Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(2 \cdot a + b\right) \cdot b + a \cdot a\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(2 \cdot a + b\right) \cdot b + a \cdot a
double f(double a, double b) {
        double r3749779 = a;
        double r3749780 = b;
        double r3749781 = r3749779 + r3749780;
        double r3749782 = r3749781 * r3749781;
        return r3749782;
}
↓
double f(double a, double b) {
        double r3749783 = 2.0;
        double r3749784 = a;
        double r3749785 = r3749783 * r3749784;
        double r3749786 = b;
        double r3749787 = r3749785 + r3749786;
        double r3749788 = r3749787 * r3749786;
        double r3749789 = r3749784 * r3749784;
        double r3749790 = r3749788 + r3749789;
        return r3749790;
}

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. Taylor expanded around -inf 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{b \cdot b + a \cdot \left(b \cdot 2 + a\right)}\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Applied associate-+r+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5 a 10) (<= 0 b 0.001))

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

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