Average Error: 41.5 → 37.6
Time: 1.6min
Precision: binary64
Cost: 482824
\[\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} \cdot \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale} - \left(4 \cdot \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} \]
↓
\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ t_1 := \sin t_0\\ t_2 := \cos t_0\\ t_3 := \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot t_1\right) \cdot t_2}{x-scale}}{y-scale}\\ t_4 := t_3 \cdot t_3 - \left(4 \cdot \frac{\frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{y-scale}}{y-scale}\\ t_5 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_6 := \sin t_5\\ t_7 := \log \left(e^{t_6}\right)\\ t_8 := \cos t_5\\ t_9 := {\left(a \cdot t_6\right)}^{2} + {\left(b \cdot t_8\right)}^{2}\\ t_10 := {\left(a \cdot t_8\right)}^{2}\\ \mathbf{if}\;t_4 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{-32}:\\ \;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{t_10 + {\left(b \cdot t_6\right)}^{2}}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot t_9}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_6 \cdot \left(2 \cdot t_8\right)\right)\right)}^{2}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t_9}{x-scale \cdot y-scale} \cdot \frac{t_10 + {\left(b \cdot t_7\right)}^{2}}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(t_7 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_8}}\right) \cdot \frac{t_8}{y-scale}\right)\\ \end{array} \]
(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 (* (/ angle 180.0) PI))
        (t_1 (sin t_0))
        (t_2 (cos t_0))
        (t_3
         (/
          (/ (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) t_1) t_2) x-scale)
          y-scale))
        (t_4
         (-
          (* t_3 t_3)
          (*
           (*
            4.0
            (/
             (/ (+ (pow (* a t_1) 2.0) (pow (* b t_2) 2.0)) x-scale)
             x-scale))
           (/
            (/ (+ (pow (* a t_2) 2.0) (pow (* b t_1) 2.0)) y-scale)
            y-scale))))
        (t_5 (* angle (* PI 0.005555555555555556)))
        (t_6 (sin t_5))
        (t_7 (log (exp t_6)))
        (t_8 (cos t_5))
        (t_9 (+ (pow (* a t_6) 2.0) (pow (* b t_8) 2.0)))
        (t_10 (pow (* a t_8) 2.0)))
   (if (<= t_4 0.0)
     t_4
     (if (<= t_4 5e-32)
       (log
        (exp
         (fma
          (/ (+ t_10 (pow (* b t_6) 2.0)) (* y-scale y-scale))
          (/ (* (/ -4.0 x-scale) t_9) x-scale)
          (pow
           (* (* (/ (+ b a) y-scale) (/ (- b a) x-scale)) (* t_6 (* 2.0 t_8)))
           2.0))))
       (fma
        (*
         (/ t_9 (* x-scale y-scale))
         (/ (+ t_10 (pow (* b t_7) 2.0)) (* x-scale y-scale)))
        -4.0
        (*
         (*
          (/ 4.0 x-scale)
          (/
           (pow (* t_7 (fma b b (- (* a a)))) 2.0)
           (* x-scale (/ y-scale t_8))))
         (/ t_8 y-scale)))))))
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 = (angle / 180.0) * ((double) M_PI);
	double t_1 = sin(t_0);
	double t_2 = cos(t_0);
	double t_3 = ((((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * t_1) * t_2) / x_45_scale) / y_45_scale;
	double t_4 = (t_3 * t_3) - ((4.0 * (((pow((a * t_1), 2.0) + pow((b * t_2), 2.0)) / x_45_scale) / x_45_scale)) * (((pow((a * t_2), 2.0) + pow((b * t_1), 2.0)) / y_45_scale) / y_45_scale));
	double t_5 = angle * (((double) M_PI) * 0.005555555555555556);
	double t_6 = sin(t_5);
	double t_7 = log(exp(t_6));
	double t_8 = cos(t_5);
	double t_9 = pow((a * t_6), 2.0) + pow((b * t_8), 2.0);
	double t_10 = pow((a * t_8), 2.0);
	double tmp;
	if (t_4 <= 0.0) {
		tmp = t_4;
	} else if (t_4 <= 5e-32) {
		tmp = log(exp(fma(((t_10 + pow((b * t_6), 2.0)) / (y_45_scale * y_45_scale)), (((-4.0 / x_45_scale) * t_9) / x_45_scale), pow(((((b + a) / y_45_scale) * ((b - a) / x_45_scale)) * (t_6 * (2.0 * t_8))), 2.0))));
	} else {
		tmp = fma(((t_9 / (x_45_scale * y_45_scale)) * ((t_10 + pow((b * t_7), 2.0)) / (x_45_scale * y_45_scale))), -4.0, (((4.0 / x_45_scale) * (pow((t_7 * fma(b, b, -(a * a))), 2.0) / (x_45_scale * (y_45_scale / t_8)))) * (t_8 / y_45_scale)));
	}
	return tmp;
}

