Average Error: 0.0 → 0.0
Time: 1.8s
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 r73619 = a;
        double r73620 = b;
        double r73621 = r73619 + r73620;
        double r73622 = r73621 * r73621;
        return r73622;
}
↓
double f(double a, double b) {
        double r73623 = a;
        double r73624 = 2.0;
        double r73625 = pow(r73623, r73624);
        double r73626 = b;
        double r73627 = r73623 * r73626;
        double r73628 = r73625 + r73627;
        double r73629 = r73623 + r73626;
        double r73630 = r73626 * r73629;
        double r73631 = r73628 + r73630;
        return r73631;
}

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)))