Average Error: 31.7 → 21.9
Time: 18.6s
Precision: binary64
Cost: 14088
\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
\[\begin{array}{l} t_0 := \sin \left(0.011111111111111112 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -2 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{-33}:\\ \;\;\;\;2 \cdot \left(\left(b + a\right) \cdot \left(\left(\left(b - a\right) \cdot 0.5\right) \cdot \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
(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
 (let* ((t_0
         (* (sin (* 0.011111111111111112 (* PI angle))) (- (* b b) (* a a)))))
   (if (<= (/ angle 180.0) -2e-8)
     t_0
     (if (<= (/ angle 180.0) 5e-33)
       (*
        2.0
        (* (+ b a) (* (* (- b a) 0.5) (* angle (* PI 0.011111111111111112)))))
       t_0))))
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) {
	double t_0 = sin((0.011111111111111112 * (((double) M_PI) * angle))) * ((b * b) - (a * a));
	double tmp;
	if ((angle / 180.0) <= -2e-8) {
		tmp = t_0;
	} else if ((angle / 180.0) <= 5e-33) {
		tmp = 2.0 * ((b + a) * (((b - a) * 0.5) * (angle * (((double) M_PI) * 0.011111111111111112))));
	} else {
		tmp = t_0;
	}
	return tmp;
}
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) {
	double t_0 = Math.sin((0.011111111111111112 * (Math.PI * angle))) * ((b * b) - (a * a));
	double tmp;
	if ((angle / 180.0) <= -2e-8) {
		tmp = t_0;
	} else if ((angle / 180.0) <= 5e-33) {
		tmp = 2.0 * ((b + a) * (((b - a) * 0.5) * (angle * (Math.PI * 0.011111111111111112))));
	} else {
		tmp = t_0;
	}
	return tmp;
}
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):
	t_0 = math.sin((0.011111111111111112 * (math.pi * angle))) * ((b * b) - (a * a))
	tmp = 0
	if (angle / 180.0) <= -2e-8:
		tmp = t_0
	elif (angle / 180.0) <= 5e-33:
		tmp = 2.0 * ((b + a) * (((b - a) * 0.5) * (angle * (math.pi * 0.011111111111111112))))
	else:
		tmp = t_0
	return tmp
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)
	t_0 = Float64(sin(Float64(0.011111111111111112 * Float64(pi * angle))) * Float64(Float64(b * b) - Float64(a * a)))
	tmp = 0.0
	if (Float64(angle / 180.0) <= -2e-8)
		tmp = t_0;
	elseif (Float64(angle / 180.0) <= 5e-33)
		tmp = Float64(2.0 * Float64(Float64(b + a) * Float64(Float64(Float64(b - a) * 0.5) * Float64(angle * Float64(pi * 0.011111111111111112)))));
	else
		tmp = t_0;
	end
	return tmp
end
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_2 = code(a, b, angle)
	t_0 = sin((0.011111111111111112 * (pi * angle))) * ((b * b) - (a * a));
	tmp = 0.0;
	if ((angle / 180.0) <= -2e-8)
		tmp = t_0;
	elseif ((angle / 180.0) <= 5e-33)
		tmp = 2.0 * ((b + a) * (((b - a) * 0.5) * (angle * (pi * 0.011111111111111112))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end
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_] := Block[{t$95$0 = N[(N[Sin[N[(0.011111111111111112 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(b * b), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(angle / 180.0), $MachinePrecision], -2e-8], t$95$0, If[LessEqual[N[(angle / 180.0), $MachinePrecision], 5e-33], N[(2.0 * N[(N[(b + a), $MachinePrecision] * N[(N[(N[(b - a), $MachinePrecision] * 0.5), $MachinePrecision] * N[(angle * N[(Pi * 0.011111111111111112), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]
\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)
\begin{array}{l}
t_0 := \sin \left(0.011111111111111112 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\\
\mathbf{if}\;\frac{angle}{180} \leq -2 \cdot 10^{-8}:\\
\;\;\;\;t_0\\

\mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{-33}:\\
\;\;\;\;2 \cdot \left(\left(b + a\right) \cdot \left(\left(\left(b - a\right) \cdot 0.5\right) \cdot \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;t_0\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes
  2. if (/.f64 angle 180) < -2e-8 or 5.00000000000000028e-33 < (/.f64 angle 180)

