Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(b + c\right) + a \cdot d\]
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 r78530 = a;
        double r78531 = b;
        double r78532 = c;
        double r78533 = r78531 + r78532;
        double r78534 = d;
        double r78535 = r78533 + r78534;
        double r78536 = r78530 * r78535;
        return r78536;
}
↓
double f(double a, double b, double c, double d) {
        double r78537 = a;
        double r78538 = b;
        double r78539 = c;
        double r78540 = r78538 + r78539;
        double r78541 = r78537 * r78540;
        double r78542 = d;
        double r78543 = r78537 * r78542;
        double r78544 = r78541 + r78543;
        return r78544;
}

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 2020039 
(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)))