Average Error: 18.3 → 0.0
Time: 2.8s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\mathsf{fma}\left(y, x - z, 0\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\mathsf{fma}\left(y, x - z, 0\right)
double f(double x, double y, double z) {
        double r607383 = x;
        double r607384 = y;
        double r607385 = r607383 * r607384;
        double r607386 = r607384 * r607384;
        double r607387 = r607385 + r607386;
        double r607388 = z;
        double r607389 = r607384 * r607388;
        double r607390 = r607387 - r607389;
        double r607391 = r607390 - r607386;
        return r607391;
}
↓
double f(double x, double y, double z) {
        double r607392 = y;
        double r607393 = x;
        double r607394 = z;
        double r607395 = r607393 - r607394;
        double r607396 = 0.0;
        double r607397 = fma(r607392, r607395, r607396);
        return r607397;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original18.3
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 18.3

    \[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, 0\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x - z, 0\right)\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))