ab-angle->ABCF C

Percentage Accurate: 79.2% → 79.2%

Time: 15.3s

Alternatives: 9

Speedup: N/A×

• 36.2% 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: 79.2% 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: 79.2% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (pow (cbrt (cos (* 0.005555555555555556 (* PI angle)))) 3.0)) 2.0)
  (pow (* b (sin (* PI (* 0.005555555555555556 angle)))) 2.0)))

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

3. Simplified 79.3%

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

   1. metadata-eval 79.3%

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

   2. div-inv 79.4%

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

   3. add-cube-cbrt 79.4%

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

   4. pow3 79.4%

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

   5. div-inv 79.3%

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

   6. metadata-eval 79.3%

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

   7. associate-*r* 79.4%

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

   8. *-commutative 79.4%

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

6. Applied egg-rr 79.4%

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

7. Final simplification 79.4%

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

Alternative 2: 79.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* b (sin (* PI (* 0.005555555555555556 angle)))) 2.0)
  (* a (* a (pow (cos (* 0.005555555555555556 (* PI angle))) 2.0)))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(0.005555555555555556 * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[(a * N[(a * N[Power[N[Cos[N[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

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

3. Simplified 79.3%

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

   1. metadata-eval 79.3%

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

   2. div-inv 79.4%

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

   3. add-cube-cbrt 79.4%

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

   4. pow3 79.4%

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

   5. div-inv 79.3%

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

   6. metadata-eval 79.3%

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

   7. associate-*r* 79.4%

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

   8. *-commutative 79.4%

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

6. Applied egg-rr 79.4%

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

   1. unpow2 79.4%

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

   2. rem-cube-cbrt 79.4%

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

   3. add-cube-cbrt 79.1%

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

   4. unpow3 79.1%

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

   5. rem-cube-cbrt 79.1%

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

   6. *-commutative 79.1%

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

   7. associate-*l* 79.1%

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

   8. unpow3 79.1%

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

   9. add-cube-cbrt 79.4%

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

8. Applied egg-rr 79.4%

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

9. Final simplification 79.4%

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

Alternative 3: 79.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ {\left(b \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)}^{2} + a \cdot \left(a \cdot \frac{1 + \cos \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)}{2}\right) \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* b (sin (* PI (* 0.005555555555555556 angle)))) 2.0)
  (* a (* a (/ (+ 1.0 (cos (* (* PI angle) 0.011111111111111112))) 2.0)))))

C

double code(double a, double b, double angle) {
	return pow((b * sin((((double) M_PI) * (0.005555555555555556 * angle)))), 2.0) + (a * (a * ((1.0 + cos(((((double) M_PI) * angle) * 0.011111111111111112))) / 2.0)));
}

Java

public static double code(double a, double b, double angle) {
	return Math.pow((b * Math.sin((Math.PI * (0.005555555555555556 * angle)))), 2.0) + (a * (a * ((1.0 + Math.cos(((Math.PI * angle) * 0.011111111111111112))) / 2.0)));
}

Python

def code(a, b, angle):
	return math.pow((b * math.sin((math.pi * (0.005555555555555556 * angle)))), 2.0) + (a * (a * ((1.0 + math.cos(((math.pi * angle) * 0.011111111111111112))) / 2.0)))

Julia

function code(a, b, angle)
	return Float64((Float64(b * sin(Float64(pi * Float64(0.005555555555555556 * angle)))) ^ 2.0) + Float64(a * Float64(a * Float64(Float64(1.0 + cos(Float64(Float64(pi * angle) * 0.011111111111111112))) / 2.0))))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = ((b * sin((pi * (0.005555555555555556 * angle)))) ^ 2.0) + (a * (a * ((1.0 + cos(((pi * angle) * 0.011111111111111112))) / 2.0)));
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(0.005555555555555556 * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[(a * N[(a * N[(N[(1.0 + N[Cos[N[(N[(Pi * angle), $MachinePrecision] * 0.011111111111111112), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

