(/ (* z1 (* z0 z0)) (* (- 1 (cos (* -2 (atan (* (/ z0 z3) (tan (* PI (- (+ z2 z2) -1/2)))))))) (- 1 z1)))

Percentage Accurate: 46.2% → 84.9%

Time: 10.3s

Alternatives: 17

Speedup: 1.4×

• 79.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (/
 (* z1 (* z0 z0))
 (*
  (-
   1.0
   (cos
    (* -2.0 (atan (* (/ z0 z3) (tan (* PI (- (+ z2 z2) -0.5))))))))
  (- 1.0 z1))))

C

double code(double z1, double z0, double z3, double z2) {
	return (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan(((z0 / z3) * tan((((double) M_PI) * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	return (z1 * (z0 * z0)) / ((1.0 - Math.cos((-2.0 * Math.atan(((z0 / z3) * Math.tan((Math.PI * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
}

Python

def code(z1, z0, z3, z2):
	return (z1 * (z0 * z0)) / ((1.0 - math.cos((-2.0 * math.atan(((z0 / z3) * math.tan((math.pi * ((z2 + z2) - -0.5)))))))) * (1.0 - z1))

Julia

function code(z1, z0, z3, z2)
	return Float64(Float64(z1 * Float64(z0 * z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(z0 / z3) * tan(Float64(pi * Float64(Float64(z2 + z2) - -0.5)))))))) * Float64(1.0 - z1)))
end

MATLAB

function tmp = code(z1, z0, z3, z2)
	tmp = (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan(((z0 / z3) * tan((pi * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
end

Wolfram

code[z1_, z0_, z3_, z2_] := N[(N[(z1 * N[(z0 * z0), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(z0 / z3), $MachinePrecision] * N[Tan[N[(Pi * N[(N[(z2 + z2), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 46.2% accurate, 1.0× speedup

Math

\[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (/
 (* z1 (* z0 z0))
 (*
  (-
   1.0
   (cos
    (* -2.0 (atan (* (/ z0 z3) (tan (* PI (- (+ z2 z2) -0.5))))))))
  (- 1.0 z1))))

C

double code(double z1, double z0, double z3, double z2) {
	return (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan(((z0 / z3) * tan((((double) M_PI) * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	return (z1 * (z0 * z0)) / ((1.0 - Math.cos((-2.0 * Math.atan(((z0 / z3) * Math.tan((Math.PI * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
}

Python

def code(z1, z0, z3, z2):
	return (z1 * (z0 * z0)) / ((1.0 - math.cos((-2.0 * math.atan(((z0 / z3) * math.tan((math.pi * ((z2 + z2) - -0.5)))))))) * (1.0 - z1))

Julia

function code(z1, z0, z3, z2)
	return Float64(Float64(z1 * Float64(z0 * z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(z0 / z3) * tan(Float64(pi * Float64(Float64(z2 + z2) - -0.5)))))))) * Float64(1.0 - z1)))
end

MATLAB

function tmp = code(z1, z0, z3, z2)
	tmp = (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan(((z0 / z3) * tan((pi * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
end

