ab-angle->ABCF C

Average Error: 20.7 → 20.7

Time: 16.1s

Precision: binary64

Cost: 39360

Math

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

↓

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

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
 (+
  (pow (* a (cos (* (* 0.005555555555555556 PI) angle))) 2.0)
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))

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

Java

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

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

Julia

function code(a, b, angle)
	return Float64((Float64(a * cos(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)
	return Float64((Float64(a * cos(Float64(Float64(0.005555555555555556 * pi) * angle))) ^ 2.0) + (Float64(b * sin(Float64(pi * Float64(angle / 180.0)))) ^ 2.0))
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)
	tmp = ((a * cos(((0.005555555555555556 * pi) * angle))) ^ 2.0) + ((b * sin((pi * (angle / 180.0)))) ^ 2.0);
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_] := N[(N[Power[N[(a * N[Cos[N[(N[(0.005555555555555556 * Pi), $MachinePrecision] * angle), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 20.7

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

2. Applied egg-rr 25.6

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

3. Applied egg-rr 20.7

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

4. Final simplification 20.7

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

Alternatives

Alternative 1
Error	20.7
Cost	39360

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

Alternative 2
Error	20.8
Cost	26368

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

Alternative 3
Error	20.7
Cost	26240

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

Alternative 4
Error	23.5
Cost	20360

\[\begin{array}{l} t_0 := {a}^{2} + {\left(angle \cdot \left(\left(1 + \pi \cdot b\right) + -1\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \mathbf{if}\;angle \leq -6.361841837595009 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq 3.7663897632145916 \cdot 10^{-35}:\\ \;\;\;\;{a}^{2} + {\left(b \cdot \left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	26.3
Cost	19840

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

Alternative 6
Error	26.3
Cost	19840

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

Alternative 7
Error	26.2
Cost	19840

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

Alternative 8
Error	26.2
Cost	19840

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

Reproduce

herbie shell --seed 2022300 
(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)))