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(angle / 180.0) * pi)
	t_1 = sin(t_0)
	t_2 = cos(t_0)
	t_3 = Float64(Float64(Float64(Float64(Float64(2.0 * Float64((b ^ 2.0) - (a ^ 2.0))) * t_1) * t_2) / x_45_scale) / y_45_scale)
	t_4 = Float64(Float64(t_3 * t_3) - Float64(Float64(4.0 * Float64(Float64(Float64((Float64(a * t_1) ^ 2.0) + (Float64(b * t_2) ^ 2.0)) / x_45_scale) / x_45_scale)) * Float64(Float64(Float64((Float64(a * t_2) ^ 2.0) + (Float64(b * t_1) ^ 2.0)) / y_45_scale) / y_45_scale)))
	t_5 = Float64(angle * Float64(pi * 0.005555555555555556))
	t_6 = sin(t_5)
	t_7 = log(exp(t_6))
	t_8 = cos(t_5)
	t_9 = Float64((Float64(a * t_6) ^ 2.0) + (Float64(b * t_8) ^ 2.0))
	t_10 = Float64(a * t_8) ^ 2.0
	tmp = 0.0
	if (t_4 <= 0.0)
		tmp = t_4;
	elseif (t_4 <= 5e-32)
		tmp = log(exp(fma(Float64(Float64(t_10 + (Float64(b * t_6) ^ 2.0)) / Float64(y_45_scale * y_45_scale)), Float64(Float64(Float64(-4.0 / x_45_scale) * t_9) / x_45_scale), (Float64(Float64(Float64(Float64(b + a) / y_45_scale) * Float64(Float64(b - a) / x_45_scale)) * Float64(t_6 * Float64(2.0 * t_8))) ^ 2.0))));
	else
		tmp = fma(Float64(Float64(t_9 / Float64(x_45_scale * y_45_scale)) * Float64(Float64(t_10 + (Float64(b * t_7) ^ 2.0)) / Float64(x_45_scale * y_45_scale))), -4.0, Float64(Float64(Float64(4.0 / x_45_scale) * Float64((Float64(t_7 * fma(b, b, Float64(-Float64(a * a)))) ^ 2.0) / Float64(x_45_scale * Float64(y_45_scale / t_8)))) * Float64(t_8 / y_45_scale)));
	end
	return tmp
end

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[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[Cos[t$95$0], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(2.0 * N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] * t$95$2), $MachinePrecision] / x$45$scale), $MachinePrecision] / y$45$scale), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 * t$95$3), $MachinePrecision] - N[(N[(4.0 * N[(N[(N[(N[Power[N[(a * t$95$1), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * t$95$2), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / x$45$scale), $MachinePrecision] / x$45$scale), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[Power[N[(a * t$95$2), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * t$95$1), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / y$45$scale), $MachinePrecision] / y$45$scale), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(angle * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[Sin[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Log[N[Exp[t$95$6], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$8 = N[Cos[t$95$5], $MachinePrecision]}, Block[{t$95$9 = N[(N[Power[N[(a * t$95$6), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * t$95$8), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[Power[N[(a * t$95$8), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[t$95$4, 0.0], t$95$4, If[LessEqual[t$95$4, 5e-32], N[Log[N[Exp[N[(N[(N[(t$95$10 + N[Power[N[(b * t$95$6), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(y$45$scale * y$45$scale), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(-4.0 / x$45$scale), $MachinePrecision] * t$95$9), $MachinePrecision] / x$45$scale), $MachinePrecision] + N[Power[N[(N[(N[(N[(b + a), $MachinePrecision] / y$45$scale), $MachinePrecision] * N[(N[(b - a), $MachinePrecision] / x$45$scale), $MachinePrecision]), $MachinePrecision] * N[(t$95$6 * N[(2.0 * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[(N[(N[(t$95$9 / N[(x$45$scale * y$45$scale), $MachinePrecision]), $MachinePrecision] * N[(N[(t$95$10 + N[Power[N[(b * t$95$7), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(x$45$scale * y$45$scale), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(N[(N[(4.0 / x$45$scale), $MachinePrecision] * N[(N[Power[N[(t$95$7 * N[(b * b + (-N[(a * a), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / N[(x$45$scale * N[(y$45$scale / t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$8 / y$45$scale), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

