Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[b \cdot a + \left(d + c\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
b \cdot a + \left(d + c\right) \cdot a
double f(double a, double b, double c, double d) {
        double r3169462 = a;
        double r3169463 = b;
        double r3169464 = c;
        double r3169465 = r3169463 + r3169464;
        double r3169466 = d;
        double r3169467 = r3169465 + r3169466;
        double r3169468 = r3169462 * r3169467;
        return r3169468;
}
↓
double f(double a, double b, double c, double d) {
        double r3169469 = b;
        double r3169470 = a;
        double r3169471 = r3169469 * r3169470;
        double r3169472 = d;
        double r3169473 = c;
        double r3169474 = r3169472 + r3169473;
        double r3169475 = r3169474 * r3169470;
        double r3169476 = r3169471 + r3169475;
        return r3169476;
}

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

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +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)))