ab-angle->ABCF A

?

Percentage Accurate: 79.8% → 79.8%
Time: 35.6s
Precision: binary64
Cost: 136512

?

\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}\\ t_1 := {t_0}^{4}\\ t_2 := \frac{angle}{180} \cdot \pi\\ {\left(a \cdot \sin t_2\right)}^{2} + {\left(b \cdot \cos \left(\left(\left(t_1 \cdot \sqrt[3]{t_1}\right) \cdot {\left(\sqrt[3]{t_0}\right)}^{2}\right) \cdot \sqrt[3]{t_2}\right)\right)}^{2} \end{array} \]
(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
  (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))
↓
(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (cbrt (cbrt (* PI (* angle 0.005555555555555556)))))
        (t_1 (pow t_0 4.0))
        (t_2 (* (/ angle 180.0) PI)))
   (+
    (pow (* a (sin t_2)) 2.0)
    (pow
     (* b (cos (* (* (* t_1 (cbrt t_1)) (pow (cbrt t_0) 2.0)) (cbrt t_2))))
     2.0))))
double code(double a, double b, double angle) {
	return pow((a * sin(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * cos(((angle / 180.0) * ((double) M_PI)))), 2.0);
}
↓
double code(double a, double b, double angle) {
	double t_0 = cbrt(cbrt((((double) M_PI) * (angle * 0.005555555555555556))));
	double t_1 = pow(t_0, 4.0);
	double t_2 = (angle / 180.0) * ((double) M_PI);
	return pow((a * sin(t_2)), 2.0) + pow((b * cos((((t_1 * cbrt(t_1)) * pow(cbrt(t_0), 2.0)) * cbrt(t_2)))), 2.0);
}

public static double code(double a, double b, double angle) {
	return Math.pow((a * Math.sin(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos(((angle / 180.0) * Math.PI))), 2.0);
}
↓
public static double code(double a, double b, double angle) {
	double t_0 = Math.cbrt(Math.cbrt((Math.PI * (angle * 0.005555555555555556))));
	double t_1 = Math.pow(t_0, 4.0);
	double t_2 = (angle / 180.0) * Math.PI;
	return Math.pow((a * Math.sin(t_2)), 2.0) + Math.pow((b * Math.cos((((t_1 * Math.cbrt(t_1)) * Math.pow(Math.cbrt(t_0), 2.0)) * Math.cbrt(t_2)))), 2.0);
}

function code(a, b, angle)
	return Float64((Float64(a * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * cos(Float64(Float64(angle / 180.0) * pi))) ^ 2.0))
end
↓
function code(a, b, angle)
	t_0 = cbrt(cbrt(Float64(pi * Float64(angle * 0.005555555555555556))))
	t_1 = t_0 ^ 4.0
	t_2 = Float64(Float64(angle / 180.0) * pi)
	return Float64((Float64(a * sin(t_2)) ^ 2.0) + (Float64(b * cos(Float64(Float64(Float64(t_1 * cbrt(t_1)) * (cbrt(t_0) ^ 2.0)) * cbrt(t_2)))) ^ 2.0))
end

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]
↓
code[a_, b_, angle_] := Block[{t$95$0 = N[Power[N[Power[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$1 = N[Power[t$95$0, 4.0], $MachinePrecision]}, Block[{t$95$2 = N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, N[(N[Power[N[(a * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[(N[(t$95$1 * N[Power[t$95$1, 1/3], $MachinePrecision]), $MachinePrecision] * N[Power[N[Power[t$95$0, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[Power[t$95$2, 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]]]

{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}
↓
\begin{array}{l}
t_0 := \sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}\\
t_1 := {t_0}^{4}\\
t_2 := \frac{angle}{180} \cdot \pi\\
{\left(a \cdot \sin t_2\right)}^{2} + {\left(b \cdot \cos \left(\left(\left(t_1 \cdot \sqrt[3]{t_1}\right) \cdot {\left(\sqrt[3]{t_0}\right)}^{2}\right) \cdot \sqrt[3]{t_2}\right)\right)}^{2}
\end{array}

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 16 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 80.0%

    \[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]

  2. Applied egg-rr80.1%

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left({\left(\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}\right)}^{3}\right)}\right)}^{2} \]
    Step-by-step derivation

