Average Error: 6.9 → 2.1
Time: 3.2s
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 r360426 = x;
        double r360427 = y;
        double r360428 = z;
        double r360429 = r360428 - r360426;
        double r360430 = r360427 * r360429;
        double r360431 = t;
        double r360432 = r360430 / r360431;
        double r360433 = r360426 + r360432;
        return r360433;
}
↓
double f(double x, double y, double z, double t) {
        double r360434 = x;
        double r360435 = y;
        double r360436 = t;
        double r360437 = r360435 / r360436;
        double r360438 = z;
        double r360439 = r360438 - r360434;
        double r360440 = r360437 * r360439;
        double r360441 = r360434 + r360440;
        return r360441;
}

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

Original6.9
Target2.1
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.9

    \[x + \frac{y \cdot \left(z - x\right)}{t}\]
  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/2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2020083 
(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)))