Average Error: 6.3 → 2.0
Time: 2.3s
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 r232539 = x;
        double r232540 = y;
        double r232541 = z;
        double r232542 = r232541 - r232539;
        double r232543 = r232540 * r232542;
        double r232544 = t;
        double r232545 = r232543 / r232544;
        double r232546 = r232539 + r232545;
        return r232546;
}
↓
double f(double x, double y, double z, double t) {
        double r232547 = y;
        double r232548 = t;
        double r232549 = r232547 / r232548;
        double r232550 = z;
        double r232551 = x;
        double r232552 = r232550 - r232551;
        double r232553 = fma(r232549, r232552, r232551);
        return r232553;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.3
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.3

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

  2. Simplified2.0

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

  3. Final simplification2.0

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

Reproduce

herbie shell --seed 2020018 +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)))