Average Error: 0.4 → 0.2
Time: 29.9s
Precision: 64
\[1.0 \le a \le 2.0 \le b \le 4.0 \le c \le 8.0 \le d \le 16.0 \le e \le 32.0\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \left(a + \left(b + c\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \left(a + \left(b + c\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r8339485 = e;
        double r8339486 = d;
        double r8339487 = r8339485 + r8339486;
        double r8339488 = c;
        double r8339489 = r8339487 + r8339488;
        double r8339490 = b;
        double r8339491 = r8339489 + r8339490;
        double r8339492 = a;
        double r8339493 = r8339491 + r8339492;
        return r8339493;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r8339494 = e;
        double r8339495 = d;
        double r8339496 = a;
        double r8339497 = b;
        double r8339498 = c;
        double r8339499 = r8339497 + r8339498;
        double r8339500 = r8339496 + r8339499;
        double r8339501 = r8339495 + r8339500;
        double r8339502 = r8339494 + r8339501;
        return r8339502;
}

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+0.4

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

  5. Applied associate-+l+0.3

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

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

Reproduce

herbie shell --seed 2019165 
(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))