Average Error: 6.6 → 2.0
Time: 3.3s
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 r313354 = x;
        double r313355 = y;
        double r313356 = z;
        double r313357 = r313356 - r313354;
        double r313358 = r313355 * r313357;
        double r313359 = t;
        double r313360 = r313358 / r313359;
        double r313361 = r313354 + r313360;
        return r313361;
}
↓
double f(double x, double y, double z, double t) {
        double r313362 = x;
        double r313363 = y;
        double r313364 = t;
        double r313365 = r313363 / r313364;
        double r313366 = z;
        double r313367 = r313366 - r313362;
        double r313368 = r313365 * r313367;
        double r313369 = r313362 + r313368;
        return r313369;
}

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

Original6.6
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

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

  3. Applied associate-/l*6.2

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

  5. Applied associate-/r/2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2020062 
(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)))