Average Error: 17.1 → 0.0
Time: 2.2s
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 r611190 = x;
        double r611191 = y;
        double r611192 = r611190 * r611191;
        double r611193 = r611191 * r611191;
        double r611194 = r611192 + r611193;
        double r611195 = z;
        double r611196 = r611191 * r611195;
        double r611197 = r611194 - r611196;
        double r611198 = r611197 - r611193;
        return r611198;
}
↓
double f(double x, double y, double z) {
        double r611199 = y;
        double r611200 = x;
        double r611201 = z;
        double r611202 = r611200 - r611201;
        double r611203 = 0.0;
        double r611204 = fma(r611199, r611202, r611203);
        return r611204;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.1

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

  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 2020057 +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)))