Average Error: 17.7 → 0.0
Time: 1.9s
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 r533112 = x;
        double r533113 = y;
        double r533114 = r533112 * r533113;
        double r533115 = r533113 * r533113;
        double r533116 = r533114 + r533115;
        double r533117 = z;
        double r533118 = r533113 * r533117;
        double r533119 = r533116 - r533118;
        double r533120 = r533119 - r533115;
        return r533120;
}
↓
double f(double x, double y, double z) {
        double r533121 = y;
        double r533122 = x;
        double r533123 = z;
        double r533124 = r533122 - r533123;
        double r533125 = 0.0;
        double r533126 = fma(r533121, r533124, r533125);
        return r533126;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.7

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

  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 2020035 +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)))