Average Error: 3.7 → 0
Time: 3.3s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(b + \left(\left(d + a\right) + c\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(b + \left(\left(d + a\right) + c\right)\right)
double f(double a, double b, double c, double d) {
        double r136469 = a;
        double r136470 = b;
        double r136471 = c;
        double r136472 = d;
        double r136473 = r136471 + r136472;
        double r136474 = r136470 + r136473;
        double r136475 = r136469 + r136474;
        double r136476 = 2.0;
        double r136477 = r136475 * r136476;
        return r136477;
}
↓
double f(double a, double b, double c, double d) {
        double r136478 = 2.0;
        double r136479 = b;
        double r136480 = d;
        double r136481 = a;
        double r136482 = r136480 + r136481;
        double r136483 = c;
        double r136484 = r136482 + r136483;
        double r136485 = r136479 + r136484;
        double r136486 = r136478 * r136485;
        return r136486;
}

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 *-un-lft-identity3.7

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

  4. Applied *-un-lft-identity3.7

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

  5. Applied distribute-lft-out3.7

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

  6. Simplified2.8

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

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

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

  9. Applied distribute-lft-out2.8

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

  10. Simplified0

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2020042 +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))