Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot \left(b + a\right) + \left(b + a\right) \cdot b\]
\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 r3150305 = a;
        double r3150306 = b;
        double r3150307 = r3150305 + r3150306;
        double r3150308 = r3150307 * r3150307;
        return r3150308;
}
↓
double f(double a, double b) {
        double r3150309 = a;
        double r3150310 = b;
        double r3150311 = r3150310 + r3150309;
        double r3150312 = r3150309 * r3150311;
        double r3150313 = r3150311 * r3150310;
        double r3150314 = r3150312 + r3150313;
        return r3150314;
}

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 2019163 +o rules:numerics
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5 a 10) (<= 0 b 0.001))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

  (* (+ a b) (+ a b)))