ab-angle->ABCF C

Percentage Accurate: 79.3% → 79.2%

Time: 25.0s

Alternatives: 5

Speedup: N/A×

• 36.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 79.2% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[a, 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 81.6%

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

2. Taylor expanded in angle around 0 81.7%

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

3. Final simplification 81.7%

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

Alternative 2: 79.1% 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 81.6%

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

2. Taylor expanded in angle around 0 81.7%

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

3. Taylor expanded in b around 0 71.2%

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

   1. unpow2 71.2%

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

   2. *-commutative 71.2%

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

   3. associate-*r* 71.2%

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

   4. *-commutative 71.2%

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

   5. *-commutative 71.2%

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

   6. unpow2 71.2%

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

   7. swap-sqr 81.6%

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

   8. unpow2 81.6%

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

   9. associate-*r* 81.6%

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

   10. *-commutative 81.6%

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

   11. *-commutative 81.6%

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

   12. *-commutative 81.6%

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

5. Simplified 81.6%

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

6. Final simplification 81.6%

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

Alternative 3: 72.6% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.6%

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

2. Taylor expanded in angle around 0 81.7%

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

3. Taylor expanded in angle around 0 76.5%

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

   1. *-commutative 76.5%

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

   2. *-commutative 76.5%

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

   3. associate-*r* 76.5%

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

5. Simplified 76.5%

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

   1. unpow2 76.5%

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

   2. associate-*r* 76.9%

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

   3. *-commutative 76.9%

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

   4. associate-*r* 76.9%

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

   5. associate-*l* 76.9%

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

   6. *-commutative 76.9%

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

   7. *-commutative 76.9%

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

   8. associate-*l* 76.9%

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

7. Applied egg-rr 76.9%

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

8. Final simplification 76.9%

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

Alternative 4: 74.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.6%

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

2. Taylor expanded in angle around 0 81.7%

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

3. Taylor expanded in angle around 0 76.5%

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

   1. *-commutative 76.5%

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

5. Simplified 76.5%

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

6. Final simplification 76.5%

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

Alternative 5: 74.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.6%

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

2. Taylor expanded in angle around 0 81.7%

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

3. Taylor expanded in angle around 0 76.5%

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

   1. metadata-eval 76.5%

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

   2. *-commutative 76.5%

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

   3. associate-/r/ 76.5%

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

   4. metadata-eval 76.5%

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

   5. metadata-eval 76.5%

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

   6. distribute-neg-frac 76.5%

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

   7. associate-/l* 76.5%

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

   8. metadata-eval 76.5%

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

   9. neg-mul-1 76.5%

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

   10. distribute-frac-neg 76.5%

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

   11. remove-double-neg 76.5%

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

   12. associate-*l/ 76.5%

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

   13. *-commutative 76.5%

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

5. Simplified 76.5%

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

6. Final simplification 76.5%

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

Reproduce

herbie shell --seed 2023321 
(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)))