Average Error: 0.1 → 0.1
Time: 11.7s
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 r2860569 = x;
        double r2860570 = y;
        double r2860571 = r2860569 + r2860570;
        double r2860572 = z;
        double r2860573 = r2860571 - r2860572;
        double r2860574 = t;
        double r2860575 = 2.0;
        double r2860576 = r2860574 * r2860575;
        double r2860577 = r2860573 / r2860576;
        return r2860577;
}
↓
double f(double x, double y, double z, double t) {
        double r2860578 = y;
        double r2860579 = t;
        double r2860580 = r2860578 / r2860579;
        double r2860581 = x;
        double r2860582 = r2860581 / r2860579;
        double r2860583 = z;
        double r2860584 = r2860583 / r2860579;
        double r2860585 = r2860582 - r2860584;
        double r2860586 = r2860580 + r2860585;
        double r2860587 = 0.5;
        double r2860588 = r2860586 * r2860587;
        return r2860588;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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

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

  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 2019192 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))