Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(a + b\right) \cdot a + \left(a + b\right) \cdot b\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(a + b\right) \cdot a + \left(a + b\right) \cdot b
double f(double a, double b) {
        double r40352 = a;
        double r40353 = b;
        double r40354 = r40352 + r40353;
        double r40355 = r40354 * r40354;
        return r40355;
}
↓
double f(double a, double b) {
        double r40356 = a;
        double r40357 = b;
        double r40358 = r40356 + r40357;
        double r40359 = r40358 * r40356;
        double r40360 = r40358 * r40357;
        double r40361 = r40359 + r40360;
        return r40361;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(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)))