ab-angle->ABCF B

Average Accuracy: 51.1% → 65.8%

Time: 24.2s

Precision: binary64

Cost: 52544

Math

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

↓

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

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 (/ (* angle (pow (cbrt PI) 2.0)) (/ 180.0 (cbrt PI))))))

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(((angle * pow(cbrt(((double) M_PI)), 2.0)) / (180.0 / cbrt(((double) M_PI)))));
}

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(((angle * Math.pow(Math.cbrt(Math.PI), 2.0)) / (180.0 / Math.cbrt(Math.PI))));
}

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(angle * (cbrt(pi) ^ 2.0)) / Float64(180.0 / cbrt(pi)))))
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[(angle * N[Power[N[Power[Pi, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(180.0 / N[Power[Pi, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 51.1%

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

2. Simplified 51.1%

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

   [Start] 51.1	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 51.1	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub-neg [=>] 51.1	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 51.1	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   neg-sub0 [=>] 51.1	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-+l- [=>] 51.1	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub0-neg [=>] 51.1	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-lft-neg-out [=>] 51.1	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-rgt-neg-in [=>] 51.1	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 51.1	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 51.1	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [=>] 51.1	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Taylor expanded in angle around inf 51.1%

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

4. Simplified 66.0%

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

   [Start] 51.1	\[ \left(-2 \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 51.1	\[ \left(-2 \cdot \left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 51.1	\[ \left(-2 \cdot \left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   difference-of-squares [=>] 51.1	\[ \left(-2 \cdot \left(\color{blue}{\left(\left(a + b\right) \cdot \left(a - b\right)\right)} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 51.1	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 51.1	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \left(\color{blue}{\left(angle \cdot 0.005555555555555556\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 51.1	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [=>] 66.0	\[ \left(-2 \cdot \color{blue}{\left(\left(a + b\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [<=] 66.0	\[ \color{blue}{\left(\left(-2 \cdot \left(a + b\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 66.0	\[ \left(\left(-2 \cdot \color{blue}{\left(b + a\right)}\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 66.0	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 66.0	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(0.005555555555555556 \cdot angle\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [<=] 66.0	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

5. Taylor expanded in angle around inf 66.1%

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

6. Applied egg-rr 65.8%

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

   [Start] 66.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \]
   *-commutative [=>] 66.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)} \]
   metadata-eval [<=] 66.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\left(angle \cdot \pi\right) \cdot \color{blue}{\frac{1}{180}}\right) \]
   div-inv [<=] 66.0	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{angle \cdot \pi}{180}\right)} \]
   add-cube-cbrt [=>] 65.8	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\frac{angle \cdot \color{blue}{\left(\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right) \cdot \sqrt[3]{\pi}\right)}}{180}\right) \]
   associate-*r* [=>] 65.8	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(angle \cdot \left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right)\right) \cdot \sqrt[3]{\pi}}}{180}\right) \]
   associate-/l* [=>] 65.8	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{angle \cdot \left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right)}{\frac{180}{\sqrt[3]{\pi}}}\right)} \]
   pow2 [=>] 65.8	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\frac{angle \cdot \color{blue}{{\left(\sqrt[3]{\pi}\right)}^{2}}}{\frac{180}{\sqrt[3]{\pi}}}\right) \]

7. Final simplification 65.8%

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

Alternatives

Alternative 1
Accuracy	66.1%
Cost	26816

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

Alternative 2
Accuracy	57.8%
Cost	14228

\[\begin{array}{l} t_0 := 2 \cdot \left(0.5 \cdot \left(b \cdot \left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\right)\right)\\ t_1 := 2 \cdot \left(-0.5 \cdot \left(a \cdot \left(a \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\right)\\ t_2 := b \cdot b - a \cdot a\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.7 \cdot 10^{-62}:\\ \;\;\;\;2 \cdot \left(\left(\pi \cdot t_2\right) \cdot \left(0.005555555555555556 \cdot angle\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-82}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 61000000:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \frac{angle \cdot \left(\left(b + a\right) \cdot \pi\right)}{\frac{b + a}{t_2}}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	55.5%
Cost	13964

\[\begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-79}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \frac{angle \cdot \pi}{\frac{1}{b \cdot b - a \cdot a}}\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-60}:\\ \;\;\;\;2 \cdot \left(-0.5 \cdot \left(a \cdot \left(a \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	66.1%
Cost	13824

\[2 \cdot \left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot 0.5\right)\right)\right) \]

Alternative 5
Accuracy	53.4%
Cost	7688

\[\begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.05 \cdot 10^{+72}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \frac{\pi}{\frac{1}{b \cdot b - a \cdot a}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	53.4%
Cost	7688

\[\begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+73}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \frac{angle \cdot \pi}{\frac{1}{b \cdot b - a \cdot a}}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	53.6%
Cost	7560

\[\begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+149}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	53.3%
Cost	7560

\[\begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+77}:\\ \;\;\;\;2 \cdot \left(\left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(0.005555555555555556 \cdot angle\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	40.3%
Cost	7305

\[\begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+36} \lor \neg \left(b \leq 3.9\right):\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	40.1%
Cost	7305

\[\begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-175} \lor \neg \left(b \leq 10^{+125}\right):\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	40.2%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-175}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+149}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	40.2%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-175}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \left(\pi \cdot \left(\left(b \cdot b\right) \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	49.3%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-29}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 10^{-60}:\\ \;\;\;\;2 \cdot \left(\left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right) \cdot -0.005555555555555556\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	32.6%
Cost	6912

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

Reproduce

herbie shell --seed 2023131 
(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)))))