Average Error: 0.4 → 0.3
Time: 4.8s
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 r67600 = e;
        double r67601 = d;
        double r67602 = r67600 + r67601;
        double r67603 = c;
        double r67604 = r67602 + r67603;
        double r67605 = b;
        double r67606 = r67604 + r67605;
        double r67607 = a;
        double r67608 = r67606 + r67607;
        return r67608;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r67609 = e;
        double r67610 = d;
        double r67611 = r67609 + r67610;
        double r67612 = c;
        double r67613 = r67611 + r67612;
        double r67614 = b;
        double r67615 = a;
        double r67616 = r67614 + r67615;
        double r67617 = r67613 + r67616;
        return r67617;
}

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 2020062 +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))