Average Error: 17.6 → 0.0
Time: 1.2s
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 r439147 = x;
        double r439148 = y;
        double r439149 = r439147 * r439148;
        double r439150 = r439148 * r439148;
        double r439151 = r439149 + r439150;
        double r439152 = z;
        double r439153 = r439148 * r439152;
        double r439154 = r439151 - r439153;
        double r439155 = r439154 - r439150;
        return r439155;
}
↓
double f(double x, double y, double z) {
        double r439156 = y;
        double r439157 = x;
        double r439158 = z;
        double r439159 = r439157 - r439158;
        double r439160 = 0.0;
        double r439161 = fma(r439156, r439159, r439160);
        return r439161;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.6

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

  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 2020065 +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)))