Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[{a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
{a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)
double f(double a, double b) {
        double r97635 = a;
        double r97636 = b;
        double r97637 = r97635 + r97636;
        double r97638 = r97637 * r97637;
        return r97638;
}
↓
double f(double a, double b) {
        double r97639 = a;
        double r97640 = 2.0;
        double r97641 = pow(r97639, r97640);
        double r97642 = b;
        double r97643 = r97639 * r97642;
        double r97644 = r97640 * r97643;
        double r97645 = pow(r97642, r97640);
        double r97646 = r97644 + r97645;
        double r97647 = r97641 + r97646;
        return r97647;
}

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 add-cbrt-cube0.5

    \[\leadsto \left(a + b\right) \cdot \color{blue}{\sqrt[3]{\left(\left(a + b\right) \cdot \left(a + b\right)\right) \cdot \left(a + b\right)}}\]

  4. Applied add-cbrt-cube0.7

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + b\right) \cdot \left(a + b\right)\right) \cdot \left(a + b\right)}} \cdot \sqrt[3]{\left(\left(a + b\right) \cdot \left(a + b\right)\right) \cdot \left(a + b\right)}\]

  5. Applied cbrt-unprod0.5

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\left(a + b\right) \cdot \left(a + b\right)\right) \cdot \left(a + b\right)\right) \cdot \left(\left(\left(a + b\right) \cdot \left(a + b\right)\right) \cdot \left(a + b\right)\right)}}\]

  6. Simplified0.5

    \[\leadsto \sqrt[3]{\color{blue}{{\left(a + b\right)}^{6}}}\]

  7. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)}\]

  8. Final simplification0.0

    \[\leadsto {a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)\]

Reproduce

herbie shell --seed 2020064 
(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)))