Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 0.001000000000000000020816681711721685132943\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot \left(b + a\right) + \left(b + a\right) \cdot b\]
\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot \left(b + a\right) + \left(b + a\right) \cdot b
double f(double a, double b) {
        double r5582395 = a;
        double r5582396 = b;
        double r5582397 = r5582395 + r5582396;
        double r5582398 = r5582397 * r5582397;
        return r5582398;
}
↓
double f(double a, double b) {
        double r5582399 = a;
        double r5582400 = b;
        double r5582401 = r5582400 + r5582399;
        double r5582402 = r5582399 * r5582401;
        double r5582403 = r5582401 * r5582400;
        double r5582404 = r5582402 + r5582403;
        return r5582404;
}

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-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 
(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)))