\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{angle}{180} \cdot \pi\\
t_1 := \sin t_0\\
t_2 := \cos t_0\\
t_3 := \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot t_1\right) \cdot t_2}{x-scale}}{y-scale}\\
t_4 := t_3 \cdot t_3 - \left(4 \cdot \frac{\frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{y-scale}}{y-scale}\\
t_5 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\
t_6 := \sin t_5\\
t_7 := \log \left(e^{t_6}\right)\\
t_8 := \cos t_5\\
t_9 := {\left(a \cdot t_6\right)}^{2} + {\left(b \cdot t_8\right)}^{2}\\
t_10 := {\left(a \cdot t_8\right)}^{2}\\
\mathbf{if}\;t_4 \leq 0:\\
\;\;\;\;t_4\\

\mathbf{elif}\;t_4 \leq 5 \cdot 10^{-32}:\\
\;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{t_10 + {\left(b \cdot t_6\right)}^{2}}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot t_9}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_6 \cdot \left(2 \cdot t_8\right)\right)\right)}^{2}\right)}\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{t_9}{x-scale \cdot y-scale} \cdot \frac{t_10 + {\left(b \cdot t_7\right)}^{2}}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(t_7 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_8}}\right) \cdot \frac{t_8}{y-scale}\right)\\


\end{array}

Error

Derivation

  1. Split input into 3 regimes

  2. if (-.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))) < 0.0

    1. Initial program 15.9

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

    if 0.0 < (-.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))) < 5e-32

    1. Initial program 58.7

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

    2. Simplified52.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot -4, \frac{b \cdot b - a \cdot a}{\frac{\frac{x-scale \cdot y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}} \cdot \frac{b \cdot b - a \cdot a}{\frac{\frac{x-scale \cdot y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}}\right)} \]
      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, 21 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, 14 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)))))))): 4 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 (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)))))))): 3 points increase in error, 7 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)))))))): 2 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 (*.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)))))))): 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 (-.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)))))))): 6 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) (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))))))))): 7 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 (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)))): 5 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))): 3 points increase in error, 3 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)))): 11 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. Applied egg-rr53.5

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

    4. Simplified55.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(a \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale} \cdot \frac{-4}{x-scale}, {\left(\frac{\left(a + b\right) \cdot \left(b - a\right)}{y-scale \cdot x-scale} \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\right)}^{2}\right)} \]
      Proof
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) x-scale) (/.f64 -4 x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) 2)): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) x-scale) (/.f64 -4 x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) 2)): 1 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) x-scale) (/.f64 -4 x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) 2)): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) x-scale) (/.f64 -4 x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) 2)): 0 points increase in error, 3 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) b) 2)) x-scale) (/.f64 -4 x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) 2)): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale))) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) 2)): 13 points increase in error, 3 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 b a)) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) 2)): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) 2)): 4 points increase in error, 2 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (*.f64 2 (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))))) 2)): 3 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 y-scale x-scale)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) 2) (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) 2)): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 y-scale x-scale)) (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2)): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (/.f64 (*.f64 y-scale x-scale) (*.f64 (*.f64 2 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))))) 2)): 2 points increase in error, 9 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (Rewrite=> times-frac_binary64 (*.f64 (/.f64 y-scale (*.f64 2 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) (/.f64 x-scale (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))))) 2)): 1 points increase in error, 5 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) (*.f64 2 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))))) 2)): 3 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 x-scale (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) y-scale)) (*.f64 2 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) 2)): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (/.f64 (Rewrite<= associate-/r/_binary64 (/.f64 x-scale (/.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) y-scale))) (*.f64 2 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) 2)): 3 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale)) (pow.f64 (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (/.f64 x-scale (/.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) y-scale))) (*.f64 2 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) 2)): 8 points increase in error, 2 points decrease in error
      (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) -4) (*.f64 x-scale x-scale))) (pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (/.f64 x-scale (/.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) y-scale))) (*.f64 2 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2))): 3 points increase in error, 7 points decrease in error

