Expression, p6

Average Error: 3.7 → 2.8

Time: 6.9s

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 r107346 = a;
        double r107347 = b;
        double r107348 = c;
        double r107349 = d;
        double r107350 = r107348 + r107349;
        double r107351 = r107347 + r107350;
        double r107352 = r107346 + r107351;
        double r107353 = 2.0;
        double r107354 = r107352 * r107353;
        return r107354;
}

↓

double f(double a, double b, double c, double d) {
        double r107355 = a;
        double r107356 = b;
        double r107357 = c;
        double r107358 = r107356 + r107357;
        double r107359 = d;
        double r107360 = r107358 + r107359;
        double r107361 = r107355 + r107360;
        double r107362 = 2.0;
        double r107363 = r107361 * r107362;
        return r107363;
}

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 
(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))