Average Error: 6.8 → 1.8
Time: 18.7s
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 r17324322 = x;
        double r17324323 = y;
        double r17324324 = z;
        double r17324325 = r17324324 - r17324322;
        double r17324326 = r17324323 * r17324325;
        double r17324327 = t;
        double r17324328 = r17324326 / r17324327;
        double r17324329 = r17324322 + r17324328;
        return r17324329;
}
↓
double f(double x, double y, double z, double t) {
        double r17324330 = x;
        double r17324331 = z;
        double r17324332 = r17324331 - r17324330;
        double r17324333 = t;
        double r17324334 = y;
        double r17324335 = r17324333 / r17324334;
        double r17324336 = r17324332 / r17324335;
        double r17324337 = r17324330 + r17324336;
        return r17324337;
}

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

Original6.8
Target1.9
Herbie1.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.8

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

  2. Taylor expanded around 0 6.8

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

  3. Simplified1.8

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

  4. Final simplification1.8

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

Reproduce

herbie shell --seed 2019174 
(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)))