Average Error: 6.4 → 1.9
Time: 18.0s
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 r272531 = x;
        double r272532 = y;
        double r272533 = z;
        double r272534 = r272533 - r272531;
        double r272535 = r272532 * r272534;
        double r272536 = t;
        double r272537 = r272535 / r272536;
        double r272538 = r272531 + r272537;
        return r272538;
}
↓
double f(double x, double y, double z, double t) {
        double r272539 = x;
        double r272540 = y;
        double r272541 = t;
        double r272542 = r272540 / r272541;
        double r272543 = z;
        double r272544 = r272543 - r272539;
        double r272545 = r272542 * r272544;
        double r272546 = r272539 + r272545;
        return r272546;
}

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

Original6.4
Target1.9
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.4

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

  3. Applied associate-/l*6.1

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

  5. Applied associate-/r/1.9

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

  6. Final simplification1.9

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

Reproduce

herbie shell --seed 2019199 
(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)))