Average Error: 0.4 → 0.5
Time: 5.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\frac{\left(\left(e + d\right) + \left(c + b\right)\right) \cdot \left(\left(e + d\right) + \left(c + b\right)\right) - a \cdot a}{\left(\left(e + d\right) + \left(c + b\right)\right) - a}\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\frac{\left(\left(e + d\right) + \left(c + b\right)\right) \cdot \left(\left(e + d\right) + \left(c + b\right)\right) - a \cdot a}{\left(\left(e + d\right) + \left(c + b\right)\right) - a}
double f(double a, double b, double c, double d, double e) {
        double r102189 = e;
        double r102190 = d;
        double r102191 = r102189 + r102190;
        double r102192 = c;
        double r102193 = r102191 + r102192;
        double r102194 = b;
        double r102195 = r102193 + r102194;
        double r102196 = a;
        double r102197 = r102195 + r102196;
        return r102197;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r102198 = e;
        double r102199 = d;
        double r102200 = r102198 + r102199;
        double r102201 = c;
        double r102202 = b;
        double r102203 = r102201 + r102202;
        double r102204 = r102200 + r102203;
        double r102205 = r102204 * r102204;
        double r102206 = a;
        double r102207 = r102206 * r102206;
        double r102208 = r102205 - r102207;
        double r102209 = r102204 - r102206;
        double r102210 = r102208 / r102209;
        return r102210;
}

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
Herbie0.5
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

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 flip-+0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2020018 
(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))