Average Error: 0.4 → 0.3
Time: 2.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[d + \left(\left(e + c\right) + \left(b + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
d + \left(\left(e + c\right) + \left(b + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r88172 = e;
        double r88173 = d;
        double r88174 = r88172 + r88173;
        double r88175 = c;
        double r88176 = r88174 + r88175;
        double r88177 = b;
        double r88178 = r88176 + r88177;
        double r88179 = a;
        double r88180 = r88178 + r88179;
        return r88180;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r88181 = d;
        double r88182 = e;
        double r88183 = c;
        double r88184 = r88182 + r88183;
        double r88185 = b;
        double r88186 = a;
        double r88187 = r88185 + r88186;
        double r88188 = r88184 + r88187;
        double r88189 = r88181 + r88188;
        return r88189;
}

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. Taylor expanded around 0 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

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

Reproduce

herbie shell --seed 2020025 +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))