ABCF->ab-angle b

Average Error: 52.2 → 30.8

Time: 20.9s

Precision: binary64

\[[A, C]=\mathsf{sort}([A, C])\]

Math

\[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq -\infty:\\ \;\;\;\;-\frac{\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt{F \cdot -0.5}\right)}{\sqrt{C}}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq -2.436086178660204 \cdot 10^{-175}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \left(2 \cdot \left(F \cdot \left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right)\right)\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq 0:\\ \;\;\;\;-\sqrt{\sqrt{-F}} \cdot \frac{\sqrt{\sqrt{-F}}}{\sqrt{C}}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq \infty:\\ \;\;\;\;\frac{\sqrt{-8 \cdot \left(C \cdot F\right)} \cdot \left(A \cdot \sqrt{2}\right)}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\sqrt{C}}{\sqrt{-F}}}\\ \end{array}\]

FPCore

(FPCore (A B C F)
 :precision binary64
 (/
  (-
   (sqrt
    (*
     (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F))
     (- (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
  (- (pow B 2.0) (* (* 4.0 A) C))))

↓

(FPCore (A B C F)
 :precision binary64
 (if (<=
      (/
       (-
        (sqrt
         (*
          (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F))
          (- (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))))))
       (- (pow B 2.0) (* (* 4.0 A) C)))
      (- INFINITY))
   (-
    (/
     (*
      (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))
      (* (cbrt (sqrt 2.0)) (sqrt (* F -0.5))))
     (sqrt C)))
   (if (<=
        (/
         (-
          (sqrt
           (*
            (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F))
            (- (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))))))
         (- (pow B 2.0) (* (* 4.0 A) C)))
        -2.436086178660204e-175)
     (/
      (-
       (sqrt
        (*
         (- (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0))))
         (* 2.0 (* F (- (* B B) (* 4.0 (* A C))))))))
      (- (pow B 2.0) (* (* 4.0 A) C)))
     (if (<=
          (/
           (-
            (sqrt
             (*
              (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F))
              (- (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))))))
           (- (pow B 2.0) (* (* 4.0 A) C)))
          0.0)
       (- (* (sqrt (sqrt (- F))) (/ (sqrt (sqrt (- F))) (sqrt C))))
       (if (<=
            (/
             (-
              (sqrt
               (*
                (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F))
                (- (+ A C) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))))))
             (- (pow B 2.0) (* (* 4.0 A) C)))
            INFINITY)
         (/
          (* (sqrt (* -8.0 (* C F))) (* A (sqrt 2.0)))
          (- (pow B 2.0) (* (* 4.0 A) C)))
         (/ -1.0 (/ (sqrt C) (sqrt (- F)))))))))

C

double code(double A, double B, double C, double F) {
	return -sqrt((2.0 * ((pow(B, 2.0) - ((4.0 * A) * C)) * F)) * ((A + C) - sqrt(pow((A - C), 2.0) + pow(B, 2.0)))) / (pow(B, 2.0) - ((4.0 * A) * C));
}

↓

double code(double A, double B, double C, double F) {
	double tmp;
	if ((-sqrt((2.0 * ((pow(B, 2.0) - ((4.0 * A) * C)) * F)) * ((A + C) - sqrt(pow(B, 2.0) + pow((A - C), 2.0)))) / (pow(B, 2.0) - ((4.0 * A) * C))) <= -((double) INFINITY)) {
		tmp = -(((cbrt(sqrt(2.0)) * cbrt(sqrt(2.0))) * (cbrt(sqrt(2.0)) * sqrt(F * -0.5))) / sqrt(C));
	} else if ((-sqrt((2.0 * ((pow(B, 2.0) - ((4.0 * A) * C)) * F)) * ((A + C) - sqrt(pow(B, 2.0) + pow((A - C), 2.0)))) / (pow(B, 2.0) - ((4.0 * A) * C))) <= -2.436086178660204e-175) {
		tmp = -sqrt(((A + C) - sqrt(pow(B, 2.0) + pow((A - C), 2.0))) * (2.0 * (F * ((B * B) - (4.0 * (A * C)))))) / (pow(B, 2.0) - ((4.0 * A) * C));
	} else if ((-sqrt((2.0 * ((pow(B, 2.0) - ((4.0 * A) * C)) * F)) * ((A + C) - sqrt(pow(B, 2.0) + pow((A - C), 2.0)))) / (pow(B, 2.0) - ((4.0 * A) * C))) <= 0.0) {
		tmp = -(sqrt(sqrt(-F)) * (sqrt(sqrt(-F)) / sqrt(C)));
	} else if ((-sqrt((2.0 * ((pow(B, 2.0) - ((4.0 * A) * C)) * F)) * ((A + C) - sqrt(pow(B, 2.0) + pow((A - C), 2.0)))) / (pow(B, 2.0) - ((4.0 * A) * C))) <= ((double) INFINITY)) {
		tmp = (sqrt(-8.0 * (C * F)) * (A * sqrt(2.0))) / (pow(B, 2.0) - ((4.0 * A) * C));
	} else {
		tmp = -1.0 / (sqrt(C) / sqrt(-F));
	}
	return tmp;
}

