Expression, p14

Average Error: 0.0 → 0.0

Time: 11.4s

Precision: 64

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

Math

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r51596 = a;
        double r51597 = b;
        double r51598 = c;
        double r51599 = r51597 + r51598;
        double r51600 = d;
        double r51601 = r51599 + r51600;
        double r51602 = r51596 * r51601;
        return r51602;
}

↓

double f(double a, double b, double c, double d) {
        double r51603 = b;
        double r51604 = a;
        double r51605 = r51603 * r51604;
        double r51606 = c;
        double r51607 = r51604 * r51606;
        double r51608 = r51605 + r51607;
        double r51609 = d;
        double r51610 = r51604 * r51609;
        double r51611 = r51608 + r51610;
        return r51611;
}

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. Simplified 0.0

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

7. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789.0 a 98765.0) (<= 0.0 b 1.0) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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