Average Error: 3.6 → 0
Time: 6.1s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(b + c\right) + \left(d + a\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(b + c\right) + \left(d + a\right)\right)
double f(double a, double b, double c, double d) {
        double r1518978 = a;
        double r1518979 = b;
        double r1518980 = c;
        double r1518981 = d;
        double r1518982 = r1518980 + r1518981;
        double r1518983 = r1518979 + r1518982;
        double r1518984 = r1518978 + r1518983;
        double r1518985 = 2.0;
        double r1518986 = r1518984 * r1518985;
        return r1518986;
}
↓
double f(double a, double b, double c, double d) {
        double r1518987 = 2.0;
        double r1518988 = b;
        double r1518989 = c;
        double r1518990 = r1518988 + r1518989;
        double r1518991 = d;
        double r1518992 = a;
        double r1518993 = r1518991 + r1518992;
        double r1518994 = r1518990 + r1518993;
        double r1518995 = r1518987 * r1518994;
        return r1518995;
}

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
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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+2.8

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

  5. Applied add-log-exp2.8

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

  6. Applied add-log-exp2.8

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

  7. Applied sum-log3.0

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

  8. Simplified0.9

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

  10. Applied rem-log-exp0

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :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))