Average Error: 14.0 → 0.7
Time: 1.1min
Precision: binary64
Cost: 33160
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)} \]
↓
\[\begin{array}{l} t_0 := \frac{1}{\sin B}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -2.202497790196905 \cdot 10^{+87}:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;t_0 \cdot \frac{F}{\mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)} - t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 - t_1\\ \end{array} \]
(FPCore (F B x)
 :precision binary64
 (+
  (- (* x (/ 1.0 (tan B))))
  (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))
↓
(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (sin B))) (t_1 (/ x (tan B))))
   (if (<= F -2.202497790196905e+87)
     (- (/ -1.0 (sin B)) t_1)
     (if (<= F 3.5e-5)
       (- (* t_0 (/ F (hypot F (sqrt (fma 2.0 x 2.0))))) t_1)
       (- t_0 t_1)))))
double code(double F, double B, double x) {
	return -(x * (1.0 / tan(B))) + ((F / sin(B)) * pow((((F * F) + 2.0) + (2.0 * x)), -(1.0 / 2.0)));
}
↓
double code(double F, double B, double x) {
	double t_0 = 1.0 / sin(B);
	double t_1 = x / tan(B);
	double tmp;
	if (F <= -2.202497790196905e+87) {
		tmp = (-1.0 / sin(B)) - t_1;
	} else if (F <= 3.5e-5) {
		tmp = (t_0 * (F / hypot(F, sqrt(fma(2.0, x, 2.0))))) - t_1;
	} else {
		tmp = t_0 - t_1;
	}
	return tmp;
}

function code(F, B, x)
	return Float64(Float64(-Float64(x * Float64(1.0 / tan(B)))) + Float64(Float64(F / sin(B)) * (Float64(Float64(Float64(F * F) + 2.0) + Float64(2.0 * x)) ^ Float64(-Float64(1.0 / 2.0)))))
end
↓
function code(F, B, x)
	t_0 = Float64(1.0 / sin(B))
	t_1 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -2.202497790196905e+87)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_1);
	elseif (F <= 3.5e-5)
		tmp = Float64(Float64(t_0 * Float64(F / hypot(F, sqrt(fma(2.0, x, 2.0))))) - t_1);
	else
		tmp = Float64(t_0 - t_1);
	end
	return tmp
end

code[F_, B_, x_] := N[((-N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) + N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], (-N[(1.0 / 2.0), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[F_, B_, x_] := Block[{t$95$0 = N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -2.202497790196905e+87], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, 3.5e-5], N[(N[(t$95$0 * N[(F / N[Sqrt[F ^ 2 + N[Sqrt[N[(2.0 * x + 2.0), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$0 - t$95$1), $MachinePrecision]]]]]

\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}
↓
\begin{array}{l}
t_0 := \frac{1}{\sin B}\\
t_1 := \frac{x}{\tan B}\\
\mathbf{if}\;F \leq -2.202497790196905 \cdot 10^{+87}:\\
\;\;\;\;\frac{-1}{\sin B} - t_1\\

\mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\
\;\;\;\;t_0 \cdot \frac{F}{\mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)} - t_1\\

\mathbf{else}:\\
\;\;\;\;t_0 - t_1\\


\end{array}

Error

Derivation

  1. Split input into 3 regimes

  2. if F < -2.20249779019690519e87

    1. Initial program 32.6

      \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)} \]

    2. Applied egg-rr25.9

      \[\leadsto \left(-x \cdot \frac{1}{\tan B}\right) + \color{blue}{\frac{F}{\frac{\sin B}{{\left(\mathsf{fma}\left(F, F, \mathsf{fma}\left(2, x, 2\right)\right)\right)}^{-0.5}}}} \]

    3. Applied egg-rr13.3

      \[\leadsto \left(-x \cdot \frac{1}{\tan B}\right) + \color{blue}{\frac{1}{\sin B} \cdot \frac{F}{\mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)}} \]

    4. Applied egg-rr13.2

      \[\leadsto \left(-\color{blue}{\frac{x}{\tan B}}\right) + \frac{1}{\sin B} \cdot \frac{F}{\mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)} \]

    5. Taylor expanded in F around -inf 0.2

      \[\leadsto \left(-\frac{x}{\tan B}\right) + \color{blue}{\frac{-1}{\sin B}} \]

    if -2.20249779019690519e87 < F < 3.4999999999999997e-5

    1. Initial program 0.8

      \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)} \]

