Average Error: 6.7 → 2.0
Time: 11.2s
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 r199390 = x;
        double r199391 = y;
        double r199392 = z;
        double r199393 = r199392 - r199390;
        double r199394 = r199391 * r199393;
        double r199395 = t;
        double r199396 = r199394 / r199395;
        double r199397 = r199390 + r199396;
        return r199397;
}
↓
double f(double x, double y, double z, double t) {
        double r199398 = y;
        double r199399 = t;
        double r199400 = r199398 / r199399;
        double r199401 = z;
        double r199402 = x;
        double r199403 = r199401 - r199402;
        double r199404 = fma(r199400, r199403, r199402);
        return r199404;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.7
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.7

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

  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 2019235 +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)))