Average Error: 0.4 → 0.3
Time: 6.4s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(d + \left(b + c\right)\right) + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(d + \left(b + c\right)\right) + a\right)
double f(double a, double b, double c, double d, double e) {
        double r104727 = e;
        double r104728 = d;
        double r104729 = r104727 + r104728;
        double r104730 = c;
        double r104731 = r104729 + r104730;
        double r104732 = b;
        double r104733 = r104731 + r104732;
        double r104734 = a;
        double r104735 = r104733 + r104734;
        return r104735;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r104736 = e;
        double r104737 = d;
        double r104738 = b;
        double r104739 = c;
        double r104740 = r104738 + r104739;
        double r104741 = r104737 + r104740;
        double r104742 = a;
        double r104743 = r104741 + r104742;
        double r104744 = r104736 + r104743;
        return r104744;
}

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

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020045 +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))