    5. Applied egg-rr22.4

      \[\leadsto \color{blue}{\log \left(e^{\mathsf{fma}\left(\frac{{\left(a \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{\left({\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}\right) \cdot \frac{-4}{x-scale}}{x-scale}, {\left(\left(\frac{a + b}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot 2\right)\right)\right)}^{2}\right)}\right)} \]

    if 5e-32 < (-.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)))

    1. Initial program 63.9

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

    2. Simplified63.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}, -4, \frac{4 \cdot \left(\left(\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\right)}{x-scale \cdot \left(y-scale \cdot \frac{x-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}\right)} \cdot \frac{\cos \left(\frac{angle}{180} \cdot \pi\right)}{y-scale}\right)} \]
      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))): 1 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) (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, 17 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, 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)) (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))): 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) (/.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))): 0 points increase in error, 6 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))): 3 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-/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))))))): 5 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)))): 11 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 (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, 5 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))): 7 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. Applied egg-rr63.6

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

    4. Simplified60.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}}{x-scale \cdot y-scale} \cdot \frac{{\left(a \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{\frac{y-scale}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)} \cdot x-scale}\right) \cdot \frac{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}{y-scale}\right)} \]
      Proof
      (fma.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 x-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 x-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 3 points increase in error, 3 points decrease in error
      (fma.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2)) (*.f64 x-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 1 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale))) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 3 points increase in error, 3 points decrease in error
      (fma.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) b) 2)) (*.f64 x-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 0 points increase in error, 1 points decrease in error
      (fma.f64 (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale)))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 22 points increase in error, 9 points decrease in error
      (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 y-scale y-scale) (*.f64 x-scale x-scale)))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 36 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 x-scale x-scale) (*.f64 y-scale y-scale)))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (*.f64 (*.f64 x-scale x-scale) (*.f64 y-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (fma.f64 b b (neg.f64 (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 2 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (*.f64 (*.f64 x-scale x-scale) (*.f64 y-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 b b) (*.f64 a a)))) 2) (*.f64 (/.f64 y-scale (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (*.f64 (*.f64 x-scale x-scale) (*.f64 y-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (-.f64 (*.f64 b b) (*.f64 a a))) 2) (*.f64 (/.f64 y-scale (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 1 points increase in error, 2 points decrease in error
      (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (*.f64 (*.f64 x-scale x-scale) (*.f64 y-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (-.f64 (*.f64 b b) (*.f64 a a))) 2) (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y-scale x-scale) (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))): 1 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (*.f64 (*.f64 x-scale x-scale) (*.f64 y-scale y-scale))) -4 (*.f64 (*.f64 (/.f64 4 x-scale) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (-.f64 (*.f64 b b) (*.f64 a a))) 2) (/.f64 (*.f64 y-scale x-scale) (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) (/.f64 (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) y-scale))): 2 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (*.f64 (*.f64 x-scale x-scale) (*.f64 y-scale y-scale))) -4 (*.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 4 (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (-.f64 (*.f64 b b) (*.f64 a a))) 2)) (*.f64 x-scale (/.f64 (*.f64 y-scale x-scale) (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))))) (/.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) y-scale))): 1 points increase in error, 6 points decrease in error
      (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2))) (*.f64 (*.f64 x-scale x-scale) (*.f64 y-scale y-scale))) -4) (*.f64 (/.f64 (*.f64 4 (pow.f64 (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (-.f64 (*.f64 b b) (*.f64 a a))) 2)) (*.f64 x-scale (/.f64 (*.f64 y-scale x-scale) (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) (/.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) y-scale)))): 0 points increase in error, 0 points decrease in error

