Average Error: 0.4 → 0.2
Time: 8.1s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(c + \left(b + a\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(c + \left(b + a\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r52897 = e;
        double r52898 = d;
        double r52899 = r52897 + r52898;
        double r52900 = c;
        double r52901 = r52899 + r52900;
        double r52902 = b;
        double r52903 = r52901 + r52902;
        double r52904 = a;
        double r52905 = r52903 + r52904;
        return r52905;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r52906 = e;
        double r52907 = d;
        double r52908 = c;
        double r52909 = b;
        double r52910 = a;
        double r52911 = r52909 + r52910;
        double r52912 = r52908 + r52911;
        double r52913 = r52907 + r52912;
        double r52914 = r52906 + r52913;
        return r52914;
}

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

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

  7. Applied associate-+l+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 +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))