Average Error: 3.7 → 0
Time: 5.1s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(a + d\right) + \left(c + b\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(a + d\right) + \left(c + b\right)\right)
double f(double a, double b, double c, double d) {
        double r65148 = a;
        double r65149 = b;
        double r65150 = c;
        double r65151 = d;
        double r65152 = r65150 + r65151;
        double r65153 = r65149 + r65152;
        double r65154 = r65148 + r65153;
        double r65155 = 2.0;
        double r65156 = r65154 * r65155;
        return r65156;
}
↓
double f(double a, double b, double c, double d) {
        double r65157 = 2.0;
        double r65158 = a;
        double r65159 = d;
        double r65160 = r65158 + r65159;
        double r65161 = c;
        double r65162 = b;
        double r65163 = r65161 + r65162;
        double r65164 = r65160 + r65163;
        double r65165 = r65157 * r65164;
        return r65165;
}

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

Original3.7
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
  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 *-un-lft-identity2.8

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

  6. Applied *-un-lft-identity2.8

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

  7. Applied distribute-lft-out2.8

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

  8. Simplified0

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

  9. Final simplification0

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14.0 a -13.0) (<= -3.0 b -2.0) (<= 3.0 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))