Average Error: 0.0 → 0.0
Time: 30.3s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[b \cdot \left(b + a \cdot 2\right) + a \cdot a\]
\left(a + b\right) \cdot \left(a + b\right)
↓
b \cdot \left(b + a \cdot 2\right) + a \cdot a
double f(double a, double b) {
        double r20745112 = a;
        double r20745113 = b;
        double r20745114 = r20745112 + r20745113;
        double r20745115 = r20745114 * r20745114;
        return r20745115;
}
↓
double f(double a, double b) {
        double r20745116 = b;
        double r20745117 = a;
        double r20745118 = 2.0;
        double r20745119 = r20745117 * r20745118;
        double r20745120 = r20745116 + r20745119;
        double r20745121 = r20745116 * r20745120;
        double r20745122 = r20745117 * r20745117;
        double r20745123 = r20745121 + r20745122;
        return r20745123;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 
(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)))