Average Error: 6.3 → 2.1
Time: 13.1s
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 r349572 = x;
        double r349573 = y;
        double r349574 = z;
        double r349575 = r349574 - r349572;
        double r349576 = r349573 * r349575;
        double r349577 = t;
        double r349578 = r349576 / r349577;
        double r349579 = r349572 + r349578;
        return r349579;
}
↓
double f(double x, double y, double z, double t) {
        double r349580 = y;
        double r349581 = t;
        double r349582 = r349580 / r349581;
        double r349583 = z;
        double r349584 = x;
        double r349585 = r349583 - r349584;
        double r349586 = fma(r349582, r349585, r349584);
        return r349586;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.3
Target2.1
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.3

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

  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 2019350 +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)))