Average Error: 0.4 → 0.3
Time: 13.1s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \frac{\left(\left(d + c\right) + b\right) \cdot \left(\left(d + c\right) + b\right) - a \cdot a}{\left(\left(d + c\right) + b\right) - a}\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \frac{\left(\left(d + c\right) + b\right) \cdot \left(\left(d + c\right) + b\right) - a \cdot a}{\left(\left(d + c\right) + b\right) - a}
double f(double a, double b, double c, double d, double e) {
        double r4978168 = e;
        double r4978169 = d;
        double r4978170 = r4978168 + r4978169;
        double r4978171 = c;
        double r4978172 = r4978170 + r4978171;
        double r4978173 = b;
        double r4978174 = r4978172 + r4978173;
        double r4978175 = a;
        double r4978176 = r4978174 + r4978175;
        return r4978176;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r4978177 = e;
        double r4978178 = d;
        double r4978179 = c;
        double r4978180 = r4978178 + r4978179;
        double r4978181 = b;
        double r4978182 = r4978180 + r4978181;
        double r4978183 = r4978182 * r4978182;
        double r4978184 = a;
        double r4978185 = r4978184 * r4978184;
        double r4978186 = r4978183 - r4978185;
        double r4978187 = r4978182 - r4978184;
        double r4978188 = r4978186 / r4978187;
        double r4978189 = r4978177 + r4978188;
        return r4978189;
}

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. Using strategy rm

  7. Applied associate-+l+0.3

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

  9. Applied flip-+0.3

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

  10. Final simplification0.3

    \[\leadsto e + \frac{\left(\left(d + c\right) + b\right) \cdot \left(\left(d + c\right) + b\right) - a \cdot a}{\left(\left(d + c\right) + b\right) - a}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1.0 a 2.0 b 4.0 c 8.0 d 16.0 e 32.0)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))