Wolfram

code[z1_, z0_, z3_, z2_] := N[(N[(z1 * N[(z0 * z0), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(z0 / z3), $MachinePrecision] * N[Tan[N[(Pi * N[(N[(z2 + z2), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left(z1 \cdot \left|z0\right|\right) \cdot \left|z0\right|}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \left({z2}^{6} \cdot {\pi}^{6}\right)\right) \cdot \left|z0\right|}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{if}\;\left|z0\right| \leq 5 \cdot 10^{-30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\left|z0\right| \leq 3.5 \cdot 10^{+154}:\\ \;\;\;\;z1 \cdot \frac{\left|z0\right| \cdot \left|z0\right|}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -0.6666666666666666 \cdot {\pi}^{4}\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-0.5 \cdot \frac{\left|z0\right|}{z3 \cdot \pi} + -0.3333333333333333 \cdot \frac{\left|z0\right| \cdot \left({z2}^{2} \cdot \pi\right)}{z3}}{z2}\right) \cdot 2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0
        (/
         (* (* z1 (fabs z0)) (fabs z0))
         (*
          (-
           1.0
           (cos
            (*
             -2.0
             (atan
              (/
               (*
                (+
                 1.0
                 (*
                  -0.08888888888888889
                  (* (pow z2 6.0) (pow PI 6.0))))
                (fabs z0))
               (* (- (sin (* (+ z2 z2) PI))) z3))))))
          (- 1.0 z1)))))
  (if (<= (fabs z0) 5e-30)
    t_0
    (if (<= (fabs z0) 3.5e+154)
      (*
       z1
       (/
        (* (fabs z0) (fabs z0))
        (*
         (- 1.0 z1)
         (-
          1.0
          (cos
           (*
            (atan
             (*
              (-
               (*
                (-
                 (*
                  (-
                   (* (* -0.08888888888888889 (* z2 z2)) (pow PI 6.0))
                   (* -0.6666666666666666 (pow PI 4.0)))
                  (* z2 z2))
                 (* 2.0 (* PI PI)))
                (* z2 z2))
               -1.0)
              (/
               (+
                (* -0.5 (/ (fabs z0) (* z3 PI)))
                (*
                 -0.3333333333333333
                 (/ (* (fabs z0) (* (pow z2 2.0) PI)) z3)))
               z2)))
            2.0))))))
      t_0))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = ((z1 * fabs(z0)) * fabs(z0)) / ((1.0 - cos((-2.0 * atan((((1.0 + (-0.08888888888888889 * (pow(z2, 6.0) * pow(((double) M_PI), 6.0)))) * fabs(z0)) / (-sin(((z2 + z2) * ((double) M_PI))) * z3)))))) * (1.0 - z1));
	double tmp;
	if (fabs(z0) <= 5e-30) {
		tmp = t_0;
	} else if (fabs(z0) <= 3.5e+154) {
		tmp = z1 * ((fabs(z0) * fabs(z0)) / ((1.0 - z1) * (1.0 - cos((atan(((((((((-0.08888888888888889 * (z2 * z2)) * pow(((double) M_PI), 6.0)) - (-0.6666666666666666 * pow(((double) M_PI), 4.0))) * (z2 * z2)) - (2.0 * (((double) M_PI) * ((double) M_PI)))) * (z2 * z2)) - -1.0) * (((-0.5 * (fabs(z0) / (z3 * ((double) M_PI)))) + (-0.3333333333333333 * ((fabs(z0) * (pow(z2, 2.0) * ((double) M_PI))) / z3))) / z2))) * 2.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = ((z1 * Math.abs(z0)) * Math.abs(z0)) / ((1.0 - Math.cos((-2.0 * Math.atan((((1.0 + (-0.08888888888888889 * (Math.pow(z2, 6.0) * Math.pow(Math.PI, 6.0)))) * Math.abs(z0)) / (-Math.sin(((z2 + z2) * Math.PI)) * z3)))))) * (1.0 - z1));
	double tmp;
	if (Math.abs(z0) <= 5e-30) {
		tmp = t_0;
	} else if (Math.abs(z0) <= 3.5e+154) {
