Average Error: 3.6 → 2.7
Time: 2.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r88961 = a;
        double r88962 = b;
        double r88963 = c;
        double r88964 = d;
        double r88965 = r88963 + r88964;
        double r88966 = r88962 + r88965;
        double r88967 = r88961 + r88966;
        double r88968 = 2.0;
        double r88969 = r88967 * r88968;
        return r88969;
}
↓
double f(double a, double b, double c, double d) {
        double r88970 = a;
        double r88971 = b;
        double r88972 = c;
        double r88973 = r88971 + r88972;
        double r88974 = d;
        double r88975 = r88973 + r88974;
        double r88976 = r88970 + r88975;
        double r88977 = 2.0;
        double r88978 = r88976 * r88977;
        return r88978;
}

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

Original3.6
Target3.8
Herbie2.7
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.6

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
  2. Using strategy rm

  3. Applied associate-+r+2.7

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
  4. Using strategy rm

  5. Applied log1p-expm1-u2.7

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2\]
  6. Using strategy rm

  7. Applied log1p-expm12.7

    \[\leadsto \color{blue}{\left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]

  8. Final simplification2.7

    \[\leadsto \left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))