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

3. Simplified 79.3%

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

   1. metadata-eval 79.3%

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

   2. div-inv 79.4%

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

   3. add-cube-cbrt 79.4%

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

   4. pow3 79.4%

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

   5. div-inv 79.3%

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

   6. metadata-eval 79.3%

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

   7. associate-*r* 79.4%

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

   8. *-commutative 79.4%

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

6. Applied egg-rr 79.4%

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

   1. unpow2 79.4%

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

   2. rem-cube-cbrt 79.4%

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

   3. add-cube-cbrt 79.1%

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

   4. unpow3 79.1%

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

   5. rem-cube-cbrt 79.1%

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

   6. *-commutative 79.1%

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

   7. associate-*l* 79.1%

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

   8. unpow3 79.1%

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

   9. add-cube-cbrt 79.4%

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

8. Applied egg-rr 79.4%

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

   1. unpow2 79.4%

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

   2. *-commutative 79.4%

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

   3. *-commutative 79.4%

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

   4. sqr-cos-a 79.4%

      \[\leadsto \left(a \cdot \color{blue}{\left(0.5 + 0.5 \cdot \cos \left(2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}\right) \cdot a + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   5. add-exp-log 42.2%

      \[\leadsto \left(a \cdot \left(0.5 + 0.5 \cdot \cos \left(2 \cdot \color{blue}{e^{\log \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\right)\right)\right) \cdot a + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   6. *-un-lft-identity 42.2%

      \[\leadsto \left(a \cdot \left(0.5 + 0.5 \cdot \cos \left(2 \cdot e^{\color{blue}{1 \cdot \log \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\right)\right)\right) \cdot a + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   7. pow-exp 42.2%

      \[\leadsto \left(a \cdot \left(0.5 + 0.5 \cdot \cos \left(2 \cdot \color{blue}{{\left(e^{1}\right)}^{\log \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\right)\right)\right) \cdot a + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   8. e-exp-1 42.2%

      \[\leadsto \left(a \cdot \left(0.5 + 0.5 \cdot \cos \left(2 \cdot {\color{blue}{e}}^{\log \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)\right) \cdot a + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

   9. sqr-cos-a 42.2%

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

10. Applied egg-rr 79.4%

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

    1. +-commutative 79.4%

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

    2. +-inverses 79.4%

       \[\leadsto \left(a \cdot \frac{\cos \color{blue}{0} + \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right) + 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}{2}\right) \cdot a + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

    3. cos-0 79.4%

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

    4. distribute-rgt-out 79.4%

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

    5. *-commutative 79.4%

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

    6. metadata-eval 79.4%

       \[\leadsto \left(a \cdot \frac{1 + \cos \left(\left(angle \cdot \pi\right) \cdot \color{blue}{0.011111111111111112}\right)}{2}\right) \cdot a + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

12. Simplified 79.4%

    \[\leadsto \left(a \cdot \color{blue}{\frac{1 + \cos \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{2}}\right) \cdot a + {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]

13. Final simplification 79.4%

    \[\leadsto {\left(b \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)}^{2} + a \cdot \left(a \cdot \frac{1 + \cos \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)}{2}\right) \]
14. Add Preprocessing

Alternative 4: 62.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.3 \cdot 10^{+154}:\\ \;\;\;\;{\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{\left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (if (<= b 1.3e+154)
   (pow (* a (cos (* 0.005555555555555556 (* PI angle)))) 2.0)
   (pow (* b (sin (* angle (* 0.005555555555555556 PI)))) 2.0)))

C

double code(double a, double b, double angle) {
	double tmp;
	if (b <= 1.3e+154) {
		tmp = pow((a * cos((0.005555555555555556 * (((double) M_PI) * angle)))), 2.0);
	} else {
		tmp = pow((b * sin((angle * (0.005555555555555556 * ((double) M_PI))))), 2.0);
	}
	return tmp;
}

Java

public static double code(double a, double b, double angle) {
	double tmp;
	if (b <= 1.3e+154) {
		tmp = Math.pow((a * Math.cos((0.005555555555555556 * (Math.PI * angle)))), 2.0);
	} else {
		tmp = Math.pow((b * Math.sin((angle * (0.005555555555555556 * Math.PI)))), 2.0);
	}
	return tmp;
}

