?

Average Error: 31.1 → 21.5
Time: 23.3s
Precision: binary64
Cost: 33280

?

\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
↓
\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left({\left(\frac{180}{angle \cdot \pi}\right)}^{-1}\right)\right)\right) \cdot \cos \left(\frac{angle \cdot \pi}{180}\right) \]
(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) (sin (pow (/ 180.0 (* angle PI)) -1.0))))
  (cos (/ (* angle PI) 180.0))))
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) {
	return ((-2.0 * (b + a)) * ((a - b) * sin(pow((180.0 / (angle * ((double) M_PI))), -1.0)))) * cos(((angle * ((double) M_PI)) / 180.0));
}

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(Math.pow((180.0 / (angle * Math.PI)), -1.0)))) * Math.cos(((angle * Math.PI) / 180.0));
}

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(math.pow((180.0 / (angle * math.pi)), -1.0)))) * math.cos(((angle * math.pi) / 180.0))

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(180.0 / Float64(angle * pi)) ^ -1.0)))) * cos(Float64(Float64(angle * pi) / 180.0)))
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 = code(a, b, angle)
	tmp = ((-2.0 * (b + a)) * ((a - b) * sin(((180.0 / (angle * pi)) ^ -1.0)))) * cos(((angle * pi) / 180.0));
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[Sin[N[Power[N[(180.0 / N[(angle * Pi), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(angle * Pi), $MachinePrecision] / 180.0), $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 \sin \left({\left(\frac{180}{angle \cdot \pi}\right)}^{-1}\right)\right)\right) \cdot \cos \left(\frac{angle \cdot \pi}{180}\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 31.1

