Simplification of discriminant from scale-rotated-ellipse

Average Error: 40.3 → 5.9

Time: 1.2min

Precision: binary64

Cost: 20432

Math

\[\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} \cdot \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} - \left(4 \cdot \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} \]

↓

\[\begin{array}{l} t_0 := \frac{\frac{b \cdot a}{y-scale}}{x-scale}\\ t_1 := \frac{y-scale \cdot x-scale}{b \cdot a}\\ t_2 := \frac{b}{x-scale} \cdot \frac{a}{y-scale}\\ \mathbf{if}\;y-scale \leq -5 \cdot 10^{+183}:\\ \;\;\;\;-4 \cdot \left(t_2 \cdot t_2\right)\\ \mathbf{elif}\;y-scale \leq -5.2 \cdot 10^{-229}:\\ \;\;\;\;-4 \cdot \left(t_0 \cdot t_0\right)\\ \mathbf{elif}\;y-scale \leq 1.35 \cdot 10^{-266}:\\ \;\;\;\;-4 \cdot \left(\left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right) \cdot \frac{\frac{b}{x-scale}}{\frac{y-scale}{a}}\right)\\ \mathbf{elif}\;y-scale \leq 1.45 \cdot 10^{-67}:\\ \;\;\;\;\frac{-4}{t_1 \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{-4 \cdot {\left(\frac{a}{x-scale} \cdot \frac{b}{y-scale}\right)}^{2}}\right)}^{3}\\ \end{array} \]

FPCore

(FPCore (a b angle x-scale y-scale)
 :precision binary64
 (-
  (*
   (/
    (/
     (*
      (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* (/ angle 180.0) PI)))
      (cos (* (/ angle 180.0) PI)))
     x-scale)
    y-scale)
   (/
    (/
     (*
      (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* (/ angle 180.0) PI)))
      (cos (* (/ angle 180.0) PI)))
     x-scale)
    y-scale))
  (*
   (*
    4.0
    (/
     (/
      (+
       (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
       (pow (* b (cos (* (/ angle 180.0) PI))) 2.0))
      x-scale)
     x-scale))
   (/
    (/
     (+
      (pow (* a (cos (* (/ angle 180.0) PI))) 2.0)
      (pow (* b (sin (* (/ angle 180.0) PI))) 2.0))
     y-scale)
    y-scale))))

↓

(FPCore (a b angle x-scale y-scale)
 :precision binary64
 (let* ((t_0 (/ (/ (* b a) y-scale) x-scale))
        (t_1 (/ (* y-scale x-scale) (* b a)))
        (t_2 (* (/ b x-scale) (/ a y-scale))))
   (if (<= y-scale -5e+183)
     (* -4.0 (* t_2 t_2))
     (if (<= y-scale -5.2e-229)
       (* -4.0 (* t_0 t_0))
       (if (<= y-scale 1.35e-266)
         (*
          -4.0
          (* (* b (/ (/ a y-scale) x-scale)) (/ (/ b x-scale) (/ y-scale a))))
         (if (<= y-scale 1.45e-67)
           (/ -4.0 (* t_1 t_1))
           (pow
            (cbrt (* -4.0 (pow (* (/ a x-scale) (/ b y-scale)) 2.0)))
            3.0)))))))

C

double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	return ((((((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(((angle / 180.0) * ((double) M_PI)))) * cos(((angle / 180.0) * ((double) M_PI)))) / x_45_scale) / y_45_scale) * (((((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(((angle / 180.0) * ((double) M_PI)))) * cos(((angle / 180.0) * ((double) M_PI)))) / x_45_scale) / y_45_scale)) - ((4.0 * (((pow((a * sin(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * cos(((angle / 180.0) * ((double) M_PI)))), 2.0)) / x_45_scale) / x_45_scale)) * (((pow((a * cos(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * sin(((angle / 180.0) * ((double) M_PI)))), 2.0)) / y_45_scale) / y_45_scale));
}

