Average Error: 0.4 → 0.3
Time: 15.3s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(c + \left(a + b\right)\right) + \left(d + e\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(c + \left(a + b\right)\right) + \left(d + e\right)
double f(double a, double b, double c, double d, double e) {
        double r5356950 = e;
        double r5356951 = d;
        double r5356952 = r5356950 + r5356951;
        double r5356953 = c;
        double r5356954 = r5356952 + r5356953;
        double r5356955 = b;
        double r5356956 = r5356954 + r5356955;
        double r5356957 = a;
        double r5356958 = r5356956 + r5356957;
        return r5356958;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r5356959 = c;
        double r5356960 = a;
        double r5356961 = b;
        double r5356962 = r5356960 + r5356961;
        double r5356963 = r5356959 + r5356962;
        double r5356964 = d;
        double r5356965 = e;
        double r5356966 = r5356964 + r5356965;
        double r5356967 = r5356963 + r5356966;
        return r5356967;
}

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. 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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019135 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))