Average Error: 6.3 → 2.1
Time: 12.5s
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 r225681 = x;
        double r225682 = y;
        double r225683 = z;
        double r225684 = r225683 - r225681;
        double r225685 = r225682 * r225684;
        double r225686 = t;
        double r225687 = r225685 / r225686;
        double r225688 = r225681 + r225687;
        return r225688;
}
↓
double f(double x, double y, double z, double t) {
        double r225689 = y;
        double r225690 = t;
        double r225691 = r225689 / r225690;
        double r225692 = z;
        double r225693 = x;
        double r225694 = r225692 - r225693;
        double r225695 = fma(r225691, r225694, r225693);
        return r225695;
}

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 2019208 +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)))