Average Error: 0.0 → 0.0
Time: 6.7s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(b \cdot a + a \cdot c\right) + a \cdot d\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(b \cdot a + a \cdot c\right) + a \cdot d
double f(double a, double b, double c, double d) {
        double r58446 = a;
        double r58447 = b;
        double r58448 = c;
        double r58449 = r58447 + r58448;
        double r58450 = d;
        double r58451 = r58449 + r58450;
        double r58452 = r58446 * r58451;
        return r58452;
}
↓
double f(double a, double b, double c, double d) {
        double r58453 = b;
        double r58454 = a;
        double r58455 = r58453 * r58454;
        double r58456 = c;
        double r58457 = r58454 * r58456;
        double r58458 = r58455 + r58457;
        double r58459 = d;
        double r58460 = r58454 * r58459;
        double r58461 = r58458 + r58460;
        return r58461;
}

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-lft-in0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789 a 98765) (<= 0.0 b 1) (<= 0.0 c 0.0016773000000000001) (<= 0.0 d 0.0016773000000000001))

  :herbie-target
  (+ (* a b) (* a (+ c d)))

  (* a (+ (+ b c) d)))