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

  2. Simplified31.1

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

    [Start]31.1

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

    *-commutative [=>]31.1

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

    sub-neg [=>]31.1

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

    +-commutative [=>]31.1

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

    neg-sub0 [=>]31.1

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

    associate-+l- [=>]31.1

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

    sub0-neg [=>]31.1

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

    distribute-lft-neg-out [=>]31.1

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

    distribute-rgt-neg-in [=>]31.1

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

    unpow2 [=>]31.1

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

    unpow2 [=>]31.1

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

    metadata-eval [=>]31.1

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

  3. Taylor expanded in angle around inf 31.2

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

  4. Simplified21.4

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

    [Start]31.2

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

    unpow2 [=>]31.2

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

    unpow2 [=>]31.2

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

    difference-of-squares [=>]31.2

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

    associate-*r* [=>]31.1

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

    *-commutative [<=]31.1

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

    *-commutative [<=]31.1

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

    associate-*l* [=>]21.3

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

    associate-*l* [<=]21.3

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

    +-commutative [=>]21.3

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

    *-commutative [=>]21.3

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

    *-commutative [=>]21.3

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

    associate-*r* [<=]21.4

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

  5. Applied egg-rr21.6

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

  6. Applied egg-rr21.5

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

  7. Applied egg-rr21.5

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

  8. Final simplification21.5

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

Alternatives

Alternative 1
Error21.3
Cost53193
\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ t_1 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+291} \lor \neg \left(t_1 \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;\cos t_0 \cdot \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sin t_0 \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)\\ \end{array} \]
Alternative 2
Error21.4
Cost53192
\[\begin{array}{l} t_0 := -2 \cdot \left(b + a\right)\\ t_1 := {b}^{2} - {a}^{2}\\ t_2 := \pi \cdot \frac{angle}{180}\\ t_3 := \cos t_2\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+291}:\\ \;\;\;\;t_3 \cdot \left(t_0 \cdot \left(\left(a - b\right) \cdot \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;2 \cdot \left(\sin t_2 \cdot \left(t_3 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(\left(a - b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right)\\ \end{array} \]
Alternative 3
Error21.4
Cost53192
\[\begin{array}{l} t_0 := -2 \cdot \left(b + a\right)\\ t_1 := {b}^{2} - {a}^{2}\\ t_2 := \pi \cdot \frac{angle}{180}\\ t_3 := \cos t_2\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+291}:\\ \;\;\;\;t_3 \cdot \left(t_0 \cdot \left(\left(a - b\right) \cdot \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(t_3 \cdot \sin t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(\left(a - b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right)\\ \end{array} \]
Alternative 4
Error21.5
Cost40072
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ t_1 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+283}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right)\\ \end{array} \]
Alternative 5
Error21.4
Cost40072
\[\begin{array}{l} t_0 := -2 \cdot \left(b + a\right)\\ t_1 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+283}:\\ \;\;\;\;\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(t_0 \cdot \left(\left(a - b\right) \cdot \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(\left(a - b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right)\\ \end{array} \]
Alternative 6
Error21.5
Cost33280
\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left({\left(\frac{180}{angle \cdot \pi}\right)}^{-1}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
Alternative 7
Error21.4
Cost26816
\[\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right)\right) \]
Alternative 8
Error21.4
Cost26816
\[\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \]
Alternative 9
Error21.4
Cost14089
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{-22} \lor \neg \left(\frac{angle}{180} \leq 4 \cdot 10^{-24}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]
Alternative 10
Error22.6
Cost13896
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ t_1 := \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{-7}:\\ \;\;\;\;\left(b \cdot b\right) \cdot t_1\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{-8}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(a \cdot \left(-a\right)\right)\\ \end{array} \]
Alternative 11
Error22.5
Cost13577
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.00011 \lor \neg \left(angle \leq 6.4 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]
Alternative 12
Error22.5
Cost13577
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.00011 \lor \neg \left(angle \leq 6.4 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]
Alternative 13
Error22.5
Cost13576
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ t_1 := \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;angle \leq -0.00011:\\ \;\;\;\;\left(b \cdot b\right) \cdot t_1\\ \mathbf{elif}\;angle \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(b \cdot t_1\right)\\ \end{array} \]
Alternative 14
Error25.7
Cost7817
\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;b \leq 1.8 \cdot 10^{-258} \lor \neg \left(b \leq 1.95 \cdot 10^{-165}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]
Alternative 15
Error29.2
Cost7561
\[\begin{array}{l} \mathbf{if}\;b \leq -2.85 \cdot 10^{+54} \lor \neg \left(b \leq 8 \cdot 10^{+117}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(angle \cdot 0.005555555555555556\right) \cdot \left(\pi \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]
Alternative 16
Error38.8
Cost7441
\[\begin{array}{l} t_0 := angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{if}\;a \leq -1.82 \cdot 10^{+50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq -122000000000:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-129} \lor \neg \left(a \leq 2.6 \cdot 10^{-111}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(\left(b \cdot b\right) \cdot 0.011111111111111112\right)\right)\\ \end{array} \]
Alternative 17
Error29.4
Cost7433
\[\begin{array}{l} \mathbf{if}\;b \leq -2.85 \cdot 10^{+54} \lor \neg \left(b \leq 4 \cdot 10^{+76}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \end{array} \]
Alternative 18
Error29.3
Cost7433
\[\begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+60} \lor \neg \left(b \leq 3.9 \cdot 10^{+76}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \end{array} \]
Alternative 19
Error29.2
Cost7433
\[\begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+60} \lor \neg \left(b \leq 10^{+79}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\left(b + a\right) \cdot \left(\pi \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]
Alternative 20
Error29.2
Cost7433
\[\begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+53} \lor \neg \left(b \leq 4.8 \cdot 10^{+94}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \end{array} \]
Alternative 21
Error32.2
Cost7177
\[\begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-15} \lor \neg \left(b \leq 1.9 \cdot 10^{-48}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]
Alternative 22
Error32.2
Cost7177
\[\begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{-14} \lor \neg \left(b \leq 4.5 \cdot 10^{-47}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot -0.011111111111111112\right) \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\\ \end{array} \]
Alternative 23
Error42.7
Cost6912
\[0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right) \]
Alternative 24
Error42.7
Cost6912
\[0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right) \]
Alternative 25
Error42.7
Cost6912
\[angle \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot 0.011111111111111112\right)\right)\right) \]
Alternative 26
Error42.7
Cost6912
\[angle \cdot \left(\pi \cdot \left(\left(b \cdot b\right) \cdot 0.011111111111111112\right)\right) \]

Error

Reproduce?

herbie shell --seed 2023039 
(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)))))