Average Error: 6.3 → 1.9
Time: 19.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{z - x}{\frac{t}{y}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{z - x}{\frac{t}{y}}
double f(double x, double y, double z, double t) {
        double r18995328 = x;
        double r18995329 = y;
        double r18995330 = z;
        double r18995331 = r18995330 - r18995328;
        double r18995332 = r18995329 * r18995331;
        double r18995333 = t;
        double r18995334 = r18995332 / r18995333;
        double r18995335 = r18995328 + r18995334;
        return r18995335;
}
↓
double f(double x, double y, double z, double t) {
        double r18995336 = x;
        double r18995337 = z;
        double r18995338 = r18995337 - r18995336;
        double r18995339 = t;
        double r18995340 = y;
        double r18995341 = r18995339 / r18995340;
        double r18995342 = r18995338 / r18995341;
        double r18995343 = r18995336 + r18995342;
        return r18995343;
}

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

Target

Original6.3
Target2.0
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.3

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

  2. Taylor expanded around 0 6.3

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

  3. Simplified1.9

    \[\leadsto x + \color{blue}{\frac{z - x}{\frac{t}{y}}}\]

  4. Final simplification1.9

    \[\leadsto x + \frac{z - x}{\frac{t}{y}}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))