ab-angle->ABCF A

Percentage Accurate: 79.6% → 79.5%

Time: 13.8s

Alternatives: 11

Speedup: 2.0×

• 36.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.4%

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

3. Taylor expanded in angle around 0

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

5. Simplified 82.5%

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

   1. lift-PI.f64 N/A

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

   2. associate-*l/ N/A

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

   3. lower-/.f64 N/A

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

   4. lower-*.f64 82.5

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

7. Applied egg-rr 82.5%

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

   1. *-rgt-identity N/A

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

   2. pow2 N/A

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

   3. lift-*.f64 82.5

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

9. Applied egg-rr 82.5%

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

Alternative 2: 79.6% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.6%

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

3. Taylor expanded in angle around 0

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

5. Simplified 79.6%

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

   1. lift-PI.f64 N/A

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

   2. associate-*l/ N/A

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

   3. lower-/.f64 N/A

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

   4. lower-*.f64 79.5

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

7. Applied egg-rr 79.5%

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

   1. *-rgt-identity N/A

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

   2. pow2 N/A

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

   3. lift-*.f64 79.5

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

9. Applied egg-rr 79.5%

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

    1. lift-PI.f64 N/A

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

    2. *-commutative N/A

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

    3. associate-/l* N/A

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

    4. div-inv N/A

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

    5. metadata-eval N/A

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

    6. lift-*.f64 N/A

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

    7. *-commutative N/A

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

    8. lift-*.f64 N/A

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

    9. lift-sin.f64 N/A

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

    10. *-commutative N/A

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

    11. lower-*.f64 79.6

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

11. Applied egg-rr 79.6%

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

12. Final simplification 79.6%

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

Reproduce

herbie shell --seed 2024218 
(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)))