Average Error: 0.4 → 0.2
Time: 12.6s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(\left(c + b\right) + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(\left(c + b\right) + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r7630938 = e;
        double r7630939 = d;
        double r7630940 = r7630938 + r7630939;
        double r7630941 = c;
        double r7630942 = r7630940 + r7630941;
        double r7630943 = b;
        double r7630944 = r7630942 + r7630943;
        double r7630945 = a;
        double r7630946 = r7630944 + r7630945;
        return r7630946;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r7630947 = e;
        double r7630948 = d;
        double r7630949 = c;
        double r7630950 = b;
        double r7630951 = r7630949 + r7630950;
        double r7630952 = a;
        double r7630953 = r7630951 + r7630952;
        double r7630954 = r7630948 + r7630953;
        double r7630955 = r7630947 + r7630954;
        return r7630955;
}

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

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

  7. Applied associate-+l+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(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))