Average Error: 0.4 → 0.2
Time: 2.1s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(a + \left(b + c\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(a + \left(b + c\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r97741 = e;
        double r97742 = d;
        double r97743 = r97741 + r97742;
        double r97744 = c;
        double r97745 = r97743 + r97744;
        double r97746 = b;
        double r97747 = r97745 + r97746;
        double r97748 = a;
        double r97749 = r97747 + r97748;
        return r97749;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r97750 = e;
        double r97751 = d;
        double r97752 = a;
        double r97753 = b;
        double r97754 = c;
        double r97755 = r97753 + r97754;
        double r97756 = r97752 + r97755;
        double r97757 = r97751 + r97756;
        double r97758 = r97750 + r97757;
        return r97758;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
  2. Using strategy rm

  3. Applied associate-+l+0.3

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

  5. Applied associate-+l+0.3

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

  6. Simplified0.3

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

  8. Applied associate-+l+0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :precision binary64
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))