Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[b \cdot a + \left(c + d\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
b \cdot a + \left(c + d\right) \cdot a
double f(double a, double b, double c, double d) {
        double r3125221 = a;
        double r3125222 = b;
        double r3125223 = c;
        double r3125224 = r3125222 + r3125223;
        double r3125225 = d;
        double r3125226 = r3125224 + r3125225;
        double r3125227 = r3125221 * r3125226;
        return r3125227;
}
↓
double f(double a, double b, double c, double d) {
        double r3125228 = b;
        double r3125229 = a;
        double r3125230 = r3125228 * r3125229;
        double r3125231 = c;
        double r3125232 = d;
        double r3125233 = r3125231 + r3125232;
        double r3125234 = r3125233 * r3125229;
        double r3125235 = r3125230 + r3125234;
        return r3125235;
}

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-lft-in0.0

    \[\leadsto \color{blue}{a \cdot \left(b + c\right) + a \cdot d}\]
  4. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 
(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)))