ab-angle->ABCF C

Percentage Accurate: 79.6% → 79.5%

Time: 24.8s

Alternatives: 15

Speedup: 1.0×

• 36.9% 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: 79.6% 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: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ {\left(a \cdot \cos \left({\left(\sqrt[3]{\sqrt[3]{\frac{\pi}{\frac{180}{angle}}}}\right)}^{9}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (cos (pow (cbrt (cbrt (/ PI (/ 180.0 angle)))) 9.0))) 2.0)
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))

C

double code(double a, double b, double angle) {
	return pow((a * cos(pow(cbrt(cbrt((((double) M_PI) / (180.0 / angle)))), 9.0))), 2.0) + pow((b * sin((((double) M_PI) * (angle / 180.0)))), 2.0);
}

Java

public static double code(double a, double b, double angle) {
	return Math.pow((a * Math.cos(Math.pow(Math.cbrt(Math.cbrt((Math.PI / (180.0 / angle)))), 9.0))), 2.0) + Math.pow((b * Math.sin((Math.PI * (angle / 180.0)))), 2.0);
}

Julia

function code(a, b, angle)
	return Float64((Float64(a * cos((cbrt(cbrt(Float64(pi / Float64(180.0 / angle)))) ^ 9.0))) ^ 2.0) + (Float64(b * sin(Float64(pi * Float64(angle / 180.0)))) ^ 2.0))
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Cos[N[Power[N[Power[N[Power[N[(Pi / N[(180.0 / angle), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 1/3], $MachinePrecision], 9.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

   1. clear-num 81.8%

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

   2. un-div-inv 81.7%

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

3. Applied egg-rr 81.7%

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

   1. div-inv 81.8%

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

   2. clear-num 81.8%

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

   3. rem-cube-cbrt 81.8%

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

   4. add-cube-cbrt 81.8%

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

   5. unpow2 81.8%

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

   6. pow-plus 81.8%

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

   7. metadata-eval 81.8%

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

   8. pow-pow 81.9%

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

   9. div-inv 82.0%

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

   10. metadata-eval 82.0%

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

   11. metadata-eval 82.0%

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

5. Applied egg-rr 82.0%

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

   1. /-rgt-identity 82.0%

      \[\leadsto {\left(a \cdot \cos \left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\frac{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}{1}}}}\right)}^{9}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   2. associate-*r* 82.0%

      \[\leadsto {\left(a \cdot \cos \left({\left(\sqrt[3]{\sqrt[3]{\frac{\color{blue}{\left(\pi \cdot angle\right) \cdot 0.005555555555555556}}{1}}}\right)}^{9}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   3. associate-/l* 82.0%

      \[\leadsto {\left(a \cdot \cos \left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\frac{\pi \cdot angle}{\frac{1}{0.005555555555555556}}}}}\right)}^{9}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   4. metadata-eval 82.0%

      \[\leadsto {\left(a \cdot \cos \left({\left(\sqrt[3]{\sqrt[3]{\frac{\pi \cdot angle}{\color{blue}{180}}}}\right)}^{9}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   5. associate-/l* 81.9%

      \[\leadsto {\left(a \cdot \cos \left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\frac{\pi}{\frac{180}{angle}}}}}\right)}^{9}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

7. Simplified 81.9%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{\frac{\pi}{\frac{180}{angle}}}}\right)}^{9}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

8. Final simplification 81.9%

   \[\leadsto {\left(a \cdot \cos \left({\left(\sqrt[3]{\sqrt[3]{\frac{\pi}{\frac{180}{angle}}}}\right)}^{9}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

Alternative 2: 40.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ {\left(b \cdot \sin t_0\right)}^{2} + {\left(a \cdot \cos \left({\left({t_0}^{0.3333333333333333}\right)}^{3}\right)\right)}^{2} \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* PI (/ angle 180.0))))
   (+
    (pow (* b (sin t_0)) 2.0)
    (pow (* a (cos (pow (pow t_0 0.3333333333333333) 3.0))) 2.0))))

