Average Error: 6.3 → 2.1
Time: 3.3s
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 r292567 = x;
        double r292568 = y;
        double r292569 = z;
        double r292570 = r292569 - r292567;
        double r292571 = r292568 * r292570;
        double r292572 = t;
        double r292573 = r292571 / r292572;
        double r292574 = r292567 + r292573;
        return r292574;
}
↓
double f(double x, double y, double z, double t) {
        double r292575 = y;
        double r292576 = t;
        double r292577 = r292575 / r292576;
        double r292578 = z;
        double r292579 = x;
        double r292580 = r292578 - r292579;
        double r292581 = fma(r292577, r292580, r292579);
        return r292581;
}

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 2020021 +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)))