Expression, p6

Average Error: 3.7 → 2.8

Time: 7.9s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]

Math

\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]

↓

\[\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]

C

double f(double a, double b, double c, double d) {
        double r143133 = a;
        double r143134 = b;
        double r143135 = c;
        double r143136 = d;
        double r143137 = r143135 + r143136;
        double r143138 = r143134 + r143137;
        double r143139 = r143133 + r143138;
        double r143140 = 2.0;
        double r143141 = r143139 * r143140;
        return r143141;
}

↓

double f(double a, double b, double c, double d) {
        double r143142 = a;
        double r143143 = b;
        double r143144 = c;
        double r143145 = r143143 + r143144;
        double r143146 = d;
        double r143147 = r143145 + r143146;
        double r143148 = r143142 + r143147;
        double r143149 = 2.0;
        double r143150 = r143148 * r143149;
        return r143150;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.7
Target	3.8
Herbie	2.8

\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

1. Initial program 3.7

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
2. Using strategy rm

3. Applied associate-+r+ 2.8

   \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]

4. Final simplification 2.8

   \[\leadsto \left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))