ab-angle->ABCF B

Average Error: 49.35% → 33.85%

Time: 22.7s

Precision: binary64

Cost: 26816

Math

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

↓

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

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
 (*
  (* (+ b a) (* (sin (* 0.005555555555555556 (* angle PI))) (* -2.0 (- 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 ((b + a) * (sin((0.005555555555555556 * (angle * ((double) M_PI)))) * (-2.0 * (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 ((b + a) * (Math.sin((0.005555555555555556 * (angle * Math.PI))) * (-2.0 * (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 ((b + a) * (math.sin((0.005555555555555556 * (angle * math.pi))) * (-2.0 * (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(b + a) * Float64(sin(Float64(0.005555555555555556 * Float64(angle * pi))) * Float64(-2.0 * 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 = ((b + a) * (sin((0.005555555555555556 * (angle * pi))) * (-2.0 * (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[(b + a), $MachinePrecision] * N[(N[Sin[N[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(-2.0 * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(Pi / N[(180.0 / angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 49.35

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

2. Simplified 49.35

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

   [Start] 49.35	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 49.35	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub-neg [=>] 49.35	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 49.35	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   neg-sub0 [=>] 49.35	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-+l- [=>] 49.35	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub0-neg [=>] 49.35	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-lft-neg-out [=>] 49.35	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-rgt-neg-in [=>] 49.35	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 49.35	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 49.35	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [=>] 49.35	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Applied egg-rr 54.54

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

4. Simplified 33.88

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

   [Start] 54.54	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 54.54	\[ \frac{\color{blue}{\left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \left(a \cdot a - b \cdot b\right)}}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-/l* [=>] 49.45	\[ \color{blue}{\frac{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}{\frac{a - b}{a \cdot a - b \cdot b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 49.45	\[ \frac{\color{blue}{\left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(a - b\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [=>] 49.45	\[ \frac{\color{blue}{-2 \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(a - b\right)\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 49.45	\[ \frac{-2 \cdot \color{blue}{\left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 49.45	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)}\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 49.45	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(0.005555555555555556 \cdot angle\right)} \cdot \pi\right)\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [<=] 49.43	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   difference-of-squares [=>] 49.43	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{a - b}{\color{blue}{\left(a + b\right) \cdot \left(a - b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 49.43	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{a - b}{\color{blue}{\left(a - b\right) \cdot \left(a + b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-/r* [=>] 33.88	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\color{blue}{\frac{\frac{a - b}{a - b}}{a + b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-inverses [=>] 33.88	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{\color{blue}{1}}{a + b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 33.88	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{1}{\color{blue}{b + a}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

5. Applied egg-rr 33.79

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

6. Applied egg-rr 33.77

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

7. Taylor expanded in angle around inf 33.85

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

8. Simplified 33.85

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

   [Start] 33.85	\[ \left(-2 \cdot \left(\left(a - b\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   associate-*r* [=>] 33.85	\[ \color{blue}{\left(\left(-2 \cdot \left(a - b\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)} \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   *-commutative [=>] 33.85	\[ \left(\left(-2 \cdot \left(a - b\right)\right) \cdot \left(\sin \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)} \cdot \left(a + b\right)\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   associate-*r* [<=] 33.75	\[ \left(\left(-2 \cdot \left(a - b\right)\right) \cdot \left(\sin \color{blue}{\left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)} \cdot \left(a + b\right)\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   rem-square-sqrt [<=] 66.91	\[ \left(\left(-2 \cdot \left(a - b\right)\right) \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \color{blue}{\left(\sqrt{a + b} \cdot \sqrt{a + b}\right)}\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   associate-*l* [<=] 66.91	\[ \color{blue}{\left(\left(\left(-2 \cdot \left(a - b\right)\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right) \cdot \left(\sqrt{a + b} \cdot \sqrt{a + b}\right)\right)} \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   *-commutative [<=] 66.91	\[ \left(\color{blue}{\left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(-2 \cdot \left(a - b\right)\right)\right)} \cdot \left(\sqrt{a + b} \cdot \sqrt{a + b}\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   *-commutative [=>] 66.91	\[ \color{blue}{\left(\left(\sqrt{a + b} \cdot \sqrt{a + b}\right) \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(-2 \cdot \left(a - b\right)\right)\right)\right)} \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   rem-square-sqrt [=>] 33.75	\[ \left(\color{blue}{\left(a + b\right)} \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(-2 \cdot \left(a - b\right)\right)\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   +-commutative [=>] 33.75	\[ \left(\color{blue}{\left(b + a\right)} \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(-2 \cdot \left(a - b\right)\right)\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   associate-*r* [=>] 33.85	\[ \left(\left(b + a\right) \cdot \left(\sin \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)} \cdot \left(-2 \cdot \left(a - b\right)\right)\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]
   *-commutative [<=] 33.85	\[ \left(\left(b + a\right) \cdot \left(\sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)} \cdot \left(-2 \cdot \left(a - b\right)\right)\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]