		tmp = z1 * ((Math.abs(z0) * Math.abs(z0)) / ((1.0 - z1) * (1.0 - Math.cos((Math.atan(((((((((-0.08888888888888889 * (z2 * z2)) * Math.pow(Math.PI, 6.0)) - (-0.6666666666666666 * Math.pow(Math.PI, 4.0))) * (z2 * z2)) - (2.0 * (Math.PI * Math.PI))) * (z2 * z2)) - -1.0) * (((-0.5 * (Math.abs(z0) / (z3 * Math.PI))) + (-0.3333333333333333 * ((Math.abs(z0) * (Math.pow(z2, 2.0) * Math.PI)) / z3))) / z2))) * 2.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = ((z1 * math.fabs(z0)) * math.fabs(z0)) / ((1.0 - math.cos((-2.0 * math.atan((((1.0 + (-0.08888888888888889 * (math.pow(z2, 6.0) * math.pow(math.pi, 6.0)))) * math.fabs(z0)) / (-math.sin(((z2 + z2) * math.pi)) * z3)))))) * (1.0 - z1))
	tmp = 0
	if math.fabs(z0) <= 5e-30:
		tmp = t_0
	elif math.fabs(z0) <= 3.5e+154:
		tmp = z1 * ((math.fabs(z0) * math.fabs(z0)) / ((1.0 - z1) * (1.0 - math.cos((math.atan(((((((((-0.08888888888888889 * (z2 * z2)) * math.pow(math.pi, 6.0)) - (-0.6666666666666666 * math.pow(math.pi, 4.0))) * (z2 * z2)) - (2.0 * (math.pi * math.pi))) * (z2 * z2)) - -1.0) * (((-0.5 * (math.fabs(z0) / (z3 * math.pi))) + (-0.3333333333333333 * ((math.fabs(z0) * (math.pow(z2, 2.0) * math.pi)) / z3))) / z2))) * 2.0)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(Float64(Float64(z1 * abs(z0)) * abs(z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(Float64(1.0 + Float64(-0.08888888888888889 * Float64((z2 ^ 6.0) * (pi ^ 6.0)))) * abs(z0)) / Float64(Float64(-sin(Float64(Float64(z2 + z2) * pi))) * z3)))))) * Float64(1.0 - z1)))
	tmp = 0.0
	if (abs(z0) <= 5e-30)
		tmp = t_0;
	elseif (abs(z0) <= 3.5e+154)
		tmp = Float64(z1 * Float64(Float64(abs(z0) * abs(z0)) / Float64(Float64(1.0 - z1) * Float64(1.0 - cos(Float64(atan(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(-0.08888888888888889 * Float64(z2 * z2)) * (pi ^ 6.0)) - Float64(-0.6666666666666666 * (pi ^ 4.0))) * Float64(z2 * z2)) - Float64(2.0 * Float64(pi * pi))) * Float64(z2 * z2)) - -1.0) * Float64(Float64(Float64(-0.5 * Float64(abs(z0) / Float64(z3 * pi))) + Float64(-0.3333333333333333 * Float64(Float64(abs(z0) * Float64((z2 ^ 2.0) * pi)) / z3))) / z2))) * 2.0))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = ((z1 * abs(z0)) * abs(z0)) / ((1.0 - cos((-2.0 * atan((((1.0 + (-0.08888888888888889 * ((z2 ^ 6.0) * (pi ^ 6.0)))) * abs(z0)) / (-sin(((z2 + z2) * pi)) * z3)))))) * (1.0 - z1));
	tmp = 0.0;
	if (abs(z0) <= 5e-30)
		tmp = t_0;
	elseif (abs(z0) <= 3.5e+154)
		tmp = z1 * ((abs(z0) * abs(z0)) / ((1.0 - z1) * (1.0 - cos((atan(((((((((-0.08888888888888889 * (z2 * z2)) * (pi ^ 6.0)) - (-0.6666666666666666 * (pi ^ 4.0))) * (z2 * z2)) - (2.0 * (pi * pi))) * (z2 * z2)) - -1.0) * (((-0.5 * (abs(z0) / (z3 * pi))) + (-0.3333333333333333 * ((abs(z0) * ((z2 ^ 2.0) * pi)) / z3))) / z2))) * 2.0)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(N[(N[(z1 * N[Abs[z0], $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(N[(1.0 + N[(-0.08888888888888889 * N[(N[Power[z2, 6.0], $MachinePrecision] * N[Power[Pi, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[((-N[Sin[N[(N[(z2 + z2), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]) * z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Abs[z0], $MachinePrecision], 5e-30], t$95$0, If[LessEqual[N[Abs[z0], $MachinePrecision], 3.5e+154], N[(z1 * N[(N[(N[Abs[z0], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - z1), $MachinePrecision] * N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(N[(N[(N[(N[(N[(N[(-0.08888888888888889 * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] * N[Power[Pi, 6.0], $MachinePrecision]), $MachinePrecision] - N[(-0.6666666666666666 * N[Power[Pi, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(Pi * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision] * N[(N[(N[(-0.5 * N[(N[Abs[z0], $MachinePrecision] / N[(z3 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 * N[(N[(N[Abs[z0], $MachinePrecision] * N[(N[Power[z2, 2.0], $MachinePrecision] * Pi), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z0 < 4.9999999999999997e-30 or 3.5000000000000002e154 < z0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 79.5%

