Average Error: 0.0 → 0.0
Time: 12.7s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot a + \left(\left(a + b\right) + a\right) \cdot b\]
\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot a + \left(\left(a + b\right) + a\right) \cdot b
double f(double a, double b) {
        double r3399111 = a;
        double r3399112 = b;
        double r3399113 = r3399111 + r3399112;
        double r3399114 = r3399113 * r3399113;
        return r3399114;
}
↓
double f(double a, double b) {
        double r3399115 = a;
        double r3399116 = r3399115 * r3399115;
        double r3399117 = b;
        double r3399118 = r3399115 + r3399117;
        double r3399119 = r3399118 + r3399115;
        double r3399120 = r3399119 * r3399117;
        double r3399121 = r3399116 + r3399120;
        return r3399121;
}

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. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019149 
(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)))