    5. Applied egg-rr60.9

      \[\leadsto \mathsf{fma}\left(\frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}}{x-scale \cdot y-scale} \cdot \frac{{\left(a \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(\color{blue}{\log \left(e^{\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}\right)} \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{\frac{y-scale}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)} \cdot x-scale}\right) \cdot \frac{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}{y-scale}\right) \]

    6. Applied egg-rr59.7

      \[\leadsto \mathsf{fma}\left(\frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}}{x-scale \cdot y-scale} \cdot \frac{{\left(a \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\color{blue}{\log \left(e^{\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}\right)} \cdot b\right)}^{2}}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(\log \left(e^{\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}\right) \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{\frac{y-scale}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)} \cdot x-scale}\right) \cdot \frac{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}{y-scale}\right) \]
  3. Recombined 3 regimes into one program.

  4. Final simplification37.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\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} \leq 0:\\ \;\;\;\;\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}\\ \mathbf{elif}\;\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} \leq 5 \cdot 10^{-32}:\\ \;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{{\left(a \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot \left({\left(a \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\right)}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(2 \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right)}^{2}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{{\left(a \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}}{x-scale \cdot y-scale} \cdot \frac{{\left(a \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2} + {\left(b \cdot \log \left(e^{\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)}\right)\right)}^{2}}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(\log \left(e^{\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)}\right) \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)}}\right) \cdot \frac{\cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)}{y-scale}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error37.6
Cost482824
\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ t_1 := \sin t_0\\ t_2 := \cos t_0\\ t_3 := \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot t_1\right) \cdot t_2}{x-scale}}{y-scale}\\ t_4 := t_3 \cdot t_3 - \left(4 \cdot \frac{\frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{y-scale}}{y-scale}\\ t_5 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_6 := \sin t_5\\ t_7 := \cos t_5\\ t_8 := {\left(a \cdot t_7\right)}^{2} + {\left(b \cdot t_6\right)}^{2}\\ t_9 := {\left(b \cdot t_7\right)}^{2}\\ t_10 := \log \left(e^{t_6}\right)\\ \mathbf{if}\;t_4 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{-32}:\\ \;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{t_8}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot \left({\left(a \cdot t_6\right)}^{2} + t_9\right)}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_6 \cdot \left(2 \cdot t_7\right)\right)\right)}^{2}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t_9 + {\left(a \cdot t_10\right)}^{2}}{x-scale \cdot y-scale} \cdot \frac{t_8}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(t_10 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_7}}\right) \cdot \frac{t_7}{y-scale}\right)\\ \end{array} \]
Alternative 2
Error38.1
Cost470024