↓

double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	double t_0 = ((b * a) / y_45_scale) / x_45_scale;
	double t_1 = (y_45_scale * x_45_scale) / (b * a);
	double t_2 = (b / x_45_scale) * (a / y_45_scale);
	double tmp;
	if (y_45_scale <= -5e+183) {
		tmp = -4.0 * (t_2 * t_2);
	} else if (y_45_scale <= -5.2e-229) {
		tmp = -4.0 * (t_0 * t_0);
	} else if (y_45_scale <= 1.35e-266) {
		tmp = -4.0 * ((b * ((a / y_45_scale) / x_45_scale)) * ((b / x_45_scale) / (y_45_scale / a)));
	} else if (y_45_scale <= 1.45e-67) {
		tmp = -4.0 / (t_1 * t_1);
	} else {
		tmp = pow(cbrt((-4.0 * pow(((a / x_45_scale) * (b / y_45_scale)), 2.0))), 3.0);
	}
	return tmp;
}

Java

public static double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	return ((((((2.0 * (Math.pow(b, 2.0) - Math.pow(a, 2.0))) * Math.sin(((angle / 180.0) * Math.PI))) * Math.cos(((angle / 180.0) * Math.PI))) / x_45_scale) / y_45_scale) * (((((2.0 * (Math.pow(b, 2.0) - Math.pow(a, 2.0))) * Math.sin(((angle / 180.0) * Math.PI))) * Math.cos(((angle / 180.0) * Math.PI))) / x_45_scale) / y_45_scale)) - ((4.0 * (((Math.pow((a * Math.sin(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos(((angle / 180.0) * Math.PI))), 2.0)) / x_45_scale) / x_45_scale)) * (((Math.pow((a * Math.cos(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.sin(((angle / 180.0) * Math.PI))), 2.0)) / y_45_scale) / y_45_scale));
}

↓

public static double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	double t_0 = ((b * a) / y_45_scale) / x_45_scale;
	double t_1 = (y_45_scale * x_45_scale) / (b * a);
	double t_2 = (b / x_45_scale) * (a / y_45_scale);
	double tmp;
	if (y_45_scale <= -5e+183) {
		tmp = -4.0 * (t_2 * t_2);
	} else if (y_45_scale <= -5.2e-229) {
		tmp = -4.0 * (t_0 * t_0);
	} else if (y_45_scale <= 1.35e-266) {
		tmp = -4.0 * ((b * ((a / y_45_scale) / x_45_scale)) * ((b / x_45_scale) / (y_45_scale / a)));
	} else if (y_45_scale <= 1.45e-67) {
		tmp = -4.0 / (t_1 * t_1);
	} else {
		tmp = Math.pow(Math.cbrt((-4.0 * Math.pow(((a / x_45_scale) * (b / y_45_scale)), 2.0))), 3.0);
	}
	return tmp;
}

Julia

function code(a, b, angle, x_45_scale, y_45_scale)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * Float64((b ^ 2.0) - (a ^ 2.0))) * sin(Float64(Float64(angle / 180.0) * pi))) * cos(Float64(Float64(angle / 180.0) * pi))) / x_45_scale) / y_45_scale) * Float64(Float64(Float64(Float64(Float64(2.0 * Float64((b ^ 2.0) - (a ^ 2.0))) * sin(Float64(Float64(angle / 180.0) * pi))) * cos(Float64(Float64(angle / 180.0) * pi))) / x_45_scale) / y_45_scale)) - Float64(Float64(4.0 * Float64(Float64(Float64((Float64(a * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * cos(Float64(Float64(angle / 180.0) * pi))) ^ 2.0)) / x_45_scale) / x_45_scale)) * Float64(Float64(Float64((Float64(a * cos(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0)) / y_45_scale) / y_45_scale)))
end

