 = r41281 - r41282;
        double r41284 = t;
        double r41285 = 2.0;
        double r41286 = r41284 * r41285;
        double r41287 = r41283 / r41286;
        return r41287;
}
↓
double f(double x, double y, double z, double t) {
        double r41288 = y;
        double r41289 = t;
        double r41290 = r41288 / r41289;
        double r41291 = x;
        double r41292 = r41291 / r41289;
        double r41293 = z;
        double r41294 = r41293 / r41289;
        double r41295 = r41292 - r41294;
        double r41296 = r41290 + r41295;
        double r41297 = 0.5;
        double r41298 = r41296 * r41297;
        return r41298;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))