Average Error: 0.0 → 0.0
Time: 4.6s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 0.001000000000000000020816681711721685132943\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(a \cdot 2 + b\right) \cdot b + a \cdot a\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(a \cdot 2 + b\right) \cdot b + a \cdot a
double f(double a, double b) {
        double r73195 = a;
        double r73196 = b;
        double r73197 = r73195 + r73196;
        double r73198 = r73197 * r73197;
        return r73198;
}
↓
double f(double a, double b) {
        double r73199 = a;
        double r73200 = 2.0;
        double r73201 = r73199 * r73200;
        double r73202 = b;
        double r73203 = r73201 + r73202;
        double r73204 = r73203 * r73202;
        double r73205 = r73199 * r73199;
        double r73206 = r73204 + r73205;
        return r73206;
}

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. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5.0 a 10.0) (<= 0.0 b 0.001))

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

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