ab-angle->ABCF A

Percentage Accurate: 79.6% → 79.5%

Time: 44.7s

Alternatives: 9

Speedup: N/A×

• 36.1% 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: 79.6% 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: 79.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ \begin{array}{l} t_0 := \sqrt[3]{\log \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)}\\ {\left(a \cdot \sin \left(\frac{angle_m}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(e^{{t_0}^{2}}\right)}^{t_0}\right)\right)}^{2} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (let* ((t_0 (cbrt (log (* PI (* angle_m 0.005555555555555556))))))
   (+
    (pow (* a (sin (* (/ angle_m 180.0) PI))) 2.0)
    (pow (* b (cos (pow (exp (pow t_0 2.0)) t_0))) 2.0))))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	double t_0 = cbrt(log((((double) M_PI) * (angle_m * 0.005555555555555556))));
	return pow((a * sin(((angle_m / 180.0) * ((double) M_PI)))), 2.0) + pow((b * cos(pow(exp(pow(t_0, 2.0)), t_0))), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	double t_0 = Math.cbrt(Math.log((Math.PI * (angle_m * 0.005555555555555556))));
	return Math.pow((a * Math.sin(((angle_m / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos(Math.pow(Math.exp(Math.pow(t_0, 2.0)), t_0))), 2.0);
}

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	t_0 = cbrt(log(Float64(pi * Float64(angle_m * 0.005555555555555556))))
	return Float64((Float64(a * sin(Float64(Float64(angle_m / 180.0) * pi))) ^ 2.0) + (Float64(b * cos((exp((t_0 ^ 2.0)) ^ t_0))) ^ 2.0))
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := Block[{t$95$0 = N[Power[N[Log[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[Power[N[(a * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[Power[N[Exp[N[Power[t$95$0, 2.0], $MachinePrecision]], $MachinePrecision], t$95$0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.9%

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

   1. add-exp-log 38.4%

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

   2. associate-*l/ 38.4%

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

   3. associate-*r/ 38.4%

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

   4. div-inv 38.4%

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

   5. metadata-eval 38.4%

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

3. Applied egg-rr 38.4%

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

   1. add-cube-cbrt 38.3%

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

   2. exp-prod 38.4%

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

   3. pow2 38.4%

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

   4. associate-*r* 38.4%

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

   5. *-commutative 38.4%

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

   6. associate-*r* 38.4%

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

   7. *-commutative 38.4%

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

5. Applied egg-rr 38.4%

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

   1. *-commutative 38.4%

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

   2. associate-*r* 38.4%

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

   3. *-commutative 38.4%

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

   4. associate-*l* 38.4%

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

   5. *-commutative 38.4%

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

   6. associate-*r* 38.4%

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

   7. *-commutative 38.4%

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

   8. associate-*l* 38.4%

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

7. Simplified 38.4%

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

8. Final simplification 38.4%

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

Alternative 2: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ {\left(a \cdot \sin \left(\frac{angle_m}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle_m \cdot 0.005555555555555556}\right)}^{2} \cdot \left(\pi \cdot {\left(angle_m \cdot 0.005555555555555556\right)}^{0.3333333333333333}\right)\right)\right)}^{2} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+
  (pow (* a (sin (* (/ angle_m 180.0) PI))) 2.0)
  (pow
   (*
    b
    (cos
     (*
      (pow (cbrt (* angle_m 0.005555555555555556)) 2.0)
      (* PI (pow (* angle_m 0.005555555555555556) 0.3333333333333333)))))
   2.0)))

C

angle_m = fabs(angle);
double code(double a, double b, double angle_m) {
	return pow((a * sin(((angle_m / 180.0) * ((double) M_PI)))), 2.0) + pow((b * cos((pow(cbrt((angle_m * 0.005555555555555556)), 2.0) * (((double) M_PI) * pow((angle_m * 0.005555555555555556), 0.3333333333333333))))), 2.0);
}

Java

angle_m = Math.abs(angle);
public static double code(double a, double b, double angle_m) {
	return Math.pow((a * Math.sin(((angle_m / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos((Math.pow(Math.cbrt((angle_m * 0.005555555555555556)), 2.0) * (Math.PI * Math.pow((angle_m * 0.005555555555555556), 0.3333333333333333))))), 2.0);
}

Julia

angle_m = abs(angle)
function code(a, b, angle_m)
	return Float64((Float64(a * sin(Float64(Float64(angle_m / 180.0) * pi))) ^ 2.0) + (Float64(b * cos(Float64((cbrt(Float64(angle_m * 0.005555555555555556)) ^ 2.0) * Float64(pi * (Float64(angle_m * 0.005555555555555556) ^ 0.3333333333333333))))) ^ 2.0))
end

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[N[(a * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[Power[N[Power[N[(angle$95$m * 0.005555555555555556), $MachinePrecision], 1/3], $MachinePrecision], 2.0], $MachinePrecision] * N[(Pi * N[Power[N[(angle$95$m * 0.005555555555555556), $MachinePrecision], 0.3333333333333333], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. add-exp-log 38.4%

