Average Error: 0.4 → 0.2
Time: 12.4s
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 r4423029 = e;
        double r4423030 = d;
        double r4423031 = r4423029 + r4423030;
        double r4423032 = c;
        double r4423033 = r4423031 + r4423032;
        double r4423034 = b;
        double r4423035 = r4423033 + r4423034;
        double r4423036 = a;
        double r4423037 = r4423035 + r4423036;
        return r4423037;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r4423038 = e;
        double r4423039 = d;
        double r4423040 = a;
        double r4423041 = b;
        double r4423042 = c;
        double r4423043 = r4423041 + r4423042;
        double r4423044 = r4423040 + r4423043;
        double r4423045 = r4423039 + r4423044;
        double r4423046 = r4423038 + r4423045;
        return r4423046;
}

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 2019168 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

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

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