↓

function code(a, b, angle, x_45_scale, y_45_scale)
	t_0 = Float64(Float64(Float64(b * a) / y_45_scale) / x_45_scale)
	t_1 = Float64(Float64(y_45_scale * x_45_scale) / Float64(b * a))
	t_2 = Float64(Float64(b / x_45_scale) * Float64(a / y_45_scale))
	tmp = 0.0
	if (y_45_scale <= -5e+183)
		tmp = Float64(-4.0 * Float64(t_2 * t_2));
	elseif (y_45_scale <= -5.2e-229)
		tmp = Float64(-4.0 * Float64(t_0 * t_0));
	elseif (y_45_scale <= 1.35e-266)
		tmp = Float64(-4.0 * Float64(Float64(b * Float64(Float64(a / y_45_scale) / x_45_scale)) * Float64(Float64(b / x_45_scale) / Float64(y_45_scale / a))));
	elseif (y_45_scale <= 1.45e-67)
		tmp = Float64(-4.0 / Float64(t_1 * t_1));
	else
		tmp = cbrt(Float64(-4.0 * (Float64(Float64(a / x_45_scale) * Float64(b / y_45_scale)) ^ 2.0))) ^ 3.0;
	end
	return tmp
end

Wolfram

code[a_, b_, angle_, x$45$scale_, y$45$scale_] := N[(N[(N[(N[(N[(N[(N[(2.0 * N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / x$45$scale), $MachinePrecision] / y$45$scale), $MachinePrecision] * N[(N[(N[(N[(N[(2.0 * N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / x$45$scale), $MachinePrecision] / y$45$scale), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(N[(N[(N[Power[N[(a * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / x$45$scale), $MachinePrecision] / x$45$scale), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[Power[N[(a * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / y$45$scale), $MachinePrecision] / y$45$scale), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[a_, b_, angle_, x$45$scale_, y$45$scale_] := Block[{t$95$0 = N[(N[(N[(b * a), $MachinePrecision] / y$45$scale), $MachinePrecision] / x$45$scale), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y$45$scale * x$45$scale), $MachinePrecision] / N[(b * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / x$45$scale), $MachinePrecision] * N[(a / y$45$scale), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$45$scale, -5e+183], N[(-4.0 * N[(t$95$2 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$45$scale, -5.2e-229], N[(-4.0 * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$45$scale, 1.35e-266], N[(-4.0 * N[(N[(b * N[(N[(a / y$45$scale), $MachinePrecision] / x$45$scale), $MachinePrecision]), $MachinePrecision] * N[(N[(b / x$45$scale), $MachinePrecision] / N[(y$45$scale / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$45$scale, 1.45e-67], N[(-4.0 / N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(-4.0 * N[Power[N[(N[(a / x$45$scale), $MachinePrecision] * N[(b / y$45$scale), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y-scale < -5.00000000000000009e183

   1. Initial program 35.4

      \[\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} \cdot \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} - \left(4 \cdot \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} \]

   2. Simplified 37.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot -4, \frac{b \cdot b - a \cdot a}{\frac{\frac{x-scale \cdot y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}} \cdot \frac{b \cdot b - a \cdot a}{\frac{\frac{x-scale \cdot y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}}\right)} \]
      Proof
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 3 points increase in error, 13 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 4 points increase in error, 16 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (Rewrite<= metadata-eval (neg.f64 4))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) 4))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (Rewrite<= associate-*r/_binary64 (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 1 points increase in error, 2 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 1 points increase in error, 5 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) 2) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) y-scale)) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 3 points increase in error, 3 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale)) y-scale) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 4 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (Rewrite<= associate-*r/_binary64 (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 2 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))))): 3 points increase in error, 3 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) 2) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) y-scale)))): 3 points increase in error, 6 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale)) y-scale))): 5 points increase in error, 2 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)))): 8 points increase in error, 9 points decrease in error
      (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in angle around 0 35.4

      \[\leadsto \color{blue}{-4 \cdot \frac{{a}^{2} \cdot {b}^{2}}{{y-scale}^{2} \cdot {x-scale}^{2}}} \]

