ab-angle->ABCF B

Average Error: 31.4 → 21.5

Time: 22.9s

Precision: binary64

Cost: 59200

Math

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

↓

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

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
   (/
    PI
    (/
     (cbrt (/ 180.0 angle))
     (pow (pow (cbrt (cbrt (* 0.005555555555555556 angle))) 3.0) 2.0))))))

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((((double) M_PI) / (cbrt((180.0 / angle)) / pow(pow(cbrt(cbrt((0.005555555555555556 * angle))), 3.0), 2.0))));
}

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.PI / (Math.cbrt((180.0 / angle)) / Math.pow(Math.pow(Math.cbrt(Math.cbrt((0.005555555555555556 * angle))), 3.0), 2.0))));
}

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(pi / Float64(cbrt(Float64(180.0 / angle)) / ((cbrt(cbrt(Float64(0.005555555555555556 * angle))) ^ 3.0) ^ 2.0)))))
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[(Pi / N[(N[Power[N[(180.0 / angle), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[N[Power[N[Power[N[Power[N[(0.005555555555555556 * angle), $MachinePrecision], 1/3], $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.4

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

2. Simplified 31.4

   \[\leadsto \color{blue}{\left(\left(\left(a \cdot a - b \cdot b\right) \cdot -2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)} \]
   Proof
   (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 a a) (*.f64 b b)) -2) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 b b)) -2) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 12 points decrease in error
   (*.f64 (*.f64 (*.f64 (-.f64 (pow.f64 a 2) (Rewrite<= unpow2_binary64 (pow.f64 b 2))) -2) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 12 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 (-.f64 (pow.f64 a 2) (pow.f64 b 2)) (Rewrite<= metadata-eval (neg.f64 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 12 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (-.f64 (pow.f64 a 2) (pow.f64 b 2)) 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 12 points decrease in error
   (*.f64 (*.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 (-.f64 (pow.f64 a 2) (pow.f64 b 2))) 2)) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 12 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 (pow.f64 a 2) (pow.f64 b 2)))) 2) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 12 points decrease in error
   (*.f64 (*.f64 (*.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 (pow.f64 a 2)) (pow.f64 b 2))) 2) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 12 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (pow.f64 a 2))) (pow.f64 b 2)) 2) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 12 points decrease in error
   (*.f64 (*.f64 (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 b 2) (neg.f64 (pow.f64 a 2)))) 2) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 12 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) 2) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 12 points decrease in error
   (*.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 12 points increase in error, 0 points decrease in error

3. Taylor expanded in angle around inf 31.4

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

4. Simplified 21.3

   \[\leadsto \color{blue}{\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   Proof
   (*.f64 (*.f64 (*.f64 -2 (+.f64 b a)) (*.f64 (-.f64 a b) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 -2 (Rewrite<= +-commutative_binary64 (+.f64 a b))) (*.f64 (-.f64 a b) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 13 points decrease in error
   (*.f64 (*.f64 (*.f64 -2 (+.f64 a b)) (*.f64 (-.f64 a b) (sin.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 1/180 angle) (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 13 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 -2 (+.f64 a b)) (*.f64 (-.f64 a b) (sin.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 angle 1/180)) (PI.f64))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 7 points increase in error, 6 points decrease in error
   (*.f64 (*.f64 (*.f64 -2 (+.f64 a b)) (*.f64 (-.f64 a b) (sin.f64 (Rewrite<= *-commutative_binary64 (*.f64 (PI.f64) (*.f64 angle 1/180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 6 points increase in error, 7 points decrease in error
   (*.f64 (Rewrite=> associate-*l*_binary64 (*.f64 -2 (*.f64 (+.f64 a b) (*.f64 (-.f64 a b) (sin.f64 (*.f64 (PI.f64) (*.f64 angle 1/180))))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 13 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 -2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (+.f64 a b) (-.f64 a b)) (sin.f64 (*.f64 (PI.f64) (*.f64 angle 1/180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 13 points decrease in error
   (*.f64 (*.f64 -2 (*.f64 (Rewrite<= difference-of-squares_binary64 (-.f64 (*.f64 a a) (*.f64 b b))) (sin.f64 (*.f64 (PI.f64) (*.f64 angle 1/180))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 7 points increase in error, 6 points decrease in error
   (*.f64 (*.f64 -2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 b b)) (sin.f64 (*.f64 (PI.f64) (*.f64 angle 1/180))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 7 points decrease in error
   (*.f64 (*.f64 -2 (*.f64 (-.f64 (pow.f64 a 2) (Rewrite<= unpow2_binary64 (pow.f64 b 2))) (sin.f64 (*.f64 (PI.f64) (*.f64 angle 1/180))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 -2 (*.f64 (-.f64 (pow.f64 a 2) (pow.f64 b 2)) (sin.f64 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 7 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 -2 (*.f64 (-.f64 (pow.f64 a 2) (pow.f64 b 2)) (sin.f64 (*.f64 (Rewrite=> *-commutative_binary64 (*.f64 1/180 angle)) (PI.f64))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 7 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 -2 (*.f64 (-.f64 (pow.f64 a 2) (pow.f64 b 2)) (sin.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/180 (*.f64 angle (PI.f64))))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 6 points increase in error, 0 points decrease in error

