Average Error: 0.4 → 0.3
Time: 10.4s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(d + \left(e + c\right)\right) + \left(b + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(d + \left(e + c\right)\right) + \left(b + a\right)
double f(double a, double b, double c, double d, double e) {
        double r68602 = e;
        double r68603 = d;
        double r68604 = r68602 + r68603;
        double r68605 = c;
        double r68606 = r68604 + r68605;
        double r68607 = b;
        double r68608 = r68606 + r68607;
        double r68609 = a;
        double r68610 = r68608 + r68609;
        return r68610;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r68611 = d;
        double r68612 = e;
        double r68613 = c;
        double r68614 = r68612 + r68613;
        double r68615 = r68611 + r68614;
        double r68616 = b;
        double r68617 = a;
        double r68618 = r68616 + r68617;
        double r68619 = r68615 + r68618;
        return r68619;
}

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. Using strategy rm

  5. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(e + d\right) + \color{blue}{1 \cdot c}\right) + \left(b + a\right)\]

  6. Applied *-un-lft-identity0.3

    \[\leadsto \left(\color{blue}{1 \cdot \left(e + d\right)} + 1 \cdot c\right) + \left(b + a\right)\]

  7. Applied distribute-lft-out0.3

    \[\leadsto \color{blue}{1 \cdot \left(\left(e + d\right) + c\right)} + \left(b + a\right)\]

  8. Simplified0.3

    \[\leadsto 1 \cdot \color{blue}{\left(d + \left(e + c\right)\right)} + \left(b + a\right)\]

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019208 +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))