Expression, p14

Average Error: 0.0 → 0.0

Time: 2.1s

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 r123838 = a;
        double r123839 = b;
        double r123840 = c;
        double r123841 = r123839 + r123840;
        double r123842 = d;
        double r123843 = r123841 + r123842;
        double r123844 = r123838 * r123843;
        return r123844;
}

↓

double f(double a, double b, double c, double d) {
        double r123845 = a;
        double r123846 = b;
        double r123847 = r123845 * r123846;
        double r123848 = c;
        double r123849 = r123845 * r123848;
        double r123850 = r123847 + r123849;
        double r123851 = d;
        double r123852 = r123845 * r123851;
        double r123853 = r123850 + r123852;
        return r123853;
}

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 2020034 
(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)))