ab-angle->ABCF C

Percentage Accurate: 80.2% → 80.2%

Time: 39.1s

Alternatives: 14

Speedup: 0.5×

• Could not converge on a ground truth

  1. reg0 = (bf #e0.1741148559334973200396490256025572307408)
  2. reg1 = (bf "4.162220192430535132532751174118990258173e248")
  3. reg2 = (bf 345117361177865257860039468436684800)

• 36.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ {\left(a \cdot \cos t\_0\right)}^{2} + {\left(b \cdot \sin t\_0\right)}^{2} \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* PI (/ angle 180.0))))
   (+ (pow (* a (cos t_0)) 2.0) (pow (* b (sin t_0)) 2.0))))

C

double code(double a, double b, double angle) {
	double t_0 = ((double) M_PI) * (angle / 180.0);
	return pow((a * cos(t_0)), 2.0) + pow((b * sin(t_0)), 2.0);
}

Java

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

Python

def code(a, b, angle):
	t_0 = math.pi * (angle / 180.0)
	return math.pow((a * math.cos(t_0)), 2.0) + math.pow((b * math.sin(t_0)), 2.0)

Julia

function code(a, b, angle)
	t_0 = Float64(pi * Float64(angle / 180.0))
	return Float64((Float64(a * cos(t_0)) ^ 2.0) + (Float64(b * sin(t_0)) ^ 2.0))
end

MATLAB

function tmp = code(a, b, angle)
	t_0 = pi * (angle / 180.0);
	tmp = ((a * cos(t_0)) ^ 2.0) + ((b * sin(t_0)) ^ 2.0);
end

Wolfram

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

Initial Program: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ {\left(a \cdot \cos t\_0\right)}^{2} + {\left(b \cdot \sin t\_0\right)}^{2} \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* PI (/ angle 180.0))))
   (+ (pow (* a (cos t_0)) 2.0) (pow (* b (sin t_0)) 2.0))))

C

double code(double a, double b, double angle) {
	double t_0 = ((double) M_PI) * (angle / 180.0);
	return pow((a * cos(t_0)), 2.0) + pow((b * sin(t_0)), 2.0);
}

Java

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

Python

def code(a, b, angle):
	t_0 = math.pi * (angle / 180.0)
	return math.pow((a * math.cos(t_0)), 2.0) + math.pow((b * math.sin(t_0)), 2.0)

Julia

function code(a, b, angle)
	t_0 = Float64(pi * Float64(angle / 180.0))
	return Float64((Float64(a * cos(t_0)) ^ 2.0) + (Float64(b * sin(t_0)) ^ 2.0))
end

MATLAB

function tmp = code(a, b, angle)
	t_0 = pi * (angle / 180.0);
	tmp = ((a * cos(t_0)) ^ 2.0) + ((b * sin(t_0)) ^ 2.0);
end

Wolfram

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

Alternative 1: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} t_0 := {\left(angle\_m \cdot 0.005555555555555556\right)}^{0.16666666666666666}\\ {\left(a \cdot \cos \left(\pi \cdot \left(t\_0 \cdot \left(t\_0 \cdot {\left(\sqrt[3]{angle\_m \cdot 0.005555555555555556}\right)}^{2}\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\right)\right)}^{2} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (let* ((t_0 (pow (* angle_m 0.005555555555555556) 0.16666666666666666)))
   (+
    (pow
     (*
      a
      (cos
       (*
        PI
        (* t_0 (* t_0 (pow (cbrt (* angle_m 0.005555555555555556)) 2.0))))))
     2.0)
    (pow (* b (sin (* PI (* angle_m 0.005555555555555556)))) 2.0))))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double t_0 = pow((angle_m * 0.005555555555555556), 0.16666666666666666);
	return pow((a * cos((((double) M_PI) * (t_0 * (t_0 * pow(cbrt((angle_m * 0.005555555555555556)), 2.0)))))), 2.0) + pow((b * sin((((double) M_PI) * (angle_m * 0.005555555555555556)))), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double t_0 = Math.pow((angle_m * 0.005555555555555556), 0.16666666666666666);
	return Math.pow((a * Math.cos((Math.PI * (t_0 * (t_0 * Math.pow(Math.cbrt((angle_m * 0.005555555555555556)), 2.0)))))), 2.0) + Math.pow((b * Math.sin((Math.PI * (angle_m * 0.005555555555555556)))), 2.0);
}

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	t_0 = Float64(angle_m * 0.005555555555555556) ^ 0.16666666666666666
	return Float64((Float64(a * cos(Float64(pi * Float64(t_0 * Float64(t_0 * (cbrt(Float64(angle_m * 0.005555555555555556)) ^ 2.0)))))) ^ 2.0) + (Float64(b * sin(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 2.0))
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := Block[{t$95$0 = N[Power[N[(angle$95$m * 0.005555555555555556), $MachinePrecision], 0.16666666666666666], $MachinePrecision]}, N[(N[Power[N[(a * N[Cos[N[(Pi * N[(t$95$0 * N[(t$95$0 * N[Power[N[Power[N[(angle$95$m * 0.005555555555555556), $MachinePrecision], 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. metadata-eval 78.4%

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

   2. div-inv 78.3%

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

   3. add-cube-cbrt 78.4%

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

   4. pow3 78.4%

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

   5. div-inv 78.5%

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

   6. metadata-eval 78.5%

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

6. Applied egg-rr 78.5%

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

   1. cube-mult 78.5%

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

   2. add-sqr-sqrt 39.4%

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

   3. associate-*l* 39.4%

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

   4. pow1/3 39.4%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(\sqrt{\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   5. sqrt-pow1 39.4%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   6. metadata-eval 39.4%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{\color{blue}{0.16666666666666666}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   7. pow1/3 39.6%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left(\sqrt{\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   8. sqrt-pow1 39.6%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   9. metadata-eval 39.6%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{\color{blue}{0.16666666666666666}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   10. pow2 39.6%

       \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \color{blue}{{\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

8. Applied egg-rr 39.6%

   \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \color{blue}{\left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}\right)\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]
9. Add Preprocessing