   4. Simplified 5.8

      \[\leadsto \color{blue}{-4 \cdot \left(\left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right) \cdot \left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right)\right)} \]
      Proof
      (*.f64 -4 (*.f64 (*.f64 (/.f64 b x-scale) (/.f64 a y-scale)) (*.f64 (/.f64 b x-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 (/.f64 b x-scale) (/.f64 b x-scale)) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale))))): 74 points increase in error, 22 points decrease in error
      (*.f64 -4 (*.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 b b) (*.f64 x-scale x-scale))) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 58 points increase in error, 6 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 x-scale x-scale)) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 x-scale 2))) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale))))): 48 points increase in error, 6 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 y-scale y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (/.f64 (pow.f64 a 2) (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 (pow.f64 a 2) (pow.f64 y-scale 2)) (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))): 10 points increase in error, 15 points decrease in error

   if -5.00000000000000009e183 < y-scale < -5.2000000000000003e-229

   1. Initial program 40.8

      \[\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} \cdot \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} - \left(4 \cdot \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} \]

   2. Simplified 44.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot -4, \frac{b \cdot b - a \cdot a}{\frac{\frac{x-scale \cdot y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}} \cdot \frac{b \cdot b - a \cdot a}{\frac{\frac{x-scale \cdot y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}}\right)} \]
      Proof
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 3 points increase in error, 13 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 4 points increase in error, 16 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (Rewrite<= metadata-eval (neg.f64 4))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) 4))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (Rewrite<= associate-*r/_binary64 (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 1 points increase in error, 2 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 1 points increase in error, 5 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) 2) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) y-scale)) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 3 points increase in error, 3 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale)) y-scale) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 4 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (Rewrite<= associate-*r/_binary64 (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 2 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))))): 3 points increase in error, 3 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) 2) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) y-scale)))): 3 points increase in error, 6 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale)) y-scale))): 5 points increase in error, 2 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)))): 8 points increase in error, 9 points decrease in error
      (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in angle around 0 36.8

      \[\leadsto \color{blue}{-4 \cdot \frac{{a}^{2} \cdot {b}^{2}}{{y-scale}^{2} \cdot {x-scale}^{2}}} \]

   4. Simplified 4.6

      \[\leadsto \color{blue}{-4 \cdot \left(\left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right) \cdot \left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right)\right)} \]
      Proof
      (*.f64 -4 (*.f64 (*.f64 (/.f64 b x-scale) (/.f64 a y-scale)) (*.f64 (/.f64 b x-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 (/.f64 b x-scale) (/.f64 b x-scale)) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale))))): 74 points increase in error, 22 points decrease in error
      (*.f64 -4 (*.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 b b) (*.f64 x-scale x-scale))) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 58 points increase in error, 6 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 x-scale x-scale)) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 x-scale 2))) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale))))): 48 points increase in error, 6 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 y-scale y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (/.f64 (pow.f64 a 2) (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 (pow.f64 a 2) (pow.f64 y-scale 2)) (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))): 10 points increase in error, 15 points decrease in error

   5. Applied egg-rr 19.9

      \[\leadsto -4 \cdot \color{blue}{\frac{\left(b \cdot \frac{a}{y-scale}\right) \cdot \left(b \cdot a\right)}{x-scale \cdot \left(x-scale \cdot y-scale\right)}} \]

   6. Applied egg-rr 4.6

      \[\leadsto -4 \cdot \color{blue}{\left(\frac{\frac{b \cdot a}{y-scale}}{x-scale} \cdot \frac{\frac{b \cdot a}{y-scale}}{x-scale}\right)} \]

   if -5.2000000000000003e-229 < y-scale < 1.34999999999999998e-266

   1. Initial program 52.6

      \[\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} \cdot \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} - \left(4 \cdot \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} \]

