ab-angle->ABCF C

Average Error: 20.1 → 20.1

Time: 29.4s

Precision: binary64

Cost: 33536

Math

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

↓

\[\begin{array}{l} t_0 := \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ {\left(a \cdot 1\right)}^{2} + \left(\frac{t_0}{2} \cdot \frac{b}{1.5}\right) \cdot \left(\left(3 \cdot b\right) \cdot t_0\right) \end{array} \]

FPCore

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

↓

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (sin (* PI (* angle 0.005555555555555556)))))
   (+ (pow (* a 1.0) 2.0) (* (* (/ t_0 2.0) (/ b 1.5)) (* (* 3.0 b) t_0)))))

C

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

↓

double code(double a, double b, double angle) {
	double t_0 = sin((((double) M_PI) * (angle * 0.005555555555555556)));
	return pow((a * 1.0), 2.0) + (((t_0 / 2.0) * (b / 1.5)) * ((3.0 * b) * t_0));
}

Java

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

↓

public static double code(double a, double b, double angle) {
	double t_0 = Math.sin((Math.PI * (angle * 0.005555555555555556)));
	return Math.pow((a * 1.0), 2.0) + (((t_0 / 2.0) * (b / 1.5)) * ((3.0 * b) * t_0));
}

Python

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

↓

def code(a, b, angle):
	t_0 = math.sin((math.pi * (angle * 0.005555555555555556)))
	return math.pow((a * 1.0), 2.0) + (((t_0 / 2.0) * (b / 1.5)) * ((3.0 * b) * t_0))

Julia

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

↓

function code(a, b, angle)
	t_0 = sin(Float64(pi * Float64(angle * 0.005555555555555556)))
	return Float64((Float64(a * 1.0) ^ 2.0) + Float64(Float64(Float64(t_0 / 2.0) * Float64(b / 1.5)) * Float64(Float64(3.0 * b) * t_0)))
end

MATLAB

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

↓

function tmp = code(a, b, angle)
	t_0 = sin((pi * (angle * 0.005555555555555556)));
	tmp = ((a * 1.0) ^ 2.0) + (((t_0 / 2.0) * (b / 1.5)) * ((3.0 * b) * t_0));
end

Wolfram

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

↓

code[a_, b_, angle_] := Block[{t$95$0 = N[Sin[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(N[Power[N[(a * 1.0), $MachinePrecision], 2.0], $MachinePrecision] + N[(N[(N[(t$95$0 / 2.0), $MachinePrecision] * N[(b / 1.5), $MachinePrecision]), $MachinePrecision] * N[(N[(3.0 * b), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 20.1

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

2. Simplified 20.1

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

3. Taylor expanded in angle around 0 20.1

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

4. Applied egg-rr 20.1

   \[\leadsto {\left(a \cdot 1\right)}^{2} + {\color{blue}{\left(\left(\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 3\right) \cdot 0.3333333333333333\right)}}^{2} \]

5. Applied egg-rr 20.1

   \[\leadsto {\left(a \cdot 1\right)}^{2} + \color{blue}{\left(\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.3333333333333333\right) \cdot \left(\left(3 \cdot b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} \]

6. Applied egg-rr 20.1

   \[\leadsto {\left(a \cdot 1\right)}^{2} + \color{blue}{\left(\frac{\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}{2} \cdot \frac{b}{1.5}\right)} \cdot \left(\left(3 \cdot b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \]

Alternatives

Alternative 1
Error	20.1
Cost	33408

\[\begin{array}{l} t_0 := \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ {\left(a \cdot 1\right)}^{2} + \left(\left(b \cdot t_0\right) \cdot 0.3333333333333333\right) \cdot \left(\left(3 \cdot b\right) \cdot t_0\right) \end{array} \]

Alternative 2
Error	20.1
Cost	33408

\[\begin{array}{l} t_0 := \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ {\left(a \cdot 1\right)}^{2} + \left(\left(t_0 \cdot 0.3333333333333333\right) \cdot b\right) \cdot \left(\left(3 \cdot b\right) \cdot t_0\right) \end{array} \]

Alternative 3
Error	20.1
Cost	26624

\[{\left(a \cdot 1\right)}^{2} + \left(3 \cdot {\left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}\right) \cdot 0.3333333333333333 \]

Alternative 4
Error	20.1
Cost	26368

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

Alternative 5
Error	33.4
Cost	20416

\[{\left(a \cdot 1\right)}^{2} + \left(\left(b \cdot angle\right) \cdot 0.3333333333333333\right) \cdot \left(\left(3 \cdot b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \]

Alternative 6
Error	34.7
Cost	20160

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

Alternative 7
Error	34.9
Cost	704

\[a \cdot a + \left(b \cdot angle\right) \cdot \left(b \cdot angle\right) \]

Alternative 8
Error	34.9
Cost	704

\[a \cdot a + \left(\left(b \cdot angle\right) \cdot b\right) \cdot angle \]

Reproduce

herbie shell --seed 2023010 
(FPCore (a b angle)
  :name "ab-angle->ABCF C"
  :precision binary64
  (+ (pow (* a (cos (* PI (/ angle 180.0)))) 2.0) (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))