ab-angle->ABCF B

Average Error: 30.7 → 20.7

Time: 20.7s

Precision: binary64

Cost: 26816

Math

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

↓

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

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
 (*
  (* (- a b) (* -2.0 (* (sin (* (* 0.005555555555555556 PI) angle)) (+ a b))))
  (cos (/ PI (/ 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 ((a - b) * (-2.0 * (sin(((0.005555555555555556 * ((double) M_PI)) * angle)) * (a + b)))) * cos((((double) M_PI) / (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 ((a - b) * (-2.0 * (Math.sin(((0.005555555555555556 * Math.PI) * angle)) * (a + b)))) * Math.cos((Math.PI / (180.0 / angle)));
}

Python

def code(a, b, 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)))

↓

def code(a, b, angle):
	return ((a - b) * (-2.0 * (math.sin(((0.005555555555555556 * math.pi) * angle)) * (a + b)))) * math.cos((math.pi / (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(a - b) * Float64(-2.0 * Float64(sin(Float64(Float64(0.005555555555555556 * pi) * angle)) * Float64(a + b)))) * cos(Float64(pi / Float64(180.0 / angle))))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = ((2.0 * ((b ^ 2.0) - (a ^ 2.0))) * sin((pi * (angle / 180.0)))) * cos((pi * (angle / 180.0)));
end

↓

function tmp = code(a, b, angle)
	tmp = ((a - b) * (-2.0 * (sin(((0.005555555555555556 * pi) * angle)) * (a + b)))) * cos((pi / (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[(a - b), $MachinePrecision] * N[(-2.0 * N[(N[Sin[N[(N[(0.005555555555555556 * Pi), $MachinePrecision] * angle), $MachinePrecision]], $MachinePrecision] * N[(a + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(Pi / N[(180.0 / angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.7

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

2. Simplified 30.7

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

   [Start] 30.7	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 30.7	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub-neg [=>] 30.7	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 30.7	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   neg-sub0 [=>] 30.7	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-+l- [=>] 30.7	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub0-neg [=>] 30.7	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-lft-neg-out [=>] 30.7	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-rgt-neg-in [=>] 30.7	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 30.7	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 30.7	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [=>] 30.7	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Applied egg-rr 34.2

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

4. Simplified 20.8

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

   [Start] 34.2	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 34.2	\[ \frac{\color{blue}{\left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \left(a \cdot a - b \cdot b\right)}}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-/l* [=>] 30.7	\[ \color{blue}{\frac{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}{\frac{a - b}{a \cdot a - b \cdot b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 30.7	\[ \frac{\color{blue}{\left(\left(a - b\right) \cdot -2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 30.7	\[ \frac{\color{blue}{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(a - b\right) \cdot -2\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 30.7	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \color{blue}{\left(-2 \cdot \left(a - b\right)\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   difference-of-squares [=>] 30.7	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\frac{a - b}{\color{blue}{\left(a + b\right) \cdot \left(a - b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 30.7	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\frac{a - b}{\color{blue}{\left(a - b\right) \cdot \left(a + b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-/r* [=>] 20.8	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\color{blue}{\frac{\frac{a - b}{a - b}}{a + b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-inverses [=>] 20.8	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\frac{\color{blue}{1}}{a + b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 20.8	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\frac{1}{\color{blue}{b + a}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

5. Taylor expanded in angle around inf 20.8

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

6. Simplified 20.7

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

   [Start] 20.8	\[ \left(-2 \cdot \left(\left(a - b\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 20.8	\[ \color{blue}{\left(\left(-2 \cdot \left(a - b\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 20.8	\[ \left(\color{blue}{\left(\left(a - b\right) \cdot -2\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [=>] 20.8	\[ \color{blue}{\left(\left(a - b\right) \cdot \left(-2 \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 20.8	\[ \left(\left(a - b\right) \cdot \left(-2 \cdot \left(\sin \left(0.005555555555555556 \cdot \color{blue}{\left(\pi \cdot angle\right)}\right) \cdot \left(a + b\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 20.7	\[ \left(\left(a - b\right) \cdot \left(-2 \cdot \left(\sin \color{blue}{\left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right)} \cdot \left(a + b\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

7. Applied egg-rr 20.7

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

8. Final simplification 20.7

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

Alternatives

Alternative 1
Error	20.7
Cost	26816

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

Alternative 2
Error	20.7
Cost	26816

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

Alternative 3
Error	20.7
Cost	26816

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

Alternative 4
Error	20.9
Cost	14345

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -0.0004 \lor \neg \left(\frac{angle}{180} \leq 5 \cdot 10^{-18}\right):\\ \;\;\;\;2 \cdot \left(\sin \left(\pi \cdot \frac{angle}{90}\right) \cdot \frac{b \cdot b - a \cdot a}{2}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(0.005555555555555556 \cdot \pi\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	21.4
Cost	14216

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -0.0004:\\ \;\;\;\;2 \cdot \left(\sin \left(\pi \cdot \frac{angle}{90}\right) \cdot \frac{b \cdot b - a \cdot a}{2}\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{-18}:\\ \;\;\;\;2 \cdot \left(\left(0.005555555555555556 \cdot \pi\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a \cdot a - b \cdot b\right)\right)\\ \end{array} \]

Alternative 6
Error	22.5
Cost	13961

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -10000 \lor \neg \left(\frac{angle}{180} \leq 2 \cdot 10^{+54}\right):\\ \;\;\;\;2 \cdot \left(b \cdot \left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(0.005555555555555556 \cdot \pi\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]

Alternative 7
Error	21.8
Cost	13824

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

Alternative 8
Error	21.7
Cost	13696

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

Alternative 9
Error	28.9
Cost	7560

\[\begin{array}{l} t_0 := \pi \cdot \left(b \cdot angle\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot t_0\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+120}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot 0.011111111111111112\right) \cdot t_0\\ \end{array} \]

Alternative 10
Error	24.6
Cost	7428

\[\begin{array}{l} \mathbf{if}\;angle \leq 4.8 \cdot 10^{+77}:\\ \;\;\;\;2 \cdot \left(\left(0.005555555555555556 \cdot \pi\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	32.4
Cost	7304

\[\begin{array}{l} t_0 := \pi \cdot \left(b \cdot angle\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{-66}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot t_0\right)\right)\\ \mathbf{elif}\;b \leq 445:\\ \;\;\;\;2 \cdot \left(\left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right) \cdot -0.005555555555555556\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot 0.011111111111111112\right) \cdot t_0\\ \end{array} \]

Alternative 12
Error	37.9
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+114} \lor \neg \left(b \leq 9.2 \cdot 10^{-176}\right):\\ \;\;\;\;\left(b \cdot 0.011111111111111112\right) \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 13
Error	37.9
Cost	7176

\[\begin{array}{l} t_0 := \pi \cdot \left(b \cdot angle\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+111}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot t_0\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-176}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot 0.011111111111111112\right) \cdot t_0\\ \end{array} \]

Alternative 14
Error	42.5
Cost	6912

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

Alternative 15
Error	42.5
Cost	6912

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

Alternative 16
Error	42.5
Cost	6912

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

Reproduce

herbie shell --seed 2023011 
(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)))))