    2. Applied egg-rr0.4

      \[\leadsto \left(-x \cdot \frac{1}{\tan B}\right) + \color{blue}{\frac{F}{\frac{\sin B}{{\left(\mathsf{fma}\left(F, F, \mathsf{fma}\left(2, x, 2\right)\right)\right)}^{-0.5}}}} \]

    3. Applied egg-rr1.0

      \[\leadsto \left(-x \cdot \frac{1}{\tan B}\right) + \color{blue}{\frac{1}{\sin B} \cdot \frac{F}{\mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)}} \]

    4. Applied egg-rr0.9

      \[\leadsto \left(-\color{blue}{\frac{x}{\tan B}}\right) + \frac{1}{\sin B} \cdot \frac{F}{\mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)} \]

    if 3.4999999999999997e-5 < F

    1. Initial program 25.3

      \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)} \]

    2. Applied egg-rr25.3

      \[\leadsto \left(-\color{blue}{\frac{1}{\frac{\tan B}{x}}}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)} \]

    3. Taylor expanded in F around inf 0.9

      \[\leadsto \left(-\frac{1}{\frac{\tan B}{x}}\right) + \color{blue}{\frac{1}{\sin B}} \]

    4. Applied egg-rr0.8

      \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;F \leq -2.202497790196905 \cdot 10^{+87}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{1}{\sin B} \cdot \frac{F}{\mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)} - \frac{x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{\tan B}\\ \end{array} \]

