Average Error: 0.4 → 0.3
Time: 3.0s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(e + d\right) + \left(c + b\right)\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(e + d\right) + \left(c + b\right)\right) + a
double f(double a, double b, double c, double d, double e) {
        double r107818 = e;
        double r107819 = d;
        double r107820 = r107818 + r107819;
        double r107821 = c;
        double r107822 = r107820 + r107821;
        double r107823 = b;
        double r107824 = r107822 + r107823;
        double r107825 = a;
        double r107826 = r107824 + r107825;
        return r107826;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r107827 = e;
        double r107828 = d;
        double r107829 = r107827 + r107828;
        double r107830 = c;
        double r107831 = b;
        double r107832 = r107830 + r107831;
        double r107833 = r107829 + r107832;
        double r107834 = a;
        double r107835 = r107833 + r107834;
        return r107835;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020034 
(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))