ab-angle->ABCF B

Average Error: 30.8 → 21.1

Time: 23.2s

Precision: binary64

Cost: 46080

Math

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

↓

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

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 (pow (* (cbrt (* 0.005555555555555556 PI)) (cbrt angle)) 3.0))))

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) {
	return ((-2.0 * (b + a)) * ((a - b) * sin((0.005555555555555556 * (angle * ((double) M_PI)))))) * cos(pow((cbrt((0.005555555555555556 * ((double) M_PI))) * cbrt(angle)), 3.0));
}

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) {
	return ((-2.0 * (b + a)) * ((a - b) * Math.sin((0.005555555555555556 * (angle * Math.PI))))) * Math.cos(Math.pow((Math.cbrt((0.005555555555555556 * Math.PI)) * Math.cbrt(angle)), 3.0));
}

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)
	return Float64(Float64(Float64(-2.0 * Float64(b + a)) * Float64(Float64(a - b) * sin(Float64(0.005555555555555556 * Float64(angle * pi))))) * cos((Float64(cbrt(Float64(0.005555555555555556 * pi)) * cbrt(angle)) ^ 3.0)))
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_] := 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[Power[N[(N[Power[N[(0.005555555555555556 * Pi), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[angle, 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.8

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

2. Simplified 30.8

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

   [Start] 30.8	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 30.8	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub-neg [=>] 30.8	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 30.8	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   neg-sub0 [=>] 30.8	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-+l- [=>] 30.8	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub0-neg [=>] 30.8	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-lft-neg-out [=>] 30.8	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-rgt-neg-in [=>] 30.8	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 30.8	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 30.8	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [=>] 30.8	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Taylor expanded in angle around inf 30.9

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

4. Simplified 21.0

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

   [Start] 30.9	\[ \left(-2 \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 30.9	\[ \left(-2 \cdot \left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 30.9	\[ \left(-2 \cdot \left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   difference-of-squares [=>] 30.9	\[ \left(-2 \cdot \left(\color{blue}{\left(\left(a + b\right) \cdot \left(a - b\right)\right)} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 30.9	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 30.9	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \left(\color{blue}{\left(angle \cdot 0.005555555555555556\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 30.9	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [=>] 21.0	\[ \left(-2 \cdot \color{blue}{\left(\left(a + b\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [<=] 21.0	\[ \color{blue}{\left(\left(-2 \cdot \left(a + b\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 21.0	\[ \left(\left(-2 \cdot \color{blue}{\left(b + a\right)}\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 21.0	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 21.0	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(0.005555555555555556 \cdot angle\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [<=] 21.0	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

5. Applied egg-rr 21.0

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

6. Applied egg-rr 21.1

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

7. Final simplification 21.1

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

Alternatives

Alternative 1
Error	21.1
Cost	39944

\[\begin{array}{l} t_0 := {b}^{2} - {a}^{2}\\ t_1 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+214}:\\ \;\;\;\;\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_1 - a \cdot t_1\right)\right)\\ \end{array} \]

Alternative 2
Error	21.0
Cost	39680

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

Alternative 3
Error	21.1
Cost	39680

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

Alternative 4
Error	21.0
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 5
Error	21.0
Cost	26816

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

Alternative 6
Error	21.8
Cost	14089

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \lor \neg \left(\frac{angle}{180} \leq 10^{-110}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 7
Error	24.3
Cost	13700

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;\frac{angle}{180} \leq -2 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(\left(b \cdot b\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 8
Error	29.1
Cost	7696

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ t_1 := a \cdot \left(a \cdot angle\right)\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+150}:\\ \;\;\;\;t_1 \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-55}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\pi \cdot t_1\right)\\ \end{array} \]

Alternative 9
Error	29.2
Cost	7696

\[\begin{array}{l} t_0 := angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ t_1 := a \cdot \left(a \cdot angle\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+124}:\\ \;\;\;\;t_1 \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-231}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-54}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\pi \cdot t_1\right)\\ \end{array} \]

Alternative 10
Error	29.1
Cost	7696

\[\begin{array}{l} t_0 := a \cdot \left(a \cdot angle\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+126}:\\ \;\;\;\;t_0 \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-229}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\left(b + a\right) \cdot \left(\pi \cdot \left(b - a\right)\right)\right)\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-53}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+68}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\pi \cdot t_0\right)\\ \end{array} \]

Alternative 11
Error	24.7
Cost	7684

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -3.9 \cdot 10^{+21}:\\ \;\;\;\;\left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right) \cdot -0.011111111111111112\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 12
Error	31.7
Cost	7308

\[\begin{array}{l} t_0 := \left(a \cdot \left(a \cdot angle\right)\right) \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-232}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(\left(b \cdot b\right) \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+23}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Error	31.7
Cost	7308

\[\begin{array}{l} t_0 := \left(a \cdot \left(a \cdot angle\right)\right) \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-225}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(\left(b \cdot b\right) \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+24}:\\ \;\;\;\;\left(b \cdot angle\right) \cdot \left(\pi \cdot \left(b \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 14
Error	31.7
Cost	7308

\[\begin{array}{l} t_0 := a \cdot \left(a \cdot angle\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-20}:\\ \;\;\;\;t_0 \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-225}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(\left(b \cdot b\right) \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;\left(b \cdot angle\right) \cdot \left(\pi \cdot \left(b \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\pi \cdot t_0\right)\\ \end{array} \]

Alternative 15
Error	38.7
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-91}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-227}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 16
Error	38.7
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+18}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-230}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 17
Error	38.2
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+119}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+55}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(\left(b \cdot b\right) \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 18
Error	38.2
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+119}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+33}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(\left(b \cdot b\right) \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 19
Error	39.7
Cost	6912

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

Reproduce

herbie shell --seed 2023060 
(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)))))