   2. Simplified 64.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot -4, \frac{b \cdot b - a \cdot a}{\frac{\frac{x-scale \cdot y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}} \cdot \frac{b \cdot b - a \cdot a}{\frac{\frac{x-scale \cdot y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}}\right)} \]
      Proof
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 3 points increase in error, 13 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) -4) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 4 points increase in error, 16 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (Rewrite<= metadata-eval (neg.f64 4))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) 4))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)))) (*.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (Rewrite<= associate-*r/_binary64 (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 1 points increase in error, 2 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 1 points increase in error, 5 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) 2) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) y-scale)) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 3 points increase in error, 3 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale)) y-scale) (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 4 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (/.f64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (/.f64 (Rewrite<= associate-*r/_binary64 (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 2 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))))): 3 points increase in error, 3 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) 2) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) y-scale)))): 3 points increase in error, 6 points decrease in error
      (fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale)) y-scale))): 5 points increase in error, 2 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)))): 8 points increase in error, 9 points decrease in error
      (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in angle around 0 64.0

      \[\leadsto \color{blue}{-4 \cdot \frac{{a}^{2} \cdot {b}^{2}}{{y-scale}^{2} \cdot {x-scale}^{2}}} \]

   4. Simplified 14.1

      \[\leadsto \color{blue}{-4 \cdot \left(\left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right) \cdot \left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right)\right)} \]
      Proof
      (*.f64 -4 (*.f64 (*.f64 (/.f64 b x-scale) (/.f64 a y-scale)) (*.f64 (/.f64 b x-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 (/.f64 b x-scale) (/.f64 b x-scale)) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale))))): 74 points increase in error, 22 points decrease in error
      (*.f64 -4 (*.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 b b) (*.f64 x-scale x-scale))) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 58 points increase in error, 6 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 x-scale x-scale)) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 x-scale 2))) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a a) (*.f64 y-scale y-scale))))): 48 points increase in error, 6 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 y-scale y-scale)))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (*.f64 (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2)) (/.f64 (pow.f64 a 2) (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 (pow.f64 a 2) (pow.f64 y-scale 2)) (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))): 10 points increase in error, 15 points decrease in error

   5. Applied egg-rr 17.5

      \[\leadsto -4 \cdot \left(\color{blue}{\frac{a}{\frac{x-scale}{b} \cdot y-scale}} \cdot \left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right)\right) \]

   6. Taylor expanded in a around 0 28.3

      \[\leadsto -4 \cdot \left(\color{blue}{\frac{a \cdot b}{x-scale \cdot y-scale}} \cdot \left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right)\right) \]

   7. Simplified 17.1

      \[\leadsto -4 \cdot \left(\color{blue}{\left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right)} \cdot \left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right)\right) \]
      Proof
      (*.f64 b (/.f64 (/.f64 a y-scale) x-scale)): 0 points increase in error, 0 points decrease in error
      (*.f64 b (Rewrite=> associate-/l/_binary64 (/.f64 a (*.f64 x-scale y-scale)))): 38 points increase in error, 54 points decrease in error
      (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 a (*.f64 x-scale y-scale)) b)): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 a b) (*.f64 x-scale y-scale))): 52 points increase in error, 36 points decrease in error

   8. Applied egg-rr 17.1

      \[\leadsto -4 \cdot \left(\left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right) \cdot \color{blue}{\frac{\frac{b}{x-scale}}{\frac{y-scale}{a}}}\right) \]

   if 1.34999999999999998e-266 < y-scale < 1.45000000000000002e-67

   1. Initial program 47.3

      \[\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} \cdot \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} - \left(4 \cdot \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} \]