9. Final simplification 33.85

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

Alternatives

Alternative 1
Error	33.85%
Cost	26816

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

Alternative 2
Error	41.65%
Cost	14216

\[\begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+135}:\\ \;\;\;\;2 \cdot \left(\left(\left(b \cdot b\right) \cdot 0.5 + \frac{a}{\frac{-2}{a}}\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(0.5 \cdot \left(b \cdot \left(b \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	45.07%
Cost	14096

\[\begin{array}{l} t_0 := \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ t_1 := 2 \cdot \left(0.5 \cdot \left(b \cdot \left(b \cdot t_0\right)\right)\right)\\ t_2 := b \cdot b - a \cdot a\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \frac{\pi \cdot \left(0.005555555555555556 \cdot angle\right)}{\frac{1}{t_2}}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-132}:\\ \;\;\;\;2 \cdot \left(-0.5 \cdot \left(t_0 \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+50}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(\left(angle \cdot \pi\right) \cdot t_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	45.04%
Cost	14096

\[\begin{array}{l} t_0 := 2 \cdot \left(0.5 \cdot \left(b \cdot \left(b \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\right)\right)\right)\\ t_1 := b \cdot b - a \cdot a\\ \mathbf{if}\;b \leq -7 \cdot 10^{+118}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \frac{\pi \cdot \left(0.005555555555555556 \cdot angle\right)}{\frac{1}{t_1}}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-132}:\\ \;\;\;\;2 \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot \left(\left(a \cdot a\right) \cdot -0.5\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+50}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(\left(angle \cdot \pi\right) \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	41.7%
Cost	14089

\[\begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+154} \lor \neg \left(b \leq 6.8 \cdot 10^{+153}\right):\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(0.5 \cdot \left(\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 6
Error	41.65%
Cost	14088

\[\begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+135}:\\ \;\;\;\;2 \cdot \left(\left(0.5 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(0.5 \cdot \left(b \cdot \left(b \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\right)\right)\right)\\ \end{array} \]

Alternative 7
Error	45.34%
Cost	13964

\[\begin{array}{l} t_0 := 2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ t_1 := b \cdot b - a \cdot a\\ \mathbf{if}\;b \leq -2 \cdot 10^{+128}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \frac{\pi \cdot \left(0.005555555555555556 \cdot angle\right)}{\frac{1}{t_1}}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-132}:\\ \;\;\;\;2 \cdot \left(-0.5 \cdot \left(\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+152}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(\left(angle \cdot \pi\right) \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	35.4%
Cost	13824

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

Alternative 9
Error	35.42%
Cost	13824

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

Alternative 10
Error	46.34%
Cost	7689

\[\begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+128} \lor \neg \left(b \leq 3.5 \cdot 10^{+138}\right):\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \frac{\pi}{\frac{1}{b \cdot b - a \cdot a}}\right)\right)\\ \end{array} \]

Alternative 11
Error	46.33%
Cost	7689

\[\begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+127} \lor \neg \left(b \leq 8.5 \cdot 10^{+137}\right):\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\pi \cdot \left(0.005555555555555556 \cdot angle\right)}{\frac{1}{b \cdot b - a \cdot a}}\\ \end{array} \]

Alternative 12
Error	46.63%
Cost	7561

\[\begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+128} \lor \neg \left(b \leq 1.22 \cdot 10^{+138}\right):\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\right)\\ \end{array} \]

Alternative 13
Error	46.58%
Cost	7561

\[\begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+154} \lor \neg \left(b \leq 1.65 \cdot 10^{+152}\right):\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(\left(angle \cdot \pi\right) \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	60.1%
Cost	7305

\[\begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-174} \lor \neg \left(b \leq 1.05 \cdot 10^{+139}\right):\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 15
Error	51.71%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{-45}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-57}:\\ \;\;\;\;2 \cdot \left(-0.005555555555555556 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\left(0.005555555555555556 \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 16
Error	51.65%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{-45}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;2 \cdot \left(\left(\pi \cdot \left(angle \cdot \left(a \cdot a\right)\right)\right) \cdot -0.005555555555555556\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\left(0.005555555555555556 \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 17
Error	67.58%
Cost	6912

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

Reproduce

herbie shell --seed 2023102 
(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)))))