Expression 1, p15

Average Error: 0.4 → 0.3

Time: 10.5s

Precision: 64

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

Math

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

↓

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

C

double f(double a, double b, double c, double d, double e) {
        double r4534557 = e;
        double r4534558 = d;
        double r4534559 = r4534557 + r4534558;
        double r4534560 = c;
        double r4534561 = r4534559 + r4534560;
        double r4534562 = b;
        double r4534563 = r4534561 + r4534562;
        double r4534564 = a;
        double r4534565 = r4534563 + r4534564;
        return r4534565;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r4534566 = a;
        double r4534567 = c;
        double r4534568 = b;
        double r4534569 = r4534567 + r4534568;
        double r4534570 = d;
        double r4534571 = e;
        double r4534572 = r4534570 + r4534571;
        double r4534573 = r4534569 + r4534572;
        double r4534574 = r4534566 + r4534573;
        return r4534574;
}

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))