Average Error: 0.0 → 0.0
Time: 5.8s
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 r65498 = a;
        double r65499 = r65498 * r65498;
        double r65500 = b;
        double r65501 = r65500 * r65500;
        double r65502 = r65499 - r65501;
        return r65502;
}
↓
double f(double a, double b) {
        double r65503 = a;
        double r65504 = b;
        double r65505 = r65503 - r65504;
        double r65506 = r65503 + r65504;
        double r65507 = r65505 * r65506;
        return r65507;
}

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 2019235 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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