Average Error: 0.0 → 0.0
Time: 820.0ms
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(\left|b\right| + \left|a\right|\right) \cdot \left(\left|a\right| + \left(-\left|b\right|\right)\right)\]
a \cdot a - b \cdot b
↓
\left(\left|b\right| + \left|a\right|\right) \cdot \left(\left|a\right| + \left(-\left|b\right|\right)\right)
double code(double a, double b) {
	return ((a * a) - (b * b));
}
↓
double code(double a, double b) {
	return ((fabs(b) + fabs(a)) * (fabs(a) + -fabs(b)));
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto a \cdot a - \color{blue}{\sqrt{b \cdot b} \cdot \sqrt{b \cdot b}}\]

  4. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{a \cdot a} \cdot \sqrt{a \cdot a}} - \sqrt{b \cdot b} \cdot \sqrt{b \cdot b}\]

  5. Applied difference-of-squares0.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020066 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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