Average Error: 6.6 → 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 r337202 = x;
        double r337203 = y;
        double r337204 = z;
        double r337205 = r337204 - r337202;
        double r337206 = r337203 * r337205;
        double r337207 = t;
        double r337208 = r337206 / r337207;
        double r337209 = r337202 + r337208;
        return r337209;
}
↓
double f(double x, double y, double z, double t) {
        double r337210 = y;
        double r337211 = t;
        double r337212 = r337210 / r337211;
        double r337213 = z;
        double r337214 = x;
        double r337215 = r337213 - r337214;
        double r337216 = fma(r337212, r337215, r337214);
        return r337216;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.6
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

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

  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 2020062 +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)))