Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left({a}^{2} + a \cdot b\right) + b \cdot \left(a + b\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left({a}^{2} + a \cdot b\right) + b \cdot \left(a + b\right)
double f(double a, double b) {
        double r80026 = a;
        double r80027 = b;
        double r80028 = r80026 + r80027;
        double r80029 = r80028 * r80028;
        return r80029;
}
↓
double f(double a, double b) {
        double r80030 = a;
        double r80031 = 2.0;
        double r80032 = pow(r80030, r80031);
        double r80033 = b;
        double r80034 = r80030 * r80033;
        double r80035 = r80032 + r80034;
        double r80036 = r80030 + r80033;
        double r80037 = r80033 * r80036;
        double r80038 = r80035 + r80037;
        return r80038;
}

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 distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied distribute-lft-in0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(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)))