Alternative 2: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} t_0 := \sqrt[3]{angle\_m \cdot 0.005555555555555556}\\ {\left(b \cdot \sin \left(\pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(a \cdot \cos \left(\pi \cdot \left(t\_0 \cdot {t\_0}^{2}\right)\right)\right)}^{2} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (let* ((t_0 (cbrt (* angle_m 0.005555555555555556))))
   (+
    (pow (* b (sin (* PI (* angle_m 0.005555555555555556)))) 2.0)
    (pow (* a (cos (* PI (* t_0 (pow t_0 2.0))))) 2.0))))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double t_0 = cbrt((angle_m * 0.005555555555555556));
	return pow((b * sin((((double) M_PI) * (angle_m * 0.005555555555555556)))), 2.0) + pow((a * cos((((double) M_PI) * (t_0 * pow(t_0, 2.0))))), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double t_0 = Math.cbrt((angle_m * 0.005555555555555556));
	return Math.pow((b * Math.sin((Math.PI * (angle_m * 0.005555555555555556)))), 2.0) + Math.pow((a * Math.cos((Math.PI * (t_0 * Math.pow(t_0, 2.0))))), 2.0);
}

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	t_0 = cbrt(Float64(angle_m * 0.005555555555555556))
	return Float64((Float64(b * sin(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 2.0) + (Float64(a * cos(Float64(pi * Float64(t_0 * (t_0 ^ 2.0))))) ^ 2.0))
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := Block[{t$95$0 = N[Power[N[(angle$95$m * 0.005555555555555556), $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[N[(Pi * N[(t$95$0 * N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. metadata-eval 78.4%

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

   2. div-inv 78.3%

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

   3. add-cube-cbrt 78.4%

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

   4. pow3 78.4%

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

   5. div-inv 78.5%

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

   6. metadata-eval 78.5%

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

6. Applied egg-rr 78.5%

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

   1. unpow3 78.5%

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

   2. pow2 78.5%

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

8. Applied egg-rr 78.5%

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

9. Final simplification 78.5%

   \[\leadsto {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(a \cdot \cos \left(\pi \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}\right)\right)\right)}^{2} \]
10. Add Preprocessing

Alternative 3: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ {\left(b \cdot \sin \left(\pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(a \cdot \cos \left(\pi \cdot {\left(\sqrt[3]{angle\_m \cdot 0.005555555555555556}\right)}^{3}\right)\right)}^{2} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+
  (pow (* b (sin (* PI (* angle_m 0.005555555555555556)))) 2.0)
  (pow
   (* a (cos (* PI (pow (cbrt (* angle_m 0.005555555555555556)) 3.0))))
   2.0)))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	return pow((b * sin((((double) M_PI) * (angle_m * 0.005555555555555556)))), 2.0) + pow((a * cos((((double) M_PI) * pow(cbrt((angle_m * 0.005555555555555556)), 3.0)))), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	return Math.pow((b * Math.sin((Math.PI * (angle_m * 0.005555555555555556)))), 2.0) + Math.pow((a * Math.cos((Math.PI * Math.pow(Math.cbrt((angle_m * 0.005555555555555556)), 3.0)))), 2.0);
}

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	return Float64((Float64(b * sin(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 2.0) + (Float64(a * cos(Float64(pi * (cbrt(Float64(angle_m * 0.005555555555555556)) ^ 3.0)))) ^ 2.0))
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[N[(Pi * N[Power[N[Power[N[(angle$95$m * 0.005555555555555556), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. metadata-eval 78.4%

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

   2. div-inv 78.3%

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

   3. add-cube-cbrt 78.4%

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

   4. pow3 78.4%

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

   5. div-inv 78.5%

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

   6. metadata-eval 78.5%

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

6. Applied egg-rr 78.5%

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

7. Final simplification 78.5%

   \[\leadsto {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(a \cdot \cos \left(\pi \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{3}\right)\right)}^{2} \]
8. Add Preprocessing

Alternative 4: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ {\left(a \cdot \cos \left(\pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(0.005555555555555556 \cdot \left(\pi \cdot angle\_m\right)\right)\right)\right)\right)}^{2} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+
  (pow (* a (cos (* PI (* angle_m 0.005555555555555556)))) 2.0)
  (pow
   (* b (sin (expm1 (log1p (* 0.005555555555555556 (* PI angle_m))))))
   2.0)))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	return pow((a * cos((((double) M_PI) * (angle_m * 0.005555555555555556)))), 2.0) + pow((b * sin(expm1(log1p((0.005555555555555556 * (((double) M_PI) * angle_m)))))), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	return Math.pow((a * Math.cos((Math.PI * (angle_m * 0.005555555555555556)))), 2.0) + Math.pow((b * Math.sin(Math.expm1(Math.log1p((0.005555555555555556 * (Math.PI * angle_m)))))), 2.0);
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	return math.pow((a * math.cos((math.pi * (angle_m * 0.005555555555555556)))), 2.0) + math.pow((b * math.sin(math.expm1(math.log1p((0.005555555555555556 * (math.pi * angle_m)))))), 2.0)

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	return Float64((Float64(a * cos(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 2.0) + (Float64(b * sin(expm1(log1p(Float64(0.005555555555555556 * Float64(pi * angle_m)))))) ^ 2.0))
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[N[(a * N[Cos[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Exp[N[Log[1 + N[(0.005555555555555556 * N[(Pi * angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. expm1-log1p-u 65.2%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}\right)}^{2} \]

   2. associate-*r* 65.2%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\left(\pi \cdot angle\right) \cdot 0.005555555555555556}\right)\right)\right)\right)}^{2} \]

   3. *-commutative 65.2%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{0.005555555555555556 \cdot \left(\pi \cdot angle\right)}\right)\right)\right)\right)}^{2} \]

6. Applied egg-rr 65.2%

   \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)\right)}\right)}^{2} \]
7. Add Preprocessing

