Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\frac{a \cdot a - b \cdot b}{\frac{\left(a - b\right) \cdot \left(a - b\right)}{a \cdot a - b \cdot b}}\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\frac{a \cdot a - b \cdot b}{\frac{\left(a - b\right) \cdot \left(a - b\right)}{a \cdot a - b \cdot b}}
double code(double a, double b) {
	return ((a + b) * (a + b));
}
↓
double code(double a, double b) {
	return (((a * a) - (b * b)) / (((a - b) * (a - b)) / ((a * a) - (b * 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
\[\left(\left(b \cdot a + b \cdot b\right) + b \cdot a\right) + a \cdot a\]

Derivation

  1. Initial program 0.0

    \[\left(a + b\right) \cdot \left(a + b\right)\]
  2. Using strategy rm

  3. Applied flip-+0.0

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

  4. Applied flip-+0.1

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

  5. Applied frac-times0.1

    \[\leadsto \color{blue}{\frac{\left(a \cdot a - b \cdot b\right) \cdot \left(a \cdot a - b \cdot b\right)}{\left(a - b\right) \cdot \left(a - b\right)}}\]
  6. Using strategy rm

  7. Applied associate-/l*0.0

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

  8. Final simplification0.0

    \[\leadsto \frac{a \cdot a - b \cdot b}{\frac{\left(a - b\right) \cdot \left(a - b\right)}{a \cdot a - b \cdot b}}\]

Reproduce

herbie shell --seed 2020106 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5 a 10) (<= 0.0 b 0.001))

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

  (* (+ a b) (+ a b)))