Average Error: 0.0 → 0.0
Time: 18.9s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[c \cdot a + \left(d + b\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
c \cdot a + \left(d + b\right) \cdot a
double f(double a, double b, double c, double d) {
        double r4898987 = a;
        double r4898988 = b;
        double r4898989 = c;
        double r4898990 = r4898988 + r4898989;
        double r4898991 = d;
        double r4898992 = r4898990 + r4898991;
        double r4898993 = r4898987 * r4898992;
        return r4898993;
}
↓
double f(double a, double b, double c, double d) {
        double r4898994 = c;
        double r4898995 = a;
        double r4898996 = r4898994 * r4898995;
        double r4898997 = d;
        double r4898998 = b;
        double r4898999 = r4898997 + r4898998;
        double r4899000 = r4898999 * r4898995;
        double r4899001 = r4898996 + r4899000;
        return r4899001;
}

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 add-sqr-sqrt0.5

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

  4. Taylor expanded around inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789.0 a 98765.0) (<= 0.0 b 1.0) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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