Average Error: 6.7 → 5.7
Time: 7.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{y}{\frac{t}{z - x}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{y}{\frac{t}{z - x}}
double f(double x, double y, double z, double t) {
        double r266591 = x;
        double r266592 = y;
        double r266593 = z;
        double r266594 = r266593 - r266591;
        double r266595 = r266592 * r266594;
        double r266596 = t;
        double r266597 = r266595 / r266596;
        double r266598 = r266591 + r266597;
        return r266598;
}
↓
double f(double x, double y, double z, double t) {
        double r266599 = x;
        double r266600 = y;
        double r266601 = t;
        double r266602 = z;
        double r266603 = r266602 - r266599;
        double r266604 = r266601 / r266603;
        double r266605 = r266600 / r266604;
        double r266606 = r266599 + r266605;
        return r266606;
}

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

Original6.7
Target1.9
Herbie5.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 8.377346974531215e+294 < (+ x (/ (* y (- z x)) t))

    1. Initial program 57.3

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

    3. Applied associate-/l*2.2

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

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 8.377346974531215e+294

    1. Initial program 0.8

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.7

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

Reproduce

herbie shell --seed 2019294 
(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)))