Average Error: 0.4 → 0.2
Time: 7.3s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(d + c\right) + \left(b + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(d + c\right) + \left(b + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r62543 = e;
        double r62544 = d;
        double r62545 = r62543 + r62544;
        double r62546 = c;
        double r62547 = r62545 + r62546;
        double r62548 = b;
        double r62549 = r62547 + r62548;
        double r62550 = a;
        double r62551 = r62549 + r62550;
        return r62551;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r62552 = e;
        double r62553 = d;
        double r62554 = c;
        double r62555 = r62553 + r62554;
        double r62556 = b;
        double r62557 = a;
        double r62558 = r62556 + r62557;
        double r62559 = r62555 + r62558;
        double r62560 = r62552 + r62559;
        return r62560;
}

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+0.4

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

  5. Applied associate-+l+0.3

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

  7. Applied associate-+l+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019291 
(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))