ab-angle->ABCF C

Percentage Accurate: 79.5% → 79.4%

Time: 29.9s

Alternatives: 5

Speedup: N/A×

• 35.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.5% 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: 79.4% accurate, 1.0× speedup

Math

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

FPCore

NOTE: angle should be positive before calling this function
(FPCore (a b angle)
 :precision binary64
 (+
  (pow a 2.0)
  (pow
   (* b (sin (* PI (pow (sqrt (* 0.005555555555555556 angle)) 2.0))))
   2.0)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: angle should be positive before calling this function
code[a_, b_, angle_] := N[(N[Power[a, 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[Power[N[Sqrt[N[(0.005555555555555556 * angle), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.0%

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

2. Taylor expanded in angle around 0 76.0%

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

3. Taylor expanded in b around 0 75.7%

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

   1. associate-*r* 76.1%

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

   2. *-commutative 76.1%

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

5. Simplified 76.1%

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

   1. *-commutative 76.1%

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

   2. metadata-eval 76.1%

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

   3. div-inv 76.0%

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

   4. add-sqr-sqrt 36.7%

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

   5. pow2 36.7%

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

   6. div-inv 36.7%

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

   7. metadata-eval 36.7%

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

   8. *-commutative 36.7%

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

7. Applied egg-rr 36.7%

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

8. Final simplification 36.7%

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

Alternative 2: 79.4% accurate, 1.5× speedup

Math

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

FPCore

NOTE: angle should be positive before calling this function
(FPCore (a b angle)
 :precision binary64
 (+ (pow a 2.0) (pow (* b (sin (* 0.005555555555555556 (* PI angle)))) 2.0)))

C

angle = abs(angle);
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

angle = Math.abs(angle);
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

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

Julia

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

MATLAB

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

Wolfram

NOTE: angle should be positive before calling this function
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 76.0%

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

2. Taylor expanded in angle around 0 76.0%

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

3. Taylor expanded in b around 0 75.7%

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

4. Final simplification 75.7%

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

Alternative 3: 79.4% accurate, 1.5× speedup

Math

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

FPCore

NOTE: angle should be positive before calling this function
(FPCore (a b angle)
 :precision binary64
 (+ (pow a 2.0) (pow (* b (sin (* PI (* 0.005555555555555556 angle)))) 2.0)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: angle should be positive before calling this function
code[a_, b_, angle_] := N[(N[Power[a, 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[(0.005555555555555556 * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.0%

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

2. Taylor expanded in angle around 0 76.0%

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

3. Taylor expanded in b around 0 75.7%

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

   1. associate-*r* 76.1%

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

   2. *-commutative 76.1%

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

5. Simplified 76.1%

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

6. Final simplification 76.1%

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

Alternative 4: 74.3% accurate, 2.0× speedup

Math

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

FPCore

NOTE: angle should be positive before calling this function
(FPCore (a b angle)
 :precision binary64
 (+ (pow a 2.0) (* (pow (* PI (* b angle)) 2.0) 3.08641975308642e-5)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: angle should be positive before calling this function
code[a_, b_, angle_] := N[(N[Power[a, 2.0], $MachinePrecision] + N[(N[Power[N[(Pi * N[(b * angle), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * 3.08641975308642e-5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.0%

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

2. Taylor expanded in angle around 0 76.0%

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

3. Taylor expanded in angle around 0 70.8%

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

   1. *-commutative 70.8%

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

   2. unpow-prod-down 70.8%

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

   3. associate-*r* 70.8%

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

   4. *-commutative 70.8%

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

   5. metadata-eval 70.8%

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

5. Applied egg-rr 70.8%

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

6. Final simplification 70.8%

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

Alternative 5: 74.3% accurate, 2.0× speedup

Math

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

FPCore

NOTE: angle should be positive before calling this function
(FPCore (a b angle)
 :precision binary64
 (+ (pow a 2.0) (pow (* b (* angle (/ PI 180.0))) 2.0)))

C

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

Java

angle = Math.abs(angle);
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

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

Julia

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

MATLAB

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

Wolfram

NOTE: angle should be positive before calling this function
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 76.0%

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

2. Taylor expanded in angle around 0 76.0%

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

3. Taylor expanded in angle around 0 70.8%

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

   1. metadata-eval 70.8%

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

   2. *-commutative 70.8%

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

   3. associate-/r/ 70.8%

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

   4. associate-/l* 70.8%

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

   5. *-commutative 70.8%

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

   6. associate-/l* 70.8%

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

   7. metadata-eval 70.8%

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

   8. *-commutative 70.8%

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

   9. associate-*r/ 70.8%

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

5. Simplified 70.8%

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

6. Final simplification 70.8%

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

Reproduce

herbie shell --seed 2023229 
(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)))