ab-angle->ABCF C

Percentage Accurate: 80.0% → 79.9%

Time: 28.3s

Alternatives: 14

Speedup: 1.0×

• 37.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% 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: 79.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (cbrt (* PI (* angle 0.005555555555555556)))))
   (+
    (pow (* a (cos (* t_0 (pow (pow (cbrt t_0) 2.0) 3.0)))) 2.0)
    (pow (* b (sin (* PI (/ angle 180.0)))) 2.0))))

C

double code(double a, double b, double angle) {
	double t_0 = cbrt((((double) M_PI) * (angle * 0.005555555555555556)));
	return pow((a * cos((t_0 * pow(pow(cbrt(t_0), 2.0), 3.0)))), 2.0) + pow((b * sin((((double) M_PI) * (angle / 180.0)))), 2.0);
}

Java

public static double code(double a, double b, double angle) {
	double t_0 = Math.cbrt((Math.PI * (angle * 0.005555555555555556)));
	return Math.pow((a * Math.cos((t_0 * Math.pow(Math.pow(Math.cbrt(t_0), 2.0), 3.0)))), 2.0) + Math.pow((b * Math.sin((Math.PI * (angle / 180.0)))), 2.0);
}

Julia

function code(a, b, angle)
	t_0 = cbrt(Float64(pi * Float64(angle * 0.005555555555555556)))
	return Float64((Float64(a * cos(Float64(t_0 * ((cbrt(t_0) ^ 2.0) ^ 3.0)))) ^ 2.0) + (Float64(b * sin(Float64(pi * Float64(angle / 180.0)))) ^ 2.0))
end

Wolfram

code[a_, b_, angle_] := Block[{t$95$0 = N[Power[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[Power[N[(a * N[Cos[N[(t$95$0 * N[Power[N[Power[N[Power[t$95$0, 1/3], $MachinePrecision], 2.0], $MachinePrecision], 3.0], $MachinePrecision]), $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 84.1%

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

   1. add-cube-cbrt 84.1%

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

   2. pow3 84.1%

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

   3. pow-to-exp 41.9%

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

   4. div-inv 41.9%

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

   5. metadata-eval 41.9%

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

3. Applied egg-rr 41.9%

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

   1. pow-to-exp 84.1%

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

   2. rem-cube-cbrt 84.2%

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

   3. add-exp-log 41.9%

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

   4. *-un-lft-identity 41.9%

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

   5. exp-prod 41.9%

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

   6. metadata-eval 41.9%

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

   7. div-inv 41.9%

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

5. Applied egg-rr 41.9%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left({\left(e^{1}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
6. Step-by-step derivation

   1. pow-exp 41.9%

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

   2. *-un-lft-identity 41.9%

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

   3. add-exp-log 84.1%

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

   4. rem-cube-cbrt 84.1%

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

   5. add-exp-log 41.7%

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

   6. add-cube-cbrt 41.7%

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

   7. unpow-prod-down 41.7%

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

7. Applied egg-rr 84.3%

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

8. Final simplification 84.3%

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

Alternative 2: 41.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\\ {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(t_0 \cdot {\left(\sqrt{\sqrt[3]{t_0}}\right)}^{12}\right)\right)}^{2} \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (cbrt (* PI (* angle 0.005555555555555556)))))
   (+
    (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)
    (pow (* a (cos (* t_0 (pow (sqrt (cbrt t_0)) 12.0)))) 2.0))))

C

double code(double a, double b, double angle) {
	double t_0 = cbrt((((double) M_PI) * (angle * 0.005555555555555556)));
	return pow((b * sin((((double) M_PI) * (angle / 180.0)))), 2.0) + pow((a * cos((t_0 * pow(sqrt(cbrt(t_0)), 12.0)))), 2.0);
}

Java

public static double code(double a, double b, double angle) {
	double t_0 = Math.cbrt((Math.PI * (angle * 0.005555555555555556)));
	return Math.pow((b * Math.sin((Math.PI * (angle / 180.0)))), 2.0) + Math.pow((a * Math.cos((t_0 * Math.pow(Math.sqrt(Math.cbrt(t_0)), 12.0)))), 2.0);
}

