Average Error: 6.8 → 1.9
Time: 13.9s
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 r22307508 = x;
        double r22307509 = y;
        double r22307510 = z;
        double r22307511 = r22307510 - r22307508;
        double r22307512 = r22307509 * r22307511;
        double r22307513 = t;
        double r22307514 = r22307512 / r22307513;
        double r22307515 = r22307508 + r22307514;
        return r22307515;
}
↓
double f(double x, double y, double z, double t) {
        double r22307516 = y;
        double r22307517 = t;
        double r22307518 = r22307516 / r22307517;
        double r22307519 = z;
        double r22307520 = x;
        double r22307521 = r22307519 - r22307520;
        double r22307522 = fma(r22307518, r22307521, r22307520);
        return r22307522;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.8
Target1.9
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. Simplified1.9

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

  3. Final simplification1.9

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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)))