Average Error: 0.4 → 0.3
Time: 24.3s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(d + \left(b + c\right)\right) + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(d + \left(b + c\right)\right) + a\right)
double f(double a, double b, double c, double d, double e) {
        double r7318119 = e;
        double r7318120 = d;
        double r7318121 = r7318119 + r7318120;
        double r7318122 = c;
        double r7318123 = r7318121 + r7318122;
        double r7318124 = b;
        double r7318125 = r7318123 + r7318124;
        double r7318126 = a;
        double r7318127 = r7318125 + r7318126;
        return r7318127;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r7318128 = e;
        double r7318129 = d;
        double r7318130 = b;
        double r7318131 = c;
        double r7318132 = r7318130 + r7318131;
        double r7318133 = r7318129 + r7318132;
        double r7318134 = a;
        double r7318135 = r7318133 + r7318134;
        double r7318136 = r7318128 + r7318135;
        return r7318136;
}

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. Using strategy rm

  5. Applied associate-+l+0.3

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

  7. Applied associate-+l+0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(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))