Average Error: 6.4 → 1.9
Time: 16.9s
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 r219541 = x;
        double r219542 = y;
        double r219543 = z;
        double r219544 = r219543 - r219541;
        double r219545 = r219542 * r219544;
        double r219546 = t;
        double r219547 = r219545 / r219546;
        double r219548 = r219541 + r219547;
        return r219548;
}
↓
double f(double x, double y, double z, double t) {
        double r219549 = y;
        double r219550 = t;
        double r219551 = r219549 / r219550;
        double r219552 = z;
        double r219553 = x;
        double r219554 = r219552 - r219553;
        double r219555 = fma(r219551, r219554, r219553);
        return r219555;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.4
Target1.9
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.4

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

  2. Simplified1.9

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

  3. Final simplification1.9

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

Reproduce

herbie shell --seed 2019199 +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)))