Average Error: 0.4 → 0.3
Time: 3.4s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(e + d\right) + c\right) + \left(b + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(e + d\right) + c\right) + \left(b + a\right)
double f(double a, double b, double c, double d, double e) {
        double r100672 = e;
        double r100673 = d;
        double r100674 = r100672 + r100673;
        double r100675 = c;
        double r100676 = r100674 + r100675;
        double r100677 = b;
        double r100678 = r100676 + r100677;
        double r100679 = a;
        double r100680 = r100678 + r100679;
        return r100680;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r100681 = e;
        double r100682 = d;
        double r100683 = r100681 + r100682;
        double r100684 = c;
        double r100685 = r100683 + r100684;
        double r100686 = b;
        double r100687 = a;
        double r100688 = r100686 + r100687;
        double r100689 = r100685 + r100688;
        return r100689;
}

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
Herbie0.3
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

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

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020083 
(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))