   2. Simplified 55.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2 \cdot \left(b \cdot b - a \cdot a\right)}{\frac{x-scale \cdot y-scale}{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}}, \frac{2 \cdot \left(b \cdot b - a \cdot a\right)}{\frac{x-scale \cdot y-scale}{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}}, -4 \cdot \left(\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}\right)\right)} \]
      Proof
      (fma.f64 (/.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (*.f64 2 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2)))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (/.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale x-scale))) (/.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 2 points increase in error, 5 points decrease in error
      (fma.f64 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale x-scale)) (/.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 1 points decrease in error
      (fma.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (/.f64 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 3 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (*.f64 2 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2)))) (/.f64 (*.f64 x-scale y-scale) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale x-scale))) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 4 points increase in error, 4 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale x-scale)) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 -4 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 6 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (*.f64 (Rewrite<= metadata-eval (neg.f64 4)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (*.f64 (neg.f64 4) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))))): 1 points increase in error, 16 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (*.f64 (neg.f64 4) (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))))): 1 points increase in error, 16 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 7 points increase in error, 10 points decrease in error

   3. Taylor expanded in angle around 0 50.4

      \[\leadsto \color{blue}{-4 \cdot \frac{{a}^{2} \cdot {b}^{2}}{{y-scale}^{2} \cdot {x-scale}^{2}}} \]

   4. Simplified 41.7

      \[\leadsto \color{blue}{\frac{-4}{\frac{y-scale \cdot \left(y-scale \cdot \left(x-scale \cdot x-scale\right)\right)}{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}}} \]
      Proof
      (/.f64 -4 (/.f64 (*.f64 y-scale (*.f64 y-scale (*.f64 x-scale x-scale))) (*.f64 (*.f64 a a) (*.f64 b b)))): 0 points increase in error, 0 points decrease in error
      (/.f64 -4 (/.f64 (*.f64 y-scale (*.f64 y-scale (Rewrite<= unpow2_binary64 (pow.f64 x-scale 2)))) (*.f64 (*.f64 a a) (*.f64 b b)))): 0 points increase in error, 0 points decrease in error
      (/.f64 -4 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y-scale y-scale) (pow.f64 x-scale 2))) (*.f64 (*.f64 a a) (*.f64 b b)))): 24 points increase in error, 3 points decrease in error
      (/.f64 -4 (/.f64 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2)) (pow.f64 x-scale 2)) (*.f64 (*.f64 a a) (*.f64 b b)))): 0 points increase in error, 0 points decrease in error
      (/.f64 -4 (/.f64 (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 b b)))): 0 points increase in error, 0 points decrease in error
      (/.f64 -4 (/.f64 (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)) (*.f64 (pow.f64 a 2) (Rewrite<= unpow2_binary64 (pow.f64 b 2))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 -4 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))): 2 points increase in error, 3 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 -4 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 8.5

      \[\leadsto \frac{-4}{\color{blue}{\frac{y-scale \cdot x-scale}{a \cdot b} \cdot \frac{y-scale \cdot x-scale}{a \cdot b}}} \]

   if 1.45000000000000002e-67 < y-scale

   1. Initial program 37.8

      \[\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} \cdot \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} - \left(4 \cdot \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} \]

   2. Simplified 42.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}, -4, \frac{4 \cdot \left(\left(\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\right)}{x-scale \cdot \left(y-scale \cdot \frac{x-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}\right)} \cdot \frac{\cos \left(\frac{angle}{180} \cdot \pi\right)}{y-scale}\right)} \]
      Proof
      (fma.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) -4 (*.f64 (/.f64 (*.f64 4 (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) -4 (*.f64 (/.f64 (*.f64 4 (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 2 points increase in error, 10 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))) -4 (*.f64 (/.f64 (*.f64 4 (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 2 points increase in error, 11 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (Rewrite<= metadata-eval (neg.f64 4)) (*.f64 (/.f64 (*.f64 4 (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 2 2)) (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (*.f64 2 2) (*.f64 (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (*.f64 2 2) (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (*.f64 2 2) (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (*.f64 2 2) (*.f64 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (Rewrite<= swap-sqr_binary64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 2 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 2 (*.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 x-scale (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) x-scale)) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 1 points increase in error, 7 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 5 points increase in error, 8 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) y-scale))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 2 points increase in error, 3 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale)) y-scale)) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))): 2 points increase in error, 2 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (/.f64 x-scale (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale))))): 7 points increase in error, 4 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x-scale y-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))): 2 points increase in error, 1 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 (*.f64 y-scale x-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)))): 5 points increase in error, 7 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 y-scale x-scale))) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))): 2 points increase in error, 2 points decrease in error
      (fma.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))): 5 points increase in error, 4 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (neg.f64 4)) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 4) (*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (neg.f64 4) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (neg.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in angle around 0 34.8

      \[\leadsto \color{blue}{-4 \cdot \frac{{a}^{2} \cdot {b}^{2}}{{x-scale}^{2} \cdot {y-scale}^{2}}} \]

