Average Error: 0.4 → 0.3
Time: 2.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(b + a\right) + \left(d + \left(e + c\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(b + a\right) + \left(d + \left(e + c\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r106807 = e;
        double r106808 = d;
        double r106809 = r106807 + r106808;
        double r106810 = c;
        double r106811 = r106809 + r106810;
        double r106812 = b;
        double r106813 = r106811 + r106812;
        double r106814 = a;
        double r106815 = r106813 + r106814;
        return r106815;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r106816 = b;
        double r106817 = a;
        double r106818 = r106816 + r106817;
        double r106819 = d;
        double r106820 = e;
        double r106821 = c;
        double r106822 = r106820 + r106821;
        double r106823 = r106819 + r106822;
        double r106824 = r106818 + r106823;
        return r106824;
}

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 *-un-lft-identity0.3

    \[\leadsto \left(\left(e + d\right) + \color{blue}{1 \cdot c}\right) + \left(b + a\right)\]

  6. Applied *-un-lft-identity0.3

    \[\leadsto \left(\color{blue}{1 \cdot \left(e + d\right)} + 1 \cdot c\right) + \left(b + a\right)\]

  7. Applied distribute-lft-out0.3

    \[\leadsto \color{blue}{1 \cdot \left(\left(e + d\right) + c\right)} + \left(b + a\right)\]

  8. Simplified0.3

    \[\leadsto 1 \cdot \color{blue}{\left(d + \left(e + c\right)\right)} + \left(b + a\right)\]

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020020 +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))