Average Error: 0.4 → 0.3
Time: 2.1s
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 r125992 = e;
        double r125993 = d;
        double r125994 = r125992 + r125993;
        double r125995 = c;
        double r125996 = r125994 + r125995;
        double r125997 = b;
        double r125998 = r125996 + r125997;
        double r125999 = a;
        double r126000 = r125998 + r125999;
        return r126000;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r126001 = e;
        double r126002 = d;
        double r126003 = r126001 + r126002;
        double r126004 = c;
        double r126005 = r126003 + r126004;
        double r126006 = b;
        double r126007 = a;
        double r126008 = r126006 + r126007;
        double r126009 = r126005 + r126008;
        return r126009;
}

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 2020062 
(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))