Average Error: 0.4 → 0.2
Time: 11.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(c + d\right) + \left(a + b\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(c + d\right) + \left(a + b\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r4960183 = e;
        double r4960184 = d;
        double r4960185 = r4960183 + r4960184;
        double r4960186 = c;
        double r4960187 = r4960185 + r4960186;
        double r4960188 = b;
        double r4960189 = r4960187 + r4960188;
        double r4960190 = a;
        double r4960191 = r4960189 + r4960190;
        return r4960191;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r4960192 = e;
        double r4960193 = c;
        double r4960194 = d;
        double r4960195 = r4960193 + r4960194;
        double r4960196 = a;
        double r4960197 = b;
        double r4960198 = r4960196 + r4960197;
        double r4960199 = r4960195 + r4960198;
        double r4960200 = r4960192 + r4960199;
        return r4960200;
}

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. Taylor expanded around 0 0.4

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

  4. Applied associate-+l+0.3

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

  6. Applied associate-+l+0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 +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))