Expression, p14

Average Error: 0.0 → 0.0

Time: 11.1s

Precision: 64

\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]

Math

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r3291401 = a;
        double r3291402 = b;
        double r3291403 = c;
        double r3291404 = r3291402 + r3291403;
        double r3291405 = d;
        double r3291406 = r3291404 + r3291405;
        double r3291407 = r3291401 * r3291406;
        return r3291407;
}

↓

double f(double a, double b, double c, double d) {
        double r3291408 = a;
        double r3291409 = b;
        double r3291410 = r3291408 * r3291409;
        double r3291411 = c;
        double r3291412 = r3291411 * r3291408;
        double r3291413 = r3291410 + r3291412;
        double r3291414 = d;
        double r3291415 = r3291408 * r3291414;
        double r3291416 = r3291413 + r3291415;
        return r3291416;
}

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 distribute-lft-in 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019132 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

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

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