Average Error: 6.4 → 1.8
Time: 18.3s
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 r270178 = x;
        double r270179 = y;
        double r270180 = z;
        double r270181 = r270180 - r270178;
        double r270182 = r270179 * r270181;
        double r270183 = t;
        double r270184 = r270182 / r270183;
        double r270185 = r270178 + r270184;
        return r270185;
}
↓
double f(double x, double y, double z, double t) {
        double r270186 = y;
        double r270187 = t;
        double r270188 = r270186 / r270187;
        double r270189 = z;
        double r270190 = x;
        double r270191 = r270189 - r270190;
        double r270192 = fma(r270188, r270191, r270190);
        return r270192;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.4
Target1.8
Herbie1.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.4

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

  2. Simplified1.8

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

  3. Final simplification1.8

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

Reproduce

herbie shell --seed 2019347 +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)))