\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ t_1 := \sin t_0\\ t_2 := \cos t_0\\ t_3 := \frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot t_1\right) \cdot t_2}{x-scale}}{y-scale}\\ t_4 := t_3 \cdot t_3 - \left(4 \cdot \frac{\frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{x-scale}}{x-scale}\right) \cdot \frac{\frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{y-scale}}{y-scale}\\ t_5 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_6 := \sin t_5\\ t_7 := \cos t_5\\ t_8 := {\left(a \cdot t_7\right)}^{2} + {\left(b \cdot t_6\right)}^{2}\\ t_9 := {\left(a \cdot t_6\right)}^{2} + {\left(b \cdot t_7\right)}^{2}\\ \mathbf{if}\;t_4 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{-32}:\\ \;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{t_8}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot t_9}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_6 \cdot \left(2 \cdot t_7\right)\right)\right)}^{2}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t_9}{x-scale \cdot y-scale} \cdot \frac{t_8}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(\log \left(e^{t_6}\right) \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_7}}\right) \cdot \frac{t_7}{y-scale}\right)\\ \end{array} \]
Alternative 3
Error40.3
Cost151808
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \cos t_0\\ t_2 := \sin t_0\\ \mathsf{fma}\left(\frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{x-scale \cdot y-scale} \cdot \frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{x-scale \cdot y-scale}, -4, \left(\frac{4}{x-scale} \cdot \frac{{\left(\log \left(e^{t_2}\right) \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_1}}\right) \cdot \frac{t_1}{y-scale}\right) \end{array} \]
Alternative 4
Error40.3
Cost145536
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \cos t_0\\ t_2 := \sin t_0\\ -4 \cdot \left(\frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{x-scale \cdot y-scale} \cdot \frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{x-scale \cdot y-scale}\right) + \frac{4}{x-scale} \cdot \left(\frac{t_1}{y-scale} \cdot \frac{{\left(\log \left(e^{t_2}\right) \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_1}}\right) \end{array} \]
Alternative 5
Error40.3
Cost139136
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \sin t_0\\ t_2 := \cos t_0\\ \mathsf{fma}\left(\frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{x-scale \cdot y-scale} \cdot \left(\left({\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}\right) \cdot \frac{1}{x-scale \cdot y-scale}\right), -4, \frac{t_2}{y-scale} \cdot \left(\frac{4}{x-scale} \cdot \frac{{\left(t_1 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_2}}\right)\right) \end{array} \]
Alternative 6
Error40.2
Cost139008
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \cos t_0\\ t_2 := \sin t_0\\ \mathsf{fma}\left(\frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{x-scale \cdot y-scale} \cdot \frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{x-scale \cdot y-scale}, -4, \frac{t_1}{y-scale} \cdot \left(\frac{4}{x-scale} \cdot \frac{{\left(t_2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_1}}\right)\right) \end{array} \]
Alternative 7
Error40.7
Cost133000
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \cos t_0\\ t_2 := \sin t_0\\ t_3 := {\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}\\ t_4 := {\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}\\ \mathbf{if}\;y-scale \leq -5.2 \cdot 10^{-40}:\\ \;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{t_3}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot t_4}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_2 \cdot \left(2 \cdot t_1\right)\right)\right)}^{2}\right)}\right)\\ \mathbf{elif}\;y-scale \leq -9 \cdot 10^{-237}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t_3}{x-scale}, \frac{t_4 \cdot \frac{-4}{y-scale}}{x-scale \cdot y-scale}, {\left(t_2 \cdot \left(b \cdot b - a \cdot a\right)\right)}^{2} \cdot \left(t_1 \cdot \frac{t_1}{y-scale \cdot \left(\left(x-scale \cdot y-scale\right) \cdot \frac{x-scale}{4}\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\frac{t_4}{x-scale \cdot y-scale} \cdot \frac{t_3}{x-scale \cdot y-scale}\right) + \frac{4}{x-scale} \cdot \left(\frac{t_1}{y-scale} \cdot \frac{{\left(t_2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{2}}{x-scale \cdot \frac{y-scale}{t_1}}\right)\\ \end{array} \]
Alternative 8
Error41.3
Cost132936
