Average Error: 0.4 → 0.3
Time: 5.4s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \left(a + \left(b + c\right)\right)\]
\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 r106302 = e;
        double r106303 = d;
        double r106304 = r106302 + r106303;
        double r106305 = c;
        double r106306 = r106304 + r106305;
        double r106307 = b;
        double r106308 = r106306 + r106307;
        double r106309 = a;
        double r106310 = r106308 + r106309;
        return r106310;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r106311 = e;
        double r106312 = d;
        double r106313 = r106311 + r106312;
        double r106314 = a;
        double r106315 = b;
        double r106316 = c;
        double r106317 = r106315 + r106316;
        double r106318 = r106314 + r106317;
        double r106319 = r106313 + r106318;
        return r106319;
}

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))