Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(b + \left(c + d\right)\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot \left(b + \left(c + d\right)\right)
double f(double a, double b, double c, double d) {
        double r93073 = a;
        double r93074 = b;
        double r93075 = c;
        double r93076 = r93074 + r93075;
        double r93077 = d;
        double r93078 = r93076 + r93077;
        double r93079 = r93073 * r93078;
        return r93079;
}
↓
double f(double a, double b, double c, double d) {
        double r93080 = a;
        double r93081 = b;
        double r93082 = c;
        double r93083 = d;
        double r93084 = r93082 + r93083;
        double r93085 = r93081 + r93084;
        double r93086 = r93080 * r93085;
        return r93086;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[a \cdot b + a \cdot \left(c + d\right)\]

Derivation

  1. Initial program 0.0

    \[a \cdot \left(\left(b + c\right) + d\right)\]
  2. Using strategy rm

  3. Applied associate-+l+0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789 a 98765) (<= 0.0 b 1) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

  (* a (+ (+ b c) d)))