Alternatives

Alternative 1
Error0.7
Cost33032
\[\begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -2.202497790196905 \cdot 10^{+87}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{F}{\mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)}}{\sin B} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \]
Alternative 2
Error0.4
Cost20616
\[\begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{F}{\sin B} \cdot {\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \]
Alternative 3
Error0.7
Cost20552
\[\begin{array}{l} t_0 := \frac{1}{\sin B}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -3.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;t_0 \cdot \left(F \cdot \sqrt{\frac{1}{2 + x \cdot 2}}\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 - t_1\\ \end{array} \]
Alternative 4
Error0.8
Cost20424
\[\begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -3.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{F}{\sin B \cdot \sqrt{2 + x \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \]
Alternative 5
Error7.5
Cost14480
\[\begin{array}{l} t_0 := \frac{F}{\sin B} \cdot {\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5} - \frac{x}{B}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -9.6 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq -4.7 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 7 \cdot 10^{-85}:\\ \;\;\;\;\cos B \cdot \frac{-x}{\sin B}\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_1\\ \end{array} \]
Alternative 6
Error6.2
Cost14344
\[\begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -6.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + {\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \]
Alternative 7
Error7.5
Cost14288
\[\begin{array}{l} t_0 := \frac{F}{\sin B} \cdot \sqrt{\frac{1}{2 + x \cdot 2}} - \frac{x}{B}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -9.6 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq -4.7 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 7 \cdot 10^{-85}:\\ \;\;\;\;\cos B \cdot \frac{-x}{\sin B}\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_1\\ \end{array} \]
Alternative 8
Error15.3
Cost13512
\[\begin{array}{l} \mathbf{if}\;F \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;\cos B \cdot \frac{-x}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{\tan B}\\ \end{array} \]
Alternative 9
Error10.8
Cost13512
\[\begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -7.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;\cos B \cdot \frac{-x}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \]
Alternative 10
Error20.2
Cost13448
\[\begin{array}{l} \mathbf{if}\;F \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;\cos B \cdot \frac{-x}{\sin B}\\ \mathbf{elif}\;F \leq 1.1201723804836918 \cdot 10^{+53}:\\ \;\;\;\;\frac{F}{F \cdot \sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.560669744230036 \cdot 10^{+125}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \]
Alternative 11
Error27.0
Cost8332
\[\begin{array}{l} t_0 := \frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{if}\;F \leq -5.4841200338751936 \cdot 10^{+66}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 4 \cdot 10^{-289}:\\ \;\;\;\;\frac{-1}{B} - x \cdot \frac{1}{\tan B}\\ \mathbf{elif}\;F \leq 8.6 \cdot 10^{-213}:\\ \;\;\;\;{\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5} \cdot \left(\frac{F}{B} + 0.16666666666666666 \cdot \left(F \cdot B\right)\right) - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 1.1201723804836918 \cdot 10^{+53}:\\ \;\;\;\;\frac{F}{F \cdot \sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.560669744230036 \cdot 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \]
Alternative 12
Error27.0
Cost7948
\[\begin{array}{l} t_0 := \frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{if}\;F \leq -5.4841200338751936 \cdot 10^{+66}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 4 \cdot 10^{-289}:\\ \;\;\;\;\frac{-1}{B} - x \cdot \frac{1}{\tan B}\\ \mathbf{elif}\;F \leq 8.6 \cdot 10^{-213}:\\ \;\;\;\;{\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 1.1201723804836918 \cdot 10^{+53}:\\ \;\;\;\;\frac{F}{F \cdot \sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.560669744230036 \cdot 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \]
Alternative 13
Error27.1
Cost7768
\[\begin{array}{l} t_0 := \frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ t_1 := \frac{1}{\sin B} - \frac{x}{B}\\ \mathbf{if}\;F \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.2 \cdot 10^{-281}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 8.6 \cdot 10^{-213}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{elif}\;F \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 1.1201723804836918 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq 6.560669744230036 \cdot 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error27.2
Cost7768
\[\begin{array}{l} t_0 := \frac{1}{\sin B} - \frac{x}{B}\\ t_1 := \frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{if}\;F \leq -5.4841200338751936 \cdot 10^{+66}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.2 \cdot 10^{-281}:\\ \;\;\;\;\frac{-1}{B} - x \cdot \frac{1}{\tan B}\\ \mathbf{elif}\;F \leq 8.6 \cdot 10^{-213}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{elif}\;F \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq 1.1201723804836918 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 6.560669744230036 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 15
Error27.2
Cost7768
\[\begin{array}{l} t_0 := \frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{if}\;F \leq -5.4841200338751936 \cdot 10^{+66}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.2 \cdot 10^{-281}:\\ \;\;\;\;\frac{-1}{B} - x \cdot \frac{1}{\tan B}\\ \mathbf{elif}\;F \leq 8.6 \cdot 10^{-213}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{elif}\;F \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 1.1201723804836918 \cdot 10^{+53}:\\ \;\;\;\;\frac{F}{F \cdot \sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.560669744230036 \cdot 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \]
Alternative 16
Error32.0
Cost7112
\[\begin{array}{l} \mathbf{if}\;F \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{-1}{\sin B}\\ \mathbf{elif}\;F \leq 8.1 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \]
Alternative 17
Error29.5
Cost7112
\[\begin{array}{l} \mathbf{if}\;F \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 8.1 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \]
Alternative 18
Error38.4
Cost6988
\[\begin{array}{l} \mathbf{if}\;F \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;B \cdot -0.16666666666666666 - \frac{x + 1}{B}\\ \mathbf{elif}\;F \leq 1.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{elif}\;F \leq 1.2844137419186442 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B}\\ \end{array} \]
Alternative 19
Error35.8
Cost6988
\[\begin{array}{l} \mathbf{if}\;F \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{-1}{\sin B}\\ \mathbf{elif}\;F \leq 1.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{elif}\;F \leq 1.2844137419186442 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B}\\ \end{array} \]
Alternative 20
Error39.5
Cost712
\[\begin{array}{l} \mathbf{if}\;F \leq -2.1 \cdot 10^{-44}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 1.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{B}\\ \end{array} \]
Alternative 21
Error39.5
Cost712
\[\begin{array}{l} \mathbf{if}\;F \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;B \cdot -0.16666666666666666 - \frac{x + 1}{B}\\ \mathbf{elif}\;F \leq 1.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{B}\\ \end{array} \]
Alternative 22
Error39.5
Cost584
\[\begin{array}{l} \mathbf{if}\;F \leq -2.1 \cdot 10^{-44}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 1.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \]
Alternative 23
Error48.8
Cost520
\[\begin{array}{l} t_0 := \frac{-x}{B}\\ \mathbf{if}\;x \leq -4.38281952032195 \cdot 10^{-266}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.266815735033279 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{B}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 24
Error43.2
Cost520
\[\begin{array}{l} \mathbf{if}\;F \leq -2.1 \cdot 10^{-44}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 1.2844137419186442 \cdot 10^{+154}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B}\\ \end{array} \]
Alternative 25
Error51.8
Cost324
\[\begin{array}{l} \mathbf{if}\;F \leq 8.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{-1}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B}\\ \end{array} \]
Alternative 26
Error57.0
Cost192
\[\frac{1}{B} \]

Error

Reproduce

herbie shell --seed 2022300 
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))