Average Error: 0.4 → 0.3
Time: 3.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(e + d\right) + \left(b + c\right)\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(e + d\right) + \left(b + c\right)\right) + a
double f(double a, double b, double c, double d, double e) {
        double r83824 = e;
        double r83825 = d;
        double r83826 = r83824 + r83825;
        double r83827 = c;
        double r83828 = r83826 + r83827;
        double r83829 = b;
        double r83830 = r83828 + r83829;
        double r83831 = a;
        double r83832 = r83830 + r83831;
        return r83832;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r83833 = e;
        double r83834 = d;
        double r83835 = r83833 + r83834;
        double r83836 = b;
        double r83837 = c;
        double r83838 = r83836 + r83837;
        double r83839 = r83835 + r83838;
        double r83840 = a;
        double r83841 = r83839 + r83840;
        return r83841;
}

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. Simplified0.3

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

  8. Applied associate-+r+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(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))