Average Error: 0.4 → 0.2
Time: 11.9s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(a + \left(b + c\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(a + \left(b + c\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r5551966 = e;
        double r5551967 = d;
        double r5551968 = r5551966 + r5551967;
        double r5551969 = c;
        double r5551970 = r5551968 + r5551969;
        double r5551971 = b;
        double r5551972 = r5551970 + r5551971;
        double r5551973 = a;
        double r5551974 = r5551972 + r5551973;
        return r5551974;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r5551975 = e;
        double r5551976 = d;
        double r5551977 = a;
        double r5551978 = b;
        double r5551979 = c;
        double r5551980 = r5551978 + r5551979;
        double r5551981 = r5551977 + r5551980;
        double r5551982 = r5551976 + r5551981;
        double r5551983 = r5551975 + r5551982;
        return r5551983;
}

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+0.3

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

  5. Applied associate-+l+0.3

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

  7. Applied associate-+l+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1.0 a 2.0 b 4.0 c 8.0 d 16.0 e 32.0)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))