Average Error: 0.0 → 0.0
Time: 10.8s
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 r41212 = x;
        double r41213 = y;
        double r41214 = r41212 + r41213;
        double r41215 = z;
        double r41216 = r41214 - r41215;
        double r41217 = t;
        double r41218 = 2.0;
        double r41219 = r41217 * r41218;
        double r41220 = r41216 / r41219;
        return r41220;
}
↓
double f(double x, double y, double z, double t) {
        double r41221 = y;
        double r41222 = t;
        double r41223 = r41221 / r41222;
        double r41224 = x;
        double r41225 = r41224 / r41222;
        double r41226 = z;
        double r41227 = r41226 / r41222;
        double r41228 = r41225 - r41227;
        double r41229 = r41223 + r41228;
        double r41230 = 0.5;
        double r41231 = r41229 * r41230;
        return r41231;
}

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)))