Average Error: 17.8 → 0.0
Time: 2.0s
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 r694220 = x;
        double r694221 = y;
        double r694222 = r694220 * r694221;
        double r694223 = r694221 * r694221;
        double r694224 = r694222 + r694223;
        double r694225 = z;
        double r694226 = r694221 * r694225;
        double r694227 = r694224 - r694226;
        double r694228 = r694227 - r694223;
        return r694228;
}
↓
double f(double x, double y, double z) {
        double r694229 = y;
        double r694230 = x;
        double r694231 = z;
        double r694232 = r694230 - r694231;
        double r694233 = 0.0;
        double r694234 = fma(r694229, r694232, r694233);
        return r694234;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.8

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

  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 2020060 +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)))