Average Error: 3.7 → 0
Time: 3.2s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(d + a\right) + \left(b + c\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(d + a\right) + \left(b + c\right)\right)
double f(double a, double b, double c, double d) {
        double r84627 = a;
        double r84628 = b;
        double r84629 = c;
        double r84630 = d;
        double r84631 = r84629 + r84630;
        double r84632 = r84628 + r84631;
        double r84633 = r84627 + r84632;
        double r84634 = 2.0;
        double r84635 = r84633 * r84634;
        return r84635;
}
↓
double f(double a, double b, double c, double d) {
        double r84636 = 2.0;
        double r84637 = d;
        double r84638 = a;
        double r84639 = r84637 + r84638;
        double r84640 = b;
        double r84641 = c;
        double r84642 = r84640 + r84641;
        double r84643 = r84639 + r84642;
        double r84644 = r84636 * r84643;
        return r84644;
}

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 distribute-lft-in2.8

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

  9. Applied associate-+r+0

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

  10. Simplified0

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2020047 
(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))