Alternative 5: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} t_0 := \pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\\ {\left(b \cdot \sin t\_0\right)}^{2} + {\left(a \cdot \cos t\_0\right)}^{2} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (let* ((t_0 (* PI (* angle_m 0.005555555555555556))))
   (+ (pow (* b (sin t_0)) 2.0) (pow (* a (cos t_0)) 2.0))))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double t_0 = ((double) M_PI) * (angle_m * 0.005555555555555556);
	return pow((b * sin(t_0)), 2.0) + pow((a * cos(t_0)), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double t_0 = Math.PI * (angle_m * 0.005555555555555556);
	return Math.pow((b * Math.sin(t_0)), 2.0) + Math.pow((a * Math.cos(t_0)), 2.0);
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	t_0 = math.pi * (angle_m * 0.005555555555555556)
	return math.pow((b * math.sin(t_0)), 2.0) + math.pow((a * math.cos(t_0)), 2.0)

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	t_0 = Float64(pi * Float64(angle_m * 0.005555555555555556))
	return Float64((Float64(b * sin(t_0)) ^ 2.0) + (Float64(a * cos(t_0)) ^ 2.0))
end

MATLAB

angle_m = abs(angle);
function tmp = code(a, b, angle_m)
	t_0 = pi * (angle_m * 0.005555555555555556);
	tmp = ((b * sin(t_0)) ^ 2.0) + ((a * cos(t_0)) ^ 2.0);
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := Block[{t$95$0 = N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, N[(N[Power[N[(b * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing

5. Final simplification 78.4%

   \[\leadsto {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]
6. Add Preprocessing

Alternative 6: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} t_0 := \pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\\ {\left(\mathsf{hypot}\left(a \cdot \cos t\_0, b \cdot \sin t\_0\right)\right)}^{2} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (let* ((t_0 (* PI (* angle_m 0.005555555555555556))))
   (pow (hypot (* a (cos t_0)) (* b (sin t_0))) 2.0)))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double t_0 = ((double) M_PI) * (angle_m * 0.005555555555555556);
	return pow(hypot((a * cos(t_0)), (b * sin(t_0))), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double t_0 = Math.PI * (angle_m * 0.005555555555555556);
	return Math.pow(Math.hypot((a * Math.cos(t_0)), (b * Math.sin(t_0))), 2.0);
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	t_0 = math.pi * (angle_m * 0.005555555555555556)
	return math.pow(math.hypot((a * math.cos(t_0)), (b * math.sin(t_0))), 2.0)

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	t_0 = Float64(pi * Float64(angle_m * 0.005555555555555556))
	return hypot(Float64(a * cos(t_0)), Float64(b * sin(t_0))) ^ 2.0
end

MATLAB

angle_m = abs(angle);
function tmp = code(a, b, angle_m)
	t_0 = pi * (angle_m * 0.005555555555555556);
	tmp = hypot((a * cos(t_0)), (b * sin(t_0))) ^ 2.0;
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := Block[{t$95$0 = N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, N[Power[N[Sqrt[N[(a * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision] ^ 2 + N[(b * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision], 2.0], $MachinePrecision]]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. metadata-eval 78.4%

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

   2. div-inv 78.3%

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

   3. add-cube-cbrt 78.4%

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

   4. pow3 78.4%

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

   5. div-inv 78.5%

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

   6. metadata-eval 78.5%

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

6. Applied egg-rr 78.5%

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

8. Applied egg-rr 78.4%

   \[\leadsto \color{blue}{{\left(\mathsf{hypot}\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right), b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}^{2}} \]
9. Add Preprocessing

Alternative 7: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ {\left(\mathsf{hypot}\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\_m\right)\right), b \cdot \sin \left(\pi \cdot \frac{angle\_m}{180}\right)\right)\right)}^{2} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (pow
  (hypot
   (* a (cos (* 0.005555555555555556 (* PI angle_m))))
   (* b (sin (* PI (/ angle_m 180.0)))))
  2.0))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	return pow(hypot((a * cos((0.005555555555555556 * (((double) M_PI) * angle_m)))), (b * sin((((double) M_PI) * (angle_m / 180.0))))), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	return Math.pow(Math.hypot((a * Math.cos((0.005555555555555556 * (Math.PI * angle_m)))), (b * Math.sin((Math.PI * (angle_m / 180.0))))), 2.0);
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	return math.pow(math.hypot((a * math.cos((0.005555555555555556 * (math.pi * angle_m)))), (b * math.sin((math.pi * (angle_m / 180.0))))), 2.0)

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	return hypot(Float64(a * cos(Float64(0.005555555555555556 * Float64(pi * angle_m)))), Float64(b * sin(Float64(pi * Float64(angle_m / 180.0))))) ^ 2.0
end

MATLAB

angle_m = abs(angle);
function tmp = code(a, b, angle_m)
	tmp = hypot((a * cos((0.005555555555555556 * (pi * angle_m)))), (b * sin((pi * (angle_m / 180.0))))) ^ 2.0;
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[Power[N[Sqrt[N[(a * N[Cos[N[(0.005555555555555556 * N[(Pi * angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2 + N[(b * N[Sin[N[(Pi * N[(angle$95$m / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision], 2.0], $MachinePrecision]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. metadata-eval 78.4%

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

   2. div-inv 78.4%

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

   3. add-cbrt-cube 54.3%

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

   4. pow1/3 42.1%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \color{blue}{\left({\left(\left(\left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \left(\pi \cdot \frac{angle}{180}\right)\right)}^{0.3333333333333333}\right)}\right)}^{2} \]

   5. pow3 42.1%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left({\color{blue}{\left({\left(\pi \cdot \frac{angle}{180}\right)}^{3}\right)}}^{0.3333333333333333}\right)\right)}^{2} \]

   6. div-inv 42.1%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left({\left({\left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)}^{3}\right)}^{0.3333333333333333}\right)\right)}^{2} \]

   7. metadata-eval 42.1%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left({\left({\left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)}^{3}\right)}^{0.3333333333333333}\right)\right)}^{2} \]

   8. associate-*r* 42.2%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left({\left({\color{blue}{\left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)}}^{3}\right)}^{0.3333333333333333}\right)\right)}^{2} \]

   9. *-commutative 42.2%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left({\left({\color{blue}{\left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}}^{3}\right)}^{0.3333333333333333}\right)\right)}^{2} \]

6. Applied egg-rr 42.2%

   \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \color{blue}{\left({\left({\left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}^{3}\right)}^{0.3333333333333333}\right)}\right)}^{2} \]
7. Step-by-step derivation

