Average Error: 17.5 → 0.0
Time: 1.1s
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 r693131 = x;
        double r693132 = y;
        double r693133 = r693131 * r693132;
        double r693134 = r693132 * r693132;
        double r693135 = r693133 + r693134;
        double r693136 = z;
        double r693137 = r693132 * r693136;
        double r693138 = r693135 - r693137;
        double r693139 = r693138 - r693134;
        return r693139;
}
↓
double f(double x, double y, double z) {
        double r693140 = y;
        double r693141 = x;
        double r693142 = z;
        double r693143 = r693141 - r693142;
        double r693144 = 0.0;
        double r693145 = fma(r693140, r693143, r693144);
        return r693145;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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 2020025 +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)))