ab-angle->ABCF A

Percentage Accurate: 80.1% → 80.0%

Time: 35.8s

Alternatives: 9

Speedup: 1.3×

• 36.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ {\left(a \cdot \sin \left(0.005555555555555556 \cdot \frac{\pi}{\frac{1}{angle}}\right)\right)}^{2} + {b}^{2} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (sin (* 0.005555555555555556 (/ PI (/ 1.0 angle))))) 2.0)
  (pow b 2.0)))

C

double code(double a, double b, double angle) {
	return pow((a * sin((0.005555555555555556 * (((double) M_PI) / (1.0 / angle))))), 2.0) + pow(b, 2.0);
}

Java

public static double code(double a, double b, double angle) {
	return Math.pow((a * Math.sin((0.005555555555555556 * (Math.PI / (1.0 / angle))))), 2.0) + Math.pow(b, 2.0);
}

Python

def code(a, b, angle):
	return math.pow((a * math.sin((0.005555555555555556 * (math.pi / (1.0 / angle))))), 2.0) + math.pow(b, 2.0)

Julia

function code(a, b, angle)
	return Float64((Float64(a * sin(Float64(0.005555555555555556 * Float64(pi / Float64(1.0 / angle))))) ^ 2.0) + (b ^ 2.0))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = ((a * sin((0.005555555555555556 * (pi / (1.0 / angle))))) ^ 2.0) + (b ^ 2.0);
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Sin[N[(0.005555555555555556 * N[(Pi / N[(1.0 / angle), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.7%

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

   1. *-commutative 76.7%

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

   2. clear-num 76.7%

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

   3. un-div-inv 76.7%

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

4. Applied egg-rr 76.7%

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

5. Taylor expanded in angle around 0 76.9%

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

   1. *-un-lft-identity 76.9%

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

   2. associate-*r/ 76.9%

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

   3. div-inv 76.9%

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

   4. times-frac 76.9%

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

   5. metadata-eval 76.9%

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

7. Applied egg-rr 76.9%

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

8. Final simplification 76.9%

   \[\leadsto {\left(a \cdot \sin \left(0.005555555555555556 \cdot \frac{\pi}{\frac{1}{angle}}\right)\right)}^{2} + {b}^{2} \]
9. Add Preprocessing

Alternative 2: 80.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

   1. *-commutative 76.7%

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

   2. clear-num 76.7%

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

   3. un-div-inv 76.7%

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

4. Applied egg-rr 76.7%

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

5. Taylor expanded in angle around 0 76.9%

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

6. Final simplification 76.9%

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

Alternative 3: 80.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

   1. *-commutative 76.7%

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

   2. clear-num 76.7%

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

   3. un-div-inv 76.7%

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

4. Applied egg-rr 76.7%

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

5. Taylor expanded in angle around 0 76.9%

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

   1. div-inv 76.8%

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

   2. clear-num 76.9%

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

   3. *-commutative 76.9%

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

   4. div-inv 76.9%

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

   5. metadata-eval 76.9%

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

7. Applied egg-rr 76.9%

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

8. Final simplification 76.9%

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

Alternative 4: 80.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

   1. associate-*l/ 76.7%

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

   2. associate-/l* 76.7%

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

   3. cos-neg 76.7%

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

   4. distribute-lft-neg-out 76.7%

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

   5. distribute-frac-neg 76.7%

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

   6. distribute-frac-neg 76.7%

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

   7. distribute-lft-neg-out 76.7%

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

   8. cos-neg 76.7%

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

   9. associate-*l/ 76.7%

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

   10. associate-/l* 76.8%

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

3. Simplified 76.8%

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

5. Taylor expanded in angle around 0 76.9%

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

6. Final simplification 76.9%

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

Alternative 5: 80.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

   1. associate-*l/ 76.7%

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

   2. associate-/l* 76.7%

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

   3. cos-neg 76.7%

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

   4. distribute-lft-neg-out 76.7%

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

   5. distribute-frac-neg 76.7%

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

   6. distribute-frac-neg 76.7%

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

   7. distribute-lft-neg-out 76.7%

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

   8. cos-neg 76.7%

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

   9. associate-*l/ 76.7%

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

   10. associate-/l* 76.8%

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

3. Simplified 76.8%

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

5. Taylor expanded in angle around 0 76.9%

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

6. Taylor expanded in angle around inf 76.8%

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

7. Final simplification 76.8%

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

Alternative 6: 75.0% accurate, 3.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

   1. associate-*l/ 76.7%

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

   2. associate-/l* 76.7%

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

   3. cos-neg 76.7%

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

   4. distribute-lft-neg-out 76.7%

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

   5. distribute-frac-neg 76.7%

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

   6. distribute-frac-neg 76.7%

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

   7. distribute-lft-neg-out 76.7%

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

   8. cos-neg 76.7%

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

   9. associate-*l/ 76.7%

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

   10. associate-/l* 76.8%

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

3. Simplified 76.8%

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

5. Taylor expanded in angle around 0 76.9%

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

6. Taylor expanded in angle around 0 71.6%

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

   1. associate-*r* 71.6%

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

8. Simplified 71.6%

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

   1. unpow2 71.6%

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

   2. associate-*l* 71.6%

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

   3. *-commutative 71.6%

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

   4. associate-*l* 71.7%

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

   5. associate-*r* 71.7%

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

   6. *-commutative 71.7%

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

   7. *-commutative 71.7%

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

   8. associate-*r* 71.6%

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

   9. *-commutative 71.6%

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

10. Applied egg-rr 71.6%

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

    1. associate-*r* 71.7%

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

    2. *-commutative 71.7%

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

    3. associate-*l* 71.6%

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

    4. *-commutative 71.6%

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

    5. *-commutative 71.6%

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

    6. *-commutative 71.6%

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

    7. associate-*l* 71.7%

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

12. Simplified 71.7%

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

13. Final simplification 71.7%

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

Alternative 7: 73.4% accurate, 3.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

