ab-angle->ABCF B

Average Accuracy: 51.2% → 66.3%

Time: 23.1s

Precision: binary64

Cost: 46464

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt[3]{angle \cdot 0.005555555555555556}\\ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{{t_0}^{2}}{\frac{\frac{1}{\pi}}{t_0}}\right) \end{array} \]

FPCore

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

↓

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (cbrt (* angle 0.005555555555555556))))
   (*
    (* (* -2.0 (+ b a)) (* (- a b) (sin (/ angle (/ 180.0 PI)))))
    (cos (/ (pow t_0 2.0) (/ (/ 1.0 PI) t_0))))))

C

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

↓

double code(double a, double b, double angle) {
	double t_0 = cbrt((angle * 0.005555555555555556));
	return ((-2.0 * (b + a)) * ((a - b) * sin((angle / (180.0 / ((double) M_PI)))))) * cos((pow(t_0, 2.0) / ((1.0 / ((double) M_PI)) / t_0)));
}

Java

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

↓

public static double code(double a, double b, double angle) {
	double t_0 = Math.cbrt((angle * 0.005555555555555556));
	return ((-2.0 * (b + a)) * ((a - b) * Math.sin((angle / (180.0 / Math.PI))))) * Math.cos((Math.pow(t_0, 2.0) / ((1.0 / Math.PI) / t_0)));
}

Julia

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

↓

function code(a, b, angle)
	t_0 = cbrt(Float64(angle * 0.005555555555555556))
	return Float64(Float64(Float64(-2.0 * Float64(b + a)) * Float64(Float64(a - b) * sin(Float64(angle / Float64(180.0 / pi))))) * cos(Float64((t_0 ^ 2.0) / Float64(Float64(1.0 / pi) / t_0))))
end

Wolfram

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

↓

code[a_, b_, angle_] := Block[{t$95$0 = N[Power[N[(angle * 0.005555555555555556), $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[(N[(-2.0 * N[(b + a), $MachinePrecision]), $MachinePrecision] * N[(N[(a - b), $MachinePrecision] * N[Sin[N[(angle / N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[Power[t$95$0, 2.0], $MachinePrecision] / N[(N[(1.0 / Pi), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 51.2%

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

2. Simplified 51.2%

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

   [Start] 51.2	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 51.2	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub-neg [=>] 51.2	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 51.2	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   neg-sub0 [=>] 51.2	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-+l- [=>] 51.2	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub0-neg [=>] 51.2	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-lft-neg-out [=>] 51.2	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-rgt-neg-in [=>] 51.2	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 51.2	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 51.2	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [=>] 51.2	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Taylor expanded in angle around inf 51.2%

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

4. Simplified 66.5%

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

   [Start] 51.2	\[ \left(-2 \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 51.2	\[ \left(-2 \cdot \left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 51.2	\[ \left(-2 \cdot \left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   difference-of-squares [=>] 51.2	\[ \left(-2 \cdot \left(\color{blue}{\left(\left(a + b\right) \cdot \left(a - b\right)\right)} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 51.2	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 51.2	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \left(\color{blue}{\left(angle \cdot 0.005555555555555556\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 51.2	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [=>] 66.4	\[ \left(-2 \cdot \color{blue}{\left(\left(a + b\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [<=] 66.4	\[ \color{blue}{\left(\left(-2 \cdot \left(a + b\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 66.4	\[ \left(\left(-2 \cdot \color{blue}{\left(b + a\right)}\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 66.4	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 66.4	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(0.005555555555555556 \cdot angle\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [<=] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

5. Applied egg-rr 66.5%

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

   [Start] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [<=] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot \color{blue}{\frac{1}{180}}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   div-inv [<=] 66.4	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\frac{angle \cdot \pi}{180}\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-/l* [=>] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\frac{angle}{\frac{180}{\pi}}\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

6. Applied egg-rr 66.3%

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{{\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\frac{1}{\pi}}{\sqrt[3]{angle \cdot 0.005555555555555556}}}\right)} \]
   Proof

