Expression 1, p15

Average Error: 0.4 → 0.3

Time: 16.0s

Precision: 64

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

Math

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

↓

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

C

double f(double a, double b, double c, double d, double e) {
        double r5375068 = e;
        double r5375069 = d;
        double r5375070 = r5375068 + r5375069;
        double r5375071 = c;
        double r5375072 = r5375070 + r5375071;
        double r5375073 = b;
        double r5375074 = r5375072 + r5375073;
        double r5375075 = a;
        double r5375076 = r5375074 + r5375075;
        return r5375076;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r5375077 = b;
        double r5375078 = a;
        double r5375079 = r5375077 + r5375078;
        double r5375080 = c;
        double r5375081 = d;
        double r5375082 = e;
        double r5375083 = r5375081 + r5375082;
        double r5375084 = r5375080 + r5375083;
        double r5375085 = r5375079 + r5375084;
        return r5375085;
}

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 2019172 
(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))