Average Error: 0.4 → 0.3
Time: 2.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(e + d\right) + c\right) + \left(b + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(e + d\right) + c\right) + \left(b + a\right)
double f(double a, double b, double c, double d, double e) {
        double r87201 = e;
        double r87202 = d;
        double r87203 = r87201 + r87202;
        double r87204 = c;
        double r87205 = r87203 + r87204;
        double r87206 = b;
        double r87207 = r87205 + r87206;
        double r87208 = a;
        double r87209 = r87207 + r87208;
        return r87209;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r87210 = e;
        double r87211 = d;
        double r87212 = r87210 + r87211;
        double r87213 = c;
        double r87214 = r87212 + r87213;
        double r87215 = b;
        double r87216 = a;
        double r87217 = r87215 + r87216;
        double r87218 = r87214 + r87217;
        return r87218;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020100 
(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))