Average Error: 0.4 → 0.3
Time: 2.3s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \left(a + \left(b + c\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + d\right) + \left(a + \left(b + c\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r100066 = e;
        double r100067 = d;
        double r100068 = r100066 + r100067;
        double r100069 = c;
        double r100070 = r100068 + r100069;
        double r100071 = b;
        double r100072 = r100070 + r100071;
        double r100073 = a;
        double r100074 = r100072 + r100073;
        return r100074;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r100075 = e;
        double r100076 = d;
        double r100077 = r100075 + r100076;
        double r100078 = a;
        double r100079 = b;
        double r100080 = c;
        double r100081 = r100079 + r100080;
        double r100082 = r100078 + r100081;
        double r100083 = r100077 + r100082;
        return r100083;
}

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

    \[\leadsto \color{blue}{\left(\left(e + d\right) + \left(c + b\right)\right)} + a\]
  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. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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))