Average Error: 6.6 → 2.0
Time: 2.4s
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 r266668 = x;
        double r266669 = y;
        double r266670 = z;
        double r266671 = r266670 - r266668;
        double r266672 = r266669 * r266671;
        double r266673 = t;
        double r266674 = r266672 / r266673;
        double r266675 = r266668 + r266674;
        return r266675;
}
↓
double f(double x, double y, double z, double t) {
        double r266676 = y;
        double r266677 = t;
        double r266678 = r266676 / r266677;
        double r266679 = z;
        double r266680 = x;
        double r266681 = r266679 - r266680;
        double r266682 = fma(r266678, r266681, r266680);
        return r266682;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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. Simplified2.0

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

  3. Final simplification2.0

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

Reproduce

herbie shell --seed 2020062 +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)))