Average Error: 0.4 → 0.3
Time: 8.0s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(d + c\right) + \left(b + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(d + c\right) + \left(b + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r78307 = e;
        double r78308 = d;
        double r78309 = r78307 + r78308;
        double r78310 = c;
        double r78311 = r78309 + r78310;
        double r78312 = b;
        double r78313 = r78311 + r78312;
        double r78314 = a;
        double r78315 = r78313 + r78314;
        return r78315;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r78316 = e;
        double r78317 = d;
        double r78318 = c;
        double r78319 = r78317 + r78318;
        double r78320 = b;
        double r78321 = a;
        double r78322 = r78320 + r78321;
        double r78323 = r78319 + r78322;
        double r78324 = r78316 + r78323;
        return r78324;
}

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. Using strategy rm

  5. Applied associate-+l+0.3

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

  7. Applied associate-+l+0.2

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

  9. Applied associate-+r+0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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))