ab-angle->ABCF A

Average Error: 20.1 → 20.2

Time: 18.5s

Precision: binary64

Cost: 39488

Math

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

↓

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

FPCore

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

↓

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (sin (/ 1.0 (/ 180.0 (* angle PI))))) 2.0)
  (pow (* b (cos (* PI (/ angle 180.0)))) 2.0)))

C

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

↓

double code(double a, double b, double angle) {
	return pow((a * sin((1.0 / (180.0 / (angle * ((double) M_PI)))))), 2.0) + pow((b * cos((((double) M_PI) * (angle / 180.0)))), 2.0);
}

Java

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

↓

public static double code(double a, double b, double angle) {
	return Math.pow((a * Math.sin((1.0 / (180.0 / (angle * Math.PI))))), 2.0) + Math.pow((b * Math.cos((Math.PI * (angle / 180.0)))), 2.0);
}

Python

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

↓

def code(a, b, angle):
	return math.pow((a * math.sin((1.0 / (180.0 / (angle * math.pi))))), 2.0) + math.pow((b * math.cos((math.pi * (angle / 180.0)))), 2.0)

Julia

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

↓

function code(a, b, angle)
	return Float64((Float64(a * sin(Float64(1.0 / Float64(180.0 / Float64(angle * pi))))) ^ 2.0) + (Float64(b * cos(Float64(pi * Float64(angle / 180.0)))) ^ 2.0))
end

MATLAB

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

↓

function tmp = code(a, b, angle)
	tmp = ((a * sin((1.0 / (180.0 / (angle * pi))))) ^ 2.0) + ((b * cos((pi * (angle / 180.0)))) ^ 2.0);
end

Wolfram

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

↓

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Sin[N[(1.0 / N[(180.0 / N[(angle * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 20.1

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

2. Applied egg-rr 20.2

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

3. Final simplification 20.2

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

Alternatives

Alternative 1
Error	20.1
Cost	39360

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

Alternative 2
Error	20.1
Cost	39360

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

Alternative 3
Error	22.8
Cost	26888

\[\begin{array}{l} t_0 := {\left(b \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot 0\right)}^{2}\\ \mathbf{if}\;\frac{angle}{180} \leq -10000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{-28}:\\ \;\;\;\;{b}^{2} + \left(\left(\left(a \cdot angle\right) \cdot \left(a \cdot angle\right)\right) \cdot {\pi}^{2}\right) \cdot 3.08641975308642 \cdot 10^{-5}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	20.2
Cost	26368

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

Alternative 5
Error	20.2
Cost	26240

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

Alternative 6
Error	20.1
Cost	26240

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

Alternative 7
Error	24.7
Cost	20360

\[\begin{array}{l} t_0 := {b}^{2} + \left(\left(\left(a \cdot angle\right) \cdot \left(a \cdot angle\right)\right) \cdot {\pi}^{2}\right) \cdot 3.08641975308642 \cdot 10^{-5}\\ \mathbf{if}\;a \leq -1.4373282556146143 \cdot 10^{-122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 8.84423320143105 \cdot 10^{-87}:\\ \;\;\;\;{b}^{2} + {\left(\left(1 + 0.005555555555555556 \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right) + -1\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	25.9
Cost	20096

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

Alternative 9
Error	23.5
Cost	20096

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

Alternative 10
Error	25.8
Cost	19840

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

Alternative 11
Error	25.8
Cost	19840

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

Reproduce

herbie shell --seed 2022294 
(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)))