Average Error: 3.7 → 0
Time: 5.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(c + b\right) + \left(d + a\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(c + b\right) + \left(d + a\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r78317 = a;
        double r78318 = b;
        double r78319 = c;
        double r78320 = d;
        double r78321 = r78319 + r78320;
        double r78322 = r78318 + r78321;
        double r78323 = r78317 + r78322;
        double r78324 = 2.0;
        double r78325 = r78323 * r78324;
        return r78325;
}
↓
double f(double a, double b, double c, double d) {
        double r78326 = c;
        double r78327 = b;
        double r78328 = r78326 + r78327;
        double r78329 = d;
        double r78330 = a;
        double r78331 = r78329 + r78330;
        double r78332 = r78328 + r78331;
        double r78333 = 2.0;
        double r78334 = r78332 * r78333;
        return r78334;
}

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. Simplified3.1

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

  4. Applied flip-+3.5

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

  5. Simplified2.8

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

  6. Simplified2.8

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

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

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

  9. Applied times-frac2.7

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

  10. Simplified0

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

  11. Simplified0

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

  12. Final simplification0

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

Reproduce

herbie shell --seed 2019195 
(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))