Expression, p14

Average Error: 0.0 → 0.0

Time: 8.4s

Precision: 64

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

\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]

Math

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r139320 = a;
        double r139321 = b;
        double r139322 = c;
        double r139323 = r139321 + r139322;
        double r139324 = d;
        double r139325 = r139323 + r139324;
        double r139326 = r139320 * r139325;
        return r139326;
}

↓

double f(double a, double b, double c, double d) {
        double r139327 = b;
        double r139328 = c;
        double r139329 = r139327 + r139328;
        double r139330 = a;
        double r139331 = r139329 * r139330;
        double r139332 = d;
        double r139333 = r139330 * r139332;
        double r139334 = r139331 + r139333;
        return r139334;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

3. Applied distribute-lft-in 0.0

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

4. Simplified 0.0

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

5. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789 a 98765) (<= 0.0 b 1) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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