Average Error: 6.6 → 2.0
Time: 3.3s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{y}{t} \cdot \left(z - x\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{y}{t} \cdot \left(z - x\right)
double f(double x, double y, double z, double t) {
        double r394187 = x;
        double r394188 = y;
        double r394189 = z;
        double r394190 = r394189 - r394187;
        double r394191 = r394188 * r394190;
        double r394192 = t;
        double r394193 = r394191 / r394192;
        double r394194 = r394187 + r394193;
        return r394194;
}
↓
double f(double x, double y, double z, double t) {
        double r394195 = x;
        double r394196 = y;
        double r394197 = t;
        double r394198 = r394196 / r394197;
        double r394199 = z;
        double r394200 = r394199 - r394195;
        double r394201 = r394198 * r394200;
        double r394202 = r394195 + r394201;
        return r394202;
}

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

Original6.6
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

    \[x + \frac{y \cdot \left(z - x\right)}{t}\]
  2. Using strategy rm

  3. Applied associate-/l*6.2

    \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}}\]
  4. Using strategy rm

  5. Applied associate-/r/2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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