Expression, p6

Average Error: 3.7 → 2.8

Time: 16.0s

Precision: 64

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

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 r6561405 = a;
        double r6561406 = b;
        double r6561407 = c;
        double r6561408 = d;
        double r6561409 = r6561407 + r6561408;
        double r6561410 = r6561406 + r6561409;
        double r6561411 = r6561405 + r6561410;
        double r6561412 = 2.0;
        double r6561413 = r6561411 * r6561412;
        return r6561413;
}

↓

double f(double a, double b, double c, double d) {
        double r6561414 = a;
        double r6561415 = b;
        double r6561416 = c;
        double r6561417 = r6561415 + r6561416;
        double r6561418 = d;
        double r6561419 = r6561417 + r6561418;
        double r6561420 = r6561414 + r6561419;
        double r6561421 = 2.0;
        double r6561422 = r6561420 * r6561421;
        return r6561422;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.7
Target	3.9
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 2019174 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14.0 a -13.0) (<= -3.0 b -2.0) (<= 3.0 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))