Average Error: 0.4 → 0.3
Time: 4.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \left(c + \left(b + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + d\right) + \left(c + \left(b + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r147629 = e;
        double r147630 = d;
        double r147631 = r147629 + r147630;
        double r147632 = c;
        double r147633 = r147631 + r147632;
        double r147634 = b;
        double r147635 = r147633 + r147634;
        double r147636 = a;
        double r147637 = r147635 + r147636;
        return r147637;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r147638 = e;
        double r147639 = d;
        double r147640 = r147638 + r147639;
        double r147641 = c;
        double r147642 = b;
        double r147643 = a;
        double r147644 = r147642 + r147643;
        double r147645 = r147641 + r147644;
        double r147646 = r147640 + r147645;
        return r147646;
}

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

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 +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))