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 79.5%

      \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   9. Taylor expanded in z2 around inf

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \color{blue}{\left({z2}^{6} \cdot {\pi}^{6}\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot \color{blue}{{\mathsf{PI}\left(\right)}^{6}}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{\color{blue}{6}}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

       3. lower-pow.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

       4. lower-pow.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

       5. lower-PI.f64 79.5%

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \left({z2}^{6} \cdot {\pi}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   11. Applied rewrites 79.5%

       \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \color{blue}{\left({z2}^{6} \cdot {\pi}^{6}\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   if 4.9999999999999997e-30 < z0 < 3.5000000000000002e154

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 70.4%

      \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -0.6666666666666666 \cdot {\pi}^{4}\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-z0}{\sin \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z3}\right) \cdot 2\right)\right)}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -0.6666666666666666 \cdot {\pi}^{4}\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \color{blue}{\frac{\frac{-1}{2} \cdot \frac{z0}{z3 \cdot \pi} + \frac{-1}{3} \cdot \frac{z0 \cdot \left({z2}^{2} \cdot \pi\right)}{z3}}{z2}}\right) \cdot 2\right)\right)} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(\frac{-4}{45} \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - \frac{-2}{3} \cdot {\pi}^{4}\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{\frac{-1}{2} \cdot \frac{z0}{z3 \cdot \mathsf{PI}\left(\right)} + \frac{-1}{3} \cdot \frac{z0 \cdot \left({z2}^{2} \cdot \mathsf{PI}\left(\right)\right)}{z3}}{\color{blue}{z2}}\right) \cdot 2\right)\right)} \]

