Average Error: 6.1 → 2.0
Time: 3.4s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{1}{\frac{\frac{t}{y}}{z - x}}
double f(double x, double y, double z, double t) {
        double r360537 = x;
        double r360538 = y;
        double r360539 = z;
        double r360540 = r360539 - r360537;
        double r360541 = r360538 * r360540;
        double r360542 = t;
        double r360543 = r360541 / r360542;
        double r360544 = r360537 + r360543;
        return r360544;
}
↓
double f(double x, double y, double z, double t) {
        double r360545 = x;
        double r360546 = 1.0;
        double r360547 = t;
        double r360548 = y;
        double r360549 = r360547 / r360548;
        double r360550 = z;
        double r360551 = r360550 - r360545;
        double r360552 = r360549 / r360551;
        double r360553 = r360546 / r360552;
        double r360554 = r360545 + r360553;
        return r360554;
}

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

Original6.1
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.1

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

  3. Applied clear-num6.2

    \[\leadsto x + \color{blue}{\frac{1}{\frac{t}{y \cdot \left(z - x\right)}}}\]
  4. Using strategy rm

  5. Applied associate-/r*2.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}}\]

  6. Final simplification2.0

    \[\leadsto x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\]

Reproduce

herbie shell --seed 2020035 
(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)))