Julia

function code(a, b, angle)
	t_0 = cbrt(Float64(pi * Float64(angle * 0.005555555555555556)))
	return Float64((Float64(b * sin(Float64(pi * Float64(angle / 180.0)))) ^ 2.0) + (Float64(a * cos(Float64(t_0 * (sqrt(cbrt(t_0)) ^ 12.0)))) ^ 2.0))
end

Wolfram

code[a_, b_, angle_] := Block[{t$95$0 = N[Power[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, 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[(t$95$0 * N[Power[N[Sqrt[N[Power[t$95$0, 1/3], $MachinePrecision]], $MachinePrecision], 12.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 84.1%

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

   1. add-cube-cbrt 84.1%

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

   2. pow3 84.1%

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

   3. pow-to-exp 41.9%

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

   4. div-inv 41.9%

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

   5. metadata-eval 41.9%

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

3. Applied egg-rr 41.9%

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

   1. pow-to-exp 84.1%

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

   2. rem-cube-cbrt 84.2%

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

   3. add-exp-log 41.9%

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

   4. *-un-lft-identity 41.9%

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

   5. exp-prod 41.9%

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

   6. metadata-eval 41.9%

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

   7. div-inv 41.9%

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

5. Applied egg-rr 41.9%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left({\left(e^{1}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
6. Step-by-step derivation

   1. pow-exp 41.9%

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

   2. *-un-lft-identity 41.9%

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

   3. add-exp-log 84.1%

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

   4. rem-cube-cbrt 84.1%

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

   5. add-exp-log 41.7%

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

   6. add-cube-cbrt 41.7%

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

   7. unpow-prod-down 41.7%

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

7. Applied egg-rr 84.3%

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

   1. pow-pow 84.1%

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

   2. add-sqr-sqrt 41.8%

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

   3. unpow-prod-down 41.9%

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

   4. metadata-eval 41.9%

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

   5. metadata-eval 41.9%

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

9. Applied egg-rr 41.9%

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

    1. pow-sqr 41.9%

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

    2. metadata-eval 41.9%

       \[\leadsto {\left(a \cdot \cos \left({\left(\sqrt{\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}}\right)}^{\color{blue}{12}} \cdot \sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

11. Simplified 41.9%

    \[\leadsto {\left(a \cdot \cos \left(\color{blue}{{\left(\sqrt{\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}}\right)}^{12}} \cdot \sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

12. Final simplification 41.9%

    \[\leadsto {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)} \cdot {\left(\sqrt{\sqrt[3]{\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}}\right)}^{12}\right)\right)}^{2} \]

Alternative 3: 41.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\left(2 \cdot \log \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}\right)\right)}^{2} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)
  (pow
   (*
    a
    (cos (pow (exp 0.5) (* 2.0 (log (* 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(pow(exp(0.5), (2.0 * log((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(Math.pow(Math.exp(0.5), (2.0 * Math.log((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(math.pow(math.exp(0.5), (2.0 * math.log((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((exp(0.5) ^ Float64(2.0 * log(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((exp(0.5) ^ (2.0 * log((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[Power[N[Exp[0.5], $MachinePrecision], N[(2.0 * N[Log[N[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.1%

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

   1. add-cube-cbrt 84.1%

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

   2. pow3 84.1%

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

   3. pow-to-exp 41.9%

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

   4. div-inv 41.9%

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

   5. metadata-eval 41.9%

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

3. Applied egg-rr 41.9%

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

   1. pow-to-exp 84.1%

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

   2. rem-cube-cbrt 84.2%

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

   3. add-exp-log 41.9%

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

   4. *-un-lft-identity 41.9%

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

   5. exp-prod 41.9%

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

   6. metadata-eval 41.9%

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

   7. div-inv 41.9%

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

5. Applied egg-rr 41.9%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left({\left(e^{1}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
6. Step-by-step derivation

