Average Error: 0.0 → 0.0
Time: 9.7s
Precision: 64
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot \left(b + a\right) + \left(b + a\right) \cdot b\]
double f(double a, double b) {
        double r5655492 = a;
        double r5655493 = b;
        double r5655494 = r5655492 + r5655493;
        double r5655495 = r5655494 * r5655494;
        return r5655495;
}
↓
double f(double a, double b) {
        double r5655496 = a;
        double r5655497 = b;
        double r5655498 = r5655497 + r5655496;
        double r5655499 = r5655496 * r5655498;
        double r5655500 = r5655498 * r5655497;
        double r5655501 = r5655499 + r5655500;
        return r5655501;
}


\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot \left(b + a\right) + \left(b + a\right) \cdot b

Error

Bits error versus a

Bits error versus b

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-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019102 +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)))