Average Error: 52.9 → 46.4
Time: 20.7s
Precision: binary64
\[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq 0:\\ \;\;\;\;\frac{\sqrt{2} \cdot \left(\sqrt{B \cdot B - \left(4 \cdot A\right) \cdot C} \cdot \sqrt{F}\right)}{\frac{B \cdot B - \left(4 \cdot A\right) \cdot C}{-\sqrt{\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}}}\\ \mathbf{elif}\;\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \leq \infty:\\ \;\;\;\;\frac{\sqrt{2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)}}{\frac{B \cdot B - \left(4 \cdot A\right) \cdot C}{-\sqrt{\left(A + C\right) + \left(C - A\right)}}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\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 0:\\
\;\;\;\;\frac{\sqrt{2} \cdot \left(\sqrt{B \cdot B - \left(4 \cdot A\right) \cdot C} \cdot \sqrt{F}\right)}{\frac{B \cdot B - \left(4 \cdot A\right) \cdot C}{-\sqrt{\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}}}\\

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

\mathbf{else}:\\
\;\;\;\;0\\

\end{array}
(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)))
      0.0)
   (/
    (* (sqrt 2.0) (* (sqrt (- (* B B) (* (* 4.0 A) C))) (sqrt F)))
    (/
     (- (* B B) (* (* 4.0 A) C))
     (- (sqrt (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (* B B))))))))
   (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 (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F)))
      (/ (- (* B B) (* (* 4.0 A) C)) (- (sqrt (+ (+ A C) (- C A))))))
     0.0)))
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))) <= 0.0) {
		tmp = (sqrt(2.0) * (sqrt((B * B) - ((4.0 * A) * C)) * sqrt(F))) / (((B * B) - ((4.0 * A) * C)) / -sqrt((A + C) + sqrt(pow((A - C), 2.0) + (B * B))));
	} 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(2.0 * ((pow(B, 2.0) - ((4.0 * A) * C)) * F)) / (((B * B) - ((4.0 * A) * C)) / -sqrt((A + C) + (C - A)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Error

Bits error versus A

Bits error versus B

Bits error versus C

Bits error versus F

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 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))) < -0.0

    1. Initial program 45.4

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

    3. Applied sqrt-prod_binary64_282241.9

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

    4. Applied distribute-rgt-neg-in_binary64_276441.9

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

    5. Applied associate-/l*_binary64_275141.9

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

    6. Simplified41.9

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

    8. Applied sqrt-prod_binary64_282241.9

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

    9. Simplified41.9

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

    11. Applied sqrt-prod_binary64_282235.0

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

    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 40.6

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

    3. Applied sqrt-prod_binary64_282238.5

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

    4. Applied distribute-rgt-neg-in_binary64_276438.5

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

    5. Applied associate-/l*_binary64_275138.5

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

    6. Simplified38.5

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

    7. Taylor expanded around -inf 37.0

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

    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 61.2

      \[\leadsto \color{blue}{0}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification46.4

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

Reproduce

herbie shell --seed 2020346 
(FPCore (A B C F)
  :name "ABCF->ab-angle a"
  :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))))