    [Start]80.0%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]

    add-cube-cbrt [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left(\left(\sqrt[3]{\frac{angle}{180} \cdot \pi} \cdot \sqrt[3]{\frac{angle}{180} \cdot \pi}\right) \cdot \sqrt[3]{\frac{angle}{180} \cdot \pi}\right)}\right)}^{2} \]

    pow3 [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\frac{angle}{180} \cdot \pi}\right)}^{3}\right)}\right)}^{2} \]

    associate-*l/ [=>]79.3%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{\color{blue}{\frac{angle \cdot \pi}{180}}}\right)}^{3}\right)\right)}^{2} \]

    div-inv [=>]79.3%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{\color{blue}{\left(angle \cdot \pi\right) \cdot \frac{1}{180}}}\right)}^{3}\right)\right)}^{2} \]

    associate-*l* [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{\color{blue}{angle \cdot \left(\pi \cdot \frac{1}{180}\right)}}\right)}^{3}\right)\right)}^{2} \]

    metadata-eval [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle \cdot \left(\pi \cdot \color{blue}{0.005555555555555556}\right)}\right)}^{3}\right)\right)}^{2} \]

  3. Applied egg-rr80.2%

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left({\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right)}^{3} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)}\right)}^{2} \]
    Step-by-step derivation

    [Start]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right)}^{2} \]

    add-cube-cbrt [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}} \cdot \sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}}^{3}\right)\right)}^{2} \]

    unpow-prod-down [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}} \cdot \sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{3} \cdot {\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{3}\right)}\right)}^{2} \]

    pow2 [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{2}\right)}}^{3} \cdot {\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{3}\right)\right)}^{2} \]

    associate-*r* [=>]79.4%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\left(angle \cdot \pi\right) \cdot 0.005555555555555556}}}\right)}^{2}\right)}^{3} \cdot {\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{3}\right)\right)}^{2} \]

    metadata-eval [<=]79.4%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\left(angle \cdot \pi\right) \cdot \color{blue}{\frac{1}{180}}}}\right)}^{2}\right)}^{3} \cdot {\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{3}\right)\right)}^{2} \]

    div-inv [<=]79.4%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\frac{angle \cdot \pi}{180}}}}\right)}^{2}\right)}^{3} \cdot {\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{3}\right)\right)}^{2} \]

    associate-*l/ [<=]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\frac{angle}{180} \cdot \pi}}}\right)}^{2}\right)}^{3} \cdot {\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{3}\right)\right)}^{2} \]

    *-commutative [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\pi \cdot \frac{angle}{180}}}}\right)}^{2}\right)}^{3} \cdot {\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}^{3}\right)\right)}^{2} \]

    pow3 [<=]80.2%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right)}^{3} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}} \cdot \sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)}\right)\right)}^{2} \]

    add-cube-cbrt [<=]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right)}^{3} \cdot \color{blue}{\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}}\right)\right)}^{2} \]

    associate-*r* [=>]79.3%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right)}^{3} \cdot \sqrt[3]{\color{blue}{\left(angle \cdot \pi\right) \cdot 0.005555555555555556}}\right)\right)}^{2} \]

    metadata-eval [<=]79.3%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right)}^{3} \cdot \sqrt[3]{\left(angle \cdot \pi\right) \cdot \color{blue}{\frac{1}{180}}}\right)\right)}^{2} \]

  4. Applied egg-rr80.2%

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\color{blue}{\left(\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}\right)}^{4} \cdot \sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}\right)}^{4}}\right) \cdot {\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}}\right)}^{2}\right)} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)\right)}^{2} \]
    Step-by-step derivation

    [Start]80.2%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right)}^{3} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)\right)}^{2} \]

    unpow3 [=>]80.2%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\color{blue}{\left(\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2} \cdot {\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right) \cdot {\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right)} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)\right)}^{2} \]

    add-cube-cbrt [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\left(\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2} \cdot {\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}} \cdot \sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}}\right)}\right) \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)\right)}^{2} \]

    associate-*r* [=>]80.1%

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\color{blue}{\left(\left(\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2} \cdot {\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}\right) \cdot \left(\sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}} \cdot \sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}}\right)\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{\pi \cdot \frac{angle}{180}}}\right)}^{2}}\right)} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)\right)}^{2} \]

