Average Error: 3.6 → 2.7
Time: 8.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)
double f(double a, double b, double c, double d) {
        double r52085 = a;
        double r52086 = b;
        double r52087 = c;
        double r52088 = d;
        double r52089 = r52087 + r52088;
        double r52090 = r52086 + r52089;
        double r52091 = r52085 + r52090;
        double r52092 = 2.0;
        double r52093 = r52091 * r52092;
        return r52093;
}
↓
double f(double a, double b, double c, double d) {
        double r52094 = 2.0;
        double r52095 = a;
        double r52096 = b;
        double r52097 = c;
        double r52098 = r52096 + r52097;
        double r52099 = d;
        double r52100 = r52098 + r52099;
        double r52101 = r52095 + r52100;
        double r52102 = r52094 * r52101;
        return r52102;
}

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 *-un-lft-identity2.7

    \[\leadsto \color{blue}{\left(1 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2\]

  6. Final simplification2.7

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

Reproduce

herbie shell --seed 2019208 +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))