ab-angle->ABCF B

Average Error: 31.0 → 31.1

Time: 1.5min

Precision: binary64

Cost: 158784

Math

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

↓

\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \frac{t_0}{-4}\\ t_2 := \sin t_0\\ t_3 := \frac{t_0}{2}\\ t_4 := \sin t_3\\ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos t_0 \cdot \left(4 \cdot t_2\right)\right) - -2 \cdot \left(t_2 \cdot \left(\left(\left(\sin \left(t_0 \cdot 0.25\right) \cdot \sin t_1 + \cos t_1 \cdot \sin \left(\frac{\pi \cdot \left(2 - angle \cdot 0.005555555555555556\right)}{4}\right)\right) \cdot \cos t_3 - t_4 \cdot t_4\right) \cdot \left({a}^{2} - {b}^{2}\right)\right)\right) \end{array} \]

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
 (let* ((t_0 (* angle (* PI 0.005555555555555556)))
        (t_1 (/ t_0 -4.0))
        (t_2 (sin t_0))
        (t_3 (/ t_0 2.0))
        (t_4 (sin t_3)))
   (-
    (* (- (pow b 2.0) (pow a 2.0)) (* (cos t_0) (* 4.0 t_2)))
    (*
     -2.0
     (*
      t_2
      (*
       (-
        (*
         (+
          (* (sin (* t_0 0.25)) (sin t_1))
          (*
           (cos t_1)
           (sin (/ (* PI (- 2.0 (* angle 0.005555555555555556))) 4.0))))
         (cos t_3))
        (* t_4 t_4))
       (- (pow a 2.0) (pow b 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) {
	double t_0 = angle * (((double) M_PI) * 0.005555555555555556);
	double t_1 = t_0 / -4.0;
	double t_2 = sin(t_0);
	double t_3 = t_0 / 2.0;
	double t_4 = sin(t_3);
	return ((pow(b, 2.0) - pow(a, 2.0)) * (cos(t_0) * (4.0 * t_2))) - (-2.0 * (t_2 * (((((sin((t_0 * 0.25)) * sin(t_1)) + (cos(t_1) * sin(((((double) M_PI) * (2.0 - (angle * 0.005555555555555556))) / 4.0)))) * cos(t_3)) - (t_4 * t_4)) * (pow(a, 2.0) - pow(b, 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) {
	double t_0 = angle * (Math.PI * 0.005555555555555556);
	double t_1 = t_0 / -4.0;
	double t_2 = Math.sin(t_0);
	double t_3 = t_0 / 2.0;
	double t_4 = Math.sin(t_3);
	return ((Math.pow(b, 2.0) - Math.pow(a, 2.0)) * (Math.cos(t_0) * (4.0 * t_2))) - (-2.0 * (t_2 * (((((Math.sin((t_0 * 0.25)) * Math.sin(t_1)) + (Math.cos(t_1) * Math.sin(((Math.PI * (2.0 - (angle * 0.005555555555555556))) / 4.0)))) * Math.cos(t_3)) - (t_4 * t_4)) * (Math.pow(a, 2.0) - Math.pow(b, 2.0)))));
}

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):
	t_0 = angle * (math.pi * 0.005555555555555556)
	t_1 = t_0 / -4.0
	t_2 = math.sin(t_0)
	t_3 = t_0 / 2.0
	t_4 = math.sin(t_3)
	return ((math.pow(b, 2.0) - math.pow(a, 2.0)) * (math.cos(t_0) * (4.0 * t_2))) - (-2.0 * (t_2 * (((((math.sin((t_0 * 0.25)) * math.sin(t_1)) + (math.cos(t_1) * math.sin(((math.pi * (2.0 - (angle * 0.005555555555555556))) / 4.0)))) * math.cos(t_3)) - (t_4 * t_4)) * (math.pow(a, 2.0) - math.pow(b, 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)
	t_0 = Float64(angle * Float64(pi * 0.005555555555555556))
	t_1 = Float64(t_0 / -4.0)
	t_2 = sin(t_0)
	t_3 = Float64(t_0 / 2.0)
	t_4 = sin(t_3)
	return Float64(Float64(Float64((b ^ 2.0) - (a ^ 2.0)) * Float64(cos(t_0) * Float64(4.0 * t_2))) - Float64(-2.0 * Float64(t_2 * Float64(Float64(Float64(Float64(Float64(sin(Float64(t_0 * 0.25)) * sin(t_1)) + Float64(cos(t_1) * sin(Float64(Float64(pi * Float64(2.0 - Float64(angle * 0.005555555555555556))) / 4.0)))) * cos(t_3)) - Float64(t_4 * t_4)) * Float64((a ^ 2.0) - (b ^ 2.0))))))
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)
	t_0 = angle * (pi * 0.005555555555555556);
	t_1 = t_0 / -4.0;
	t_2 = sin(t_0);
	t_3 = t_0 / 2.0;
	t_4 = sin(t_3);
	tmp = (((b ^ 2.0) - (a ^ 2.0)) * (cos(t_0) * (4.0 * t_2))) - (-2.0 * (t_2 * (((((sin((t_0 * 0.25)) * sin(t_1)) + (cos(t_1) * sin(((pi * (2.0 - (angle * 0.005555555555555556))) / 4.0)))) * cos(t_3)) - (t_4 * t_4)) * ((a ^ 2.0) - (b ^ 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_] := Block[{t$95$0 = N[(angle * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 / -4.0), $MachinePrecision]}, Block[{t$95$2 = N[Sin[t$95$0], $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 / 2.0), $MachinePrecision]}, Block[{t$95$4 = N[Sin[t$95$3], $MachinePrecision]}, N[(N[(N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[t$95$0], $MachinePrecision] * N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-2.0 * N[(t$95$2 * N[(N[(N[(N[(N[(N[Sin[N[(t$95$0 * 0.25), $MachinePrecision]], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[t$95$1], $MachinePrecision] * N[Sin[N[(N[(Pi * N[(2.0 - N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 4.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$3], $MachinePrecision]), $MachinePrecision] - N[(t$95$4 * t$95$4), $MachinePrecision]), $MachinePrecision] * N[(N[Power[a, 2.0], $MachinePrecision] - N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Initial program 31.0

