Average Error: 0.4 → 0.2
Time: 6.9s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(c + \left(b + a\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(c + \left(b + a\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r133141 = e;
        double r133142 = d;
        double r133143 = r133141 + r133142;
        double r133144 = c;
        double r133145 = r133143 + r133144;
        double r133146 = b;
        double r133147 = r133145 + r133146;
        double r133148 = a;
        double r133149 = r133147 + r133148;
        return r133149;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r133150 = e;
        double r133151 = d;
        double r133152 = c;
        double r133153 = b;
        double r133154 = a;
        double r133155 = r133153 + r133154;
        double r133156 = r133152 + r133155;
        double r133157 = r133151 + r133156;
        double r133158 = r133150 + r133157;
        return r133158;
}

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
Herbie0.2
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

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. Using strategy rm

  7. Applied associate-+l+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019347 +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))