Average Error: 0.4 → 0.2
Time: 8.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(d + c\right) + \left(b + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(d + c\right) + \left(b + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r93861 = e;
        double r93862 = d;
        double r93863 = r93861 + r93862;
        double r93864 = c;
        double r93865 = r93863 + r93864;
        double r93866 = b;
        double r93867 = r93865 + r93866;
        double r93868 = a;
        double r93869 = r93867 + r93868;
        return r93869;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r93870 = e;
        double r93871 = d;
        double r93872 = c;
        double r93873 = r93871 + r93872;
        double r93874 = b;
        double r93875 = a;
        double r93876 = r93874 + r93875;
        double r93877 = r93873 + r93876;
        double r93878 = r93870 + r93877;
        return r93878;
}

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

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

  5. Applied associate-+l+0.3

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

  7. Applied associate-+l+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019305 +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))