Average Error: 6.8 → 2.1
Time: 17.0s
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 r304255 = x;
        double r304256 = y;
        double r304257 = z;
        double r304258 = r304257 - r304255;
        double r304259 = r304256 * r304258;
        double r304260 = t;
        double r304261 = r304259 / r304260;
        double r304262 = r304255 + r304261;
        return r304262;
}
↓
double f(double x, double y, double z, double t) {
        double r304263 = x;
        double r304264 = 1.0;
        double r304265 = t;
        double r304266 = y;
        double r304267 = r304265 / r304266;
        double r304268 = z;
        double r304269 = r304268 - r304263;
        double r304270 = r304267 / r304269;
        double r304271 = r304264 / r304270;
        double r304272 = r304263 + r304271;
        return r304272;
}

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
Target2.2
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.8

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

  3. Applied clear-num6.9

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

  5. Applied associate-/r*2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2019198 
(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)))