Average Error: 0.0 → 0.0
Time: 11.3s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\mathsf{fma}\left(a, a, \left(-b \cdot b\right)\right)\]
a \cdot a - b \cdot b
↓
\mathsf{fma}\left(a, a, \left(-b \cdot b\right)\right)
double f(double a, double b) {
        double r2512132 = a;
        double r2512133 = r2512132 * r2512132;
        double r2512134 = b;
        double r2512135 = r2512134 * r2512134;
        double r2512136 = r2512133 - r2512135;
        return r2512136;
}
↓
double f(double a, double b) {
        double r2512137 = a;
        double r2512138 = b;
        double r2512139 = r2512138 * r2512138;
        double r2512140 = -r2512139;
        double r2512141 = fma(r2512137, r2512137, r2512140);
        return r2512141;
}

Error

Bits error versus a

Bits error versus b

Target

Original0.0
Target0.0
Herbie0.0
\[\left(a + b\right) \cdot \left(a - b\right)\]

Derivation

  1. Initial program 0.0

    \[a \cdot a - b \cdot b\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(a, a, \left(-b \cdot b\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(a, a, \left(-b \cdot b\right)\right)\]

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

  :herbie-target
  (* (+ a b) (- a b))

  (- (* a a) (* b b)))