Average Error: 0.4 → 0.3
Time: 4.3s
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 r117755 = e;
        double r117756 = d;
        double r117757 = r117755 + r117756;
        double r117758 = c;
        double r117759 = r117757 + r117758;
        double r117760 = b;
        double r117761 = r117759 + r117760;
        double r117762 = a;
        double r117763 = r117761 + r117762;
        return r117763;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r117764 = e;
        double r117765 = d;
        double r117766 = b;
        double r117767 = c;
        double r117768 = r117766 + r117767;
        double r117769 = r117765 + r117768;
        double r117770 = a;
        double r117771 = r117769 + r117770;
        double r117772 = r117764 + r117771;
        return r117772;
}

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+0.4

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

  5. Applied associate-+l+0.3

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

  6. Simplified0.3

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020001 +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))