Average Error: 0.4 → 0.3
Time: 5.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \left(a + \left(b + c\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + d\right) + \left(a + \left(b + c\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r133014 = e;
        double r133015 = d;
        double r133016 = r133014 + r133015;
        double r133017 = c;
        double r133018 = r133016 + r133017;
        double r133019 = b;
        double r133020 = r133018 + r133019;
        double r133021 = a;
        double r133022 = r133020 + r133021;
        return r133022;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r133023 = e;
        double r133024 = d;
        double r133025 = r133023 + r133024;
        double r133026 = a;
        double r133027 = b;
        double r133028 = c;
        double r133029 = r133027 + r133028;
        double r133030 = r133026 + r133029;
        double r133031 = r133025 + r133030;
        return r133031;
}

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+0.4

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

  4. Simplified0.4

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

  6. Applied associate-+l+0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020042 
(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))