Error

Bits error versus A

Bits error versus B

Bits error versus C

Bits error versus F

Derivation

1. Split input into 5 regimes

2. if (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < -inf.0

   1. Initial program 64.0

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

   2. Taylor expanded around -inf 33.8

      \[\leadsto \color{blue}{-1 \cdot \left(\sqrt{-0.5 \cdot \frac{F}{C}} \cdot \sqrt{2}\right)}\]

   3. Simplified 33.8

      \[\leadsto \color{blue}{-\sqrt{2} \cdot \sqrt{-0.5 \cdot \frac{F}{C}}}\]
   4. Using strategy rm

   5. Applied associate-*r/_binary64 33.8

      \[\leadsto -\sqrt{2} \cdot \sqrt{\color{blue}{\frac{-0.5 \cdot F}{C}}}\]

   6. Applied sqrt-div_binary64 22.7

      \[\leadsto -\sqrt{2} \cdot \color{blue}{\frac{\sqrt{-0.5 \cdot F}}{\sqrt{C}}}\]

   7. Applied associate-*r/_binary64 22.7

      \[\leadsto -\color{blue}{\frac{\sqrt{2} \cdot \sqrt{-0.5 \cdot F}}{\sqrt{C}}}\]

   8. Simplified 22.7

      \[\leadsto -\frac{\color{blue}{\sqrt{2} \cdot \sqrt{F \cdot -0.5}}}{\sqrt{C}}\]
   9. Using strategy rm

   10. Applied add-cube-cbrt_binary64 22.7

       \[\leadsto -\frac{\color{blue}{\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \sqrt[3]{\sqrt{2}}\right)} \cdot \sqrt{F \cdot -0.5}}{\sqrt{C}}\]

   11. Applied associate-*l*_binary64 22.7

       \[\leadsto -\frac{\color{blue}{\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt{F \cdot -0.5}\right)}}{\sqrt{C}}\]

   12. Simplified 22.7

       \[\leadsto -\frac{\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \color{blue}{\left(\sqrt{F \cdot -0.5} \cdot \sqrt[3]{\sqrt{2}}\right)}}{\sqrt{C}}\]

   if -inf.0 < (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < -2.43608617866020407e-175

   1. Initial program 1.5

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]
   2. Using strategy rm

   3. Applied *-un-lft-identity_binary64 1.5

      \[\leadsto \frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot \color{blue}{\left(1 \cdot F\right)}\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

   4. Applied associate-*r*_binary64 1.5

      \[\leadsto \frac{-\sqrt{\left(2 \cdot \color{blue}{\left(\left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot 1\right) \cdot F\right)}\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

   5. Simplified 1.5

      \[\leadsto \frac{-\sqrt{\left(2 \cdot \left(\color{blue}{\left(B \cdot B - \left(C \cdot A\right) \cdot 4\right)} \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

   if -2.43608617866020407e-175 < (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < 0.0

   1. Initial program 57.7

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

   2. Taylor expanded around -inf 34.7

      \[\leadsto \color{blue}{-1 \cdot \left(\sqrt{-0.5 \cdot \frac{F}{C}} \cdot \sqrt{2}\right)}\]

   3. Simplified 34.7

      \[\leadsto \color{blue}{-\sqrt{2} \cdot \sqrt{-0.5 \cdot \frac{F}{C}}}\]
   4. Using strategy rm

   5. Applied associate-*r/_binary64 34.7

      \[\leadsto -\sqrt{2} \cdot \sqrt{\color{blue}{\frac{-0.5 \cdot F}{C}}}\]

   6. Applied sqrt-div_binary64 30.4

      \[\leadsto -\sqrt{2} \cdot \color{blue}{\frac{\sqrt{-0.5 \cdot F}}{\sqrt{C}}}\]

   7. Applied associate-*r/_binary64 30.4

      \[\leadsto -\color{blue}{\frac{\sqrt{2} \cdot \sqrt{-0.5 \cdot F}}{\sqrt{C}}}\]

   8. Simplified 30.4

      \[\leadsto -\frac{\color{blue}{\sqrt{2} \cdot \sqrt{F \cdot -0.5}}}{\sqrt{C}}\]
   9. Using strategy rm

