ab-angle->ABCF C

Percentage Accurate: 79.8% → 79.7%

Time: 31.7s

Alternatives: 9

Speedup: N/A×

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

• could not determine a ground truth

  1. a = 9.865569452358299e+76
  2. b = 8.599544234028783e+125
  3. angle = -3.0358477393644936e+171

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 79.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Cos[N[Power[N[Power[N[(angle * N[(N[Power[N[Sqrt[Pi], $MachinePrecision], 2.0], $MachinePrecision] * -0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

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

   1. add-cube-cbrt 80.4%

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

   2. pow3 80.4%

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

4. Applied egg-rr 80.4%

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

   1. add-sqr-sqrt 80.4%

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

   2. pow2 80.4%

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

6. Applied egg-rr 80.4%

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

7. Final simplification 80.4%

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

Alternative 2: 79.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[N[(-0.005555555555555556 * N[(angle * N[Power[N[Power[Pi, 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

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

   1. add-cube-cbrt 80.4%

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

   2. pow3 80.4%

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

4. Applied egg-rr 80.4%

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

   1. rem-cube-cbrt 80.3%

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

   2. associate-*r* 80.3%

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

6. Applied egg-rr 80.3%

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

   1. add-cbrt-cube 80.3%

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

   2. pow3 80.3%

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

8. Applied egg-rr 80.3%

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

9. Final simplification 80.3%

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

Alternative 3: 79.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[N[Power[N[Power[N[(angle * N[(Pi * -0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

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

   1. add-cube-cbrt 80.4%

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

   2. pow3 80.4%

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

4. Applied egg-rr 80.4%

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

5. Final simplification 80.4%

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

Alternative 4: 79.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(a, b, angle):
	return math.pow((b * math.sin((math.pi * (angle / 180.0)))), 2.0) + math.pow((a * math.cos(((angle * math.pi) * 0.005555555555555556))), 2.0)

Julia

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

MATLAB

function tmp = code(a, b, angle)
	tmp = ((b * sin((pi * (angle / 180.0)))) ^ 2.0) + ((a * cos(((angle * pi) * 0.005555555555555556))) ^ 2.0);
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(a * N[Cos[N[(N[(angle * Pi), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

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

3. Taylor expanded in angle around inf 80.3%

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

4. Final simplification 80.3%

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

Alternative 5: 79.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (cos (* angle (/ PI -180.0)))) 2.0)
  (pow (* b (sin (* -0.005555555555555556 (* angle PI)))) 2.0)))

C

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

Java

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

Python

def code(a, b, angle):
	return math.pow((a * math.cos((angle * (math.pi / -180.0)))), 2.0) + math.pow((b * math.sin((-0.005555555555555556 * (angle * math.pi)))), 2.0)

Julia

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

MATLAB

function tmp = code(a, b, angle)
	tmp = ((a * cos((angle * (pi / -180.0)))) ^ 2.0) + ((b * sin((-0.005555555555555556 * (angle * pi)))) ^ 2.0);
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Cos[N[(angle * N[(Pi / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(-0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

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

3. Simplified 80.3%

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

5. Taylor expanded in angle around inf 80.3%

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

6. Final simplification 80.3%

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

Alternative 6: 79.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.3%

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

3. Simplified 80.3%

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

5. Taylor expanded in angle around 0 80.2%

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

6. Taylor expanded in b around 0 80.2%

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

7. Final simplification 80.2%

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

Alternative 7: 74.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.3%

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

3. Simplified 80.3%

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

5. Taylor expanded in angle around 0 80.2%

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

6. Taylor expanded in angle around 0 75.3%

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

7. Final simplification 75.3%

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

Alternative 8: 74.4% accurate, 3.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.3%

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

3. Simplified 80.3%

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

5. Taylor expanded in angle around 0 80.2%

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

6. Taylor expanded in angle around 0 75.3%

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

   1. unpow2 75.3%

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

   2. *-commutative 75.3%

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

   3. associate-*l* 75.3%

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

   4. *-commutative 75.3%

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

   5. *-commutative 75.3%

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

   6. associate-*l* 75.3%

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

   7. *-commutative 75.3%

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

8. Applied egg-rr 75.3%

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

9. Taylor expanded in b around 0 75.3%

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

10. Final simplification 75.3%

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

Alternative 9: 74.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := b \cdot \left(angle \cdot \pi\right)\\ {a}^{2} + t\_0 \cdot \left(-0.005555555555555556 \cdot \left(-0.005555555555555556 \cdot t\_0\right)\right) \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* b (* angle PI))))
   (+
    (pow a 2.0)
    (* t_0 (* -0.005555555555555556 (* -0.005555555555555556 t_0))))))

C

double code(double a, double b, double angle) {
	double t_0 = b * (angle * ((double) M_PI));
	return pow(a, 2.0) + (t_0 * (-0.005555555555555556 * (-0.005555555555555556 * t_0)));
}

Java

public static double code(double a, double b, double angle) {
	double t_0 = b * (angle * Math.PI);
	return Math.pow(a, 2.0) + (t_0 * (-0.005555555555555556 * (-0.005555555555555556 * t_0)));
}

Python

def code(a, b, angle):
	t_0 = b * (angle * math.pi)
	return math.pow(a, 2.0) + (t_0 * (-0.005555555555555556 * (-0.005555555555555556 * t_0)))

Julia

function code(a, b, angle)
	t_0 = Float64(b * Float64(angle * pi))
	return Float64((a ^ 2.0) + Float64(t_0 * Float64(-0.005555555555555556 * Float64(-0.005555555555555556 * t_0))))
end

MATLAB

function tmp = code(a, b, angle)
	t_0 = b * (angle * pi);
	tmp = (a ^ 2.0) + (t_0 * (-0.005555555555555556 * (-0.005555555555555556 * t_0)));
end

Wolfram

code[a_, b_, angle_] := Block[{t$95$0 = N[(b * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]}, N[(N[Power[a, 2.0], $MachinePrecision] + N[(t$95$0 * N[(-0.005555555555555556 * N[(-0.005555555555555556 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 80.3%

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

3. Simplified 80.3%

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

5. Taylor expanded in angle around 0 80.2%

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

6. Taylor expanded in angle around 0 75.3%

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

   1. unpow2 75.3%

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

   2. associate-*r* 75.3%

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

   3. *-commutative 75.3%

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

   4. associate-*l* 75.3%

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

   5. *-commutative 75.3%

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

   6. *-commutative 75.3%

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

   7. associate-*l* 75.3%

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

   8. *-commutative 75.3%

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

8. Applied egg-rr 75.3%

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

9. Final simplification 75.3%

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

Reproduce

herbie shell --seed 2024046 
(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)))