Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(b + \left(d + c\right)\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(b + \left(d + c\right)\right) \cdot a
double f(double a, double b, double c, double d) {
        double r2479022 = a;
        double r2479023 = b;
        double r2479024 = c;
        double r2479025 = r2479023 + r2479024;
        double r2479026 = d;
        double r2479027 = r2479025 + r2479026;
        double r2479028 = r2479022 * r2479027;
        return r2479028;
}
↓
double f(double a, double b, double c, double d) {
        double r2479029 = b;
        double r2479030 = d;
        double r2479031 = c;
        double r2479032 = r2479030 + r2479031;
        double r2479033 = r2479029 + r2479032;
        double r2479034 = a;
        double r2479035 = r2479033 * r2479034;
        return r2479035;
}

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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019141 +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)))