Average Error: 0.0 → 0.0
Time: 22.2s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\mathsf{fma}\left(a, a, -b \cdot b\right)\]
a \cdot a - b \cdot b
↓
\mathsf{fma}\left(a, a, -b \cdot b\right)
double f(double a, double b) {
        double r5103226 = a;
        double r5103227 = r5103226 * r5103226;
        double r5103228 = b;
        double r5103229 = r5103228 * r5103228;
        double r5103230 = r5103227 - r5103229;
        return r5103230;
}
↓
double f(double a, double b) {
        double r5103231 = a;
        double r5103232 = b;
        double r5103233 = r5103232 * r5103232;
        double r5103234 = -r5103233;
        double r5103235 = fma(r5103231, r5103231, r5103234);
        return r5103235;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019138 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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