ab-angle->ABCF A

Average Error: 20.2 → 20.2

Time: 19.9s

Precision: binary64

Cost: 39616

Math

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

↓

\[\begin{array}{l} t_0 := \frac{\frac{\pi}{180}}{\frac{1}{angle}}\\ {\left(a \cdot \sin t_0\right)}^{2} + {\left(b \cdot \cos t_0\right)}^{2} \end{array} \]

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
 (let* ((t_0 (/ (/ PI 180.0) (/ 1.0 angle))))
   (+ (pow (* a (sin t_0)) 2.0) (pow (* b (cos t_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) {
	double t_0 = (((double) M_PI) / 180.0) / (1.0 / angle);
	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) {
	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) {
	double t_0 = (Math.PI / 180.0) / (1.0 / angle);
	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):
	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):
	t_0 = (math.pi / 180.0) / (1.0 / angle)
	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)
	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)
	t_0 = Float64(Float64(pi / 180.0) / Float64(1.0 / angle))
	return Float64((Float64(a * sin(t_0)) ^ 2.0) + (Float64(b * cos(t_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)
	t_0 = (pi / 180.0) / (1.0 / angle);
	tmp = ((a * sin(t_0)) ^ 2.0) + ((b * cos(t_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_] := Block[{t$95$0 = N[(N[(Pi / 180.0), $MachinePrecision] / N[(1.0 / angle), $MachinePrecision]), $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]]

Derivation

1. Initial program 20.2

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

2. Applied egg-rr 20.2

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

3. Applied egg-rr 20.2

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

4. Final simplification 20.2

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

Alternatives

Alternative 1
Error	20.2
Cost	39488

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

Alternative 2
Error	20.2
Cost	39488

\[{\left(a \cdot \sin \left(\frac{\pi}{\frac{1}{angle}} \cdot 0.005555555555555556\right)\right)}^{2} + {\left(b \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

Alternative 3
Error	20.2
Cost	39360

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

Alternative 4
Error	20.2
Cost	39360

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

Alternative 5
Error	20.4
Cost	26368

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

Alternative 6
Error	20.3
Cost	26240

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

Alternative 7
Error	20.3
Cost	26240

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

Alternative 8
Error	20.6
Cost	20488

\[\begin{array}{l} \mathbf{if}\;angle \leq -1450000:\\ \;\;\;\;{b}^{2} + \frac{a}{\frac{2}{a}} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 1.12 \cdot 10^{-13}:\\ \;\;\;\;{b}^{2} + \left(0.005555555555555556 \cdot \left(\pi \cdot \left(0.005555555555555556 \cdot \left(a \cdot angle\right)\right)\right)\right) \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + \frac{a \cdot a}{2} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	20.6
Cost	20425

\[\begin{array}{l} \mathbf{if}\;angle \leq -1450000 \lor \neg \left(angle \leq 1.12 \cdot 10^{-13}\right):\\ \;\;\;\;{b}^{2} + \frac{a}{\frac{2}{a}} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + {\left(0.005555555555555556 \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)}^{2}\\ \end{array} \]

Alternative 10
Error	20.6
Cost	20424

\[\begin{array}{l} \mathbf{if}\;angle \leq -1450000:\\ \;\;\;\;{b}^{2} + \frac{a}{\frac{2}{a}} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 1.12 \cdot 10^{-13}:\\ \;\;\;\;{b}^{2} + {\left(0.005555555555555556 \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + \frac{a \cdot a}{2} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	21.9
Cost	20105

\[\begin{array}{l} \mathbf{if}\;angle \leq -3.35 \cdot 10^{+35} \lor \neg \left(angle \leq 1.25 \cdot 10^{+24}\right):\\ \;\;\;\;b \cdot b\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + {\left(0.005555555555555556 \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)}^{2}\\ \end{array} \]

Alternative 12
Error	22.0
Cost	20041

\[\begin{array}{l} \mathbf{if}\;angle \leq -3.2 \cdot 10^{+29} \lor \neg \left(angle \leq 3 \cdot 10^{+26}\right):\\ \;\;\;\;b \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.08641975308642 \cdot 10^{-5}, {\left(\pi \cdot \left(a \cdot angle\right)\right)}^{2}, b \cdot b\right)\\ \end{array} \]

Alternative 13
Error	21.9
Cost	20041

\[\begin{array}{l} \mathbf{if}\;angle \leq -1.1 \cdot 10^{+30} \lor \neg \left(angle \leq 6.8 \cdot 10^{+24}\right):\\ \;\;\;\;b \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, b, {\left(\pi \cdot \left(0.005555555555555556 \cdot \left(a \cdot angle\right)\right)\right)}^{2}\right)\\ \end{array} \]

Alternative 14
Error	21.9
Cost	19977

\[\begin{array}{l} \mathbf{if}\;angle \leq -1.08 \cdot 10^{+32} \lor \neg \left(angle \leq 1.3 \cdot 10^{+23}\right):\\ \;\;\;\;b \cdot b\\ \mathbf{else}:\\ \;\;\;\;{\left(\mathsf{hypot}\left(\pi \cdot \left(angle \cdot \left(a \cdot 0.005555555555555556\right)\right), b\right)\right)}^{2}\\ \end{array} \]

Alternative 15
Error	30.0
Cost	14025

\[\begin{array}{l} \mathbf{if}\;angle \leq 6 \cdot 10^{-104} \lor \neg \left(angle \leq 8.5 \cdot 10^{+23}\right):\\ \;\;\;\;b \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot b + 3.08641975308642 \cdot 10^{-5} \cdot \left(\left(\left(a \cdot a\right) \cdot \left(angle \cdot angle\right)\right) \cdot {\pi}^{2}\right)\\ \end{array} \]

Alternative 16
Error	31.6
Cost	192

\[b \cdot b \]

Reproduce

herbie shell --seed 2023028 
(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)))