   [Start] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{angle}{180} \cdot \pi\right)} \]
   associate-/r/ [<=] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{angle}{\frac{180}{\pi}}\right)} \]
   div-inv [=>] 66.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{angle}{\color{blue}{180 \cdot \frac{1}{\pi}}}\right) \]
   associate-/r* [=>] 66.4	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{\frac{angle}{180}}{\frac{1}{\pi}}\right)} \]
   add-cube-cbrt [=>] 66.3	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\frac{angle}{180}}\right) \cdot \sqrt[3]{\frac{angle}{180}}}}{\frac{1}{\pi}}\right) \]
   associate-/l* [=>] 66.3	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\frac{angle}{180}}}{\frac{\frac{1}{\pi}}{\sqrt[3]{\frac{angle}{180}}}}\right)} \]
   pow2 [=>] 66.3	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{\color{blue}{{\left(\sqrt[3]{\frac{angle}{180}}\right)}^{2}}}{\frac{\frac{1}{\pi}}{\sqrt[3]{\frac{angle}{180}}}}\right) \]
   div-inv [=>] 66.3	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{{\left(\sqrt[3]{\color{blue}{angle \cdot \frac{1}{180}}}\right)}^{2}}{\frac{\frac{1}{\pi}}{\sqrt[3]{\frac{angle}{180}}}}\right) \]
   metadata-eval [=>] 66.3	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{{\left(\sqrt[3]{angle \cdot \color{blue}{0.005555555555555556}}\right)}^{2}}{\frac{\frac{1}{\pi}}{\sqrt[3]{\frac{angle}{180}}}}\right) \]
   div-inv [=>] 66.3	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{{\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\frac{1}{\pi}}{\sqrt[3]{\color{blue}{angle \cdot \frac{1}{180}}}}}\right) \]
   metadata-eval [=>] 66.3	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{{\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\frac{1}{\pi}}{\sqrt[3]{angle \cdot \color{blue}{0.005555555555555556}}}}\right) \]

7. Final simplification 66.3%

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{{\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\frac{1}{\pi}}{\sqrt[3]{angle \cdot 0.005555555555555556}}}\right) \]

Alternatives

Alternative 1
Accuracy	66.2%
Cost	46336

\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\frac{\frac{{\left(\sqrt[3]{angle}\right)}^{2}}{180}}{\frac{1}{\pi \cdot \sqrt[3]{angle}}}\right) \]

Alternative 2
Accuracy	65.5%
Cost	27336

\[\begin{array}{l} t_0 := -2 \cdot \left(b + a\right)\\ \mathbf{if}\;\frac{angle}{180} \leq 10^{-24}:\\ \;\;\;\;t_0 \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{+184}:\\ \;\;\;\;2 \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	66.5%
Cost	26944

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

Alternative 4
Accuracy	66.4%
Cost	26944

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

Alternative 5
Accuracy	66.5%
Cost	26816

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

Alternative 6
Accuracy	66.5%
Cost	26816

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

Alternative 7
Accuracy	66.5%
Cost	26816

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

Alternative 8
Accuracy	66.2%
Cost	13833

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -5 \cdot 10^{-40} \lor \neg \left(angle \leq 10^{-22}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	64.8%
Cost	13696

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

Alternative 10
Accuracy	61.3%
Cost	13572

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq 1.8 \cdot 10^{+56}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(-2 \cdot \left(a \cdot a\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	61.4%
Cost	13572

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(\frac{angle}{\frac{180}{\pi}}\right) \cdot \left(-2 \cdot \left(a \cdot a\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	60.7%
Cost	7684

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq 6 \cdot 10^{+56}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 13
Accuracy	53.8%
Cost	7561

\[\begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+88} \lor \neg \left(b \leq 1.85 \cdot 10^{+96}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(angle \cdot 0.005555555555555556\right) \cdot \left(\pi \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	53.9%
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+89} \lor \neg \left(b \leq 2.8 \cdot 10^{+98}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	53.6%
Cost	7432

\[\begin{array}{l} t_0 := b \cdot \left(b \cdot angle\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+57}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot t_0\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+100}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot t_0\right)\\ \end{array} \]

Alternative 16
Accuracy	40.3%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+47} \lor \neg \left(b \leq 2 \cdot 10^{+73}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 17
Accuracy	40.0%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+158} \lor \neg \left(b \leq 3.5 \cdot 10^{+73}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 18
Accuracy	48.7%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-50} \lor \neg \left(b \leq 1.15 \cdot 10^{-87}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 19
Accuracy	48.7%
Cost	7176

\[\begin{array}{l} t_0 := b \cdot \left(b \cdot angle\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{-50}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot t_0\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-88}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot t_0\right)\\ \end{array} \]

Alternative 20
Accuracy	48.7%
Cost	7176

\[\begin{array}{l} t_0 := b \cdot \left(b \cdot angle\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot t_0\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-91}:\\ \;\;\;\;\left(angle \cdot -0.011111111111111112\right) \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot t_0\right)\\ \end{array} \]

Alternative 21
Accuracy	32.5%
Cost	6912

\[0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right) \]

Reproduce

herbie shell --seed 2023137 
(FPCore (a b angle)
  :name "ab-angle->ABCF B"
  :precision binary64
  (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0)))) (cos (* PI (/ angle 180.0)))))