Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(a + b\right) \cdot \left(a + b\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(a + b\right) \cdot \left(a + b\right)
double f(double a, double b) {
        double r77951 = a;
        double r77952 = b;
        double r77953 = r77951 + r77952;
        double r77954 = r77953 * r77953;
        return r77954;
}
↓
double f(double a, double b) {
        double r77955 = a;
        double r77956 = b;
        double r77957 = r77955 + r77956;
        double r77958 = r77957 * r77957;
        return r77958;
}

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

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(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)))