Average Error: 0.4 → 0.3
Time: 3.3s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + \left(d + \left(b + c\right)\right)\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + \left(d + \left(b + c\right)\right)\right) + a
double f(double a, double b, double c, double d, double e) {
        double r93091 = e;
        double r93092 = d;
        double r93093 = r93091 + r93092;
        double r93094 = c;
        double r93095 = r93093 + r93094;
        double r93096 = b;
        double r93097 = r93095 + r93096;
        double r93098 = a;
        double r93099 = r93097 + r93098;
        return r93099;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r93100 = e;
        double r93101 = d;
        double r93102 = b;
        double r93103 = c;
        double r93104 = r93102 + r93103;
        double r93105 = r93101 + r93104;
        double r93106 = r93100 + r93105;
        double r93107 = a;
        double r93108 = r93106 + r93107;
        return r93108;
}

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

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

  5. Applied associate-+l+0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020060 +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))