   4. Simplified 23.6

      \[\leadsto \color{blue}{\left(\frac{a}{x-scale} \cdot \frac{a}{x-scale}\right) \cdot \left(\frac{\frac{b \cdot b}{y-scale}}{y-scale} \cdot -4\right)} \]
      Proof
      (*.f64 (*.f64 (/.f64 a x-scale) (/.f64 a x-scale)) (*.f64 (/.f64 (/.f64 (*.f64 b b) y-scale) y-scale) -4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a a) (*.f64 x-scale x-scale))) (*.f64 (/.f64 (/.f64 (*.f64 b b) y-scale) y-scale) -4)): 43 points increase in error, 4 points decrease in error
      (*.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 x-scale x-scale)) (*.f64 (/.f64 (/.f64 (*.f64 b b) y-scale) y-scale) -4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (pow.f64 a 2) (Rewrite<= unpow2_binary64 (pow.f64 x-scale 2))) (*.f64 (/.f64 (/.f64 (*.f64 b b) y-scale) y-scale) -4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (pow.f64 a 2) (pow.f64 x-scale 2)) (*.f64 (/.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) y-scale) y-scale) -4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (pow.f64 a 2) (pow.f64 x-scale 2)) (*.f64 (Rewrite<= associate-/r*_binary64 (/.f64 (pow.f64 b 2) (*.f64 y-scale y-scale))) -4)): 17 points increase in error, 2 points decrease in error
      (*.f64 (/.f64 (pow.f64 a 2) (pow.f64 x-scale 2)) (*.f64 (/.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2))) -4)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 (pow.f64 a 2) (pow.f64 x-scale 2)) (/.f64 (pow.f64 b 2) (pow.f64 y-scale 2))) -4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) -4): 10 points increase in error, 13 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 -4 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 4.6

      \[\leadsto \color{blue}{{\left(\sqrt[3]{-4 \cdot {\left(\frac{a}{x-scale} \cdot \frac{b}{y-scale}\right)}^{2}}\right)}^{3}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 5.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;y-scale \leq -5 \cdot 10^{+183}:\\ \;\;\;\;-4 \cdot \left(\left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right) \cdot \left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right)\right)\\ \mathbf{elif}\;y-scale \leq -5.2 \cdot 10^{-229}:\\ \;\;\;\;-4 \cdot \left(\frac{\frac{b \cdot a}{y-scale}}{x-scale} \cdot \frac{\frac{b \cdot a}{y-scale}}{x-scale}\right)\\ \mathbf{elif}\;y-scale \leq 1.35 \cdot 10^{-266}:\\ \;\;\;\;-4 \cdot \left(\left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right) \cdot \frac{\frac{b}{x-scale}}{\frac{y-scale}{a}}\right)\\ \mathbf{elif}\;y-scale \leq 1.45 \cdot 10^{-67}:\\ \;\;\;\;\frac{-4}{\frac{y-scale \cdot x-scale}{b \cdot a} \cdot \frac{y-scale \cdot x-scale}{b \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{-4 \cdot {\left(\frac{a}{x-scale} \cdot \frac{b}{y-scale}\right)}^{2}}\right)}^{3}\\ \end{array} \]

