Expression 1, p15

Average Error: 0.4 → 0.3

Time: 11.7s

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 r4576530 = e;
        double r4576531 = d;
        double r4576532 = r4576530 + r4576531;
        double r4576533 = c;
        double r4576534 = r4576532 + r4576533;
        double r4576535 = b;
        double r4576536 = r4576534 + r4576535;
        double r4576537 = a;
        double r4576538 = r4576536 + r4576537;
        return r4576538;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r4576539 = a;
        double r4576540 = c;
        double r4576541 = b;
        double r4576542 = r4576540 + r4576541;
        double r4576543 = d;
        double r4576544 = e;
        double r4576545 = r4576543 + r4576544;
        double r4576546 = r4576542 + r4576545;
        double r4576547 = r4576539 + r4576546;
        return r4576547;
}

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 2019163 
(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))