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 r284704 = x;
        double r284705 = y;
        double r284706 = z;
        double r284707 = r284706 - r284704;
        double r284708 = r284705 * r284707;
        double r284709 = t;
        double r284710 = r284708 / r284709;
        double r284711 = r284704 + r284710;
        return r284711;
}
↓
double f(double x, double y, double z, double t) {
        double r284712 = y;
        double r284713 = t;
        double r284714 = r284712 / r284713;
        double r284715 = z;
        double r284716 = x;
        double r284717 = r284715 - r284716;
        double r284718 = fma(r284714, r284717, r284716);
        return r284718;
}

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 2020039 +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)))