Average Error: 0.4 → 0.3
Time: 19.1s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(b + a\right) + \left(\left(c + d\right) + e\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(b + a\right) + \left(\left(c + d\right) + e\right)
double f(double a, double b, double c, double d, double e) {
        double r5365845 = e;
        double r5365846 = d;
        double r5365847 = r5365845 + r5365846;
        double r5365848 = c;
        double r5365849 = r5365847 + r5365848;
        double r5365850 = b;
        double r5365851 = r5365849 + r5365850;
        double r5365852 = a;
        double r5365853 = r5365851 + r5365852;
        return r5365853;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r5365854 = b;
        double r5365855 = a;
        double r5365856 = r5365854 + r5365855;
        double r5365857 = c;
        double r5365858 = d;
        double r5365859 = r5365857 + r5365858;
        double r5365860 = e;
        double r5365861 = r5365859 + r5365860;
        double r5365862 = r5365856 + r5365861;
        return r5365862;
}

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. Using strategy rm

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019200 +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))