Expression 1, p15

Average Error: 0.4 → 0.3

Time: 19.5s

Precision: 64

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

Math

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

↓

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

C

double f(double a, double b, double c, double d, double e) {
        double r6007551 = e;
        double r6007552 = d;
        double r6007553 = r6007551 + r6007552;
        double r6007554 = c;
        double r6007555 = r6007553 + r6007554;
        double r6007556 = b;
        double r6007557 = r6007555 + r6007556;
        double r6007558 = a;
        double r6007559 = r6007557 + r6007558;
        return r6007559;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r6007560 = b;
        double r6007561 = a;
        double r6007562 = r6007560 + r6007561;
        double r6007563 = c;
        double r6007564 = d;
        double r6007565 = e;
        double r6007566 = r6007564 + r6007565;
        double r6007567 = r6007563 + r6007566;
        double r6007568 = r6007562 + r6007567;
        return r6007568;
}

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

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

4. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019139 
(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))