   1. unpow1/3 54.4%

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

   2. rem-cbrt-cube 78.3%

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

   3. *-commutative 78.3%

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

   4. metadata-eval 78.3%

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

   5. div-inv 78.3%

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

   6. add-cube-cbrt 78.1%

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

   7. associate-/l* 78.0%

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

   8. pow2 78.0%

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

8. Applied egg-rr 78.0%

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

   1. *-un-lft-identity 78.0%

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

   2. add-sqr-sqrt 78.0%

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

   3. pow2 78.0%

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

10. Applied egg-rr 78.3%

    \[\leadsto \color{blue}{1 \cdot {\left(\mathsf{hypot}\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right), b \cdot \sin \left(\frac{\pi \cdot angle}{180}\right)\right)\right)}^{2}} \]
11. Step-by-step derivation

    1. *-lft-identity 78.3%

       \[\leadsto \color{blue}{{\left(\mathsf{hypot}\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right), b \cdot \sin \left(\frac{\pi \cdot angle}{180}\right)\right)\right)}^{2}} \]

    2. *-commutative 78.3%

       \[\leadsto {\left(\mathsf{hypot}\left(a \cdot \cos \color{blue}{\left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)}, b \cdot \sin \left(\frac{\pi \cdot angle}{180}\right)\right)\right)}^{2} \]

    3. *-commutative 78.3%

       \[\leadsto {\left(\mathsf{hypot}\left(a \cdot \cos \left(\color{blue}{\left(0.005555555555555556 \cdot angle\right)} \cdot \pi\right), b \cdot \sin \left(\frac{\pi \cdot angle}{180}\right)\right)\right)}^{2} \]

    4. associate-*r* 78.2%

       \[\leadsto {\left(\mathsf{hypot}\left(a \cdot \cos \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}, b \cdot \sin \left(\frac{\pi \cdot angle}{180}\right)\right)\right)}^{2} \]

    5. associate-/l* 78.3%

       \[\leadsto {\left(\mathsf{hypot}\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right), b \cdot \sin \color{blue}{\left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} \]

12. Simplified 78.3%

    \[\leadsto \color{blue}{{\left(\mathsf{hypot}\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right), b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)}^{2}} \]

13. Final simplification 78.3%

    \[\leadsto {\left(\mathsf{hypot}\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right), b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)}^{2} \]
14. Add Preprocessing

Alternative 8: 80.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ {\left(b \cdot \sin \left(\pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\right)\right)}^{2} + {a}^{2} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+ (pow (* b (sin (* PI (* angle_m 0.005555555555555556)))) 2.0) (pow a 2.0)))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	return pow((b * sin((((double) M_PI) * (angle_m * 0.005555555555555556)))), 2.0) + pow(a, 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	return Math.pow((b * Math.sin((Math.PI * (angle_m * 0.005555555555555556)))), 2.0) + Math.pow(a, 2.0);
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	return math.pow((b * math.sin((math.pi * (angle_m * 0.005555555555555556)))), 2.0) + math.pow(a, 2.0)

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	return Float64((Float64(b * sin(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 2.0) + (a ^ 2.0))
end

MATLAB

angle_m = abs(angle);
function tmp = code(a, b, angle_m)
	tmp = ((b * sin((pi * (angle_m * 0.005555555555555556)))) ^ 2.0) + (a ^ 2.0);
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing

5. Taylor expanded in angle around 0 78.2%

   \[\leadsto {\color{blue}{a}}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

6. Final simplification 78.2%

   \[\leadsto {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {a}^{2} \]
7. Add Preprocessing

Alternative 9: 58.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} \mathbf{if}\;a \leq 1.85 \cdot 10^{-153}:\\ \;\;\;\;{\left(b \cdot \sin \left(angle\_m \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(b \cdot \left(0.005555555555555556 \cdot \left(\pi \cdot angle\_m\right)\right)\right)}^{2}\\ \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (if (<= a 1.85e-153)
   (pow (* b (sin (* angle_m (* PI 0.005555555555555556)))) 2.0)
   (+ (pow a 2.0) (pow (* b (* 0.005555555555555556 (* PI angle_m))) 2.0))))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double tmp;
	if (a <= 1.85e-153) {
		tmp = pow((b * sin((angle_m * (((double) M_PI) * 0.005555555555555556)))), 2.0);
	} else {
		tmp = pow(a, 2.0) + pow((b * (0.005555555555555556 * (((double) M_PI) * angle_m))), 2.0);
	}
	return tmp;
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double tmp;
	if (a <= 1.85e-153) {
		tmp = Math.pow((b * Math.sin((angle_m * (Math.PI * 0.005555555555555556)))), 2.0);
	} else {
		tmp = Math.pow(a, 2.0) + Math.pow((b * (0.005555555555555556 * (Math.PI * angle_m))), 2.0);
	}
	return tmp;
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	tmp = 0
	if a <= 1.85e-153:
		tmp = math.pow((b * math.sin((angle_m * (math.pi * 0.005555555555555556)))), 2.0)
	else:
		tmp = math.pow(a, 2.0) + math.pow((b * (0.005555555555555556 * (math.pi * angle_m))), 2.0)
	return tmp

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	tmp = 0.0
	if (a <= 1.85e-153)
		tmp = Float64(b * sin(Float64(angle_m * Float64(pi * 0.005555555555555556)))) ^ 2.0;
	else
		tmp = Float64((a ^ 2.0) + (Float64(b * Float64(0.005555555555555556 * Float64(pi * angle_m))) ^ 2.0));
	end
	return tmp
end

MATLAB

angle_m = abs(angle);
function tmp_2 = code(a, b, angle_m)
	tmp = 0.0;
	if (a <= 1.85e-153)
		tmp = (b * sin((angle_m * (pi * 0.005555555555555556)))) ^ 2.0;
	else
		tmp = (a ^ 2.0) + ((b * (0.005555555555555556 * (pi * angle_m))) ^ 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := If[LessEqual[a, 1.85e-153], N[Power[N[(b * N[Sin[N[(angle$95$m * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[(N[Power[a, 2.0], $MachinePrecision] + N[Power[N[(b * N[(0.005555555555555556 * N[(Pi * angle$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.8500000000000001e-153

