ab-angle->ABCF A

Average Error: 31.66% → 31.73%

Time: 21.7s

Precision: binary64

Cost: 58752

Math

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

↓

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

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 (/ PI (/ 180.0 angle)))) 2.0)
  (pow
   (* b (cos (/ (cbrt angle) (/ (/ 180.0 PI) (pow (cbrt angle) 2.0)))))
   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((((double) M_PI) / (180.0 / angle)))), 2.0) + pow((b * cos((cbrt(angle) / ((180.0 / ((double) M_PI)) / pow(cbrt(angle), 2.0))))), 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((Math.PI / (180.0 / angle)))), 2.0) + Math.pow((b * Math.cos((Math.cbrt(angle) / ((180.0 / Math.PI) / Math.pow(Math.cbrt(angle), 2.0))))), 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(pi / Float64(180.0 / angle)))) ^ 2.0) + (Float64(b * cos(Float64(cbrt(angle) / Float64(Float64(180.0 / pi) / (cbrt(angle) ^ 2.0))))) ^ 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[(Pi / N[(180.0 / angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[Power[angle, 1/3], $MachinePrecision] / N[(N[(180.0 / Pi), $MachinePrecision] / N[Power[N[Power[angle, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.66

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

2. Applied egg-rr 31.73

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

3. Applied egg-rr 31.73

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

4. Final simplification 31.73

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

Alternatives

Alternative 1
Error	31.74%
Cost	58624

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

Alternative 2
Error	31.74%
Cost	52160

\[{\left(a \cdot \sin \left(\frac{\pi}{\frac{180}{angle}}\right)\right)}^{2} + {\left(b \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right)}^{2} \]

Alternative 3
Error	31.63%
Cost	39360

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

Alternative 4
Error	31.74%
Cost	39360

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

Alternative 5
Error	31.73%
Cost	39360

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

Alternative 6
Error	31.61%
Cost	33280

\[{\left(a \cdot \sin \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2} + \frac{b \cdot b}{2} \cdot \left(1 + \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right) \]

Alternative 7
Error	31.81%
Cost	19904

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

Alternative 8
Error	31.76%
Cost	19904

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

Alternative 9
Error	31.87%
Cost	19904

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

Alternative 10
Error	31.84%
Cost	14153

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(a \cdot angle\right)\\ \mathbf{if}\;angle \leq -0.005 \lor \neg \left(angle \leq 0.0049\right):\\ \;\;\;\;b \cdot b + \frac{a \cdot a}{2} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot b + \left(t_0 \cdot t_0\right) \cdot {\pi}^{2}\\ \end{array} \]

Alternative 11
Error	31.98%
Cost	14089

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.005 \lor \neg \left(angle \leq 0.0049\right):\\ \;\;\;\;b \cdot b + \frac{a}{\frac{2}{a}} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot b + {\left(angle \cdot \left(a \cdot \pi\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]

Alternative 12
Error	31.99%
Cost	14089

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.005 \lor \neg \left(angle \leq 0.0049\right):\\ \;\;\;\;b \cdot b + \frac{a \cdot a}{2} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot b + {\left(angle \cdot \left(a \cdot \pi\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]

Alternative 13
Error	34.72%
Cost	13769

\[\begin{array}{l} \mathbf{if}\;angle \leq -7 \cdot 10^{+55} \lor \neg \left(angle \leq 4.6 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot b + {\left(a \cdot 0\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;b \cdot b + 3.08641975308642 \cdot 10^{-5} \cdot {\left(a \cdot \left(\pi \cdot angle\right)\right)}^{2}\\ \end{array} \]

Alternative 14
Error	34.72%
Cost	13769

\[\begin{array}{l} \mathbf{if}\;angle \leq -7 \cdot 10^{+55} \lor \neg \left(angle \leq 4.6 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot b + {\left(a \cdot 0\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;b \cdot b + {\left(angle \cdot \left(a \cdot \pi\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]

Alternative 15
Error	49.83%
Cost	6912

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

Reproduce

herbie shell --seed 2023089 
(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)))