   1. add-sqr-sqrt 41.8%

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

   2. unpow-prod-down 41.8%

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

   3. add-exp-log 41.8%

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

   4. pow1/2 41.8%

      \[\leadsto {\left(a \cdot \cos \left({\left(e^{\log \color{blue}{\left({\left(e^{1}\right)}^{0.5}\right)}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)} \cdot {\left(\sqrt{e^{1}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   5. log-pow 41.8%

      \[\leadsto {\left(a \cdot \cos \left({\left(e^{\color{blue}{0.5 \cdot \log \left(e^{1}\right)}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)} \cdot {\left(\sqrt{e^{1}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   6. add-log-exp 41.8%

      \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5 \cdot \color{blue}{1}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)} \cdot {\left(\sqrt{e^{1}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   7. metadata-eval 41.8%

      \[\leadsto {\left(a \cdot \cos \left({\left(e^{\color{blue}{0.5}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)} \cdot {\left(\sqrt{e^{1}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   8. div-inv 41.8%

      \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)} \cdot {\left(\sqrt{e^{1}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   9. metadata-eval 41.8%

      \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)} \cdot {\left(\sqrt{e^{1}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   10. add-exp-log 41.8%

       \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot {\color{blue}{\left(e^{\log \left(\sqrt{e^{1}}\right)}\right)}}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   11. pow1/2 41.8%

       \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot {\left(e^{\log \color{blue}{\left({\left(e^{1}\right)}^{0.5}\right)}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   12. log-pow 41.8%

       \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot {\left(e^{\color{blue}{0.5 \cdot \log \left(e^{1}\right)}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   13. add-log-exp 41.8%

       \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot {\left(e^{0.5 \cdot \color{blue}{1}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   14. metadata-eval 41.8%

       \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot {\left(e^{\color{blue}{0.5}}\right)}^{\log \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   15. div-inv 41.8%

       \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot {\left(e^{0.5}\right)}^{\log \left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   16. metadata-eval 41.8%

       \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot {\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

7. Applied egg-rr 41.8%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left({\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot {\left(e^{0.5}\right)}^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
8. Step-by-step derivation

   1. pow-sqr 41.8%

      \[\leadsto {\left(a \cdot \cos \color{blue}{\left({\left(e^{0.5}\right)}^{\left(2 \cdot \log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   2. associate-*r* 41.8%

      \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\left(2 \cdot \log \color{blue}{\left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   3. *-commutative 41.8%

      \[\leadsto {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\left(2 \cdot \log \color{blue}{\left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

9. Simplified 41.8%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left({\left(e^{0.5}\right)}^{\left(2 \cdot \log \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

10. Final simplification 41.8%

    \[\leadsto {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left({\left(e^{0.5}\right)}^{\left(2 \cdot \log \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}\right)\right)}^{2} \]

Alternative 4: 41.1% accurate, 0.7× speedup

Math

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

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 E (log 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(pow(((double) M_E), log(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(Math.pow(Math.E, Math.log(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(math.pow(math.e, math.log(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((exp(1) ^ log(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((2.71828182845904523536 ^ log(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[N[Power[E, N[Log[t$95$0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 84.1%

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

   1. add-cube-cbrt 84.1%

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

   2. pow3 84.1%

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

   3. pow-to-exp 41.9%

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

   4. div-inv 41.9%

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

   5. metadata-eval 41.9%

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

3. Applied egg-rr 41.9%

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

   1. pow-to-exp 84.1%

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

   2. rem-cube-cbrt 84.2%

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

   3. add-exp-log 41.9%

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

   4. *-un-lft-identity 41.9%

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

   5. exp-prod 41.9%

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

   6. metadata-eval 41.9%

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

   7. div-inv 41.9%

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

5. Applied egg-rr 41.9%

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

6. Final simplification 41.9%

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

Alternative 5: 79.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(angle \cdot \left(\sqrt[3]{-1.7146776406035666 \cdot 10^{-7}} \cdot \left(-\pi\right)\right)\right)\right)}^{2} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)
  (pow (* a (cos (* angle (* (cbrt -1.7146776406035666e-7) (- PI))))) 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((angle * (cbrt(-1.7146776406035666e-7) * -((double) M_PI))))), 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((angle * (Math.cbrt(-1.7146776406035666e-7) * -Math.PI)))), 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(angle * Float64(cbrt(-1.7146776406035666e-7) * Float64(-pi))))) ^ 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[(angle * N[(N[Power[-1.7146776406035666e-7, 1/3], $MachinePrecision] * (-Pi)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.1%

