Average Error: 0.4 → 0.2
Time: 3.8s
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 r96693 = e;
        double r96694 = d;
        double r96695 = r96693 + r96694;
        double r96696 = c;
        double r96697 = r96695 + r96696;
        double r96698 = b;
        double r96699 = r96697 + r96698;
        double r96700 = a;
        double r96701 = r96699 + r96700;
        return r96701;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r96702 = e;
        double r96703 = d;
        double r96704 = c;
        double r96705 = r96703 + r96704;
        double r96706 = b;
        double r96707 = a;
        double r96708 = r96706 + r96707;
        double r96709 = r96705 + r96708;
        double r96710 = r96702 + r96709;
        return r96710;
}

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 2019322 
(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))