Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(\left(b + c\right) + d\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot \left(\left(b + c\right) + d\right)
double f(double a, double b, double c, double d) {
        double r91931 = a;
        double r91932 = b;
        double r91933 = c;
        double r91934 = r91932 + r91933;
        double r91935 = d;
        double r91936 = r91934 + r91935;
        double r91937 = r91931 * r91936;
        return r91937;
}
↓
double f(double a, double b, double c, double d) {
        double r91938 = a;
        double r91939 = b;
        double r91940 = c;
        double r91941 = r91939 + r91940;
        double r91942 = d;
        double r91943 = r91941 + r91942;
        double r91944 = r91938 * r91943;
        return r91944;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(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)))