Average Error: 3.7 → 0
Time: 8.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(b + c\right) + \left(d + a\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(b + c\right) + \left(d + a\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r11478 = a;
        double r11479 = b;
        double r11480 = c;
        double r11481 = d;
        double r11482 = r11480 + r11481;
        double r11483 = r11479 + r11482;
        double r11484 = r11478 + r11483;
        double r11485 = 2.0;
        double r11486 = r11484 * r11485;
        return r11486;
}
↓
double f(double a, double b, double c, double d) {
        double r11487 = b;
        double r11488 = c;
        double r11489 = r11487 + r11488;
        double r11490 = d;
        double r11491 = a;
        double r11492 = r11490 + r11491;
        double r11493 = r11489 + r11492;
        double r11494 = 2.0;
        double r11495 = r11493 * r11494;
        return r11495;
}

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
Target3.9
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 +-commutative2.8

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

  7. Applied associate-+l+0

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

  8. Final simplification0

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

Reproduce

herbie shell --seed 2019310 +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))