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

2. Simplified 31.0

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

   [Start] 31.0	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   rational_best-simplify-1 [=>] 31.0	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
   rational_best-simplify-50 [=>] 31.0	\[ \color{blue}{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]

3. Applied egg-rr 31.0

   \[\leadsto \color{blue}{\left(\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) + \cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)\right)} \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

4. Simplified 31.0

   \[\leadsto \color{blue}{\left(-2 \cdot \left(-\cos \left(angle \cdot \left(\pi \cdot 0.002777777777777778\right)\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.002777777777777778\right)\right)\right)\right)} \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   Proof

   [Start] 31.0	\[ \left(\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) + \cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-59 [=>] 31.0	\[ \color{blue}{\left(\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) - \left(-\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)\right)\right)} \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-13 [=>] 31.0	\[ \left(\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) - \color{blue}{\frac{\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)}{-1}}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-45 [=>] 31.0	\[ \color{blue}{\left(\left(-1 + -1\right) \cdot \frac{\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)}{-1}\right)} \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   metadata-eval [=>] 31.0	\[ \left(\color{blue}{-2} \cdot \frac{\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)}{-1}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-13 [<=] 31.0	\[ \left(-2 \cdot \color{blue}{\left(-\cos \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)\right)}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-50 [=>] 31.1	\[ \left(-2 \cdot \left(-\cos \color{blue}{\left(0.002777777777777778 \cdot \left(angle \cdot \pi\right)\right)} \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)\right)\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-1 [=>] 31.1	\[ \left(-2 \cdot \left(-\cos \left(0.002777777777777778 \cdot \color{blue}{\left(\pi \cdot angle\right)}\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)\right)\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-50 [=>] 31.0	\[ \left(-2 \cdot \left(-\cos \color{blue}{\left(angle \cdot \left(\pi \cdot 0.002777777777777778\right)\right)} \cdot \sin \left(\pi \cdot \left(angle \cdot 0.002777777777777778\right)\right)\right)\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-50 [=>] 31.1	\[ \left(-2 \cdot \left(-\cos \left(angle \cdot \left(\pi \cdot 0.002777777777777778\right)\right) \cdot \sin \color{blue}{\left(0.002777777777777778 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-1 [=>] 31.1	\[ \left(-2 \cdot \left(-\cos \left(angle \cdot \left(\pi \cdot 0.002777777777777778\right)\right) \cdot \sin \left(0.002777777777777778 \cdot \color{blue}{\left(\pi \cdot angle\right)}\right)\right)\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   rational_best-simplify-50 [=>] 31.0	\[ \left(-2 \cdot \left(-\cos \left(angle \cdot \left(\pi \cdot 0.002777777777777778\right)\right) \cdot \sin \color{blue}{\left(angle \cdot \left(\pi \cdot 0.002777777777777778\right)\right)}\right)\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

5. Applied egg-rr 31.0

   \[\leadsto \color{blue}{\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot 4\right)\right) - -2 \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)} \]

6. Simplified 30.9

   \[\leadsto \color{blue}{\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(4 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) - -2 \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left({a}^{2} - {b}^{2}\right)\right)\right)} \]
   Proof

   [Start] 31.0	\[ \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot 4\right)\right) - -2 \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) \]
   rational_best-simplify-1 [=>] 31.0	\[ \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \color{blue}{\left(\left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot 4\right) \cdot \left({b}^{2} - {a}^{2}\right)\right)} - -2 \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) \]
   rational_best-simplify-50 [=>] 30.9	\[ \color{blue}{\left({b}^{2} - {a}^{2}\right) \cdot \left(\left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot 4\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)} - -2 \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) \]
   rational_best-simplify-1 [<=] 30.9	\[ \left({b}^{2} - {a}^{2}\right) \cdot \color{blue}{\left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot 4\right)\right)} - -2 \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) \]
   rational_best-simplify-1 [=>] 30.9	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \color{blue}{\left(4 \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}\right) - -2 \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) \]
   rational_best-simplify-50 [<=] 30.9	\[ \left({b}^{2} - {a}^{2}\right) \cdot \color{blue}{\left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(4 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)} - -2 \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) \]
   rational_best-simplify-50 [=>] 30.9	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(4 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) - -2 \cdot \color{blue}{\left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)} \]

