Expression, p14

Average Error: 0.0 → 0.0

Time: 8.1s

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

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r62270 = a;
        double r62271 = b;
        double r62272 = c;
        double r62273 = r62271 + r62272;
        double r62274 = d;
        double r62275 = r62273 + r62274;
        double r62276 = r62270 * r62275;
        return r62276;
}

↓

double f(double a, double b, double c, double d) {
        double r62277 = a;
        double r62278 = d;
        double r62279 = r62277 * r62278;
        double r62280 = b;
        double r62281 = c;
        double r62282 = r62280 + r62281;
        double r62283 = r62277 * r62282;
        double r62284 = r62279 + r62283;
        return r62284;
}

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. Using strategy rm

5. Applied +-commutative 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020042 
(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)))