Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot a + b \cdot \left(a + \left(a + b\right)\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot a + b \cdot \left(a + \left(a + b\right)\right)
double f(double a, double b) {
        double r85170 = a;
        double r85171 = b;
        double r85172 = r85170 + r85171;
        double r85173 = r85172 * r85172;
        return r85173;
}
↓
double f(double a, double b) {
        double r85174 = a;
        double r85175 = r85174 * r85174;
        double r85176 = b;
        double r85177 = r85174 + r85176;
        double r85178 = r85174 + r85177;
        double r85179 = r85176 * r85178;
        double r85180 = r85175 + r85179;
        return r85180;
}

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. Applied associate-+l+0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020024 
(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)))