   1. Initial program 81.0%

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

   3. Simplified 81.0%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. metadata-eval 81.0%

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

      2. div-inv 81.0%

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

      3. add-cube-cbrt 81.2%

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

      4. pow3 81.2%

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

      5. div-inv 81.1%

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

      6. metadata-eval 81.1%

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

   6. Applied egg-rr 81.1%

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

      1. cube-mult 81.2%

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

      2. add-sqr-sqrt 40.0%

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

      3. associate-*l* 39.9%

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

      4. pow1/3 40.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(\sqrt{\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      5. sqrt-pow1 40.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      6. metadata-eval 40.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{\color{blue}{0.16666666666666666}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      7. pow1/3 40.1%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left(\sqrt{\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      8. sqrt-pow1 40.1%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      9. metadata-eval 40.1%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{\color{blue}{0.16666666666666666}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      10. pow2 40.1%

          \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \color{blue}{{\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   8. Applied egg-rr 40.1%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \color{blue}{\left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}\right)\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   9. Taylor expanded in a around 0 40.3%

      \[\leadsto \color{blue}{{b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}} \]
   10. Step-by-step derivation

       1. unpow2 40.3%

          \[\leadsto \color{blue}{\left(b \cdot b\right)} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \]

       2. associate-*r* 40.3%

          \[\leadsto \left(b \cdot b\right) \cdot {\sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}}^{2} \]

       3. *-commutative 40.3%

          \[\leadsto \left(b \cdot b\right) \cdot {\sin \left(\color{blue}{\left(angle \cdot 0.005555555555555556\right)} \cdot \pi\right)}^{2} \]

       4. *-commutative 40.3%

          \[\leadsto \left(b \cdot b\right) \cdot {\sin \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}}^{2} \]

       5. unpow2 40.3%

          \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} \]

       6. swap-sqr 48.8%

          \[\leadsto \color{blue}{\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} \]

       7. unpow2 48.8%

          \[\leadsto \color{blue}{{\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]

   11. Simplified 48.8%

       \[\leadsto \color{blue}{{\left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}} \]

   if 1.8500000000000001e-153 < a

   1. Initial program 72.9%

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

   3. Simplified 73.0%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. metadata-eval 73.0%

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

      2. div-inv 73.0%

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

      3. add-cube-cbrt 72.8%

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

      4. pow3 72.9%

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

      5. div-inv 73.1%

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

      6. metadata-eval 73.1%

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

   6. Applied egg-rr 73.1%

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

      1. cube-mult 73.0%

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

      2. add-sqr-sqrt 38.3%

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

      3. associate-*l* 38.4%

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

      4. pow1/3 38.2%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(\sqrt{\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      5. sqrt-pow1 38.2%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      6. metadata-eval 38.2%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{\color{blue}{0.16666666666666666}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      7. pow1/3 38.5%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left(\sqrt{\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      8. sqrt-pow1 38.6%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      9. metadata-eval 38.6%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{\color{blue}{0.16666666666666666}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      10. pow2 38.6%

          \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \color{blue}{{\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   8. Applied egg-rr 38.6%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \color{blue}{\left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}\right)\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   9. Taylor expanded in angle around 0 36.4%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}\right)\right)\right)\right)}^{2} + {\left(b \cdot \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}^{2} \]

   10. Taylor expanded in angle around 0 68.7%

       \[\leadsto {\color{blue}{a}}^{2} + {\left(b \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.85 \cdot 10^{-153}:\\ \;\;\;\;{\left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(b \cdot \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{+157}:\\ \;\;\;\;{\left(a \cdot \cos \left(\pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{\left(b \cdot \sin \left(angle\_m \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (if (<= b 4.8e+157)
   (pow (* a (cos (* PI (* angle_m 0.005555555555555556)))) 2.0)
   (pow (* b (sin (* angle_m (* PI 0.005555555555555556)))) 2.0)))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double tmp;
	if (b <= 4.8e+157) {
		tmp = pow((a * cos((((double) M_PI) * (angle_m * 0.005555555555555556)))), 2.0);
	} else {
		tmp = pow((b * sin((angle_m * (((double) M_PI) * 0.005555555555555556)))), 2.0);
	}
	return tmp;
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double tmp;
	if (b <= 4.8e+157) {
		tmp = Math.pow((a * Math.cos((Math.PI * (angle_m * 0.005555555555555556)))), 2.0);
	} else {
		tmp = Math.pow((b * Math.sin((angle_m * (Math.PI * 0.005555555555555556)))), 2.0);
	}
	return tmp;
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	tmp = 0
	if b <= 4.8e+157:
		tmp = math.pow((a * math.cos((math.pi * (angle_m * 0.005555555555555556)))), 2.0)
	else:
		tmp = math.pow((b * math.sin((angle_m * (math.pi * 0.005555555555555556)))), 2.0)
	return tmp

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	tmp = 0.0
	if (b <= 4.8e+157)
		tmp = Float64(a * cos(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 2.0;
	else
		tmp = Float64(b * sin(Float64(angle_m * Float64(pi * 0.005555555555555556)))) ^ 2.0;
	end
	return tmp
end

MATLAB

angle_m = abs(angle);
function tmp_2 = code(a, b, angle_m)
	tmp = 0.0;
	if (b <= 4.8e+157)
		tmp = (a * cos((pi * (angle_m * 0.005555555555555556)))) ^ 2.0;
	else
		tmp = (b * sin((angle_m * (pi * 0.005555555555555556)))) ^ 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := If[LessEqual[b, 4.8e+157], N[Power[N[(a * N[Cos[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[Power[N[(b * N[Sin[N[(angle$95$m * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.7999999999999999e157

   1. Initial program 74.7%

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

   3. Simplified 74.8%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. metadata-eval 74.8%

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

      2. div-inv 74.8%

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

      3. add-cube-cbrt 74.9%

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

      4. pow3 74.9%

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

      5. div-inv 74.9%

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

      6. metadata-eval 74.9%

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

   6. Applied egg-rr 74.9%

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

   7. Taylor expanded in a around inf 59.4%

      \[\leadsto \color{blue}{{a}^{2} \cdot {\cos \left(angle \cdot \left(\pi \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}^{2}} \]
   8. Step-by-step derivation

