Expression, p6

Average Error: 3.6 → 2.7

Time: 2.7s

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 r92019 = a;
        double r92020 = b;
        double r92021 = c;
        double r92022 = d;
        double r92023 = r92021 + r92022;
        double r92024 = r92020 + r92023;
        double r92025 = r92019 + r92024;
        double r92026 = 2.0;
        double r92027 = r92025 * r92026;
        return r92027;
}

↓

double f(double a, double b, double c, double d) {
        double r92028 = a;
        double r92029 = b;
        double r92030 = c;
        double r92031 = r92029 + r92030;
        double r92032 = d;
        double r92033 = r92031 + r92032;
        double r92034 = r92028 + r92033;
        double r92035 = 2.0;
        double r92036 = r92034 * r92035;
        return r92036;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.6
Target	3.8
Herbie	2.7

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

Derivation

1. Initial program 3.6

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

3. Applied associate-+r+ 2.7

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

4. Final simplification 2.7

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

Reproduce

herbie shell --seed 2020057 
(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))