Average Error: 0.4 → 0.2
Time: 2.1s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(a + \left(b + c\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(a + \left(b + c\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r84263 = e;
        double r84264 = d;
        double r84265 = r84263 + r84264;
        double r84266 = c;
        double r84267 = r84265 + r84266;
        double r84268 = b;
        double r84269 = r84267 + r84268;
        double r84270 = a;
        double r84271 = r84269 + r84270;
        return r84271;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r84272 = e;
        double r84273 = d;
        double r84274 = a;
        double r84275 = b;
        double r84276 = c;
        double r84277 = r84275 + r84276;
        double r84278 = r84274 + r84277;
        double r84279 = r84273 + r84278;
        double r84280 = r84272 + r84279;
        return r84280;
}

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
Herbie0.2
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

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 associate-+l+0.3

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

  6. Simplified0.3

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

  8. Applied associate-+l+0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020065 
(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))