      1. pow-prod-down 59.4%

         \[\leadsto \color{blue}{{\left(a \cdot \cos \left(angle \cdot \left(\pi \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)\right)}^{2}} \]

      2. associate-*r* 59.3%

         \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\left(angle \cdot \pi\right) \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)}\right)}^{2} \]

      3. *-commutative 59.3%

         \[\leadsto {\left(a \cdot \cos \left(\color{blue}{\left(\pi \cdot angle\right)} \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}^{2} \]

      4. associate-*r* 59.4%

         \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\pi \cdot \left(angle \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}\right)}^{2} \]

      5. rem-cube-cbrt 59.5%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)\right)}^{2} \]

   9. Applied egg-rr 59.5%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]

   if 4.7999999999999999e157 < b

   1. Initial program 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. metadata-eval 99.6%

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

      2. div-inv 99.6%

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

      3. add-cube-cbrt 99.6%

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

      4. pow3 99.6%

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

      5. div-inv 99.6%

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

      6. metadata-eval 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. cube-mult 99.6%

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

      2. add-sqr-sqrt 54.0%

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

      3. associate-*l* 54.0%

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

      4. pow1/3 54.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(\sqrt{\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      5. sqrt-pow1 54.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      6. metadata-eval 54.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{\color{blue}{0.16666666666666666}} \cdot \left(\sqrt{\sqrt[3]{angle \cdot 0.005555555555555556}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      7. pow1/3 54.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left(\sqrt{\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      8. sqrt-pow1 54.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      9. metadata-eval 54.0%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{\color{blue}{0.16666666666666666}} \cdot \left(\sqrt[3]{angle \cdot 0.005555555555555556} \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

      10. pow2 54.0%

          \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \color{blue}{{\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}\right)\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   8. Applied egg-rr 54.0%

      \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \color{blue}{\left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot \left({\left(angle \cdot 0.005555555555555556\right)}^{0.16666666666666666} \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}\right)\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   9. Taylor expanded in a around 0 63.0%

      \[\leadsto \color{blue}{{b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}} \]
   10. Step-by-step derivation

       1. unpow2 63.0%

          \[\leadsto \color{blue}{\left(b \cdot b\right)} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \]

       2. associate-*r* 63.0%

          \[\leadsto \left(b \cdot b\right) \cdot {\sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}}^{2} \]

       3. *-commutative 63.0%

          \[\leadsto \left(b \cdot b\right) \cdot {\sin \left(\color{blue}{\left(angle \cdot 0.005555555555555556\right)} \cdot \pi\right)}^{2} \]

       4. *-commutative 63.0%

          \[\leadsto \left(b \cdot b\right) \cdot {\sin \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}}^{2} \]

       5. unpow2 63.0%

          \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} \]

       6. swap-sqr 91.7%

          \[\leadsto \color{blue}{\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} \]

       7. unpow2 91.7%

          \[\leadsto \color{blue}{{\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]

   11. Simplified 91.8%

       \[\leadsto \color{blue}{{\left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{+157}:\\ \;\;\;\;{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{\left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} \mathbf{if}\;b \leq 7.8 \cdot 10^{+157}:\\ \;\;\;\;{\left(a \cdot \cos \left(\pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\_m\right)\right)\right)}^{2}\\ \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (if (<= b 7.8e+157)
   (pow (* a (cos (* PI (* angle_m 0.005555555555555556)))) 2.0)
   (pow (* b (sin (* 0.005555555555555556 (* PI angle_m)))) 2.0)))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double tmp;
	if (b <= 7.8e+157) {
		tmp = pow((a * cos((((double) M_PI) * (angle_m * 0.005555555555555556)))), 2.0);
	} else {
		tmp = pow((b * sin((0.005555555555555556 * (((double) M_PI) * angle_m)))), 2.0);
	}
	return tmp;
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double tmp;
	if (b <= 7.8e+157) {
		tmp = Math.pow((a * Math.cos((Math.PI * (angle_m * 0.005555555555555556)))), 2.0);
	} else {
		tmp = Math.pow((b * Math.sin((0.005555555555555556 * (Math.PI * angle_m)))), 2.0);
	}
	return tmp;
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	tmp = 0
	if b <= 7.8e+157:
		tmp = math.pow((a * math.cos((math.pi * (angle_m * 0.005555555555555556)))), 2.0)
	else:
		tmp = math.pow((b * math.sin((0.005555555555555556 * (math.pi * angle_m)))), 2.0)
	return tmp

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	tmp = 0.0
	if (b <= 7.8e+157)
		tmp = Float64(a * cos(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 2.0;
	else
		tmp = Float64(b * sin(Float64(0.005555555555555556 * Float64(pi * angle_m)))) ^ 2.0;
	end
	return tmp
end

MATLAB

angle_m = abs(angle);
function tmp_2 = code(a, b, angle_m)
	tmp = 0.0;
	if (b <= 7.8e+157)
		tmp = (a * cos((pi * (angle_m * 0.005555555555555556)))) ^ 2.0;
	else
		tmp = (b * sin((0.005555555555555556 * (pi * angle_m)))) ^ 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := If[LessEqual[b, 7.8e+157], N[Power[N[(a * N[Cos[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[Power[N[(b * N[Sin[N[(0.005555555555555556 * N[(Pi * angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.79999999999999941e157

   1. Initial program 74.7%

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

   3. Simplified 74.8%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. metadata-eval 74.8%

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

      2. div-inv 74.8%

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

      3. add-cube-cbrt 74.9%

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

      4. pow3 74.9%

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

      5. div-inv 74.9%

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

      6. metadata-eval 74.9%

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

   6. Applied egg-rr 74.9%

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

   7. Taylor expanded in a around inf 59.4%

      \[\leadsto \color{blue}{{a}^{2} \cdot {\cos \left(angle \cdot \left(\pi \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}^{2}} \]
   8. Step-by-step derivation

      1. pow-prod-down 59.4%

         \[\leadsto \color{blue}{{\left(a \cdot \cos \left(angle \cdot \left(\pi \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)\right)}^{2}} \]

      2. associate-*r* 59.3%

         \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\left(angle \cdot \pi\right) \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)}\right)}^{2} \]

