Average Error: 0.0 → 0.0
Time: 13.8s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(b + c\right) + a \cdot d\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot \left(b + c\right) + a \cdot d
double f(double a, double b, double c, double d) {
        double r6711527 = a;
        double r6711528 = b;
        double r6711529 = c;
        double r6711530 = r6711528 + r6711529;
        double r6711531 = d;
        double r6711532 = r6711530 + r6711531;
        double r6711533 = r6711527 * r6711532;
        return r6711533;
}
↓
double f(double a, double b, double c, double d) {
        double r6711534 = a;
        double r6711535 = b;
        double r6711536 = c;
        double r6711537 = r6711535 + r6711536;
        double r6711538 = r6711534 * r6711537;
        double r6711539 = d;
        double r6711540 = r6711534 * r6711539;
        double r6711541 = r6711538 + r6711540;
        return r6711541;
}

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 distribute-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789.0 a 98765.0) (<= 0.0 b 1.0) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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