Average Error: 6.8 → 1.9
Time: 15.4s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x - \frac{1}{\frac{\frac{t}{y}}{x - z}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x - \frac{1}{\frac{\frac{t}{y}}{x - z}}
double f(double x, double y, double z, double t) {
        double r222297 = x;
        double r222298 = y;
        double r222299 = z;
        double r222300 = r222299 - r222297;
        double r222301 = r222298 * r222300;
        double r222302 = t;
        double r222303 = r222301 / r222302;
        double r222304 = r222297 + r222303;
        return r222304;
}
↓
double f(double x, double y, double z, double t) {
        double r222305 = x;
        double r222306 = 1.0;
        double r222307 = t;
        double r222308 = y;
        double r222309 = r222307 / r222308;
        double r222310 = z;
        double r222311 = r222305 - r222310;
        double r222312 = r222309 / r222311;
        double r222313 = r222306 / r222312;
        double r222314 = r222305 - r222313;
        return r222314;
}

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

Original6.8
Target2.0
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.8

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

  2. Simplified6.8

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

  4. Applied associate-/l*6.2

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

  6. Applied clear-num6.2

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

  7. Simplified1.9

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

  8. Final simplification1.9

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

Reproduce

herbie shell --seed 2019195 
(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)))