Expression 1, p15

Average Error: 0.4 → 0.3

Time: 12.0s

Precision: 64

\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]

Math

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

↓

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

C

double f(double a, double b, double c, double d, double e) {
        double r5146511 = e;
        double r5146512 = d;
        double r5146513 = r5146511 + r5146512;
        double r5146514 = c;
        double r5146515 = r5146513 + r5146514;
        double r5146516 = b;
        double r5146517 = r5146515 + r5146516;
        double r5146518 = a;
        double r5146519 = r5146517 + r5146518;
        return r5146519;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r5146520 = a;
        double r5146521 = c;
        double r5146522 = b;
        double r5146523 = r5146521 + r5146522;
        double r5146524 = d;
        double r5146525 = e;
        double r5146526 = r5146524 + r5146525;
        double r5146527 = r5146523 + r5146526;
        double r5146528 = r5146520 + r5146527;
        return r5146528;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Target

Original	0.4
Target	0.2
Herbie	0.3

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

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. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))