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

   1. add-cbrt-cube 63.3%

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

   2. pow1/3 49.9%

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

   3. pow3 49.9%

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

   4. div-inv 49.9%

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

   5. metadata-eval 49.9%

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

3. Applied egg-rr 49.9%

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

4. Taylor expanded in angle around -inf 84.2%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left(-1 \cdot \left(angle \cdot \left(\sqrt[3]{-1.7146776406035666 \cdot 10^{-7}} \cdot \pi\right)\right)\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
5. Step-by-step derivation

   1. associate-*r* 84.2%

      \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\left(-1 \cdot angle\right) \cdot \left(\sqrt[3]{-1.7146776406035666 \cdot 10^{-7}} \cdot \pi\right)\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   2. neg-mul-1 84.2%

      \[\leadsto {\left(a \cdot \cos \left(\color{blue}{\left(-angle\right)} \cdot \left(\sqrt[3]{-1.7146776406035666 \cdot 10^{-7}} \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

   3. *-commutative 84.2%

      \[\leadsto {\left(a \cdot \cos \left(\left(-angle\right) \cdot \color{blue}{\left(\pi \cdot \sqrt[3]{-1.7146776406035666 \cdot 10^{-7}}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

6. Simplified 84.2%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\left(-angle\right) \cdot \left(\pi \cdot \sqrt[3]{-1.7146776406035666 \cdot 10^{-7}}\right)\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

7. Final simplification 84.2%

   \[\leadsto {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(angle \cdot \left(\sqrt[3]{-1.7146776406035666 \cdot 10^{-7}} \cdot \left(-\pi\right)\right)\right)\right)}^{2} \]

Alternative 6: 80.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)
  (pow (* a (cos (* PI (* angle 0.005555555555555556)))) 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 * 0.005555555555555556)))), 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 * 0.005555555555555556)))), 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 * 0.005555555555555556)))), 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(pi * Float64(angle * 0.005555555555555556)))) ^ 2.0))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = ((b * sin((pi * (angle / 180.0)))) ^ 2.0) + ((a * cos((pi * (angle * 0.005555555555555556)))) ^ 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[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.1%

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

2. Taylor expanded in angle around inf 84.0%

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

   1. *-commutative 84.0%

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

   2. *-commutative 84.0%

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

   3. associate-*r* 84.2%

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

4. Simplified 84.2%

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

5. Final simplification 84.2%

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

Alternative 7: 80.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)
  (pow (* a (cos (/ PI (/ 180.0 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((((double) M_PI) / (180.0 / 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((Math.PI / (180.0 / 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((math.pi / (180.0 / 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(pi / Float64(180.0 / angle)))) ^ 2.0))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = ((b * sin((pi * (angle / 180.0)))) ^ 2.0) + ((a * cos((pi / (180.0 / 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[(Pi / N[(180.0 / angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.1%

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

   1. clear-num 84.1%

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

   2. un-div-inv 84.2%

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

3. Applied egg-rr 84.2%

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

4. Final simplification 84.2%

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

Alternative 8: 80.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow a 2.0)
  (pow (* b (log1p (expm1 (sin (* PI (* angle 0.005555555555555556)))))) 2.0)))

C

double code(double a, double b, double angle) {
	return pow(a, 2.0) + pow((b * log1p(expm1(sin((((double) M_PI) * (angle * 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.log1p(Math.expm1(Math.sin((Math.PI * (angle * 0.005555555555555556)))))), 2.0);
}

Python

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

Julia

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[a, 2.0], $MachinePrecision] + N[Power[N[(b * N[Log[1 + N[(Exp[N[Sin[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.1%

