Average Error: 0.0 → 0.0
Time: 9.6s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[\mathsf{fma}\left(y, y, x \cdot \left(2 + x\right)\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
\mathsf{fma}\left(y, y, x \cdot \left(2 + x\right)\right)
double f(double x, double y) {
        double r15118113 = x;
        double r15118114 = 2.0;
        double r15118115 = r15118113 * r15118114;
        double r15118116 = r15118113 * r15118113;
        double r15118117 = r15118115 + r15118116;
        double r15118118 = y;
        double r15118119 = r15118118 * r15118118;
        double r15118120 = r15118117 + r15118119;
        return r15118120;
}
↓
double f(double x, double y) {
        double r15118121 = y;
        double r15118122 = x;
        double r15118123 = 2.0;
        double r15118124 = r15118123 + r15118122;
        double r15118125 = r15118122 * r15118124;
        double r15118126 = fma(r15118121, r15118121, r15118125);
        return r15118126;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0.0
\[y \cdot y + \left(2 \cdot x + x \cdot x\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, y, \left(2 + x\right) \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, y, x \cdot \left(2 + x\right)\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

  (+ (+ (* x 2.0) (* x x)) (* y y)))