  5. Final simplification80.2%

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\left(\left({\left(\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}\right)}^{4} \cdot \sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}\right)}^{4}}\right) \cdot {\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}}\right)}^{2}\right) \cdot \sqrt[3]{\frac{angle}{180} \cdot \pi}\right)\right)}^{2} \]

Alternatives

Alternative 1
Accuracy79.8%
Cost136512
\[\begin{array}{l} t_0 := \sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}\\ t_1 := {t_0}^{4}\\ t_2 := \frac{angle}{180} \cdot \pi\\ {\left(a \cdot \sin t_2\right)}^{2} + {\left(b \cdot \cos \left(\left(\left(t_1 \cdot \sqrt[3]{t_1}\right) \cdot {\left(\sqrt[3]{t_0}\right)}^{2}\right) \cdot \sqrt[3]{t_2}\right)\right)}^{2} \end{array} \]
Alternative 2
Accuracy79.8%
Cost91072
\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ {\left(a \cdot \sin t_0\right)}^{2} + {\left(b \cdot \cos \left(\sqrt[3]{t_0} \cdot {\left({\left(\sqrt[3]{\sqrt[3]{\frac{angle}{180} \cdot \sqrt[3]{{\pi}^{3}}}}\right)}^{2}\right)}^{3}\right)\right)}^{2} \end{array} \]
Alternative 3
Accuracy79.8%
Cost78208
\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ t_1 := \sqrt[3]{t_0}\\ {\left(a \cdot \sin t_0\right)}^{2} + {\left(b \cdot \cos \left(t_1 \cdot {\left({\left(\sqrt[3]{t_1}\right)}^{2}\right)}^{3}\right)\right)}^{2} \end{array} \]
Alternative 4
Accuracy79.8%
Cost78144
\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ {\left(a \cdot \sin t_0\right)}^{2} + {\left(b \cdot \cos \left(\sqrt[3]{t_0} \cdot e^{\log \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{2}\right)}\right)\right)}^{2} \end{array} \]
Alternative 5
Accuracy79.8%
Cost52224
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right)}^{2} \]
Alternative 6
Accuracy79.8%
Cost52160
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \log \left(e^{\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)}\right)\right)}^{2} \]
Alternative 7
Accuracy79.9%
Cost52160
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right)}^{2} \]
Alternative 8
Accuracy79.8%
Cost39360
\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ {\left(a \cdot \sin t_0\right)}^{2} + {\left(b \cdot \cos t_0\right)}^{2} \end{array} \]
Alternative 9
Accuracy79.8%
Cost39360
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right)\right)}^{2} \]
Alternative 10
Accuracy79.7%
Cost26240
\[{b}^{2} + {\left(a \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} \]
Alternative 11
Accuracy79.8%
Cost26240
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {b}^{2} \]
Alternative 12
Accuracy77.1%
Cost20488
\[\begin{array}{l} t_0 := \pi \cdot \left(a \cdot angle\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-32}:\\ \;\;\;\;{b}^{2} + {\left(0.005555555555555556 \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)}^{2}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-87}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot 0\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + t_0 \cdot \left(0.005555555555555556 \cdot \left(0.005555555555555556 \cdot t_0\right)\right)\\ \end{array} \]
Alternative 13
Accuracy77.0%
Cost20105
\[\begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-32} \lor \neg \left(a \leq 1.26 \cdot 10^{-86}\right):\\ \;\;\;\;{b}^{2} + {\left(\pi \cdot \left(a \cdot angle\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot 0\right)}^{2}\\ \end{array} \]
Alternative 14
Accuracy77.1%
Cost20104
\[\begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-32}:\\ \;\;\;\;{b}^{2} + {\left(0.005555555555555556 \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)}^{2}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-87}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot 0\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + {\left(\pi \cdot \left(a \cdot angle\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]
Alternative 15
Accuracy77.1%
Cost20104
\[\begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-33}:\\ \;\;\;\;{b}^{2} + {\left(0.005555555555555556 \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)}^{2}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-86}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot 0\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot \frac{angle}{\frac{180}{\pi}}\right)}^{2}\\ \end{array} \]
Alternative 16
Accuracy56.1%
Cost13248
\[{b}^{2} + {\left(a \cdot 0\right)}^{2} \]

Reproduce?

herbie shell --seed 2023271 
(FPCore (a b angle)
  :name "ab-angle->ABCF A"
  :precision binary64
  (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))