Average Error: 0.4 → 0.2
Time: 5.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(\left(b + c\right) + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(\left(b + c\right) + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r109339 = e;
        double r109340 = d;
        double r109341 = r109339 + r109340;
        double r109342 = c;
        double r109343 = r109341 + r109342;
        double r109344 = b;
        double r109345 = r109343 + r109344;
        double r109346 = a;
        double r109347 = r109345 + r109346;
        return r109347;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r109348 = e;
        double r109349 = d;
        double r109350 = b;
        double r109351 = c;
        double r109352 = r109350 + r109351;
        double r109353 = a;
        double r109354 = r109352 + r109353;
        double r109355 = r109349 + r109354;
        double r109356 = r109348 + r109355;
        return r109356;
}

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
Herbie0.2
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

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. Using strategy rm

  7. Applied associate-+l+0.2

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

  9. Applied associate-+r+0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(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))