Average Error: 6.9 → 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 r319321 = x;
        double r319322 = y;
        double r319323 = z;
        double r319324 = r319323 - r319321;
        double r319325 = r319322 * r319324;
        double r319326 = t;
        double r319327 = r319325 / r319326;
        double r319328 = r319321 + r319327;
        return r319328;
}
↓
double f(double x, double y, double z, double t) {
        double r319329 = y;
        double r319330 = t;
        double r319331 = r319329 / r319330;
        double r319332 = z;
        double r319333 = x;
        double r319334 = r319332 - r319333;
        double r319335 = fma(r319331, r319334, r319333);
        return r319335;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.9
Target2.1
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.9

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

  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 2020083 +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)))