Average Error: 0.4 → 0.3
Time: 14.1s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \left(\left(b + c\right) + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + d\right) + \left(\left(b + c\right) + a\right)
double f(double a, double b, double c, double d, double e) {
        double r105502 = e;
        double r105503 = d;
        double r105504 = r105502 + r105503;
        double r105505 = c;
        double r105506 = r105504 + r105505;
        double r105507 = b;
        double r105508 = r105506 + r105507;
        double r105509 = a;
        double r105510 = r105508 + r105509;
        return r105510;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r105511 = e;
        double r105512 = d;
        double r105513 = r105511 + r105512;
        double r105514 = b;
        double r105515 = c;
        double r105516 = r105514 + r105515;
        double r105517 = a;
        double r105518 = r105516 + r105517;
        double r105519 = r105513 + r105518;
        return r105519;
}

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. Simplified0.3

    \[\leadsto \left(\left(e + d\right) + \color{blue}{\left(b + c\right)}\right) + a\]
  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1.0 a 2.0 b 4.0 c 8.0 d 16.0 e 32.0)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))