Average Error: 0.0 → 0.0
Time: 7.5s
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 r59880 = a;
        double r59881 = b;
        double r59882 = c;
        double r59883 = r59881 + r59882;
        double r59884 = d;
        double r59885 = r59883 + r59884;
        double r59886 = r59880 * r59885;
        return r59886;
}
↓
double f(double a, double b, double c, double d) {
        double r59887 = c;
        double r59888 = a;
        double r59889 = r59887 * r59888;
        double r59890 = d;
        double r59891 = b;
        double r59892 = r59890 + r59891;
        double r59893 = r59892 * r59888;
        double r59894 = r59889 + r59893;
        return r59894;
}

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. Simplified0.0

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

  4. Applied add-sqr-sqrt0.5

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

  5. Simplified0.5

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

  6. Simplified0.5

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

  7. Taylor expanded around inf 0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))