      3. *-commutative 59.3%

         \[\leadsto {\left(a \cdot \cos \left(\color{blue}{\left(\pi \cdot angle\right)} \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}^{2} \]

      4. associate-*r* 59.4%

         \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\pi \cdot \left(angle \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}\right)}^{2} \]

      5. rem-cube-cbrt 59.5%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)\right)}^{2} \]

   9. Applied egg-rr 59.5%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]

   if 7.79999999999999941e157 < b

   1. Initial program 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 63.0%

      \[\leadsto \color{blue}{{b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}} \]
   6. Step-by-step derivation

      1. unpow2 63.0%

         \[\leadsto \color{blue}{\left(b \cdot b\right)} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \]

      2. *-commutative 63.0%

         \[\leadsto \left(b \cdot b\right) \cdot {\sin \left(0.005555555555555556 \cdot \color{blue}{\left(\pi \cdot angle\right)}\right)}^{2} \]

      3. unpow2 63.0%

         \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)} \]

      4. swap-sqr 91.8%

         \[\leadsto \color{blue}{\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) \cdot \left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)} \]

      5. unpow2 91.8%

         \[\leadsto \color{blue}{{\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}} \]

      6. *-commutative 91.8%

         \[\leadsto {\left(b \cdot \sin \left(0.005555555555555556 \cdot \color{blue}{\left(angle \cdot \pi\right)}\right)\right)}^{2} \]

   7. Simplified 91.8%

      \[\leadsto \color{blue}{{\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7.8 \cdot 10^{+157}:\\ \;\;\;\;{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} \mathbf{if}\;b \leq 1.3 \cdot 10^{+169}:\\ \;\;\;\;{\left(a \cdot \cos \left(\pi \cdot \left(angle\_m \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{a}^{6}}\\ \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (if (<= b 1.3e+169)
   (pow (* a (cos (* PI (* angle_m 0.005555555555555556)))) 2.0)
   (cbrt (pow a 6.0))))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double tmp;
	if (b <= 1.3e+169) {
		tmp = pow((a * cos((((double) M_PI) * (angle_m * 0.005555555555555556)))), 2.0);
	} else {
		tmp = cbrt(pow(a, 6.0));
	}
	return tmp;
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double tmp;
	if (b <= 1.3e+169) {
		tmp = Math.pow((a * Math.cos((Math.PI * (angle_m * 0.005555555555555556)))), 2.0);
	} else {
		tmp = Math.cbrt(Math.pow(a, 6.0));
	}
	return tmp;
}

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	tmp = 0.0
	if (b <= 1.3e+169)
		tmp = Float64(a * cos(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 2.0;
	else
		tmp = cbrt((a ^ 6.0));
	end
	return tmp
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := If[LessEqual[b, 1.3e+169], N[Power[N[(a * N[Cos[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[Power[N[Power[a, 6.0], $MachinePrecision], 1/3], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.3e169

   1. Initial program 75.1%

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

   3. Simplified 75.1%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. metadata-eval 75.1%

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

      2. div-inv 75.1%

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

      3. add-cube-cbrt 75.2%

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

      4. pow3 75.2%

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

      5. div-inv 75.3%

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

      6. metadata-eval 75.3%

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

   6. Applied egg-rr 75.3%

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

   7. Taylor expanded in a around inf 58.6%

      \[\leadsto \color{blue}{{a}^{2} \cdot {\cos \left(angle \cdot \left(\pi \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}^{2}} \]
   8. Step-by-step derivation

      1. pow-prod-down 58.6%

         \[\leadsto \color{blue}{{\left(a \cdot \cos \left(angle \cdot \left(\pi \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)\right)}^{2}} \]

      2. associate-*r* 58.5%

         \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\left(angle \cdot \pi\right) \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)}\right)}^{2} \]

      3. *-commutative 58.5%

         \[\leadsto {\left(a \cdot \cos \left(\color{blue}{\left(\pi \cdot angle\right)} \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}^{2} \]

      4. associate-*r* 58.6%

         \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\pi \cdot \left(angle \cdot {\left(\sqrt[3]{0.005555555555555556}\right)}^{3}\right)\right)}\right)}^{2} \]

      5. rem-cube-cbrt 58.7%

         \[\leadsto {\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)\right)}^{2} \]

   9. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]

   if 1.3e169 < b

   1. Initial program 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in angle around 0 31.7%

      \[\leadsto \color{blue}{{a}^{2}} \]
   6. Step-by-step derivation

      1. add-sqr-sqrt 31.7%

         \[\leadsto \color{blue}{\sqrt{{a}^{2}} \cdot \sqrt{{a}^{2}}} \]

      2. sqrt-unprod 39.8%

         \[\leadsto \color{blue}{\sqrt{{a}^{2} \cdot {a}^{2}}} \]

      3. pow-prod-up 39.8%

         \[\leadsto \sqrt{\color{blue}{{a}^{\left(2 + 2\right)}}} \]

      4. metadata-eval 39.8%

         \[\leadsto \sqrt{{a}^{\color{blue}{4}}} \]

   7. Applied egg-rr 39.8%

      \[\leadsto \color{blue}{\sqrt{{a}^{4}}} \]
   8. Step-by-step derivation

      1. add-cbrt-cube 39.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt{{a}^{4}} \cdot \sqrt{{a}^{4}}\right) \cdot \sqrt{{a}^{4}}}} \]

      2. pow1/3 39.8%

         \[\leadsto \color{blue}{{\left(\left(\sqrt{{a}^{4}} \cdot \sqrt{{a}^{4}}\right) \cdot \sqrt{{a}^{4}}\right)}^{0.3333333333333333}} \]

      3. add-sqr-sqrt 39.8%

         \[\leadsto {\left(\color{blue}{{a}^{4}} \cdot \sqrt{{a}^{4}}\right)}^{0.3333333333333333} \]

      4. sqrt-pow1 39.8%

         \[\leadsto {\left({a}^{4} \cdot \color{blue}{{a}^{\left(\frac{4}{2}\right)}}\right)}^{0.3333333333333333} \]