C

double code(double a, double b, double angle) {
	double t_0 = ((double) M_PI) * (angle / 180.0);
	return pow((b * sin(t_0)), 2.0) + pow((a * cos(pow(pow(t_0, 0.3333333333333333), 3.0))), 2.0);
}

Java

public static double code(double a, double b, double angle) {
	double t_0 = Math.PI * (angle / 180.0);
	return Math.pow((b * Math.sin(t_0)), 2.0) + Math.pow((a * Math.cos(Math.pow(Math.pow(t_0, 0.3333333333333333), 3.0))), 2.0);
}

Python

def code(a, b, angle):
	t_0 = math.pi * (angle / 180.0)
	return math.pow((b * math.sin(t_0)), 2.0) + math.pow((a * math.cos(math.pow(math.pow(t_0, 0.3333333333333333), 3.0))), 2.0)

Julia

function code(a, b, angle)
	t_0 = Float64(pi * Float64(angle / 180.0))
	return Float64((Float64(b * sin(t_0)) ^ 2.0) + (Float64(a * cos(((t_0 ^ 0.3333333333333333) ^ 3.0))) ^ 2.0))
end

MATLAB

function tmp = code(a, b, angle)
	t_0 = pi * (angle / 180.0);
	tmp = ((b * sin(t_0)) ^ 2.0) + ((a * cos(((t_0 ^ 0.3333333333333333) ^ 3.0))) ^ 2.0);
end

Wolfram

code[a_, b_, angle_] := Block[{t$95$0 = N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]}, N[(N[Power[N[(b * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[N[Power[N[Power[t$95$0, 0.3333333333333333], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 81.8%

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

   1. add-cube-cbrt 81.8%

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

   2. pow3 81.8%

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

   3. div-inv 81.8%

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

   4. metadata-eval 81.8%

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

3. Applied egg-rr 81.8%

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

   1. pow1/3 42.5%

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

   2. metadata-eval 42.5%

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

   3. div-inv 42.6%

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

5. Applied egg-rr 42.6%

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

6. Final simplification 42.6%

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

Alternative 3: 79.6% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)
  (pow
   (* a (cos (pow (cbrt (* PI (* angle 0.005555555555555556))) 3.0)))
   2.0)))

C

double code(double a, double b, double angle) {
	return pow((b * sin((((double) M_PI) * (angle / 180.0)))), 2.0) + pow((a * cos(pow(cbrt((((double) M_PI) * (angle * 0.005555555555555556))), 3.0))), 2.0);
}

Java

public static double code(double a, double b, double angle) {
	return Math.pow((b * Math.sin((Math.PI * (angle / 180.0)))), 2.0) + Math.pow((a * Math.cos(Math.pow(Math.cbrt((Math.PI * (angle * 0.005555555555555556))), 3.0))), 2.0);
}

Julia

function code(a, b, angle)
	return Float64((Float64(b * sin(Float64(pi * Float64(angle / 180.0)))) ^ 2.0) + (Float64(a * cos((cbrt(Float64(pi * Float64(angle * 0.005555555555555556))) ^ 3.0))) ^ 2.0))
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[N[Power[N[Power[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

   1. add-cube-cbrt 81.8%

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

   2. pow3 81.8%

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

   3. div-inv 81.8%

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

   4. metadata-eval 81.8%

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

3. Applied egg-rr 81.8%

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

4. Final simplification 81.8%

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

Alternative 4: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)
  (pow (* a (cos (* 0.005555555555555556 (* PI angle)))) 2.0)))

C

double code(double a, double b, double angle) {
	return pow((b * sin((((double) M_PI) * (angle / 180.0)))), 2.0) + pow((a * 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 * (angle / 180.0)))), 2.0) + Math.pow((a * Math.cos((0.005555555555555556 * (Math.PI * angle)))), 2.0);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[N[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around inf 81.8%

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

3. Final simplification 81.8%

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

Alternative 5: 79.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp = code(a, b, angle)
	t_0 = pi * (angle / 180.0);
	tmp = ((b * sin(t_0)) ^ 2.0) + ((a * cos(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[(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 81.8%