   1. associate-*l/ 76.7%

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

   2. associate-/l* 76.7%

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

   3. cos-neg 76.7%

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

   4. distribute-lft-neg-out 76.7%

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

   5. distribute-frac-neg 76.7%

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

   6. distribute-frac-neg 76.7%

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

   7. distribute-lft-neg-out 76.7%

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

   8. cos-neg 76.7%

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

   9. associate-*l/ 76.7%

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

   10. associate-/l* 76.8%

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

3. Simplified 76.8%

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

5. Taylor expanded in angle around 0 76.9%

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

6. Taylor expanded in angle around 0 71.6%

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

   1. associate-*r* 71.6%

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

8. Simplified 71.6%

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

   1. unpow2 71.6%

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

   2. associate-*l* 71.6%

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

   3. *-commutative 71.6%

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

   4. associate-*l* 71.7%

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

   5. associate-*r* 71.7%

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

   6. *-commutative 71.7%

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

   7. *-commutative 71.7%

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

   8. associate-*r* 71.6%

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

   9. *-commutative 71.6%

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

10. Applied egg-rr 71.6%

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

    1. associate-*r* 71.7%

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

    2. *-commutative 71.7%

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

    3. associate-*l* 71.6%

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

    4. *-commutative 71.6%

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

    5. *-commutative 71.6%

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

    6. associate-*l* 68.8%

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

    7. *-commutative 68.8%

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

    8. associate-*r* 68.8%

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

    9. associate-*l* 68.8%

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

12. Simplified 68.8%

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

13. Final simplification 68.8%

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

Alternative 8: 73.3% accurate, 3.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

   1. associate-*l/ 76.7%

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

   2. associate-/l* 76.7%

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

   3. cos-neg 76.7%

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

   4. distribute-lft-neg-out 76.7%

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

   5. distribute-frac-neg 76.7%

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

   6. distribute-frac-neg 76.7%

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

   7. distribute-lft-neg-out 76.7%

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

   8. cos-neg 76.7%

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

   9. associate-*l/ 76.7%

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

   10. associate-/l* 76.8%

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

3. Simplified 76.8%

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

5. Taylor expanded in angle around 0 76.9%

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

6. Taylor expanded in angle around 0 71.6%

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

   1. associate-*r* 71.6%

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

8. Simplified 71.6%

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

   1. unpow2 71.6%

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

   2. associate-*l* 71.6%

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

   3. *-commutative 71.6%

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

   4. associate-*l* 71.7%

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

   5. associate-*r* 71.7%

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

   6. *-commutative 71.7%

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

   7. *-commutative 71.7%

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

   8. associate-*r* 71.6%

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

   9. *-commutative 71.6%

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

10. Applied egg-rr 71.6%

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

    1. associate-*l* 68.7%

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

    2. *-commutative 68.7%

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

    3. associate-*l* 68.7%

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

12. Simplified 68.7%

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

13. Taylor expanded in angle around 0 68.7%

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

    1. *-commutative 68.7%

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

    2. *-commutative 68.7%

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

    3. *-commutative 68.7%

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

    4. associate-*l* 68.8%

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

15. Simplified 68.8%

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

16. Final simplification 68.8%

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

Alternative 9: 73.3% accurate, 3.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

   1. associate-*l/ 76.7%

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

   2. associate-/l* 76.7%

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

   3. cos-neg 76.7%

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

   4. distribute-lft-neg-out 76.7%

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

   5. distribute-frac-neg 76.7%

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

   6. distribute-frac-neg 76.7%

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

   7. distribute-lft-neg-out 76.7%

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

   8. cos-neg 76.7%

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

   9. associate-*l/ 76.7%

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

   10. associate-/l* 76.8%

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

3. Simplified 76.8%

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

5. Taylor expanded in angle around 0 76.9%

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

6. Taylor expanded in angle around 0 71.6%

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

   1. associate-*r* 71.6%

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

8. Simplified 71.6%

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

   1. unpow2 71.6%

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

   2. associate-*l* 71.6%

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

   3. *-commutative 71.6%

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

   4. associate-*l* 71.7%

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

   5. associate-*r* 71.7%

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

   6. *-commutative 71.7%

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

   7. *-commutative 71.7%

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

   8. associate-*r* 71.6%

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

   9. *-commutative 71.6%

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

10. Applied egg-rr 71.6%

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

    1. associate-*l* 68.7%

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

    2. *-commutative 68.7%

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

    3. associate-*l* 68.7%

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

12. Simplified 68.7%

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

13. Taylor expanded in angle around 0 68.7%

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

14. Final simplification 68.7%

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

Reproduce

herbie shell --seed 2024086 
(FPCore (a b angle)
  :name "ab-angle->ABCF A"
  :precision binary64
  (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))