Average Error: 0.4 → 0.3
Time: 2.7s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(e + d\right) + c\right) + \left(b + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(e + d\right) + c\right) + \left(b + a\right)
double f(double a, double b, double c, double d, double e) {
        double r112626 = e;
        double r112627 = d;
        double r112628 = r112626 + r112627;
        double r112629 = c;
        double r112630 = r112628 + r112629;
        double r112631 = b;
        double r112632 = r112630 + r112631;
        double r112633 = a;
        double r112634 = r112632 + r112633;
        return r112634;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r112635 = e;
        double r112636 = d;
        double r112637 = r112635 + r112636;
        double r112638 = c;
        double r112639 = r112637 + r112638;
        double r112640 = b;
        double r112641 = a;
        double r112642 = r112640 + r112641;
        double r112643 = r112639 + r112642;
        return r112643;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020081 
(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))