Average Error: 0.0 → 0.0
Time: 16.1s
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 r3844215 = a;
        double r3844216 = b;
        double r3844217 = c;
        double r3844218 = r3844216 + r3844217;
        double r3844219 = d;
        double r3844220 = r3844218 + r3844219;
        double r3844221 = r3844215 * r3844220;
        return r3844221;
}
↓
double f(double a, double b, double c, double d) {
        double r3844222 = a;
        double r3844223 = d;
        double r3844224 = r3844222 * r3844223;
        double r3844225 = c;
        double r3844226 = b;
        double r3844227 = r3844225 + r3844226;
        double r3844228 = r3844227 * r3844222;
        double r3844229 = r3844224 + r3844228;
        return r3844229;
}

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 2019162 +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)))