?

Average Error: 31.4 → 21.5
Time: 24.0s
Precision: binary64
Cost: 65536

?

\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
↓
\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\right)\right) \cdot \cos \left(\frac{\pi \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\sqrt[3]{180}}{\sqrt[3]{angle}}}\right) \]
(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) (log1p (expm1 (sin (* angle (* 0.005555555555555556 PI)))))))
  (cos
   (/
    (* PI (pow (cbrt (* angle 0.005555555555555556)) 2.0))
    (/ (cbrt 180.0) (cbrt angle))))))
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) * log1p(expm1(sin((angle * (0.005555555555555556 * ((double) M_PI)))))))) * cos(((((double) M_PI) * pow(cbrt((angle * 0.005555555555555556)), 2.0)) / (cbrt(180.0) / cbrt(angle))));
}

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.log1p(Math.expm1(Math.sin((angle * (0.005555555555555556 * Math.PI))))))) * Math.cos(((Math.PI * Math.pow(Math.cbrt((angle * 0.005555555555555556)), 2.0)) / (Math.cbrt(180.0) / Math.cbrt(angle))));
}

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) * log1p(expm1(sin(Float64(angle * Float64(0.005555555555555556 * pi))))))) * cos(Float64(Float64(pi * (cbrt(Float64(angle * 0.005555555555555556)) ^ 2.0)) / Float64(cbrt(180.0) / cbrt(angle)))))
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_] := N[(N[(N[(-2.0 * N[(b + a), $MachinePrecision]), $MachinePrecision] * N[(N[(a - b), $MachinePrecision] * N[Log[1 + N[(Exp[N[Sin[N[(angle * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(Pi * N[Power[N[Power[N[(angle * 0.005555555555555556), $MachinePrecision], 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(N[Power[180.0, 1/3], $MachinePrecision] / N[Power[angle, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

\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 \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\right)\right) \cdot \cos \left(\frac{\pi \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\sqrt[3]{180}}{\sqrt[3]{angle}}}\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified31.4

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

    [Start]31.4

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

    *-commutative [=>]31.4

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

    sub-neg [=>]31.4

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

    +-commutative [=>]31.4

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

    neg-sub0 [=>]31.4

    \[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

    associate-+l- [=>]31.4

    \[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

    sub0-neg [=>]31.4

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

    distribute-lft-neg-out [=>]31.4

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

    distribute-rgt-neg-in [=>]31.4

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

    unpow2 [=>]31.4

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

    unpow2 [=>]31.4

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

    metadata-eval [=>]31.4

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

  3. Taylor expanded in angle around inf 31.5

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

  4. Simplified21.5

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

    [Start]31.5

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

    unpow2 [=>]31.5

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

    unpow2 [=>]31.5

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

    difference-of-squares [=>]31.5

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

    associate-*r* [=>]31.5

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

    *-commutative [<=]31.5

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

    *-commutative [<=]31.5

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

    associate-*l* [=>]21.5

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

    associate-*l* [<=]21.5

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

    +-commutative [=>]21.5

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

    *-commutative [=>]21.5

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

    *-commutative [=>]21.5

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

    associate-*r* [<=]21.5

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

  5. Applied egg-rr21.6

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

  6. Simplified21.6

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

    [Start]21.6

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

    associate-/l* [=>]21.6

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

  7. Applied egg-rr21.5

    \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)}\right)\right) \cdot \cos \left(\frac{\pi \cdot {\left(\sqrt[3]{0.005555555555555556 \cdot angle}\right)}^{2}}{\frac{\sqrt[3]{180}}{\sqrt[3]{angle}}}\right) \]

  8. Final simplification21.5

    \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\right)\right) \cdot \cos \left(\frac{\pi \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\sqrt[3]{180}}{\sqrt[3]{angle}}}\right) \]

Alternatives

Alternative 1
Error21.6
Cost52736
\[\cos \left(\frac{\pi \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\sqrt[3]{180}}{\sqrt[3]{angle}}}\right) \cdot \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
Alternative 2
Error21.5
Cost52736
\[\cos \left(\frac{\pi \cdot {\left(\sqrt[3]{angle \cdot 0.005555555555555556}\right)}^{2}}{\frac{\sqrt[3]{180}}{\sqrt[3]{angle}}}\right) \cdot \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right) \]
Alternative 3
Error21.5
Cost26816
\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
Alternative 4
Error21.4
Cost26816
\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
Alternative 5
Error22.5
Cost13833
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -55000 \lor \neg \left(angle \leq 0.00088\right):\\ \;\;\;\;2 \cdot \left(b \cdot \left(b \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]
Alternative 6
Error21.8
Cost13833
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -2 \cdot 10^{-49} \lor \neg \left(angle \leq 2.1 \cdot 10^{-58}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]
Alternative 7
Error23.7
Cost13705
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{-133} \lor \neg \left(a \leq 4.6 \cdot 10^{-132}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\\ \end{array} \]
Alternative 8
Error22.3
Cost13696
\[\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \]
Alternative 9
Error24.9
Cost7684
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq 10000000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]
Alternative 10
Error29.2
Cost7432
\[\begin{array}{l} \mathbf{if}\;b \leq -1.52 \cdot 10^{+128}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+133}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\left(angle \cdot 0.005555555555555556\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]
Alternative 11
Error29.2
Cost7432
\[\begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+128}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+135}:\\ \;\;\;\;angle \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\left(angle \cdot 0.005555555555555556\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]
Alternative 12
Error33.5
Cost7304
\[\begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{-119}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(\left(angle \cdot 0.005555555555555556\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]
Alternative 13
Error33.5
Cost7177
\[\begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-118} \lor \neg \left(b \leq 1.2 \cdot 10^{+19}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]
Alternative 14
Error33.5
Cost7176
\[\begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-118}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+17}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \end{array} \]
Alternative 15
Error33.5
Cost7176
\[\begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-118}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \end{array} \]
Alternative 16
Error43.4
Cost6912
\[0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right) \]
Alternative 17
Error39.7
Cost6912
\[0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right) \]
Alternative 18
Error39.7
Cost6912
\[0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right) \]

Error

Reproduce?

herbie shell --seed 2023066 
(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)))))