Average Error: 0.4 → 0.2
Time: 6.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(d + \left(b + c\right)\right) + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(d + \left(b + c\right)\right) + a\right)
double f(double a, double b, double c, double d, double e) {
        double r70871 = e;
        double r70872 = d;
        double r70873 = r70871 + r70872;
        double r70874 = c;
        double r70875 = r70873 + r70874;
        double r70876 = b;
        double r70877 = r70875 + r70876;
        double r70878 = a;
        double r70879 = r70877 + r70878;
        return r70879;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r70880 = e;
        double r70881 = d;
        double r70882 = b;
        double r70883 = c;
        double r70884 = r70882 + r70883;
        double r70885 = r70881 + r70884;
        double r70886 = a;
        double r70887 = r70885 + r70886;
        double r70888 = r70880 + r70887;
        return r70888;
}

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

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

  5. Applied associate-+l+0.3

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

  6. Simplified0.3

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

  8. Applied associate-+l+0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019297 
(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))