Average Error: 0.4 → 0.3
Time: 5.3s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \left(c + \left(b + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + d\right) + \left(c + \left(b + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r94157 = e;
        double r94158 = d;
        double r94159 = r94157 + r94158;
        double r94160 = c;
        double r94161 = r94159 + r94160;
        double r94162 = b;
        double r94163 = r94161 + r94162;
        double r94164 = a;
        double r94165 = r94163 + r94164;
        return r94165;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r94166 = e;
        double r94167 = d;
        double r94168 = r94166 + r94167;
        double r94169 = c;
        double r94170 = b;
        double r94171 = a;
        double r94172 = r94170 + r94171;
        double r94173 = r94169 + r94172;
        double r94174 = r94168 + r94173;
        return r94174;
}

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

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

Reproduce

herbie shell --seed 2019351 +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))