Average Error: 0.4 → 0.3
Time: 2.9s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \left(a + \left(b + c\right)\right)\]
\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 r97516 = e;
        double r97517 = d;
        double r97518 = r97516 + r97517;
        double r97519 = c;
        double r97520 = r97518 + r97519;
        double r97521 = b;
        double r97522 = r97520 + r97521;
        double r97523 = a;
        double r97524 = r97522 + r97523;
        return r97524;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r97525 = e;
        double r97526 = d;
        double r97527 = r97525 + r97526;
        double r97528 = a;
        double r97529 = b;
        double r97530 = c;
        double r97531 = r97529 + r97530;
        double r97532 = r97528 + r97531;
        double r97533 = r97527 + r97532;
        return r97533;
}

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 associate-+l+0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020036 
(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))