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

2. Taylor expanded in angle around 0 84.0%

   \[\leadsto {\left(a \cdot \color{blue}{1}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
3. Step-by-step derivation

   1. log1p-expm1-u 84.1%

      \[\leadsto {\left(a \cdot 1\right)}^{2} + {\left(b \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)}\right)}^{2} \]

   2. div-inv 84.1%

      \[\leadsto {\left(a \cdot 1\right)}^{2} + {\left(b \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)\right)\right)\right)}^{2} \]

   3. metadata-eval 84.1%

      \[\leadsto {\left(a \cdot 1\right)}^{2} + {\left(b \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)\right)\right)\right)}^{2} \]

4. Applied egg-rr 84.1%

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\left(b \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}\right)}^{2} \]

5. Final simplification 84.1%

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

Alternative 9: 80.0% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

2. Taylor expanded in angle around 0 84.0%

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

3. Taylor expanded in angle around inf 84.1%

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

4. Final simplification 84.1%

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

Alternative 10: 74.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.75 \cdot 10^{+207}:\\ \;\;\;\;{a}^{2} + \left(angle \cdot 0.005555555555555556\right) \cdot \left(\left(\pi \cdot b\right) \cdot \left(angle \cdot \left(0.005555555555555556 \cdot \left(\pi \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(b \cdot \left(\pi \cdot angle\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (if (<= b 1.75e+207)
   (+
    (pow a 2.0)
    (*
     (* angle 0.005555555555555556)
     (* (* PI b) (* angle (* 0.005555555555555556 (* PI b))))))
   (+ (pow a 2.0) (* (pow (* b (* PI angle)) 2.0) 3.08641975308642e-5))))

C

double code(double a, double b, double angle) {
	double tmp;
	if (b <= 1.75e+207) {
		tmp = pow(a, 2.0) + ((angle * 0.005555555555555556) * ((((double) M_PI) * b) * (angle * (0.005555555555555556 * (((double) M_PI) * b)))));
	} else {
		tmp = pow(a, 2.0) + (pow((b * (((double) M_PI) * angle)), 2.0) * 3.08641975308642e-5);
	}
	return tmp;
}

Java

public static double code(double a, double b, double angle) {
	double tmp;
	if (b <= 1.75e+207) {
		tmp = Math.pow(a, 2.0) + ((angle * 0.005555555555555556) * ((Math.PI * b) * (angle * (0.005555555555555556 * (Math.PI * b)))));
	} else {
		tmp = Math.pow(a, 2.0) + (Math.pow((b * (Math.PI * angle)), 2.0) * 3.08641975308642e-5);
	}
	return tmp;
}

Python

def code(a, b, angle):
	tmp = 0
	if b <= 1.75e+207:
		tmp = math.pow(a, 2.0) + ((angle * 0.005555555555555556) * ((math.pi * b) * (angle * (0.005555555555555556 * (math.pi * b)))))
	else:
		tmp = math.pow(a, 2.0) + (math.pow((b * (math.pi * angle)), 2.0) * 3.08641975308642e-5)
	return tmp

Julia

function code(a, b, angle)
	tmp = 0.0
	if (b <= 1.75e+207)
		tmp = Float64((a ^ 2.0) + Float64(Float64(angle * 0.005555555555555556) * Float64(Float64(pi * b) * Float64(angle * Float64(0.005555555555555556 * Float64(pi * b))))));
	else
		tmp = Float64((a ^ 2.0) + Float64((Float64(b * Float64(pi * angle)) ^ 2.0) * 3.08641975308642e-5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, angle)
	tmp = 0.0;
	if (b <= 1.75e+207)
		tmp = (a ^ 2.0) + ((angle * 0.005555555555555556) * ((pi * b) * (angle * (0.005555555555555556 * (pi * b)))));
	else
		tmp = (a ^ 2.0) + (((b * (pi * angle)) ^ 2.0) * 3.08641975308642e-5);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, angle_] := If[LessEqual[b, 1.75e+207], N[(N[Power[a, 2.0], $MachinePrecision] + N[(N[(angle * 0.005555555555555556), $MachinePrecision] * N[(N[(Pi * b), $MachinePrecision] * N[(angle * N[(0.005555555555555556 * N[(Pi * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[a, 2.0], $MachinePrecision] + N[(N[Power[N[(b * N[(Pi * angle), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * 3.08641975308642e-5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.75000000000000014e207

