Average Error: 0.4 → 0.3
Time: 12.4s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[a + \left(e + \left(\left(c + d\right) + b\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
a + \left(e + \left(\left(c + d\right) + b\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r247673 = e;
        double r247674 = d;
        double r247675 = r247673 + r247674;
        double r247676 = c;
        double r247677 = r247675 + r247676;
        double r247678 = b;
        double r247679 = r247677 + r247678;
        double r247680 = a;
        double r247681 = r247679 + r247680;
        return r247681;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r247682 = a;
        double r247683 = e;
        double r247684 = c;
        double r247685 = d;
        double r247686 = r247684 + r247685;
        double r247687 = b;
        double r247688 = r247686 + r247687;
        double r247689 = r247683 + r247688;
        double r247690 = r247682 + r247689;
        return r247690;
}

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. Simplified0.3

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

  4. Applied associate-+r+0.3

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

  6. Applied associate-+r+0.4

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019194 
(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))