Python

def code(a, b, angle):
	tmp = 0
	if b <= 1.3e+154:
		tmp = math.pow((a * math.cos((0.005555555555555556 * (math.pi * angle)))), 2.0)
	else:
		tmp = math.pow((b * math.sin((angle * (0.005555555555555556 * math.pi)))), 2.0)
	return tmp

Julia

function code(a, b, angle)
	tmp = 0.0
	if (b <= 1.3e+154)
		tmp = Float64(a * cos(Float64(0.005555555555555556 * Float64(pi * angle)))) ^ 2.0;
	else
		tmp = Float64(b * sin(Float64(angle * Float64(0.005555555555555556 * pi)))) ^ 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, angle)
	tmp = 0.0;
	if (b <= 1.3e+154)
		tmp = (a * cos((0.005555555555555556 * (pi * angle)))) ^ 2.0;
	else
		tmp = (b * sin((angle * (0.005555555555555556 * pi)))) ^ 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, angle_] := If[LessEqual[b, 1.3e+154], N[Power[N[(a * N[Cos[N[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[Power[N[(b * N[Sin[N[(angle * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.29999999999999994e154

   1. Initial program 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in a around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. unpow2 56.1%

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

      3. unpow2 56.1%

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

      4. swap-sqr 56.1%

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

      5. unpow2 56.1%

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

      6. *-commutative 56.1%

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

   7. Simplified 56.1%

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

   if 1.29999999999999994e154 < b

   1. Initial program 99.1%

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

   3. Simplified 99.2%

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

      1. metadata-eval 99.2%

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

      2. div-inv 99.2%

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

      3. add-cube-cbrt 99.2%

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

      4. pow3 99.2%

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

      5. div-inv 99.2%

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

      6. metadata-eval 99.2%

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

      7. associate-*r* 99.2%

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

      8. *-commutative 99.2%

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

   6. Applied egg-rr 99.2%

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

      1. unpow2 99.2%

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

      2. rem-cube-cbrt 99.2%

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

      3. add-cube-cbrt 99.2%

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

      4. unpow3 99.2%

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

      5. rem-cube-cbrt 99.2%

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

      6. *-commutative 99.2%

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

      7. associate-*l* 99.2%

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

      8. unpow3 99.2%

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

      9. add-cube-cbrt 99.2%

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

   8. Applied egg-rr 99.2%

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

   9. Taylor expanded in a around 0 56.9%

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

       1. unpow2 56.9%

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

       2. *-commutative 56.9%

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

       3. unpow2 56.9%

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

       4. swap-sqr 95.5%

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

       5. unpow2 95.5%

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

       6. associate-*r* 95.5%

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

       7. *-commutative 95.5%

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

   11. Simplified 95.5%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.3 \cdot 10^{+154}:\\ \;\;\;\;{\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{\left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\\ \mathbf{if}\;b \leq 1.5 \cdot 10^{+154}:\\ \;\;\;\;{\left(a \cdot \cos t\_0\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{\left(b \cdot \sin t\_0\right)}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* 0.005555555555555556 (* PI angle))))
   (if (<= b 1.5e+154) (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 = 0.005555555555555556 * (((double) M_PI) * angle);
	double tmp;
	if (b <= 1.5e+154) {
		tmp = pow((a * cos(t_0)), 2.0);
	} else {
		tmp = pow((b * sin(t_0)), 2.0);
	}
	return tmp;
}

Java

public static double code(double a, double b, double angle) {
	double t_0 = 0.005555555555555556 * (Math.PI * angle);
	double tmp;
	if (b <= 1.5e+154) {
		tmp = Math.pow((a * Math.cos(t_0)), 2.0);
	} else {
		tmp = Math.pow((b * Math.sin(t_0)), 2.0);
	}
	return tmp;
}

