Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 0.001000000000000000020816681711721685132943\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(b + a\right) \cdot \left(b + a\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(b + a\right) \cdot \left(b + a\right)
double f(double a, double b) {
        double r3509683 = a;
        double r3509684 = b;
        double r3509685 = r3509683 + r3509684;
        double r3509686 = r3509685 * r3509685;
        return r3509686;
}
↓
double f(double a, double b) {
        double r3509687 = b;
        double r3509688 = a;
        double r3509689 = r3509687 + r3509688;
        double r3509690 = r3509689 * r3509689;
        return r3509690;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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)))