Average Error: 0.0 → 0.0
Time: 6.1s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(a - b\right) \cdot \left(a + b\right)\]
a \cdot a - b \cdot b
↓
\left(a - b\right) \cdot \left(a + b\right)
double f(double a, double b) {
        double r104948 = a;
        double r104949 = r104948 * r104948;
        double r104950 = b;
        double r104951 = r104950 * r104950;
        double r104952 = r104949 - r104951;
        return r104952;
}
↓
double f(double a, double b) {
        double r104953 = a;
        double r104954 = b;
        double r104955 = r104953 - r104954;
        double r104956 = r104953 + r104954;
        double r104957 = r104955 * r104956;
        return r104957;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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