Average Error: 0.4 → 0.2
Time: 9.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(\left(c + b\right) + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(\left(c + b\right) + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r52327 = e;
        double r52328 = d;
        double r52329 = r52327 + r52328;
        double r52330 = c;
        double r52331 = r52329 + r52330;
        double r52332 = b;
        double r52333 = r52331 + r52332;
        double r52334 = a;
        double r52335 = r52333 + r52334;
        return r52335;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r52336 = e;
        double r52337 = d;
        double r52338 = c;
        double r52339 = b;
        double r52340 = r52338 + r52339;
        double r52341 = a;
        double r52342 = r52340 + r52341;
        double r52343 = r52337 + r52342;
        double r52344 = r52336 + r52343;
        return r52344;
}

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+0.2

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

  7. Applied associate-+l+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 +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))