Alternatives

Alternative 1
Error	5.9
Cost	1748

\[\begin{array}{l} t_0 := \frac{\frac{b \cdot a}{y-scale}}{x-scale}\\ t_1 := -4 \cdot \left(t_0 \cdot t_0\right)\\ t_2 := \frac{a}{\frac{y-scale \cdot x-scale}{b}}\\ t_3 := \frac{b}{x-scale} \cdot \frac{a}{y-scale}\\ t_4 := -4 \cdot \left(t_3 \cdot t_3\right)\\ \mathbf{if}\;y-scale \leq -4.3 \cdot 10^{+181}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y-scale \leq -6.5 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y-scale \leq 1.45 \cdot 10^{-284}:\\ \;\;\;\;-4 \cdot \left(\left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right) \cdot \frac{\frac{b}{x-scale}}{\frac{y-scale}{a}}\right)\\ \mathbf{elif}\;y-scale \leq 3.1 \cdot 10^{-78}:\\ \;\;\;\;-4 \cdot \left(t_2 \cdot t_2\right)\\ \mathbf{elif}\;y-scale \leq 10^{+214}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	5.9
Cost	1748

\[\begin{array}{l} t_0 := \frac{\frac{b \cdot a}{y-scale}}{x-scale}\\ t_1 := -4 \cdot \left(t_0 \cdot t_0\right)\\ t_2 := \frac{y-scale \cdot x-scale}{b \cdot a}\\ t_3 := \frac{b}{x-scale} \cdot \frac{a}{y-scale}\\ t_4 := -4 \cdot \left(t_3 \cdot t_3\right)\\ \mathbf{if}\;y-scale \leq -8 \cdot 10^{+179}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y-scale \leq -3.6 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y-scale \leq 5 \cdot 10^{-268}:\\ \;\;\;\;-4 \cdot \left(\left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right) \cdot \frac{\frac{b}{x-scale}}{\frac{y-scale}{a}}\right)\\ \mathbf{elif}\;y-scale \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\frac{-4}{t_2 \cdot t_2}\\ \mathbf{elif}\;y-scale \leq 10^{+214}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	5.8
Cost	1484

\[\begin{array}{l} t_0 := \frac{a}{\frac{y-scale \cdot x-scale}{b}}\\ t_1 := -4 \cdot \left(t_0 \cdot t_0\right)\\ t_2 := \frac{b}{x-scale} \cdot \frac{a}{y-scale}\\ \mathbf{if}\;a \leq 10^{-293}:\\ \;\;\;\;-4 \cdot \left(t_2 \cdot t_2\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+254}:\\ \;\;\;\;-4 \cdot \left(\left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right) \cdot \frac{\frac{b}{x-scale}}{\frac{y-scale}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	7.2
Cost	1088

\[-4 \cdot \left(\left(\frac{b}{x-scale} \cdot \frac{a}{y-scale}\right) \cdot \left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right)\right) \]

Alternative 5
Error	7.2
Cost	1088

\[-4 \cdot \left(\left(b \cdot \frac{\frac{a}{y-scale}}{x-scale}\right) \cdot \frac{\frac{b}{x-scale}}{\frac{y-scale}{a}}\right) \]

Alternative 6
Error	5.6
Cost	1088

\[\begin{array}{l} t_0 := \frac{b}{x-scale} \cdot \frac{a}{y-scale}\\ -4 \cdot \left(t_0 \cdot t_0\right) \end{array} \]

Alternative 7
Error	30.1
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2022330 
(FPCore (a b angle x-scale y-scale)
  :name "Simplification of discriminant from scale-rotated-ellipse"
  :precision binary64
  (- (* (/ (/ (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* (/ angle 180.0) PI))) (cos (* (/ angle 180.0) PI))) x-scale) y-scale) (/ (/ (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* (/ angle 180.0) PI))) (cos (* (/ angle 180.0) PI))) x-scale) y-scale)) (* (* 4.0 (/ (/ (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)) x-scale) x-scale)) (/ (/ (+ (pow (* a (cos (* (/ angle 180.0) PI))) 2.0) (pow (* b (sin (* (/ angle 180.0) PI))) 2.0)) y-scale) y-scale))))