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

2. Final simplification 81.8%

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

Alternative 6: 79.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

   1. associate-*r/ 81.8%

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

3. Applied egg-rr 81.8%

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

4. Final simplification 81.8%

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

Alternative 7: 79.5% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Taylor expanded in angle around inf 81.7%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\left(b \cdot \color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}^{2} \]
4. Step-by-step derivation

   1. associate-*r* 81.7%

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

   2. *-commutative 81.7%

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

   3. associate-*l* 81.7%

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

5. Simplified 81.7%

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

6. Final simplification 81.7%

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

Alternative 8: 79.5% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Final simplification 81.8%

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

Alternative 9: 74.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Taylor expanded in angle around 0 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)}}^{2} \]
4. Step-by-step derivation

   1. *-commutative 78.1%

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

5. Simplified 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot b\right)\right)\right)}}^{2} \]
6. Step-by-step derivation

   1. unpow2 78.1%

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

   2. associate-*r* 78.1%

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

   3. associate-*r* 78.1%

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

   4. *-commutative 78.1%

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

   5. metadata-eval 78.1%

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

   6. div-inv 78.1%

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

   7. *-commutative 78.1%

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

   8. associate-*r* 78.1%

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

   9. div-inv 78.1%

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

   10. metadata-eval 78.1%

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

   11. *-commutative 78.1%

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

   12. associate-*l* 78.1%

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

7. Applied egg-rr 78.1%

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

8. Final simplification 78.1%

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

Alternative 10: 74.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Taylor expanded in angle around 0 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)}}^{2} \]
4. Step-by-step derivation

   1. *-commutative 78.1%

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

5. Simplified 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot b\right)\right)\right)}}^{2} \]
6. Step-by-step derivation

   1. unpow2 78.1%

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

   2. *-commutative 78.1%

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

   3. associate-*r* 78.1%

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

   4. associate-*r* 78.1%

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

   5. *-commutative 78.1%

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

   6. metadata-eval 78.1%

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

   7. div-inv 78.1%

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

   8. *-commutative 78.1%

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

   9. associate-*r* 78.1%

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

   10. div-inv 78.1%

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

   11. metadata-eval 78.1%

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

   12. *-commutative 78.1%

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

   13. associate-*l* 78.1%

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

7. Applied egg-rr 78.1%

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

8. Final simplification 78.1%

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

Alternative 11: 74.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ {a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+ (pow a 2.0) (* 3.08641975308642e-5 (pow (* angle (* PI b)) 2.0))))

C

double code(double a, double b, double angle) {
	return pow(a, 2.0) + (3.08641975308642e-5 * pow((angle * (((double) M_PI) * b)), 2.0));
}

Java

public static double code(double a, double b, double angle) {
	return Math.pow(a, 2.0) + (3.08641975308642e-5 * Math.pow((angle * (Math.PI * b)), 2.0));
}

Python

def code(a, b, angle):
	return math.pow(a, 2.0) + (3.08641975308642e-5 * math.pow((angle * (math.pi * b)), 2.0))

Julia

function code(a, b, angle)
	return Float64((a ^ 2.0) + Float64(3.08641975308642e-5 * (Float64(angle * Float64(pi * b)) ^ 2.0)))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = (a ^ 2.0) + (3.08641975308642e-5 * ((angle * (pi * b)) ^ 2.0));
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[a, 2.0], $MachinePrecision] + N[(3.08641975308642e-5 * N[Power[N[(angle * N[(Pi * b), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Taylor expanded in angle around 0 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)}}^{2} \]
4. Step-by-step derivation

   1. *-commutative 78.1%

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

5. Simplified 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot b\right)\right)\right)}}^{2} \]
6. Step-by-step derivation

   1. *-commutative 78.1%

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

   2. unpow-prod-down 78.0%

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

   3. *-commutative 78.0%

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

   4. associate-*l* 78.1%

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

   5. metadata-eval 78.1%

      \[\leadsto {\left(a \cdot 1\right)}^{2} + {\left(\pi \cdot \left(b \cdot angle\right)\right)}^{2} \cdot \color{blue}{3.08641975308642 \cdot 10^{-5}} \]