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

   2. associate-*l/ 38.4%

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

   3. associate-*r/ 38.4%

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

   4. div-inv 38.4%

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

   5. metadata-eval 38.4%

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

3. Applied egg-rr 38.4%

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

   1. rem-exp-log 80.0%

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

   2. metadata-eval 80.0%

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

   3. div-inv 80.0%

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

   4. associate-*r/ 80.0%

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

   5. associate-*l/ 79.9%

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

   6. add-cube-cbrt 80.1%

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

   7. associate-*l* 79.9%

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

   8. pow2 79.9%

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

   9. div-inv 80.0%

      \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{\color{blue}{angle \cdot \frac{1}{180}}}\right)}^{2} \cdot \left(\sqrt[3]{\frac{angle}{180}} \cdot \pi\right)\right)\right)}^{2} \]

   10. metadata-eval 80.0%

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

   11. div-inv 79.9%

       \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2} \cdot \left(\sqrt[3]{\color{blue}{angle \cdot \frac{1}{180}}} \cdot \pi\right)\right)\right)}^{2} \]

   12. metadata-eval 79.9%

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

5. Applied egg-rr 79.9%

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

   1. pow1/3 38.4%

      \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2} \cdot \left(\color{blue}{{\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}} \cdot \pi\right)\right)\right)}^{2} \]

   2. *-commutative 38.4%

      \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2} \cdot \left({\color{blue}{\left(0.005555555555555556 \cdot angle\right)}}^{0.3333333333333333} \cdot \pi\right)\right)\right)}^{2} \]

7. Applied egg-rr 38.4%

   \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2} \cdot \left(\color{blue}{{\left(0.005555555555555556 \cdot angle\right)}^{0.3333333333333333}} \cdot \pi\right)\right)\right)}^{2} \]

8. Final simplification 38.4%

   \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2} \cdot \left(\pi \cdot {\left(angle \cdot 0.005555555555555556\right)}^{0.3333333333333333}\right)\right)\right)}^{2} \]

Alternative 3: 79.5% accurate, 0.8× speedup

Math

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

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+
  (pow (* a (sin (* (/ angle_m 180.0) PI))) 2.0)
  (pow (* b (cos (exp (log (* angle_m (* PI 0.005555555555555556)))))) 2.0)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[N[(a * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[Exp[N[Log[N[(angle$95$m * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. add-exp-log 38.4%

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

   2. associate-*l/ 38.4%

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

   3. associate-*r/ 38.4%

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

   4. div-inv 38.4%

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

   5. metadata-eval 38.4%

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

3. Applied egg-rr 38.4%

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

4. Final simplification 38.4%

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

Alternative 4: 79.4% accurate, 1.5× speedup

Math

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

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+ (pow b 2.0) (pow (* a (sin (* 0.005555555555555556 (* angle_m PI)))) 2.0)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[b, 2.0], $MachinePrecision] + N[Power[N[(a * N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. *-commutative 79.9%

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

   2. associate-*r/ 79.9%

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

   3. associate-*l/ 80.0%

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

   4. *-commutative 80.0%

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

   5. *-commutative 80.0%

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

   6. associate-*r/ 80.0%

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

   7. associate-*l/ 80.0%

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

   8. *-commutative 80.0%

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

3. Simplified 80.0%

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

4. Taylor expanded in angle around 0 80.1%

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

5. Taylor expanded in angle around inf 80.0%

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

6. Final simplification 80.0%

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

Alternative 5: 79.5% accurate, 1.5× speedup

Math

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

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+ (pow b 2.0) (pow (* a (sin (* angle_m (/ PI 180.0)))) 2.0)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[b, 2.0], $MachinePrecision] + N[Power[N[(a * N[Sin[N[(angle$95$m * N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. *-commutative 79.9%

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

   2. associate-*r/ 79.9%

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

   3. associate-*l/ 80.0%

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

   4. *-commutative 80.0%

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

   5. *-commutative 80.0%

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

   6. associate-*r/ 80.0%

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

   7. associate-*l/ 80.0%

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

   8. *-commutative 80.0%

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

3. Simplified 80.0%

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

4. Taylor expanded in angle around 0 80.1%

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

5. Final simplification 80.1%

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

Alternative 6: 79.5% accurate, 1.5× speedup

Math

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

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+ (pow (* a (sin (* PI (* angle_m 0.005555555555555556)))) 2.0) (pow b 2.0)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[N[(a * N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. *-commutative 79.9%

