ab-angle->ABCF B

Average Error: 31.4 → 21.5

Time: 22.1s

Precision: binary64

Cost: 26816

Math

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

↓

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

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 (* angle (* 0.005555555555555556 PI)))))
  (cos (* PI (/ angle 180.0)))))

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((angle * (0.005555555555555556 * ((double) M_PI)))))) * cos((((double) M_PI) * (angle / 180.0)));
}

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((angle * (0.005555555555555556 * Math.PI))))) * Math.cos((Math.PI * (angle / 180.0)));
}

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

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(angle * Float64(0.005555555555555556 * pi))))) * cos(Float64(pi * Float64(angle / 180.0))))
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 = ((-2.0 * (b + a)) * ((a - b) * sin((angle * (0.005555555555555556 * pi))))) * cos((pi * (angle / 180.0)));
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[(angle * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(Pi * N[(angle / 180.0), $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)))): 12 points increase in error, 0 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)))): 0 points increase in error, 12 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)))): 12 points increase in error, 0 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)))): 0 points increase in error, 12 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)))): 12 points increase in error, 0 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)))): 0 points increase in error, 12 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 21.6

   \[\leadsto \color{blue}{\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   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)))): 13 points increase in error, 0 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)))): 13 points increase in error, 0 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)))): 0 points increase in error, 13 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)))): 10 points increase in error, 3 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)))): 0 points increase in error, 13 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)))): 13 points increase in error, 0 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, 13 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)))): 0 points increase in error, 13 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)))): 13 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)))): 0 points increase in error, 13 points decrease in error

5. Applied egg-rr 49.7

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)} - 1\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

6. Simplified 21.5

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \color{blue}{\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   Proof
   (*.f64 (*.f64 (*.f64 -2 (+.f64 b a)) (*.f64 (-.f64 a b) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (*.f64 -2 (+.f64 b a)) (*.f64 (-.f64 a b) (Rewrite<= expm1-log1p_binary64 (expm1.f64 (log1p.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 1 points increase in error, 2 points decrease in error
   (*.f64 (*.f64 (*.f64 -2 (+.f64 b a)) (*.f64 (-.f64 a b) (Rewrite<= expm1-def_binary64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) 1)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))): 2 points increase in error, 1 points decrease in error

7. Final simplification 21.5

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

Alternatives

Alternative 1
Error	21.6
Cost	26816

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

Alternative 2
Error	21.8
Cost	14089

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;\frac{angle}{180} \leq -4 \cdot 10^{-52} \lor \neg \left(\frac{angle}{180} \leq 2 \cdot 10^{-26}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 3
Error	23.3
Cost	13960

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\left(a \cdot \left(-a\right)\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10000000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(b \cdot b\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \end{array} \]

Alternative 4
Error	23.3
Cost	13960

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\left(a \cdot \left(-a\right)\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10000000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(b \cdot b\right) \cdot \sin \left(\frac{\pi}{\frac{180}{angle}}\right)\right)\\ \end{array} \]

Alternative 5
Error	23.4
Cost	13960

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;\frac{angle}{180} \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(-2 \cdot \left(a \cdot a\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10000000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(b \cdot b\right) \cdot \sin \left(\frac{\pi}{\frac{180}{angle}}\right)\right)\\ \end{array} \]

Alternative 6
Error	22.6
Cost	13696

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

Alternative 7
Error	23.0
Cost	13641

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.065 \lor \neg \left(angle \leq 0.68\right):\\ \;\;\;\;\left(a \cdot \left(-a\right)\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 8
Error	25.3
Cost	7684

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq 8 \cdot 10^{+19}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(a \cdot a\right)\right) \cdot \left(angle \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 9
Error	29.8
Cost	7432

\[\begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+138}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+112}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(a \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	30.0
Cost	7432

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+82}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+112}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(a \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	30.0
Cost	7432

\[\begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+82}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.78 \cdot 10^{+112}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\left(b + a\right) \cdot \left(\pi \cdot \left(b - a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(a \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	29.9
Cost	7432

\[\begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+137}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+111}:\\ \;\;\;\;\left(angle \cdot 0.011111111111111112\right) \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(a \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 13
Error	33.2
Cost	7304

\[\begin{array}{l} t_0 := a \cdot \left(angle \cdot -0.011111111111111112\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(\pi \cdot t_0\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;2 \cdot \left(\left(angle \cdot 0.005555555555555556\right) \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(a \cdot t_0\right)\\ \end{array} \]

Alternative 14
Error	39.1
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -6.7 \cdot 10^{+152}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+101}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(a \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 15
Error	39.1
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+153}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+41}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 16
Error	33.2
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-59}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-30}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 17
Error	33.3
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-61}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-28}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 18
Error	33.2
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-26}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 19
Error	33.2
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-30}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(a \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 20
Error	33.2
Cost	7176

\[\begin{array}{l} t_0 := a \cdot \left(angle \cdot -0.011111111111111112\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(\pi \cdot t_0\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-28}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(a \cdot t_0\right)\\ \end{array} \]

Alternative 21
Error	40.4
Cost	6912

\[-0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \pi\right)\right)\right) \]

Reproduce

herbie shell --seed 2022340 
(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)))))