Average Error: 0.4 → 0.3
Time: 11.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(c + b\right) + a\right) + \left(d + e\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(c + b\right) + a\right) + \left(d + e\right)
double f(double a, double b, double c, double d, double e) {
        double r4836679 = e;
        double r4836680 = d;
        double r4836681 = r4836679 + r4836680;
        double r4836682 = c;
        double r4836683 = r4836681 + r4836682;
        double r4836684 = b;
        double r4836685 = r4836683 + r4836684;
        double r4836686 = a;
        double r4836687 = r4836685 + r4836686;
        return r4836687;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r4836688 = c;
        double r4836689 = b;
        double r4836690 = r4836688 + r4836689;
        double r4836691 = a;
        double r4836692 = r4836690 + r4836691;
        double r4836693 = d;
        double r4836694 = e;
        double r4836695 = r4836693 + r4836694;
        double r4836696 = r4836692 + r4836695;
        return r4836696;
}

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

    \[\leadsto \color{blue}{\left(\left(e + d\right) + \left(c + b\right)\right)} + a\]
  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1.0 a 2.0 b 4.0 c 8.0 d 16.0 e 32.0)

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

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