5. Applied egg-rr 21.4

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{\left(\pi \cdot {\left(\sqrt[3]{0.005555555555555556 \cdot angle}\right)}^{2}\right) \cdot 1}{\sqrt[3]{\frac{180}{angle}}}\right)} \]

6. Simplified 21.3

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{\pi}{\frac{\sqrt[3]{\frac{180}{angle}}}{{\left(\sqrt[3]{0.005555555555555556 \cdot angle}\right)}^{2}}}\right)} \]
   Proof
   (*.f64 (*.f64 (*.f64 -2 (+.f64 b a)) (*.f64 (-.f64 a b) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (/.f64 (PI.f64) (/.f64 (cbrt.f64 (/.f64 180 angle)) (pow.f64 (cbrt.f64 (*.f64 1/180 angle)) 2))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 -2 (+.f64 b a)) (*.f64 (-.f64 a b) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (*.f64 1/180 angle)) 2)) (cbrt.f64 (/.f64 180 angle)))))): 0 points increase in error, 3 points decrease in error
   (*.f64 (*.f64 (*.f64 -2 (+.f64 b a)) (*.f64 (-.f64 a b) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (*.f64 1/180 angle)) 2)) 1)) (cbrt.f64 (/.f64 180 angle))))): 3 points increase in error, 0 points decrease in error

7. Applied egg-rr 21.5

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

8. Final simplification 21.5

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

Alternatives

Alternative 1
Error	21.5
Cost	13956

\[\begin{array}{l} t_0 := b \cdot b - a \cdot a\\ t_1 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -6 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \frac{t_0}{\frac{2}{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}}\\ \mathbf{elif}\;angle \leq 1.65 \cdot 10^{-54}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_1 - a \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 2
Error	21.3
Cost	13952

\[\frac{1}{\frac{2}{\left(b + a\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)}} \cdot \left(2 \cdot \left(b - a\right)\right) \]

Alternative 3
Error	21.5
Cost	13833

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -2.3 \cdot 10^{-18} \lor \neg \left(angle \leq 3.5 \cdot 10^{-55}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 4
Error	21.5
Cost	13832

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ t_1 := b \cdot b - a \cdot a\\ \mathbf{if}\;angle \leq -9.5 \cdot 10^{-7}:\\ \;\;\;\;\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot t_1\\ \mathbf{elif}\;angle \leq 3.8 \cdot 10^{-55}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 5
Error	21.5
Cost	13824

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

Alternative 6
Error	21.3
Cost	13824

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

Alternative 7
Error	21.2
Cost	13824

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

Alternative 8
Error	22.8
Cost	13640

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.0038:\\ \;\;\;\;\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot \left(b \cdot b\right)\\ \mathbf{elif}\;angle \leq 1.45 \cdot 10^{-23}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(-a\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	22.6
Cost	13577

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.0038 \lor \neg \left(angle \leq 3800000000\right):\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 10
Error	22.6
Cost	13576

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.0014:\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;angle \leq 3800000000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	22.6
Cost	13576

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.0031:\\ \;\;\;\;\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot \left(b \cdot b\right)\\ \mathbf{elif}\;angle \leq 3800000000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	23.8
Cost	7817

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -2.25 \cdot 10^{+30} \lor \neg \left(angle \leq 1020000000000\right):\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 13
Error	29.6
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+108} \lor \neg \left(b \leq 1.48 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	29.6
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+108} \lor \neg \left(b \leq 1.5 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(angle \cdot \pi\right) \cdot \left(b \cdot b - a \cdot a\right)\right)\\ \end{array} \]

Alternative 15
Error	29.6
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+108} \lor \neg \left(b \leq 1.25 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 16
Error	38.0
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-104} \lor \neg \left(a \leq 0.72\right):\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 17
Error	33.1
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -33000000000000 \lor \neg \left(b \leq 1150000000\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 18
Error	33.1
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -32000000000000 \lor \neg \left(b \leq 45000000\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot -0.011111111111111112\right) \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\\ \end{array} \]

Alternative 19
Error	43.0
Cost	6912

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

Alternative 20
Error	43.0
Cost	6912

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

Alternative 21
Error	43.0
Cost	6912

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

Alternative 22
Error	42.9
Cost	6912

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

Reproduce

herbie shell --seed 2022343 
(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)))))