Average Error: 6.2 → 2.1
Time: 2.2s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)
double f(double x, double y, double z, double t) {
        double r303700 = x;
        double r303701 = y;
        double r303702 = z;
        double r303703 = r303702 - r303700;
        double r303704 = r303701 * r303703;
        double r303705 = t;
        double r303706 = r303704 / r303705;
        double r303707 = r303700 + r303706;
        return r303707;
}
↓
double f(double x, double y, double z, double t) {
        double r303708 = y;
        double r303709 = t;
        double r303710 = r303708 / r303709;
        double r303711 = z;
        double r303712 = x;
        double r303713 = r303711 - r303712;
        double r303714 = fma(r303710, r303713, r303712);
        return r303714;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.2
Target2.1
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.2

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

  2. Simplified2.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]

  3. Final simplification2.1

    \[\leadsto \mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\]

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(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)))