Average Error: 0.0 → 0.0
Time: 15.2s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(\left(b + c\right) + d\right) \cdot a
double f(double a, double b, double c, double d) {
        double r2535044 = a;
        double r2535045 = b;
        double r2535046 = c;
        double r2535047 = r2535045 + r2535046;
        double r2535048 = d;
        double r2535049 = r2535047 + r2535048;
        double r2535050 = r2535044 * r2535049;
        return r2535050;
}
↓
double f(double a, double b, double c, double d) {
        double r2535051 = b;
        double r2535052 = c;
        double r2535053 = r2535051 + r2535052;
        double r2535054 = d;
        double r2535055 = r2535053 + r2535054;
        double r2535056 = a;
        double r2535057 = r2535055 * r2535056;
        return r2535057;
}

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

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

Reproduce

herbie shell --seed 2019130 +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)))