Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot b + \left(c + d\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot b + \left(c + d\right) \cdot a
double f(double a, double b, double c, double d) {
        double r3646349 = a;
        double r3646350 = b;
        double r3646351 = c;
        double r3646352 = r3646350 + r3646351;
        double r3646353 = d;
        double r3646354 = r3646352 + r3646353;
        double r3646355 = r3646349 * r3646354;
        return r3646355;
}
↓
double f(double a, double b, double c, double d) {
        double r3646356 = a;
        double r3646357 = b;
        double r3646358 = r3646356 * r3646357;
        double r3646359 = c;
        double r3646360 = d;
        double r3646361 = r3646359 + r3646360;
        double r3646362 = r3646361 * r3646356;
        double r3646363 = r3646358 + r3646362;
        return r3646363;
}

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. Using strategy rm

  5. Applied *-commutative0.0

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

  7. Applied distribute-lft-in0.0

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

  8. Applied associate-+l+0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(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)))