\[\begin{array}{l} t_0 := b \cdot b - a \cdot a\\ t_1 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_2 := \cos t_1\\ t_3 := \sin t_1\\ t_4 := {\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_3\right)}^{2}\\ t_5 := {\left(a \cdot t_3\right)}^{2} + {\left(b \cdot t_2\right)}^{2}\\ \mathbf{if}\;y-scale \leq -4.2 \cdot 10^{-40}:\\ \;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{t_4}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot t_5}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_3 \cdot \left(2 \cdot t_2\right)\right)\right)}^{2}\right)}\right)\\ \mathbf{elif}\;y-scale \leq 9.2 \cdot 10^{-210}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{t_5}{\frac{x-scale \cdot x-scale}{t_4}}}{y-scale}, \frac{-4}{y-scale}, {\left(2 \cdot \left(t_0 \cdot \frac{t_2}{\frac{x-scale \cdot y-scale}{t_3}}\right)\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t_5}{x-scale \cdot y-scale} \cdot \frac{t_4}{x-scale \cdot y-scale}, -4, \frac{4}{x-scale} \cdot \frac{{\left(t_3 \cdot t_0\right)}^{2}}{\frac{\frac{x-scale \cdot y-scale}{t_2}}{\frac{t_2}{y-scale}}}\right)\\ \end{array} \]
Alternative 9
Error41.4
Cost132804
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \cos t_0\\ t_2 := \sin t_0\\ t_3 := {\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}\\ t_4 := {\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}\\ t_5 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_6 := \sin t_5\\ t_7 := \cos t_5\\ \mathbf{if}\;angle \leq 1.2 \cdot 10^{-189}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t_3}{x-scale} \cdot \frac{t_4}{y-scale \cdot \left(x-scale \cdot y-scale\right)}, -4, t_1 \cdot \left(\frac{4}{x-scale} \cdot \frac{{\left(t_2 \cdot \left(b \cdot b - a \cdot a\right)\right)}^{2}}{\frac{x-scale \cdot y-scale}{\frac{t_1}{y-scale}}}\right)\right)\\ \mathbf{elif}\;angle \leq 1.55 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{{\left(a \cdot t_6\right)}^{2} + {\left(b \cdot t_7\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{{\left(a \cdot t_7\right)}^{2} + {\left(b \cdot t_6\right)}^{2}}{y-scale}}{y-scale}, -4, {\left(\frac{t_6}{\frac{y-scale}{\left(b + a\right) \cdot \left(2 \cdot \left(b - a\right)\right)}} \cdot \frac{t_7}{x-scale}\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{t_4}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot t_3}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_2 \cdot \left(2 \cdot t_1\right)\right)\right)}^{2}\right)}\right)\\ \end{array} \]
Alternative 10
Error40.6
Cost132804
\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_2 := \cos t_1\\ t_3 := \cos t_0\\ t_4 := \sin t_0\\ t_5 := \sin t_1\\ t_6 := {\left(a \cdot t_5\right)}^{2} + {\left(b \cdot t_2\right)}^{2}\\ t_7 := {\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_5\right)}^{2}\\ \mathbf{if}\;angle \leq 1.2 \cdot 10^{-189}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t_6}{x-scale \cdot y-scale}, -4 \cdot \frac{t_7}{x-scale \cdot y-scale}, \frac{4}{x-scale} \cdot \left(\frac{{\left(t_5 \cdot \left(b \cdot b - a \cdot a\right)\right)}^{2}}{\frac{y-scale}{t_2}} \cdot \frac{\frac{t_2}{y-scale}}{x-scale}\right)\right)\\ \mathbf{elif}\;angle \leq 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{{\left(a \cdot t_4\right)}^{2} + {\left(b \cdot t_3\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{{\left(a \cdot t_3\right)}^{2} + {\left(b \cdot t_4\right)}^{2}}{y-scale}}{y-scale}, -4, {\left(\frac{t_4}{\frac{y-scale}{\left(b + a\right) \cdot \left(2 \cdot \left(b - a\right)\right)}} \cdot \frac{t_3}{x-scale}\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(e^{\mathsf{fma}\left(\frac{t_7}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot t_6}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_5 \cdot \left(2 \cdot t_2\right)\right)\right)}^{2}\right)}\right)\\ \end{array} \]
Alternative 11
Error40.9
Cost132360