7. Applied egg-rr 30.9

   \[\leadsto \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(4 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) - -2 \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\color{blue}{\left(\cos \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right) \cdot \cos \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right) - \sin \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right) \cdot \sin \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right)\right)} \cdot \left({a}^{2} - {b}^{2}\right)\right)\right) \]

8. Applied egg-rr 31.1

   \[\leadsto \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(4 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) - -2 \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left(\color{blue}{\left(\sin \left(\left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot 0.25\right) \cdot \sin \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{-4}\right) + \cos \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{-4}\right) \cdot \sin \left(\frac{\pi \cdot \left(2 - angle \cdot 0.005555555555555556\right)}{4}\right)\right)} \cdot \cos \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right) - \sin \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right) \cdot \sin \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right)\right) \cdot \left({a}^{2} - {b}^{2}\right)\right)\right) \]

9. Final simplification 31.1

   \[\leadsto \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(4 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right) - -2 \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left(\left(\sin \left(\left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot 0.25\right) \cdot \sin \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{-4}\right) + \cos \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{-4}\right) \cdot \sin \left(\frac{\pi \cdot \left(2 - angle \cdot 0.005555555555555556\right)}{4}\right)\right) \cdot \cos \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right) - \sin \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right) \cdot \sin \left(\frac{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}{2}\right)\right) \cdot \left({a}^{2} - {b}^{2}\right)\right)\right) \]

Alternatives

Alternative 1
Error	30.9
Cost	79040

\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \sin t_0\\ t_2 := \cos t_0\\ \left({b}^{2} - {a}^{2}\right) \cdot \left(t_2 \cdot \left(4 \cdot t_1\right)\right) - -2 \cdot \left(t_1 \cdot \left(t_2 \cdot \left({a}^{2} - {b}^{2}\right)\right)\right) \end{array} \]

Alternative 2
Error	31.0
Cost	52800

\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.002777777777777778\right)\\ \left(-2 \cdot \left(-\cos t_0 \cdot \sin t_0\right)\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \end{array} \]

Alternative 3
Error	31.0
Cost	39488

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ 2 \cdot \left(\cos t_0 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \sin t_0\right)\right) \end{array} \]

Alternative 4
Error	31.3
Cost	32900

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -4 \cdot 10^{-262}:\\ \;\;\;\;{a}^{2} \cdot \left(-\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} \cdot \sin \left(\pi \cdot \left(0.011111111111111112 \cdot angle\right)\right)\\ \end{array} \]

Alternative 5
Error	31.0
Cost	26368

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

Alternative 6
Error	36.1
Cost	26244

\[\begin{array}{l} \mathbf{if}\;{b}^{2} \leq 1.25 \cdot 10^{-89}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\\ \end{array} \]

Alternative 7
Error	35.0
Cost	26244

\[\begin{array}{l} \mathbf{if}\;{b}^{2} \leq 1.9 \cdot 10^{-88}:\\ \;\;\;\;{a}^{2} \cdot \sin \left(\pi \cdot \left(angle \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\\ \end{array} \]

Alternative 8
Error	35.0
Cost	26244

\[\begin{array}{l} \mathbf{if}\;{b}^{2} \leq 3.7 \cdot 10^{-88}:\\ \;\;\;\;{a}^{2} \cdot \sin \left(\pi \cdot \left(angle \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 9
Error	35.0
Cost	19912

\[\begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{-48}:\\ \;\;\;\;{b}^{2} \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-45}:\\ \;\;\;\;{a}^{2} \cdot \sin \left(\pi \cdot \left(angle \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} \cdot \sin \left(\pi \cdot \left(0.011111111111111112 \cdot angle\right)\right)\\ \end{array} \]

Alternative 10
Error	37.5
Cost	13512

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{if}\;b \leq -0.092:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 1.96 \cdot 10^{-44}:\\ \;\;\;\;-0.011111111111111112 \cdot \left({a}^{2} \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	37.5
Cost	13512

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{if}\;b \leq -0.29:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-44}:\\ \;\;\;\;angle \cdot \left(\left(\pi \cdot {a}^{2}\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	37.4
Cost	13512

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{if}\;b \leq -0.215:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-44}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Error	37.4
Cost	13512

\[\begin{array}{l} t_0 := \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\\ \mathbf{if}\;b \leq -0.59:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-45}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 14
Error	43.0
Cost	13248

\[-0.011111111111111112 \cdot \left(angle \cdot \left({a}^{2} \cdot \pi\right)\right) \]

Alternative 15
Error	43.0
Cost	13248

\[-0.011111111111111112 \cdot \left({a}^{2} \cdot \left(angle \cdot \pi\right)\right) \]

Reproduce

herbie shell --seed 2023099 
(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)))))