Average Error: 0.4 → 0.3
Time: 3.9s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(d + \left(e + \left(b + c\right)\right)\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(d + \left(e + \left(b + c\right)\right)\right) + a
double f(double a, double b, double c, double d, double e) {
        double r112839 = e;
        double r112840 = d;
        double r112841 = r112839 + r112840;
        double r112842 = c;
        double r112843 = r112841 + r112842;
        double r112844 = b;
        double r112845 = r112843 + r112844;
        double r112846 = a;
        double r112847 = r112845 + r112846;
        return r112847;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r112848 = d;
        double r112849 = e;
        double r112850 = b;
        double r112851 = c;
        double r112852 = r112850 + r112851;
        double r112853 = r112849 + r112852;
        double r112854 = r112848 + r112853;
        double r112855 = a;
        double r112856 = r112854 + r112855;
        return r112856;
}

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-+r+0.4

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

  6. Simplified0.4

    \[\leadsto \left(\color{blue}{\left(d + \left(e + c\right)\right)} + b\right) + a\]
  7. Using strategy rm

  8. Applied associate-+l+0.4

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020033 +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))