Expression, p14

Average Error: 0.0 → 0.0

Time: 9.1s

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 r53289 = a;
        double r53290 = b;
        double r53291 = c;
        double r53292 = r53290 + r53291;
        double r53293 = d;
        double r53294 = r53292 + r53293;
        double r53295 = r53289 * r53294;
        return r53295;
}

↓

double f(double a, double b, double c, double d) {
        double r53296 = b;
        double r53297 = c;
        double r53298 = r53296 + r53297;
        double r53299 = a;
        double r53300 = r53298 * r53299;
        double r53301 = d;
        double r53302 = r53299 * r53301;
        double r53303 = r53300 + r53302;
        return r53303;
}

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)))