    1. Initial program 47.5

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
    2. Simplified47.5

      \[\leadsto \color{blue}{\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      Proof
      (*.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (*.f64 (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 2 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a))) (*.f64 (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 2 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2)))) (*.f64 (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
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.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))))): 10 points increase in error, 11 points decrease in error
    3. Applied egg-rr47.5

      \[\leadsto \color{blue}{0 + \left(b \cdot b - a \cdot a\right) \cdot \sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} \]
    4. Simplified47.4

      \[\leadsto \color{blue}{\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)} \]
      Proof
      (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (*.f64 angle (PI.f64)) 1/90))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (*.f64 angle (PI.f64)) (Rewrite<= metadata-eval (*.f64 1/180 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 angle (PI.f64)) 1/180) 2)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (*.f64 (Rewrite=> *-commutative_binary64 (*.f64 (PI.f64) angle)) 1/180) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (PI.f64) (*.f64 angle 1/180))) 2))): 28 points increase in error, 25 points decrease in error
      (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (*.f64 (PI.f64) (*.f64 angle 1/180)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-lft-identity_binary64 (+.f64 0 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 2 (*.f64 (PI.f64) (*.f64 angle 1/180))))))): 0 points increase in error, 0 points decrease in error

    if -2e-8 < (/.f64 angle 180) < 5.00000000000000028e-33

    1. Initial program 18.4

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
    2. Simplified18.4

      \[\leadsto \color{blue}{2 \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \left(\sin \left(\frac{\pi \cdot angle}{180}\right) \cdot \cos \left(\frac{\pi \cdot angle}{180}\right)\right)\right)} \]
      Proof
      (*.f64 2 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (*.f64 (sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180)) (cos.f64 (/.f64 (*.f64 (PI.f64) angle) 180))))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (*.f64 (sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180)) (cos.f64 (/.f64 (*.f64 (PI.f64) angle) 180))))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (*.f64 (sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180)) (cos.f64 (/.f64 (*.f64 (PI.f64) angle) 180))))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (*.f64 (sin.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (/.f64 (*.f64 (PI.f64) angle) 180))))): 39 points increase in error, 25 points decrease in error
      (*.f64 2 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (cos.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (PI.f64) (/.f64 angle 180))))))): 11 points increase in error, 23 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))): 0 points increase in error, 1 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.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))))): 10 points increase in error, 11 points decrease in error
    3. Applied egg-rr10.2

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(b + a, \left(b - a\right) \cdot \left(\left(\sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right) + 0\right) \cdot 0.5\right), \mathsf{fma}\left(a, -a, a \cdot a\right) \cdot \left(\left(\sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right) + 0\right) \cdot 0.5\right)\right)} \]
    4. Taylor expanded in a around 0 0.4

      \[\leadsto 2 \cdot \mathsf{fma}\left(b + a, \left(b - a\right) \cdot \left(\left(\sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right) + 0\right) \cdot 0.5\right), \color{blue}{0} \cdot \left(\left(\sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right) + 0\right) \cdot 0.5\right)\right) \]
    5. Applied egg-rr0.4

      \[\leadsto 2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)\right)} \]
    6. Taylor expanded in angle around 0 0.4

      \[\leadsto 2 \cdot \left(\left(b + a\right) \cdot \left(\color{blue}{\left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)} \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)\right) \]
    7. Simplified0.3

      \[\leadsto 2 \cdot \left(\left(b + a\right) \cdot \left(\color{blue}{\left(angle \cdot \left(0.011111111111111112 \cdot \pi\right)\right)} \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)\right) \]
      Proof
      (*.f64 angle (*.f64 1/90 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/90) (PI.f64))): 42 points increase in error, 34 points decrease in error
      (*.f64 (Rewrite=> *-commutative_binary64 (*.f64 1/90 angle)) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 1/90 (*.f64 angle (PI.f64)))): 42 points increase in error, 45 points decrease in error
  3. Recombined 2 regimes into one program.
  4. Final simplification21.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -2 \cdot 10^{-8}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{-33}:\\ \;\;\;\;2 \cdot \left(\left(b + a\right) \cdot \left(\left(\left(b - a\right) \cdot 0.5\right) \cdot \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\\ \end{array} \]

