ab-angle->ABCF A

Percentage Accurate: 79.5% → 79.4%

Time: 19.5s

Alternatives: 5

Speedup: N/A×

• 37.1% 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: 79.5% 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: 79.4% accurate, 2.0× 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 82.3%

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

2. Taylor expanded in angle around 0 82.7%

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

   1. associate-*l/ 82.8%

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

4. Applied egg-rr 82.8%

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

5. Taylor expanded in b around 0 82.8%

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

   1. unpow2 82.8%

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

7. Simplified 82.8%

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

8. Final simplification 82.8%

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

Alternative 2: 79.4% accurate, 2.0× speedup

Math

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

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(Float64(angle * 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[(N[(angle * Pi), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.3%

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

2. Taylor expanded in angle around 0 82.7%

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

   1. associate-*l/ 82.8%

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

4. Applied egg-rr 82.8%

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

5. Taylor expanded in b around 0 82.8%

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

   1. unpow2 82.8%

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

7. Simplified 82.8%

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

   1. div-inv 82.7%

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

   2. metadata-eval 82.7%

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

9. Applied egg-rr 82.7%

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

10. Final simplification 82.7%

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

Alternative 3: 74.2% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.3%

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

2. Taylor expanded in angle around 0 82.7%

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

   1. associate-*l/ 82.8%

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

4. Applied egg-rr 82.8%

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

5. Taylor expanded in b around 0 82.8%

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

   1. unpow2 82.8%

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

7. Simplified 82.8%

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

8. Taylor expanded in angle around 0 79.6%

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

   1. *-commutative 79.6%

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

10. Simplified 79.6%

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

11. Final simplification 79.6%

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

Alternative 4: 74.2% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.3%

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

2. Taylor expanded in angle around 0 82.7%

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

3. Taylor expanded in angle around 0 79.6%

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

   1. associate-*r* 79.6%

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

5. Simplified 79.6%

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

6. Taylor expanded in b around 0 79.6%

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

   1. unpow2 82.8%

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

8. Simplified 79.6%

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

9. Final simplification 79.6%

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

Alternative 5: 56.6% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ b \cdot b + {\left(a \cdot 0\right)}^{2} \end{array} \]

FPCore

(FPCore (a b angle) :precision binary64 (+ (* b b) (pow (* a 0.0) 2.0)))

C

double code(double a, double b, double angle) {
	return (b * b) + pow((a * 0.0), 2.0);
}

Fortran

real(8) function code(a, b, angle)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: angle
    code = (b * b) + ((a * 0.0d0) ** 2.0d0)
end function

Java

public static double code(double a, double b, double angle) {
	return (b * b) + Math.pow((a * 0.0), 2.0);
}

Python

def code(a, b, angle):
	return (b * b) + math.pow((a * 0.0), 2.0)

Julia

function code(a, b, angle)
	return Float64(Float64(b * b) + (Float64(a * 0.0) ^ 2.0))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = (b * b) + ((a * 0.0) ^ 2.0);
end

Wolfram

code[a_, b_, angle_] := N[(N[(b * b), $MachinePrecision] + N[Power[N[(a * 0.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.3%

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

2. Taylor expanded in angle around 0 82.7%

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

   1. add-cube-cbrt 82.7%

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

   2. pow3 82.7%

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

   3. div-inv 82.7%

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

   4. metadata-eval 82.7%

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

4. Applied egg-rr 82.7%

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

5. Taylor expanded in angle around 0 62.2%

   \[\leadsto {\left(a \cdot \color{blue}{0}\right)}^{2} + {\left(b \cdot 1\right)}^{2} \]

6. Taylor expanded in b around 0 62.2%

   \[\leadsto {\left(a \cdot 0\right)}^{2} + \color{blue}{{b}^{2}} \]
7. Step-by-step derivation

   1. unpow2 82.8%

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

8. Simplified 62.2%

   \[\leadsto {\left(a \cdot 0\right)}^{2} + \color{blue}{b \cdot b} \]

9. Final simplification 62.2%

   \[\leadsto b \cdot b + {\left(a \cdot 0\right)}^{2} \]

Reproduce

herbie shell --seed 2023207 
(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)))