Average Error: 0.4 → 0.2
Time: 6.0s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(\left(b + c\right) + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(\left(b + c\right) + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r67632 = e;
        double r67633 = d;
        double r67634 = r67632 + r67633;
        double r67635 = c;
        double r67636 = r67634 + r67635;
        double r67637 = b;
        double r67638 = r67636 + r67637;
        double r67639 = a;
        double r67640 = r67638 + r67639;
        return r67640;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r67641 = e;
        double r67642 = d;
        double r67643 = b;
        double r67644 = c;
        double r67645 = r67643 + r67644;
        double r67646 = a;
        double r67647 = r67645 + r67646;
        double r67648 = r67642 + r67647;
        double r67649 = r67641 + r67648;
        return r67649;
}

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. Using strategy rm

  9. Applied associate-+r+0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(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))