Alternatives

Alternative 1
Error21.9
Cost33472
\[\begin{array}{l} t_0 := \sin \left(0.011111111111111112 \cdot \left(\pi \cdot angle\right)\right) \cdot 0.5\\ 2 \cdot \mathsf{fma}\left(b + a, \left(b - a\right) \cdot t_0, 0 \cdot t_0\right) \end{array} \]
Alternative 2
Error23.3
Cost14088
\[\begin{array}{l} t_0 := 2 \cdot \frac{\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)}{\frac{2}{b \cdot b}}\\ \mathbf{if}\;\frac{angle}{180} \leq -0.1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{-13}:\\ \;\;\;\;2 \cdot \left(\left(b + a\right) \cdot \left(\left(\left(b - a\right) \cdot 0.5\right) \cdot \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error23.1
Cost13832
\[\begin{array}{l} t_0 := 2 \cdot \left(-0.5 \cdot \left(a \cdot \left(a \cdot \sin \left(0.011111111111111112 \cdot \left(\pi \cdot angle\right)\right)\right)\right)\right)\\ \mathbf{if}\;angle \leq -48:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq 0.17:\\ \;\;\;\;2 \cdot \left(\left(b + a\right) \cdot \left(\left(\left(b - a\right) \cdot 0.5\right) \cdot \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error23.3
Cost13832
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.011111111111111112\right)\\ t_1 := 2 \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \sin t_0\right)\right)\right)\\ \mathbf{if}\;angle \leq -0.0062:\\ \;\;\;\;t_1\\ \mathbf{elif}\;angle \leq 7.8 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(\left(b + a\right) \cdot \left(\left(\left(b - a\right) \cdot 0.5\right) \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 5
Error23.3
Cost13832
\[\begin{array}{l} t_0 := 2 \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\right)\right)\\ \mathbf{if}\;angle \leq -0.0067:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq 7.8 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(\left(b + a\right) \cdot \left(\left(\left(b - a\right) \cdot 0.5\right) \cdot \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 6
Error21.9
Cost13824
\[2 \cdot \left(\left(b + a\right) \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot \left(\left(b - a\right) \cdot 0.5\right)\right)\right) \]
Alternative 7
Error24.4
Cost7688
\[\begin{array}{l} \mathbf{if}\;angle \leq -520000:\\ \;\;\;\;\left(a \cdot \left(a \cdot \pi\right)\right) \cdot \left(angle \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;angle \leq 4.5 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(\left(b + a\right) \cdot \left(\left(\left(b - a\right) \cdot 0.5\right) \cdot \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(1 + \pi \cdot \left(b \cdot b\right)\right) + -1\right)\right)\\ \end{array} \]
Alternative 8
Error30.4
Cost7432
\[\begin{array}{l} t_0 := -0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot \left(a \cdot angle\right)\right)\right)\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+144}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 9
Error24.7
Cost7432
\[\begin{array}{l} \mathbf{if}\;angle \leq -520000:\\ \;\;\;\;\left(a \cdot \left(a \cdot \pi\right)\right) \cdot \left(angle \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;angle \leq 7.8 \cdot 10^{-8}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\pi \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(1 + \pi \cdot \left(b \cdot b\right)\right) + -1\right)\right)\\ \end{array} \]
Alternative 10
Error39.3
Cost7176
\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(b \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{-129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 7800000:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 11
Error34.0
Cost7176
\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(b \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{-128}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 12
Error34.0
Cost7176
\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(b \cdot \left(angle \cdot \left(b \cdot \pi\right)\right)\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{-128}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-22}:\\ \;\;\;\;\left(a \cdot \left(a \cdot \pi\right)\right) \cdot \left(angle \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 13
Error34.0
Cost7176
\[\begin{array}{l} t_0 := angle \cdot \left(b \cdot \pi\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{-128}:\\ \;\;\;\;t_0 \cdot \left(b \cdot 0.011111111111111112\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;\left(a \cdot \left(a \cdot \pi\right)\right) \cdot \left(angle \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot t_0\right)\\ \end{array} \]
Alternative 14
Error33.3
Cost7176
\[\begin{array}{l} t_0 := -0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot \left(a \cdot angle\right)\right)\right)\\ \mathbf{if}\;a \leq -1.82 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;\pi \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 15
Error44.2
Cost6912
\[0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right) \]

Error

Reproduce

herbie shell --seed 2022329 
(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)))))