Python

def code(a, b, angle):
	t_0 = 0.005555555555555556 * (math.pi * angle)
	tmp = 0
	if b <= 1.5e+154:
		tmp = math.pow((a * math.cos(t_0)), 2.0)
	else:
		tmp = math.pow((b * math.sin(t_0)), 2.0)
	return tmp

Julia

function code(a, b, angle)
	t_0 = Float64(0.005555555555555556 * Float64(pi * angle))
	tmp = 0.0
	if (b <= 1.5e+154)
		tmp = Float64(a * cos(t_0)) ^ 2.0;
	else
		tmp = Float64(b * sin(t_0)) ^ 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, angle)
	t_0 = 0.005555555555555556 * (pi * angle);
	tmp = 0.0;
	if (b <= 1.5e+154)
		tmp = (a * cos(t_0)) ^ 2.0;
	else
		tmp = (b * sin(t_0)) ^ 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, angle_] := Block[{t$95$0 = N[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, 1.5e+154], 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]]]

Derivation

1. Split input into 2 regimes

2. if b < 1.50000000000000013e154

   1. Initial program 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in a around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. unpow2 56.1%

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

      3. unpow2 56.1%

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

      4. swap-sqr 56.1%

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

      5. unpow2 56.1%

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

      6. *-commutative 56.1%

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

   7. Simplified 56.1%

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

   if 1.50000000000000013e154 < b

   1. Initial program 99.1%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around 0 56.9%

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

      1. unpow2 56.9%

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

      2. *-commutative 56.9%

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

      3. unpow2 56.9%

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

      4. swap-sqr 95.5%

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

      5. unpow2 95.5%

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

      6. *-commutative 95.5%

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

   7. Simplified 95.5%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.5 \cdot 10^{+154}:\\ \;\;\;\;{\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{+172}:\\ \;\;\;\;{\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{a}^{6}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (if (<= b 2.6e+172)
   (pow (* a (cos (* 0.005555555555555556 (* PI angle)))) 2.0)
   (cbrt (pow a 6.0))))

C

double code(double a, double b, double angle) {
	double tmp;
	if (b <= 2.6e+172) {
		tmp = pow((a * cos((0.005555555555555556 * (((double) M_PI) * angle)))), 2.0);
	} else {
		tmp = cbrt(pow(a, 6.0));
	}
	return tmp;
}

Java

public static double code(double a, double b, double angle) {
	double tmp;
	if (b <= 2.6e+172) {
		tmp = Math.pow((a * Math.cos((0.005555555555555556 * (Math.PI * angle)))), 2.0);
	} else {
		tmp = Math.cbrt(Math.pow(a, 6.0));
	}
	return tmp;
}

Julia

function code(a, b, angle)
	tmp = 0.0
	if (b <= 2.6e+172)
		tmp = Float64(a * cos(Float64(0.005555555555555556 * Float64(pi * angle)))) ^ 2.0;
	else
		tmp = cbrt((a ^ 6.0));
	end
	return tmp
end

Wolfram

code[a_, b_, angle_] := If[LessEqual[b, 2.6e+172], N[Power[N[(a * N[Cos[N[(0.005555555555555556 * N[(Pi * angle), $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 < 2.6e172

   1. Initial program 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in a around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. unpow2 55.7%

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

      3. unpow2 55.7%

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

      4. swap-sqr 55.7%

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

      5. unpow2 55.7%

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

      6. *-commutative 55.7%

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

   7. Simplified 55.7%

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

   if 2.6e172 < b

   1. Initial program 99.1%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in angle around 0 20.4%

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

      1. add-sqr-sqrt 20.4%

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

      2. sqrt-unprod 24.6%

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

      3. pow-prod-up 24.6%

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

      4. metadata-eval 24.6%

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

   7. Applied egg-rr 24.6%

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

      1. add-cbrt-cube 28.4%

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

      2. pow1/3 28.4%

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

      3. add-sqr-sqrt 28.4%

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

      4. sqrt-pow1 28.4%

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

      5. metadata-eval 28.4%

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

      6. pow-prod-up 28.4%

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

      7. metadata-eval 28.4%

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

   9. Applied egg-rr 28.4%

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

       1. unpow1/3 28.4%

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

   11. Simplified 28.4%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{+172}:\\ \;\;\;\;{\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{a}^{6}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.2% accurate, 2.0× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (+ (pow (* b (sin (* PI (* 0.005555555555555556 angle)))) 2.0) (* a a)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(0.005555555555555556 * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[(a * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

