Average Error: 0.4 → 0.3
Time: 7.4s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[d + \left(\left(e + c\right) + \left(b + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
d + \left(\left(e + c\right) + \left(b + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r69804 = e;
        double r69805 = d;
        double r69806 = r69804 + r69805;
        double r69807 = c;
        double r69808 = r69806 + r69807;
        double r69809 = b;
        double r69810 = r69808 + r69809;
        double r69811 = a;
        double r69812 = r69810 + r69811;
        return r69812;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r69813 = d;
        double r69814 = e;
        double r69815 = c;
        double r69816 = r69814 + r69815;
        double r69817 = b;
        double r69818 = a;
        double r69819 = r69817 + r69818;
        double r69820 = r69816 + r69819;
        double r69821 = r69813 + r69820;
        return r69821;
}

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. Taylor expanded around 0 0.3

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

  6. Applied associate-+l+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019322 
(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))