ab-angle->ABCF C

Percentage Accurate: 80.2% → 80.1%

Time: 39.2s

Alternatives: 7

Speedup: N/A×

• 37.0% 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: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ {\left(a \cdot \cos t\_0\right)}^{2} + {\left(b \cdot \sin t\_0\right)}^{2} \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ {a}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{-1}{\frac{-180}{angle}}\right)\right)}^{2} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+ (pow a 2.0) (pow (* b (sin (* PI (/ -1.0 (/ -180.0 angle))))) 2.0)))

C

double code(double a, double b, double angle) {
	return pow(a, 2.0) + pow((b * sin((((double) M_PI) * (-1.0 / (-180.0 / 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((Math.PI * (-1.0 / (-180.0 / angle))))), 2.0);
}

Python

def code(a, b, angle):
	return math.pow(a, 2.0) + math.pow((b * math.sin((math.pi * (-1.0 / (-180.0 / angle))))), 2.0)

Julia

function code(a, b, angle)
	return Float64((a ^ 2.0) + (Float64(b * sin(Float64(pi * Float64(-1.0 / Float64(-180.0 / angle))))) ^ 2.0))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = (a ^ 2.0) + ((b * sin((pi * (-1.0 / (-180.0 / angle))))) ^ 2.0);
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[a, 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[(-1.0 / N[(-180.0 / angle), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.1%

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

3. Simplified 78.1%

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

5. Taylor expanded in angle around 0 78.3%

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

   1. metadata-eval 78.3%

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

   2. div-inv 78.4%

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

   3. clear-num 78.4%

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

   4. un-div-inv 78.4%

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

7. Applied egg-rr 78.4%

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

   1. frac-2neg 78.4%

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

   2. div-inv 78.4%

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

   3. distribute-neg-frac 78.4%

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

   4. metadata-eval 78.4%

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

9. Applied egg-rr 78.4%

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

10. Final simplification 78.4%

    \[\leadsto {a}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{-1}{\frac{-180}{angle}}\right)\right)}^{2} \]
11. Add Preprocessing

Alternative 2: 80.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

3. Simplified 78.1%

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

5. Taylor expanded in angle around 0 78.3%

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

   1. metadata-eval 78.3%

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

   2. div-inv 78.4%

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

   3. clear-num 78.4%

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

   4. un-div-inv 78.4%

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

7. Applied egg-rr 78.4%

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

8. Final simplification 78.4%

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

Alternative 3: 80.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

3. Simplified 78.1%

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

5. Taylor expanded in angle around 0 78.3%

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

   1. *-commutative 78.3%

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

   2. associate-*r* 78.4%

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

7. Applied egg-rr 78.4%

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

8. Final simplification 78.4%

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

Alternative 4: 80.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp = code(a, b, angle)
	tmp = (a ^ 2.0) + ((b * sin((pi * (angle * 0.005555555555555556)))) ^ 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 * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.1%

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

3. Simplified 78.1%

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

5. Taylor expanded in angle around 0 78.3%

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

6. Final simplification 78.3%

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

Alternative 5: 73.4% accurate, 3.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

3. Simplified 78.1%

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

5. Taylor expanded in angle around 0 78.3%

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

6. Taylor expanded in angle around 0 72.3%

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

   1. unpow2 72.3%

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

   2. associate-*r* 72.4%

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

   3. associate-*r* 72.6%

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

   4. *-commutative 72.6%

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

   5. associate-*l* 72.6%

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

   6. *-commutative 72.6%

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

8. Applied egg-rr 72.6%

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

9. Final simplification 72.6%

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

Alternative 6: 73.3% accurate, 3.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

3. Simplified 78.1%

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

5. Taylor expanded in angle around 0 78.3%

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

6. Taylor expanded in angle around 0 72.3%

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

   1. unpow2 72.3%

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

   2. associate-*r* 72.4%

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

   3. associate-*l* 70.9%

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

   4. *-commutative 70.9%

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

   5. *-commutative 70.9%

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

   6. associate-*l* 70.9%

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

8. Applied egg-rr 70.9%

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

   1. *-commutative 70.9%

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

   2. associate-*r* 72.6%

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

   3. *-commutative 72.6%

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

   4. *-commutative 72.6%

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

   5. associate-*l* 72.6%

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

   6. associate-*l* 72.6%

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

10. Applied egg-rr 72.6%

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

11. Final simplification 72.6%

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

Alternative 7: 75.1% accurate, 3.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

3. Simplified 78.1%

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

5. Taylor expanded in angle around 0 78.3%

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

6. Taylor expanded in angle around 0 72.3%

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

   1. unpow2 72.3%

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

   2. associate-*r* 72.4%

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

   3. associate-*l* 70.9%

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

   4. *-commutative 70.9%

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

   5. *-commutative 70.9%

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

   6. associate-*l* 70.9%

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

8. Applied egg-rr 70.9%

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

   1. *-commutative 70.9%

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

   2. associate-*r* 70.9%

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

   3. associate-*l* 72.4%

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

   4. associate-*l* 72.4%

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

   5. associate-*r* 72.4%

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

   6. *-commutative 72.4%

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

   7. associate-*l* 72.4%

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

10. Applied egg-rr 72.4%

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

    1. *-commutative 72.4%

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

    2. associate-*r* 72.3%

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

    3. *-commutative 72.3%

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

    4. associate-*l* 72.4%

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

    5. *-commutative 72.4%

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

    6. metadata-eval 72.4%

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

    7. associate-/r/ 72.3%

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

    8. associate-*l/ 72.4%

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

    9. *-lft-identity 72.4%

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

    10. *-commutative 72.4%

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

    11. remove-double-div 72.4%

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

    12. associate-/r/ 72.4%

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

    13. metadata-eval 72.4%

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

    14. times-frac 72.4%

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

    15. metadata-eval 72.4%

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

    16. *-lft-identity 72.4%

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

    17. associate-*l/ 72.4%

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

    18. remove-double-div 72.4%

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

12. Simplified 72.4%

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

13. Final simplification 72.4%

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

Reproduce

herbie shell --seed 2024096 
(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)))