Expression, p14

Average Error: 0.0 → 0.0

Time: 2.5s

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

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r98597 = a;
        double r98598 = b;
        double r98599 = c;
        double r98600 = r98598 + r98599;
        double r98601 = d;
        double r98602 = r98600 + r98601;
        double r98603 = r98597 * r98602;
        return r98603;
}

↓

double f(double a, double b, double c, double d) {
        double r98604 = a;
        double r98605 = b;
        double r98606 = r98604 * r98605;
        double r98607 = c;
        double r98608 = r98604 * r98607;
        double r98609 = r98606 + r98608;
        double r98610 = d;
        double r98611 = r98604 * r98610;
        double r98612 = r98609 + r98611;
        return r98612;
}

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

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

Reproduce

herbie shell --seed 2020062 
(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)))