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

3. Simplified 79.3%

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

   1. metadata-eval 79.3%

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

   2. div-inv 79.4%

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

   3. add-cube-cbrt 79.4%

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

   4. pow3 79.4%

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

   5. div-inv 79.3%

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

   6. metadata-eval 79.3%

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

   7. associate-*r* 79.4%

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

   8. *-commutative 79.4%

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

6. Applied egg-rr 79.4%

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

   1. unpow2 79.4%

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

   2. rem-cube-cbrt 79.4%

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

   3. add-cube-cbrt 79.1%

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

   4. unpow3 79.1%

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

   5. rem-cube-cbrt 79.1%

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

   6. *-commutative 79.1%

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

   7. associate-*l* 79.1%

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

   8. unpow3 79.1%

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

   9. add-cube-cbrt 79.4%

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

8. Applied egg-rr 79.4%

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

9. Taylor expanded in angle around 0 78.9%

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

10. Final simplification 78.9%

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

Alternative 8: 57.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.38 \cdot 10^{+172}:\\ \;\;\;\;a \cdot a\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{a}^{6}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (if (<= b 1.38e+172) (* a a) (cbrt (pow a 6.0))))

C

double code(double a, double b, double angle) {
	double tmp;
	if (b <= 1.38e+172) {
		tmp = a * a;
	} else {
		tmp = cbrt(pow(a, 6.0));
	}
	return tmp;
}

Java

public static double code(double a, double b, double angle) {
	double tmp;
	if (b <= 1.38e+172) {
		tmp = a * a;
	} else {
		tmp = Math.cbrt(Math.pow(a, 6.0));
	}
	return tmp;
}

Julia

function code(a, b, angle)
	tmp = 0.0
	if (b <= 1.38e+172)
		tmp = Float64(a * a);
	else
		tmp = cbrt((a ^ 6.0));
	end
	return tmp
end

Wolfram

code[a_, b_, angle_] := If[LessEqual[b, 1.38e+172], 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 < 1.38000000000000002e172

   1. Initial program 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in angle around 0 55.1%

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

      1. unpow2 55.1%

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

   7. Applied egg-rr 55.1%

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

   if 1.38000000000000002e172 < b

   1. Initial program 99.1%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in angle around 0 20.4%

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

      1. add-sqr-sqrt 20.4%

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

      2. sqrt-unprod 24.6%

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

      3. pow-prod-up 24.6%

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

      4. metadata-eval 24.6%

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

   7. Applied egg-rr 24.6%

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

      1. add-cbrt-cube 28.4%

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

      2. pow1/3 28.4%

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

      3. add-sqr-sqrt 28.4%

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

      4. sqrt-pow1 28.4%

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

      5. metadata-eval 28.4%

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

      6. pow-prod-up 28.4%

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

      7. metadata-eval 28.4%

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

   9. Applied egg-rr 28.4%

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

       1. unpow1/3 28.4%

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

   11. Simplified 28.4%

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

Alternative 9: 56.6% accurate, 139.0× speedup

Math

\[\begin{array}{l} \\ a \cdot a \end{array} \]

FPCore

(FPCore (a b angle) :precision binary64 (* a a))

C

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

Fortran

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

Java

public static double code(double a, double b, double angle) {
	return a * a;
}

Python

def code(a, b, angle):
	return a * a

Julia

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

MATLAB

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

Wolfram

code[a_, b_, angle_] := N[(a * a), $MachinePrecision]

Derivation

1. Initial program 79.3%

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

3. Simplified 79.3%

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

5. Taylor expanded in angle around 0 52.0%

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

   1. unpow2 52.0%

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

7. Applied egg-rr 52.0%

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

Reproduce

herbie shell --seed 2024132 
(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)))