Average Error: 6.7 → 2.0
Time: 2.5s
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 r282093 = x;
        double r282094 = y;
        double r282095 = z;
        double r282096 = r282095 - r282093;
        double r282097 = r282094 * r282096;
        double r282098 = t;
        double r282099 = r282097 / r282098;
        double r282100 = r282093 + r282099;
        return r282100;
}
↓
double f(double x, double y, double z, double t) {
        double r282101 = y;
        double r282102 = t;
        double r282103 = r282101 / r282102;
        double r282104 = z;
        double r282105 = x;
        double r282106 = r282104 - r282105;
        double r282107 = fma(r282103, r282106, r282105);
        return r282107;
}

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 2020047 +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)))