Average Error: 0.4 → 0.3
Time: 19.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(c + e\right) + \left(a + b\right)\right) + d\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(c + e\right) + \left(a + b\right)\right) + d
double f(double a, double b, double c, double d, double e) {
        double r7018711 = e;
        double r7018712 = d;
        double r7018713 = r7018711 + r7018712;
        double r7018714 = c;
        double r7018715 = r7018713 + r7018714;
        double r7018716 = b;
        double r7018717 = r7018715 + r7018716;
        double r7018718 = a;
        double r7018719 = r7018717 + r7018718;
        return r7018719;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r7018720 = c;
        double r7018721 = e;
        double r7018722 = r7018720 + r7018721;
        double r7018723 = a;
        double r7018724 = b;
        double r7018725 = r7018723 + r7018724;
        double r7018726 = r7018722 + r7018725;
        double r7018727 = d;
        double r7018728 = r7018726 + r7018727;
        return r7018728;
}

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. Taylor expanded around 0 0.4

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

  4. Applied associate-+l+0.3

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

  6. Applied associate-+l+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019200 
(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))