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

   2. associate-*r/ 79.9%

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

   3. associate-*l/ 80.0%

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

   4. *-commutative 80.0%

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

   5. *-commutative 80.0%

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

   6. associate-*r/ 80.0%

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

   7. associate-*l/ 80.0%

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

   8. *-commutative 80.0%

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

3. Simplified 80.0%

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

4. Taylor expanded in angle around 0 80.1%

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

   1. add-exp-log 79.3%

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

   2. associate-*r/ 79.3%

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

   3. associate-*l/ 79.3%

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

   4. add-sqr-sqrt 50.4%

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

   5. add-sqr-sqrt 79.3%

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

   6. associate-*l/ 79.3%

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

   7. associate-*r/ 79.3%

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

   8. div-inv 79.3%

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

   9. metadata-eval 79.3%

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

6. Applied egg-rr 79.3%

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

   1. add-sqr-sqrt 79.3%

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

   2. pow2 79.3%

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

   3. rem-exp-log 80.1%

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

   4. sqrt-pow1 80.1%

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

   5. metadata-eval 80.1%

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

   6. pow1 80.1%

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

   7. *-commutative 80.1%

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

   8. associate-*r* 80.1%

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

8. Applied egg-rr 80.1%

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

9. Final simplification 80.1%

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

Alternative 7: 74.4% accurate, 1.9× speedup

Math

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

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+
  (pow b 2.0)
  (*
   (* a (* angle_m (* PI 0.005555555555555556)))
   (* 0.005555555555555556 (* PI (* a angle_m))))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[b, 2.0], $MachinePrecision] + N[(N[(a * N[(angle$95$m * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.005555555555555556 * N[(Pi * N[(a * angle$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. *-commutative 79.9%

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

   2. associate-*r/ 79.9%

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

   3. associate-*l/ 80.0%

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

   4. *-commutative 80.0%

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

   5. *-commutative 80.0%

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

   6. associate-*r/ 80.0%

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

   7. associate-*l/ 80.0%

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

   8. *-commutative 80.0%

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

3. Simplified 80.0%

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

4. Taylor expanded in angle around 0 80.1%

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

5. Taylor expanded in angle around 0 75.0%

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

   1. *-commutative 75.0%

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

7. Simplified 75.0%

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

   1. unpow2 75.0%

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

   2. associate-*l* 75.0%

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

   3. *-commutative 75.0%

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

   4. associate-*l* 75.0%

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

   5. *-commutative 75.0%

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

   6. *-commutative 75.0%

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

   7. associate-*l* 75.0%

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

   8. associate-*r* 75.0%

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

   9. *-commutative 75.0%

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

   10. associate-*r* 75.0%

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

9. Applied egg-rr 75.0%

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

    1. associate-*r* 75.1%

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

    2. *-commutative 75.1%

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

    3. associate-*r* 75.1%

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

    4. *-commutative 75.1%

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

    5. *-commutative 75.1%

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

11. Simplified 75.1%

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

12. Final simplification 75.1%

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

Alternative 8: 74.3% accurate, 2.0× speedup

Math

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

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+ (pow b 2.0) (* (pow (* a (* angle_m PI)) 2.0) 3.08641975308642e-5)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[b, 2.0], $MachinePrecision] + N[(N[Power[N[(a * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * 3.08641975308642e-5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. *-commutative 79.9%

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

   2. associate-*r/ 79.9%

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

   3. associate-*l/ 80.0%

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

   4. *-commutative 80.0%

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

   5. *-commutative 80.0%

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

   6. associate-*r/ 80.0%

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

   7. associate-*l/ 80.0%

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

   8. *-commutative 80.0%

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

3. Simplified 80.0%

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

4. Taylor expanded in angle around 0 80.1%

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

5. Taylor expanded in angle around 0 75.0%

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

   1. *-commutative 75.0%

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

7. Simplified 75.0%

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

   1. *-commutative 75.0%

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

   2. unpow-prod-down 75.0%

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

   3. *-commutative 75.0%

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

   4. associate-*l* 75.0%

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

   5. metadata-eval 75.0%

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

9. Applied egg-rr 75.0%

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

10. Taylor expanded in angle around 0 75.0%

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

11. Final simplification 75.0%

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

Alternative 9: 74.4% accurate, 2.0× speedup

Math

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

FPCore

angle_m = (fabs.f64 angle)
(FPCore (a b angle_m)
 :precision binary64
 (+ (pow b 2.0) (pow (* (* PI 0.005555555555555556) (* a angle_m)) 2.0)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

angle_m = N[Abs[angle], $MachinePrecision]
code[a_, b_, angle$95$m_] := N[(N[Power[b, 2.0], $MachinePrecision] + N[Power[N[(N[(Pi * 0.005555555555555556), $MachinePrecision] * N[(a * angle$95$m), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. *-commutative 79.9%

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

   2. associate-*r/ 79.9%

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

   3. associate-*l/ 80.0%

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

   4. *-commutative 80.0%

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

   5. *-commutative 80.0%

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

   6. associate-*r/ 80.0%

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

   7. associate-*l/ 80.0%

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

   8. *-commutative 80.0%

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

3. Simplified 80.0%

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

4. Taylor expanded in angle around 0 80.1%

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

5. Taylor expanded in angle around 0 75.0%

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

   1. *-commutative 75.0%

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

   2. associate-*r* 75.0%

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

   3. associate-*l* 75.1%

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

   4. *-commutative 75.1%

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

7. Simplified 75.1%

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

8. Final simplification 75.1%

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

Reproduce

herbie shell --seed 2023333 
(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)))