Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(b + a\right) \cdot \left(a - b\right)\]
double f(double a, double b) {
        double r11953947 = a;
        double r11953948 = r11953947 * r11953947;
        double r11953949 = b;
        double r11953950 = r11953949 * r11953949;
        double r11953951 = r11953948 - r11953950;
        return r11953951;
}
↓
double f(double a, double b) {
        double r11953952 = b;
        double r11953953 = a;
        double r11953954 = r11953952 + r11953953;
        double r11953955 = r11953953 - r11953952;
        double r11953956 = r11953954 * r11953955;
        return r11953956;
}


a \cdot a - b \cdot b
↓
\left(b + a\right) \cdot \left(a - b\right)

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 difference-of-squares0.0

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

  4. Final simplification0.0

    \[\leadsto \left(b + a\right) \cdot \left(a - b\right)\]

Reproduce

herbie shell --seed 2019102 
(FPCore (a b)
  :name "Difference of squares"

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

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