Average Error: 0.4 → 0.3
Time: 8.0s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(d + \left(c + b\right)\right) + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(d + \left(c + b\right)\right) + a\right)
double f(double a, double b, double c, double d, double e) {
        double r72837 = e;
        double r72838 = d;
        double r72839 = r72837 + r72838;
        double r72840 = c;
        double r72841 = r72839 + r72840;
        double r72842 = b;
        double r72843 = r72841 + r72842;
        double r72844 = a;
        double r72845 = r72843 + r72844;
        return r72845;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r72846 = e;
        double r72847 = d;
        double r72848 = c;
        double r72849 = b;
        double r72850 = r72848 + r72849;
        double r72851 = r72847 + r72850;
        double r72852 = a;
        double r72853 = r72851 + r72852;
        double r72854 = r72846 + r72853;
        return r72854;
}

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-+l+0.3

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

  7. Applied associate-+l+0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019322 +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))