ab-angle->ABCF B

Average Error: 49.86% → 34.49%

Time: 22.1s

Precision: binary64

Cost: 59200

Math

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

↓

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

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

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

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) {
	return ((-2.0 * (b + a)) * ((a - b) * Math.sin((0.005555555555555556 * (angle * Math.PI))))) * Math.cos(((Math.cbrt(Math.PI) / Math.pow(Math.cbrt(((180.0 / angle) / Math.PI)), 2.0)) / Math.cbrt((180.0 / angle))));
}

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)
	return Float64(Float64(Float64(-2.0 * Float64(b + a)) * Float64(Float64(a - b) * sin(Float64(0.005555555555555556 * Float64(angle * pi))))) * cos(Float64(Float64(cbrt(pi) / (cbrt(Float64(Float64(180.0 / angle) / pi)) ^ 2.0)) / cbrt(Float64(180.0 / angle)))))
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_] := N[(N[(N[(-2.0 * N[(b + a), $MachinePrecision]), $MachinePrecision] * N[(N[(a - b), $MachinePrecision] * N[Sin[N[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[Power[Pi, 1/3], $MachinePrecision] / N[Power[N[Power[N[(N[(180.0 / angle), $MachinePrecision] / Pi), $MachinePrecision], 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[Power[N[(180.0 / angle), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 49.86

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

2. Simplified 49.86

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

   [Start] 49.86	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 49.86	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub-neg [=>] 49.86	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 49.86	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   neg-sub0 [=>] 49.86	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-+l- [=>] 49.86	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub0-neg [=>] 49.86	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-lft-neg-out [=>] 49.86	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-rgt-neg-in [=>] 49.86	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 49.86	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 49.86	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [=>] 49.86	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Taylor expanded in angle around inf 49.93

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

4. Simplified 34.38

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

   [Start] 49.93	\[ \left(-2 \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 49.93	\[ \left(-2 \cdot \left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 49.93	\[ \left(-2 \cdot \left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   difference-of-squares [=>] 49.92	\[ \left(-2 \cdot \left(\color{blue}{\left(\left(a + b\right) \cdot \left(a - b\right)\right)} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 49.92	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 49.92	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \left(\color{blue}{\left(\pi \cdot angle\right)} \cdot 0.005555555555555556\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [<=] 49.86	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [=>] 34.33	\[ \left(-2 \cdot \color{blue}{\left(\left(a + b\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [<=] 34.32	\[ \color{blue}{\left(\left(-2 \cdot \left(a + b\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 34.32	\[ \left(\left(-2 \cdot \color{blue}{\left(b + a\right)}\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 34.38	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 34.38	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(angle \cdot \pi\right)} \cdot 0.005555555555555556\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 34.38	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

5. Applied egg-rr 34.32

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

6. Applied egg-rr 34.47

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

7. Simplified 34.49

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

   [Start] 34.47	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\frac{\frac{1}{{\left(\sqrt[3]{\frac{\frac{180}{angle}}{\pi}}\right)}^{2}}}{\sqrt[3]{\frac{180}{angle}}} \cdot \sqrt[3]{\pi}\right) \]
   associate-*l/ [=>] 34.5	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{\frac{1}{{\left(\sqrt[3]{\frac{\frac{180}{angle}}{\pi}}\right)}^{2}} \cdot \sqrt[3]{\pi}}{\sqrt[3]{\frac{180}{angle}}}\right)} \]
   associate-*l/ [=>] 34.49	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\frac{\color{blue}{\frac{1 \cdot \sqrt[3]{\pi}}{{\left(\sqrt[3]{\frac{\frac{180}{angle}}{\pi}}\right)}^{2}}}}{\sqrt[3]{\frac{180}{angle}}}\right) \]
   *-lft-identity [=>] 34.49	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\frac{\frac{\color{blue}{\sqrt[3]{\pi}}}{{\left(\sqrt[3]{\frac{\frac{180}{angle}}{\pi}}\right)}^{2}}}{\sqrt[3]{\frac{180}{angle}}}\right) \]

8. Final simplification 34.49

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

Alternatives

Alternative 1
Error	34.38%
Cost	26816

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

Alternative 2
Error	35.1%
Cost	13956

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{\frac{1}{b \cdot b - a \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	35.96%
Cost	13828

\[\begin{array}{l} \mathbf{if}\;angle \leq -2.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{\frac{1}{b \cdot b - a \cdot a}}\\ \mathbf{elif}\;angle \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;\left(\left(b + a\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \left(a \cdot a\right)\right) \cdot 0\\ \end{array} \]

Alternative 4
Error	35.94%
Cost	13700

\[\begin{array}{l} \mathbf{if}\;angle \leq -8.5 \cdot 10^{-8}:\\ \;\;\;\;\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;angle \leq 8.6 \cdot 10^{+42}:\\ \;\;\;\;\left(\left(b + a\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \left(a \cdot a\right)\right) \cdot 0\\ \end{array} \]

Alternative 5
Error	37.53%
Cost	13572

\[\begin{array}{l} \mathbf{if}\;angle \leq -390000:\\ \;\;\;\;2 \cdot \left(b \cdot \left(b \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;angle \leq 7.8 \cdot 10^{+39}:\\ \;\;\;\;\left(\left(b + a\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \left(a \cdot a\right)\right) \cdot 0\\ \end{array} \]

Alternative 6
Error	47.78%
Cost	7696

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right)\right)\\ t_1 := \pi \cdot \left(a \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-87}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+33}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	37.83%
Cost	7433

\[\begin{array}{l} \mathbf{if}\;angle \leq -1.05 \cdot 10^{+61} \lor \neg \left(angle \leq 9.2 \cdot 10^{+42}\right):\\ \;\;\;\;\left(-2 \cdot \left(a \cdot a\right)\right) \cdot 0\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(\left(b + a\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	37.76%
Cost	7433

\[\begin{array}{l} \mathbf{if}\;angle \leq -6.3 \cdot 10^{+60} \lor \neg \left(angle \leq 7.6 \cdot 10^{+42}\right):\\ \;\;\;\;\left(-2 \cdot \left(a \cdot a\right)\right) \cdot 0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b + a\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 9
Error	60.35%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;angle \leq -3.3 \cdot 10^{+85} \lor \neg \left(angle \leq 7 \cdot 10^{+35}\right):\\ \;\;\;\;\left(-2 \cdot \left(a \cdot a\right)\right) \cdot 0\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	60.31%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;angle \leq -6.2 \cdot 10^{+84} \lor \neg \left(angle \leq 22000000000\right):\\ \;\;\;\;\left(-2 \cdot \left(a \cdot a\right)\right) \cdot 0\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	52.09%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-8} \lor \neg \left(a \leq 7 \cdot 10^{-51}\right):\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	52.08%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-9} \lor \neg \left(a \leq 5.5 \cdot 10^{-53}\right):\\ \;\;\;\;\pi \cdot \left(a \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 13
Error	52.07%
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	82.12%
Cost	448

\[\left(-2 \cdot \left(a \cdot a\right)\right) \cdot 0 \]

Alternative 15
Error	84.65%
Cost	256

\[a \cdot \left(-a\right) \]

Reproduce

herbie shell --seed 2023090 
(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)))))