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \cos t_0\\ t_2 := \sin t_0\\ t_3 := \log \left(e^{\mathsf{fma}\left(\frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{y-scale \cdot y-scale}, \frac{\frac{-4}{x-scale} \cdot \left({\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}\right)}{x-scale}, {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_2 \cdot \left(2 \cdot t_1\right)\right)\right)}^{2}\right)}\right)\\ t_4 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_5 := \sin t_4\\ t_6 := \cos t_4\\ \mathbf{if}\;y-scale \leq -4.4 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y-scale \leq 3.2 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{{\left(a \cdot t_5\right)}^{2} + {\left(b \cdot t_6\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{{\left(a \cdot t_6\right)}^{2} + {\left(b \cdot t_5\right)}^{2}}{y-scale}}{y-scale}, -4, {\left(\frac{t_5}{\frac{y-scale}{\left(b + a\right) \cdot \left(2 \cdot \left(b - a\right)\right)}} \cdot \frac{t_6}{x-scale}\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 12
Error42.5
Cost125956
\[\begin{array}{l} t_0 := \frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\\ t_1 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_2 := \cos t_1\\ t_3 := 2 \cdot t_2\\ t_4 := \sin t_1\\ t_5 := {\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_4\right)}^{2}\\ t_6 := {\left(a \cdot t_4\right)}^{2} + {\left(b \cdot t_2\right)}^{2}\\ t_7 := \frac{t_5}{y-scale \cdot y-scale} \cdot \frac{\frac{-4}{x-scale} \cdot t_6}{x-scale}\\ \mathbf{if}\;y-scale \leq -6.8 \cdot 10^{+196}:\\ \;\;\;\;t_7 + {\left(t_0 \cdot \left(t_3 \cdot \log \left(e^{t_4}\right)\right)\right)}^{2}\\ \mathbf{elif}\;y-scale \leq 2.1 \cdot 10^{-124}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{t_6}{\frac{x-scale \cdot x-scale}{t_5}}}{y-scale}, \frac{-4}{y-scale}, {\left(2 \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \frac{t_2}{\frac{x-scale \cdot y-scale}{t_4}}\right)\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(t_0 \cdot \left(t_4 \cdot t_3\right)\right)}^{2} + t_7\\ \end{array} \]
Alternative 13
Error41.9
Cost119560
\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := \sin t_0\\ t_2 := \cos t_0\\ t_3 := \mathsf{fma}\left(\frac{\frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{y-scale}}{y-scale}, -4, {\left(\frac{t_1}{\frac{y-scale}{\left(b + a\right) \cdot \left(2 \cdot \left(b - a\right)\right)}} \cdot \frac{t_2}{x-scale}\right)}^{2}\right)\\ t_4 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_5 := \sin t_4\\ t_6 := \cos t_4\\ \mathbf{if}\;x-scale \leq -7.5 \cdot 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x-scale \leq 3.2 \cdot 10^{-200}:\\ \;\;\;\;{\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_5 \cdot \left(2 \cdot t_6\right)\right)\right)}^{2} + \frac{{\left(a \cdot t_6\right)}^{2} + {\left(b \cdot t_5\right)}^{2}}{y-scale \cdot y-scale} \cdot \frac{\frac{-4}{x-scale} \cdot \left({\left(a \cdot t_5\right)}^{2} + {\left(b \cdot t_6\right)}^{2}\right)}{x-scale}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 14
Error43.2
Cost119428
\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := \sin t_0\\ t_2 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_3 := \cos t_2\\ t_4 := \sin t_2\\ t_5 := \cos t_0\\ \mathbf{if}\;angle \leq 9.2 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{{\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_5\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{{\left(a \cdot t_5\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{y-scale}}{y-scale}, -4, {\left(\frac{t_1}{\frac{y-scale}{\left(b + a\right) \cdot \left(2 \cdot \left(b - a\right)\right)}} \cdot \frac{t_5}{x-scale}\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{{\left(a \cdot t_3\right)}^{2} + {\left(b \cdot t_4\right)}^{2}}{y-scale \cdot y-scale}, \frac{-4}{x-scale} \cdot \frac{{\left(a \cdot t_4\right)}^{2} + {\left(b \cdot t_3\right)}^{2}}{x-scale}, {\left(\left(t_4 \cdot \left(2 \cdot t_3\right)\right) \cdot \frac{\left(b + a\right) \cdot \left(b - a\right)}{x-scale \cdot y-scale}\right)}^{2}\right)\\ \end{array} \]
Alternative 15
Error43.8
Cost113024
\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \sin t_0\\ t_2 := \cos t_0\\ {\left(\left(\frac{b + a}{y-scale} \cdot \frac{b - a}{x-scale}\right) \cdot \left(t_1 \cdot \left(2 \cdot t_2\right)\right)\right)}^{2} + \frac{{\left(a \cdot t_2\right)}^{2} + {\left(b \cdot t_1\right)}^{2}}{y-scale \cdot y-scale} \cdot \frac{\frac{-4}{x-scale} \cdot \left({\left(a \cdot t_1\right)}^{2} + {\left(b \cdot t_2\right)}^{2}\right)}{x-scale} \end{array} \]

Error

Reproduce

herbie shell --seed 2022334 
(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))))