   10. Applied sqrt-unprod_binary64 30.4

       \[\leadsto -\frac{\color{blue}{\sqrt{2 \cdot \left(F \cdot -0.5\right)}}}{\sqrt{C}}\]

   11. Simplified 30.4

       \[\leadsto -\frac{\sqrt{\color{blue}{-F}}}{\sqrt{C}}\]
   12. Using strategy rm

   13. Applied *-un-lft-identity_binary64 30.4

       \[\leadsto -\frac{\sqrt{-F}}{\color{blue}{1 \cdot \sqrt{C}}}\]

   14. Applied add-sqr-sqrt_binary64 30.5

       \[\leadsto -\frac{\color{blue}{\sqrt{\sqrt{-F}} \cdot \sqrt{\sqrt{-F}}}}{1 \cdot \sqrt{C}}\]

   15. Applied times-frac_binary64 30.5

       \[\leadsto -\color{blue}{\frac{\sqrt{\sqrt{-F}}}{1} \cdot \frac{\sqrt{\sqrt{-F}}}{\sqrt{C}}}\]

   if 0.0 < (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C))) < +inf.0

   1. Initial program 36.2

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

   2. Taylor expanded around -inf 13.8

      \[\leadsto \frac{-\color{blue}{-1 \cdot \left(\sqrt{-8 \cdot \left(C \cdot F\right)} \cdot \left(A \cdot \sqrt{2}\right)\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

   if +inf.0 < (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))

   1. Initial program 64.0

      \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]

   2. Taylor expanded around -inf 51.8

      \[\leadsto \color{blue}{-1 \cdot \left(\sqrt{-0.5 \cdot \frac{F}{C}} \cdot \sqrt{2}\right)}\]

   3. Simplified 51.8

      \[\leadsto \color{blue}{-\sqrt{2} \cdot \sqrt{-0.5 \cdot \frac{F}{C}}}\]
   4. Using strategy rm

   5. Applied associate-*r/_binary64 51.8

      \[\leadsto -\sqrt{2} \cdot \sqrt{\color{blue}{\frac{-0.5 \cdot F}{C}}}\]

   6. Applied sqrt-div_binary64 47.8

      \[\leadsto -\sqrt{2} \cdot \color{blue}{\frac{\sqrt{-0.5 \cdot F}}{\sqrt{C}}}\]

   7. Applied associate-*r/_binary64 47.8

      \[\leadsto -\color{blue}{\frac{\sqrt{2} \cdot \sqrt{-0.5 \cdot F}}{\sqrt{C}}}\]

   8. Simplified 47.8

      \[\leadsto -\frac{\color{blue}{\sqrt{2} \cdot \sqrt{F \cdot -0.5}}}{\sqrt{C}}\]
   9. Using strategy rm

   10. Applied sqrt-unprod_binary64 47.8

       \[\leadsto -\frac{\color{blue}{\sqrt{2 \cdot \left(F \cdot -0.5\right)}}}{\sqrt{C}}\]

   11. Simplified 47.8

       \[\leadsto -\frac{\sqrt{\color{blue}{-F}}}{\sqrt{C}}\]
   12. Using strategy rm

   13. Applied *-un-lft-identity_binary64 47.8

       \[\leadsto -\frac{\sqrt{\color{blue}{1 \cdot \left(-F\right)}}}{\sqrt{C}}\]

   14. Applied sqrt-prod_binary64 47.8

       \[\leadsto -\frac{\color{blue}{\sqrt{1} \cdot \sqrt{-F}}}{\sqrt{C}}\]

   15. Applied associate-/l*_binary64 47.8

       \[\leadsto -\color{blue}{\frac{\sqrt{1}}{\frac{\sqrt{C}}{\sqrt{-F}}}}\]
3. Recombined 5 regimes into one program.

4. Final simplification 30.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq -\infty:\\ \;\;\;\;-\frac{\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt{F \cdot -0.5}\right)}{\sqrt{C}}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq -2.436086178660204 \cdot 10^{-175}:\\ \;\;\;\;\frac{-\sqrt{\left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \left(2 \cdot \left(F \cdot \left(B \cdot B - 4 \cdot \left(A \cdot C\right)\right)\right)\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq 0:\\ \;\;\;\;-\sqrt{\sqrt{-F}} \cdot \frac{\sqrt{\sqrt{-F}}}{\sqrt{C}}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq \infty:\\ \;\;\;\;\frac{\sqrt{-8 \cdot \left(C \cdot F\right)} \cdot \left(A \cdot \sqrt{2}\right)}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\sqrt{C}}{\sqrt{-F}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021173 
(FPCore (A B C F)
  :name "ABCF->ab-angle b"
  :precision binary64
  (/ (- (sqrt (* (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F)) (- (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))) (- (pow B 2.0) (* (* 4.0 A) C))))