Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot d + \left(c + b\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot d + \left(c + b\right) \cdot a
double f(double a, double b, double c, double d) {
        double r1243970 = a;
        double r1243971 = b;
        double r1243972 = c;
        double r1243973 = r1243971 + r1243972;
        double r1243974 = d;
        double r1243975 = r1243973 + r1243974;
        double r1243976 = r1243970 * r1243975;
        return r1243976;
}
↓
double f(double a, double b, double c, double d) {
        double r1243977 = a;
        double r1243978 = d;
        double r1243979 = r1243977 * r1243978;
        double r1243980 = c;
        double r1243981 = b;
        double r1243982 = r1243980 + r1243981;
        double r1243983 = r1243982 * r1243977;
        double r1243984 = r1243979 + r1243983;
        return r1243984;
}

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-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

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

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