7. Applied egg-rr 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + \color{blue}{{\left(\pi \cdot \left(b \cdot angle\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}} \]

8. Taylor expanded in b around 0 78.0%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(angle \cdot \left(b \cdot \pi\right)\right)}}^{2} \cdot 3.08641975308642 \cdot 10^{-5} \]

9. Final simplification 78.0%

   \[\leadsto {a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \]

Alternative 12: 74.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ {a}^{2} + {\left(\pi \cdot \left(angle \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+ (pow a 2.0) (* (pow (* PI (* angle b)) 2.0) 3.08641975308642e-5)))

C

double code(double a, double b, double angle) {
	return pow(a, 2.0) + (pow((((double) M_PI) * (angle * b)), 2.0) * 3.08641975308642e-5);
}

Java

public static double code(double a, double b, double angle) {
	return Math.pow(a, 2.0) + (Math.pow((Math.PI * (angle * b)), 2.0) * 3.08641975308642e-5);
}

Python

def code(a, b, angle):
	return math.pow(a, 2.0) + (math.pow((math.pi * (angle * b)), 2.0) * 3.08641975308642e-5)

Julia

function code(a, b, angle)
	return Float64((a ^ 2.0) + Float64((Float64(pi * Float64(angle * b)) ^ 2.0) * 3.08641975308642e-5))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = (a ^ 2.0) + (((pi * (angle * b)) ^ 2.0) * 3.08641975308642e-5);
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[a, 2.0], $MachinePrecision] + N[(N[Power[N[(Pi * N[(angle * b), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * 3.08641975308642e-5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Taylor expanded in angle around 0 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)}}^{2} \]
4. Step-by-step derivation

   1. *-commutative 78.1%

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

5. Simplified 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot b\right)\right)\right)}}^{2} \]
6. Step-by-step derivation

   1. *-commutative 78.1%

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

   2. unpow-prod-down 78.0%

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

   3. *-commutative 78.0%

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

   4. associate-*l* 78.1%

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

   5. metadata-eval 78.1%

      \[\leadsto {\left(a \cdot 1\right)}^{2} + {\left(\pi \cdot \left(b \cdot angle\right)\right)}^{2} \cdot \color{blue}{3.08641975308642 \cdot 10^{-5}} \]

7. Applied egg-rr 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + \color{blue}{{\left(\pi \cdot \left(b \cdot angle\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}} \]

8. Final simplification 78.1%

   \[\leadsto {a}^{2} + {\left(\pi \cdot \left(angle \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5} \]

Alternative 13: 74.2% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Taylor expanded in angle around 0 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)}}^{2} \]
4. Step-by-step derivation

   1. *-commutative 78.1%

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

5. Simplified 78.1%

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

6. Final simplification 78.1%

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

Alternative 14: 74.2% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Taylor expanded in angle around 0 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)}}^{2} \]
4. Step-by-step derivation

   1. associate-*r* 78.1%

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

   2. *-commutative 78.1%

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

5. Simplified 78.1%

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

6. Final simplification 78.1%

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

Alternative 15: 74.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ {a}^{2} + {\left(\frac{\pi \cdot b}{\frac{180}{angle}}\right)}^{2} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[a, 2.0], $MachinePrecision] + N[Power[N[(N[(Pi * b), $MachinePrecision] / N[(180.0 / angle), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

2. Taylor expanded in angle around 0 81.8%

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

3. Taylor expanded in angle around 0 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)}}^{2} \]
4. Step-by-step derivation

   1. *-commutative 78.1%

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

5. Simplified 78.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot b\right)\right)\right)}}^{2} \]
6. Step-by-step derivation

   1. associate-*r* 78.1%

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

   2. metadata-eval 78.1%

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

   3. associate-/r/ 78.1%

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

   4. associate-*l/ 78.1%

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

   5. *-un-lft-identity 78.1%

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

7. Applied egg-rr 78.1%

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

8. Final simplification 78.1%

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

Reproduce

herbie shell --seed 2023207 
(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)))