Average Error: 0.4 → 0.3
Time: 8.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(e + d\right) + \left(c + b\right)\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(e + d\right) + \left(c + b\right)\right) + a
double f(double a, double b, double c, double d, double e) {
        double r54705 = e;
        double r54706 = d;
        double r54707 = r54705 + r54706;
        double r54708 = c;
        double r54709 = r54707 + r54708;
        double r54710 = b;
        double r54711 = r54709 + r54710;
        double r54712 = a;
        double r54713 = r54711 + r54712;
        return r54713;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r54714 = e;
        double r54715 = d;
        double r54716 = r54714 + r54715;
        double r54717 = c;
        double r54718 = b;
        double r54719 = r54717 + r54718;
        double r54720 = r54716 + r54719;
        double r54721 = a;
        double r54722 = r54720 + r54721;
        return r54722;
}

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

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019298 
(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))