   1. Initial program 82.4%

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

   2. Taylor expanded in angle around 0 82.3%

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

   3. Taylor expanded in angle around 0 75.8%

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

      1. *-commutative 75.8%

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

   5. Simplified 75.8%

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

      1. unpow2 75.8%

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

      2. associate-*r* 75.8%

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

      3. *-commutative 75.8%

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

      4. metadata-eval 75.8%

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

      5. div-inv 75.8%

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

      6. associate-*l* 77.1%

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

      7. div-inv 77.1%

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

      8. metadata-eval 77.1%

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

      9. associate-*r* 77.1%

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

      10. *-commutative 77.1%

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

      11. associate-*l* 77.1%

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

   7. Applied egg-rr 77.1%

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

   if 1.75000000000000014e207 < b

   1. Initial program 99.8%

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

   2. Taylor expanded in angle around 0 99.8%

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

   3. Taylor expanded in angle around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. unpow-prod-down 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*l* 99.9%

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

      6. metadata-eval 99.9%

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

   7. Applied egg-rr 99.9%

      \[\leadsto {\left(a \cdot 1\right)}^{2} + \color{blue}{{\left(b \cdot \left(\pi \cdot angle\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.75 \cdot 10^{+207}:\\ \;\;\;\;{a}^{2} + \left(angle \cdot 0.005555555555555556\right) \cdot \left(\left(\pi \cdot b\right) \cdot \left(angle \cdot \left(0.005555555555555556 \cdot \left(\pi \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(b \cdot \left(\pi \cdot angle\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]

Alternative 11: 74.8% 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 84.1%

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

2. Taylor expanded in angle around 0 84.0%

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

3. Taylor expanded in angle around 0 78.2%

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

   1. *-commutative 78.2%

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

5. Simplified 78.2%

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

6. Taylor expanded in angle around 0 66.0%

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

   1. associate-*r* 66.1%

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

   2. associate-*r* 66.0%

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

   3. *-commutative 66.0%

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

   4. associate-*l* 66.0%

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

   5. unpow2 66.0%

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

   6. unpow2 66.0%

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

   7. unpow2 66.0%

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

   8. unswap-sqr 66.0%

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

   9. swap-sqr 78.2%

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

   10. unpow2 78.2%

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

   11. *-commutative 78.2%

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

   12. associate-*l* 78.2%

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

8. Simplified 78.2%

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

9. Taylor expanded in angle around 0 78.2%

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

10. Final simplification 78.2%

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

Alternative 12: 74.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

2. Taylor expanded in angle around 0 84.0%

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

3. Taylor expanded in angle around 0 78.2%

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

   1. *-commutative 78.2%

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

5. Simplified 78.2%

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

   1. *-commutative 78.2%

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

   2. unpow-prod-down 78.2%

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

   3. *-commutative 78.2%

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

   4. *-commutative 78.2%

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

   5. associate-*l* 78.2%

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

   6. metadata-eval 78.2%

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

7. Applied egg-rr 78.2%

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

8. Final simplification 78.2%

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

Alternative 13: 74.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

2. Taylor expanded in angle around 0 84.0%

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

3. Taylor expanded in angle around 0 78.2%

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

   1. *-commutative 78.2%

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

   2. associate-*l* 78.2%

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

   3. *-commutative 78.2%

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

5. Simplified 78.2%

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

6. Final simplification 78.2%

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

Alternative 14: 74.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

2. Taylor expanded in angle around 0 84.0%

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

3. Taylor expanded in angle around 0 78.2%

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

   1. *-commutative 78.2%

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

   2. associate-*l* 78.2%

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

5. Simplified 78.2%

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

6. Final simplification 78.2%

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

Reproduce

herbie shell --seed 2023230 
(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)))