      5. metadata-eval 39.8%

         \[\leadsto {\left({a}^{4} \cdot {a}^{\color{blue}{2}}\right)}^{0.3333333333333333} \]

      6. pow-prod-up 39.8%

         \[\leadsto {\color{blue}{\left({a}^{\left(4 + 2\right)}\right)}}^{0.3333333333333333} \]

      7. metadata-eval 39.8%

         \[\leadsto {\left({a}^{\color{blue}{6}}\right)}^{0.3333333333333333} \]

   9. Applied egg-rr 39.8%

      \[\leadsto \color{blue}{{\left({a}^{6}\right)}^{0.3333333333333333}} \]
   10. Step-by-step derivation

       1. unpow1/3 39.8%

          \[\leadsto \color{blue}{\sqrt[3]{{a}^{6}}} \]

   11. Simplified 39.8%

       \[\leadsto \color{blue}{\sqrt[3]{{a}^{6}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 57.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} \mathbf{if}\;b \leq 1.45 \cdot 10^{+169}:\\ \;\;\;\;a \cdot a\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{a}^{6}}\\ \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (if (<= b 1.45e+169) (* a a) (cbrt (pow a 6.0))))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double tmp;
	if (b <= 1.45e+169) {
		tmp = a * a;
	} else {
		tmp = cbrt(pow(a, 6.0));
	}
	return tmp;
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double tmp;
	if (b <= 1.45e+169) {
		tmp = a * a;
	} else {
		tmp = Math.cbrt(Math.pow(a, 6.0));
	}
	return tmp;
}

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	tmp = 0.0
	if (b <= 1.45e+169)
		tmp = Float64(a * a);
	else
		tmp = cbrt((a ^ 6.0));
	end
	return tmp
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := If[LessEqual[b, 1.45e+169], N[(a * a), $MachinePrecision], N[Power[N[Power[a, 6.0], $MachinePrecision], 1/3], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.45e169

   1. Initial program 75.1%

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

   3. Simplified 75.1%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in angle around 0 59.1%

      \[\leadsto \color{blue}{{a}^{2}} \]
   6. Step-by-step derivation

      1. unpow2 59.1%

         \[\leadsto \color{blue}{a \cdot a} \]

   7. Applied egg-rr 59.1%

      \[\leadsto \color{blue}{a \cdot a} \]

   if 1.45e169 < b

   1. Initial program 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in angle around 0 31.7%

      \[\leadsto \color{blue}{{a}^{2}} \]
   6. Step-by-step derivation

      1. add-sqr-sqrt 31.7%

         \[\leadsto \color{blue}{\sqrt{{a}^{2}} \cdot \sqrt{{a}^{2}}} \]

      2. sqrt-unprod 39.8%

         \[\leadsto \color{blue}{\sqrt{{a}^{2} \cdot {a}^{2}}} \]

      3. pow-prod-up 39.8%

         \[\leadsto \sqrt{\color{blue}{{a}^{\left(2 + 2\right)}}} \]

      4. metadata-eval 39.8%

         \[\leadsto \sqrt{{a}^{\color{blue}{4}}} \]

   7. Applied egg-rr 39.8%

      \[\leadsto \color{blue}{\sqrt{{a}^{4}}} \]
   8. Step-by-step derivation

      1. add-cbrt-cube 39.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt{{a}^{4}} \cdot \sqrt{{a}^{4}}\right) \cdot \sqrt{{a}^{4}}}} \]

      2. pow1/3 39.8%

         \[\leadsto \color{blue}{{\left(\left(\sqrt{{a}^{4}} \cdot \sqrt{{a}^{4}}\right) \cdot \sqrt{{a}^{4}}\right)}^{0.3333333333333333}} \]

      3. add-sqr-sqrt 39.8%

         \[\leadsto {\left(\color{blue}{{a}^{4}} \cdot \sqrt{{a}^{4}}\right)}^{0.3333333333333333} \]

      4. sqrt-pow1 39.8%

         \[\leadsto {\left({a}^{4} \cdot \color{blue}{{a}^{\left(\frac{4}{2}\right)}}\right)}^{0.3333333333333333} \]

      5. metadata-eval 39.8%

         \[\leadsto {\left({a}^{4} \cdot {a}^{\color{blue}{2}}\right)}^{0.3333333333333333} \]

      6. pow-prod-up 39.8%

         \[\leadsto {\color{blue}{\left({a}^{\left(4 + 2\right)}\right)}}^{0.3333333333333333} \]

      7. metadata-eval 39.8%

         \[\leadsto {\left({a}^{\color{blue}{6}}\right)}^{0.3333333333333333} \]

   9. Applied egg-rr 39.8%

      \[\leadsto \color{blue}{{\left({a}^{6}\right)}^{0.3333333333333333}} \]
   10. Step-by-step derivation

       1. unpow1/3 39.8%

          \[\leadsto \color{blue}{\sqrt[3]{{a}^{6}}} \]

   11. Simplified 39.8%

       \[\leadsto \color{blue}{\sqrt[3]{{a}^{6}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 57.2% accurate, 139.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ a \cdot a \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m) :precision binary64 (* a a))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	return a * a;
}

Fortran

angle_m = abs(angle)
real(8) function code(a, b, angle_m)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: angle_m
    code = a * a
end function

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	return a * a;
}

Python

angle_m = math.fabs(angle)
def code(a, b, angle_m):
	return a * a

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	return Float64(a * a)
end

MATLAB

angle_m = abs(angle);
function tmp = code(a, b, angle_m)
	tmp = a * a;
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(a * a), $MachinePrecision]

Derivation

1. Initial program 78.3%

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

3. Simplified 78.4%

   \[\leadsto \color{blue}{{\left(a \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}} \]
4. Add Preprocessing

5. Taylor expanded in angle around 0 55.4%

   \[\leadsto \color{blue}{{a}^{2}} \]
6. Step-by-step derivation

   1. unpow2 55.4%

      \[\leadsto \color{blue}{a \cdot a} \]

7. Applied egg-rr 55.4%

   \[\leadsto \color{blue}{a \cdot a} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024143 
(FPCore (a b angle)
  :name "ab-angle->ABCF C"
  :precision binary64
  (+ (pow (* a (cos (* PI (/ angle 180.0)))) 2.0) (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))