Average Error: 0.4 → 0.2
Time: 5.9s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(\left(b + c\right) + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(\left(b + c\right) + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r99150 = e;
        double r99151 = d;
        double r99152 = r99150 + r99151;
        double r99153 = c;
        double r99154 = r99152 + r99153;
        double r99155 = b;
        double r99156 = r99154 + r99155;
        double r99157 = a;
        double r99158 = r99156 + r99157;
        return r99158;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r99159 = e;
        double r99160 = d;
        double r99161 = b;
        double r99162 = c;
        double r99163 = r99161 + r99162;
        double r99164 = a;
        double r99165 = r99163 + r99164;
        double r99166 = r99160 + r99165;
        double r99167 = r99159 + r99166;
        return r99167;
}

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. Using strategy rm

  9. Applied associate-+r+0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(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))