ab-angle->ABCF B

Average Error: 31.5 → 21.6

Time: 21.2s

Precision: binary64

Cost: 26816

Math

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

↓

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

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

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

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

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 ((math.sin((math.pi * (angle / 180.0))) * (-2.0 * (a - b))) * (b + a)) * math.cos((angle * (math.pi * 0.005555555555555556)))

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(sin(Float64(pi * Float64(angle / 180.0))) * Float64(-2.0 * Float64(a - b))) * Float64(b + a)) * cos(Float64(angle * Float64(pi * 0.005555555555555556))))
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 = ((sin((pi * (angle / 180.0))) * (-2.0 * (a - b))) * (b + a)) * cos((angle * (pi * 0.005555555555555556)));
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[(N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(-2.0 * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(angle * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.5

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

2. Simplified 31.5

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

   [Start] 31.5	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 31.5	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub-neg [=>] 31.5	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 31.5	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   neg-sub0 [=>] 31.5	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-+l- [=>] 31.5	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub0-neg [=>] 31.5	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-lft-neg-out [=>] 31.5	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-rgt-neg-in [=>] 31.5	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 31.5	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 31.5	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [=>] 31.5	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Applied egg-rr 35.2

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

4. Simplified 21.6

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

   [Start] 35.2	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 35.2	\[ \frac{\color{blue}{\left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \left(a \cdot a - b \cdot b\right)}}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-/l* [=>] 31.5	\[ \color{blue}{\frac{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}{\frac{a - b}{a \cdot a - b \cdot b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 31.5	\[ \frac{\color{blue}{\left(\left(a - b\right) \cdot -2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 31.5	\[ \frac{\color{blue}{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(a - b\right) \cdot -2\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 31.5	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \color{blue}{\left(-2 \cdot \left(a - b\right)\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   difference-of-squares [=>] 31.5	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\frac{a - b}{\color{blue}{\left(a + b\right) \cdot \left(a - b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 31.5	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\frac{a - b}{\color{blue}{\left(a - b\right) \cdot \left(a + b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-/r* [=>] 21.6	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\color{blue}{\frac{\frac{a - b}{a - b}}{a + b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-inverses [=>] 21.6	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\frac{\color{blue}{1}}{a + b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 21.6	\[ \frac{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)}{\frac{1}{\color{blue}{b + a}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

5. Applied egg-rr 21.6

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

6. Taylor expanded in angle around 0 21.7

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

7. Simplified 21.6

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

   [Start] 21.7	\[ \left(\left(b + a\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \]
   *-commutative [=>] 21.7	\[ \left(\left(b + a\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \color{blue}{\left(\pi \cdot angle\right)}\right) \]
   associate-*r* [=>] 21.6	\[ \left(\left(b + a\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(-2 \cdot \left(a - b\right)\right)\right)\right) \cdot \cos \color{blue}{\left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right)} \]

8. Final simplification 21.6

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

Alternatives

Alternative 1
Error	21.6
Cost	26816

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

Alternative 2
Error	21.8
Cost	14089

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{-43} \lor \neg \left(\frac{angle}{180} \leq 10^{-14}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\frac{\pi \cdot angle}{90}\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(a - b\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	22.6
Cost	13696

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

Alternative 4
Error	22.9
Cost	13577

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.0067 \lor \neg \left(angle \leq 0.037\right):\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(a - b\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	22.9
Cost	13577

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.027 \lor \neg \left(angle \leq 0.072\right):\\ \;\;\;\;\left(b \cdot b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(a - b\right)\right)\right)\\ \end{array} \]

Alternative 6
Error	22.9
Cost	13576

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.0195:\\ \;\;\;\;\left(b \cdot b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;angle \leq 0.135:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(a - b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \sin \left(\frac{\pi \cdot angle}{90}\right)\\ \end{array} \]

Alternative 7
Error	22.8
Cost	13576

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.18:\\ \;\;\;\;a \cdot \left(\left(-a\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 0.0085:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(a - b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \sin \left(\frac{\pi \cdot angle}{90}\right)\\ \end{array} \]

Alternative 8
Error	22.8
Cost	13576

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.23:\\ \;\;\;\;\left(a \cdot \left(-a\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;angle \leq 0.082:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(a - b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \sin \left(\frac{\pi \cdot angle}{90}\right)\\ \end{array} \]

Alternative 9
Error	22.8
Cost	13576

\[\begin{array}{l} t_0 := \sin \left(\frac{\pi \cdot angle}{90}\right)\\ \mathbf{if}\;angle \leq -0.17:\\ \;\;\;\;\left(a \cdot a\right) \cdot \left(-t_0\right)\\ \mathbf{elif}\;angle \leq 0.049:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(a - b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot t_0\\ \end{array} \]

Alternative 10
Error	29.5
Cost	7432

\[\begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+151}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+147}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	29.5
Cost	7432

\[\begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+153}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{+153}:\\ \;\;\;\;\left(angle \cdot 0.011111111111111112\right) \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	25.2
Cost	7300

\[\begin{array}{l} \mathbf{if}\;angle \leq -9.5 \cdot 10^{+37}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot 0.011111111111111112\right) \cdot \left(\left(angle \cdot \left(b + a\right)\right) \cdot \left(b - a\right)\right)\\ \end{array} \]

Alternative 13
Error	25.3
Cost	7300

\[\begin{array}{l} \mathbf{if}\;angle \leq -2.55 \cdot 10^{+38}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(a - b\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	38.3
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+152} \lor \neg \left(b \leq 2 \cdot 10^{+43}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 15
Error	36.3
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-16} \lor \neg \left(a \leq 5.5 \cdot 10^{-6}\right):\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 16
Error	36.3
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-14} \lor \neg \left(a \leq 7.6 \cdot 10^{-5}\right):\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 17
Error	36.3
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-15} \lor \neg \left(a \leq 1.95\right):\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(b \cdot \left(b \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 18
Error	36.3
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-11} \lor \neg \left(a \leq 7 \cdot 10^{-7}\right):\\ \;\;\;\;\left(\pi \cdot \left(a \cdot a\right)\right) \cdot \left(angle \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(b \cdot \left(b \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 19
Error	36.3
Cost	7176

\[\begin{array}{l} t_0 := \pi \cdot \left(a \cdot a\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{-14}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot t_0\right)\\ \mathbf{elif}\;a \leq 0.00023:\\ \;\;\;\;\pi \cdot \left(b \cdot \left(b \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot t_0\right)\\ \end{array} \]

Alternative 20
Error	36.2
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-14}:\\ \;\;\;\;\pi \cdot \left(\left(a \cdot a\right) \cdot \left(angle \cdot -0.011111111111111112\right)\right)\\ \mathbf{elif}\;a \leq 6.9 \cdot 10^{-7}:\\ \;\;\;\;\pi \cdot \left(b \cdot \left(b \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(a \cdot a\right)\right) \cdot \left(angle \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 21
Error	43.2
Cost	6912

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

Alternative 22
Error	43.2
Cost	6912

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

Alternative 23
Error	43.2
Cost	6912

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

Reproduce

herbie shell --seed 2023031 
(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)))))