Average Error: 0.4 → 0.3
Time: 9.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(\left(d + c\right) + b\right) + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(\left(d + c\right) + b\right) + a\right)
double f(double a, double b, double c, double d, double e) {
        double r115852 = e;
        double r115853 = d;
        double r115854 = r115852 + r115853;
        double r115855 = c;
        double r115856 = r115854 + r115855;
        double r115857 = b;
        double r115858 = r115856 + r115857;
        double r115859 = a;
        double r115860 = r115858 + r115859;
        return r115860;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r115861 = e;
        double r115862 = d;
        double r115863 = c;
        double r115864 = r115862 + r115863;
        double r115865 = b;
        double r115866 = r115864 + r115865;
        double r115867 = a;
        double r115868 = r115866 + r115867;
        double r115869 = r115861 + r115868;
        return r115869;
}

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+0.4

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

  5. Applied associate-+l+0.3

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

  7. Applied associate-+l+0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(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))