   11. Applied rewrites 74.2%

       \[\leadsto z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -0.6666666666666666 \cdot {\pi}^{4}\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \color{blue}{\frac{-0.5 \cdot \frac{z0}{z3 \cdot \pi} + -0.3333333333333333 \cdot \frac{z0 \cdot \left({z2}^{2} \cdot \pi\right)}{z3}}{z2}}\right) \cdot 2\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \sin \left(\left(z2 + z2\right) \cdot \pi\right)\\ t_1 := \frac{\left(z1 \cdot \left|z0\right|\right) \cdot \left|z0\right|}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \left({z2}^{6} \cdot {\pi}^{6}\right)\right) \cdot \left|z0\right|}{\left(-t\_0\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{if}\;\left|z0\right| \leq 5 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\left|z0\right| \leq 3.5 \cdot 10^{+154}:\\ \;\;\;\;z1 \cdot \frac{\left|z0\right| \cdot \left|z0\right|}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -64.9393940226683\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-\left|z0\right|}{t\_0 \cdot z3}\right) \cdot 2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0 (sin (* (+ z2 z2) PI)))
       (t_1
        (/
         (* (* z1 (fabs z0)) (fabs z0))
         (*
          (-
           1.0
           (cos
            (*
             -2.0
             (atan
              (/
               (*
                (+
                 1.0
                 (*
                  -0.08888888888888889
                  (* (pow z2 6.0) (pow PI 6.0))))
                (fabs z0))
               (* (- t_0) z3))))))
          (- 1.0 z1)))))
  (if (<= (fabs z0) 5e-30)
    t_1
    (if (<= (fabs z0) 3.5e+154)
      (*
       z1
       (/
        (* (fabs z0) (fabs z0))
        (*
         (- 1.0 z1)
         (-
          1.0
          (cos
           (*
            (atan
             (*
              (-
               (*
                (-
                 (*
                  (-
                   (* (* -0.08888888888888889 (* z2 z2)) (pow PI 6.0))
                   -64.9393940226683)
                  (* z2 z2))
                 (* 2.0 (* PI PI)))
                (* z2 z2))
               -1.0)
              (/ (- (fabs z0)) (* t_0 z3))))
            2.0))))))
      t_1))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = sin(((z2 + z2) * ((double) M_PI)));
	double t_1 = ((z1 * fabs(z0)) * fabs(z0)) / ((1.0 - cos((-2.0 * atan((((1.0 + (-0.08888888888888889 * (pow(z2, 6.0) * pow(((double) M_PI), 6.0)))) * fabs(z0)) / (-t_0 * z3)))))) * (1.0 - z1));
	double tmp;
	if (fabs(z0) <= 5e-30) {
		tmp = t_1;
	} else if (fabs(z0) <= 3.5e+154) {
		tmp = z1 * ((fabs(z0) * fabs(z0)) / ((1.0 - z1) * (1.0 - cos((atan(((((((((-0.08888888888888889 * (z2 * z2)) * pow(((double) M_PI), 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (((double) M_PI) * ((double) M_PI)))) * (z2 * z2)) - -1.0) * (-fabs(z0) / (t_0 * z3)))) * 2.0)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = Math.sin(((z2 + z2) * Math.PI));
	double t_1 = ((z1 * Math.abs(z0)) * Math.abs(z0)) / ((1.0 - Math.cos((-2.0 * Math.atan((((1.0 + (-0.08888888888888889 * (Math.pow(z2, 6.0) * Math.pow(Math.PI, 6.0)))) * Math.abs(z0)) / (-t_0 * z3)))))) * (1.0 - z1));
	double tmp;
	if (Math.abs(z0) <= 5e-30) {
		tmp = t_1;
	} else if (Math.abs(z0) <= 3.5e+154) {
		tmp = z1 * ((Math.abs(z0) * Math.abs(z0)) / ((1.0 - z1) * (1.0 - Math.cos((Math.atan(((((((((-0.08888888888888889 * (z2 * z2)) * Math.pow(Math.PI, 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (Math.PI * Math.PI))) * (z2 * z2)) - -1.0) * (-Math.abs(z0) / (t_0 * z3)))) * 2.0)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = math.sin(((z2 + z2) * math.pi))
	t_1 = ((z1 * math.fabs(z0)) * math.fabs(z0)) / ((1.0 - math.cos((-2.0 * math.atan((((1.0 + (-0.08888888888888889 * (math.pow(z2, 6.0) * math.pow(math.pi, 6.0)))) * math.fabs(z0)) / (-t_0 * z3)))))) * (1.0 - z1))
	tmp = 0
	if math.fabs(z0) <= 5e-30:
		tmp = t_1
	elif math.fabs(z0) <= 3.5e+154:
		tmp = z1 * ((math.fabs(z0) * math.fabs(z0)) / ((1.0 - z1) * (1.0 - math.cos((math.atan(((((((((-0.08888888888888889 * (z2 * z2)) * math.pow(math.pi, 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (math.pi * math.pi))) * (z2 * z2)) - -1.0) * (-math.fabs(z0) / (t_0 * z3)))) * 2.0)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = sin(Float64(Float64(z2 + z2) * pi))
	t_1 = Float64(Float64(Float64(z1 * abs(z0)) * abs(z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(Float64(1.0 + Float64(-0.08888888888888889 * Float64((z2 ^ 6.0) * (pi ^ 6.0)))) * abs(z0)) / Float64(Float64(-t_0) * z3)))))) * Float64(1.0 - z1)))
	tmp = 0.0
	if (abs(z0) <= 5e-30)
		tmp = t_1;
	elseif (abs(z0) <= 3.5e+154)
		tmp = Float64(z1 * Float64(Float64(abs(z0) * abs(z0)) / Float64(Float64(1.0 - z1) * Float64(1.0 - cos(Float64(atan(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(-0.08888888888888889 * Float64(z2 * z2)) * (pi ^ 6.0)) - -64.9393940226683) * Float64(z2 * z2)) - Float64(2.0 * Float64(pi * pi))) * Float64(z2 * z2)) - -1.0) * Float64(Float64(-abs(z0)) / Float64(t_0 * z3)))) * 2.0))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = sin(((z2 + z2) * pi));
	t_1 = ((z1 * abs(z0)) * abs(z0)) / ((1.0 - cos((-2.0 * atan((((1.0 + (-0.08888888888888889 * ((z2 ^ 6.0) * (pi ^ 6.0)))) * abs(z0)) / (-t_0 * z3)))))) * (1.0 - z1));
	tmp = 0.0;
	if (abs(z0) <= 5e-30)
		tmp = t_1;
	elseif (abs(z0) <= 3.5e+154)
		tmp = z1 * ((abs(z0) * abs(z0)) / ((1.0 - z1) * (1.0 - cos((atan(((((((((-0.08888888888888889 * (z2 * z2)) * (pi ^ 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (pi * pi))) * (z2 * z2)) - -1.0) * (-abs(z0) / (t_0 * z3)))) * 2.0)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[Sin[N[(N[(z2 + z2), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(z1 * N[Abs[z0], $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(N[(1.0 + N[(-0.08888888888888889 * N[(N[Power[z2, 6.0], $MachinePrecision] * N[Power[Pi, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[((-t$95$0) * z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Abs[z0], $MachinePrecision], 5e-30], t$95$1, If[LessEqual[N[Abs[z0], $MachinePrecision], 3.5e+154], N[(z1 * N[(N[(N[Abs[z0], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - z1), $MachinePrecision] * N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(N[(N[(N[(N[(N[(N[(-0.08888888888888889 * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] * N[Power[Pi, 6.0], $MachinePrecision]), $MachinePrecision] - -64.9393940226683), $MachinePrecision] * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(Pi * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision] * N[((-N[Abs[z0], $MachinePrecision]) / N[(t$95$0 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z0 < 4.9999999999999997e-30 or 3.5000000000000002e154 < z0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 79.5%

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 79.5%

      \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   9. Taylor expanded in z2 around inf

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \color{blue}{\left({z2}^{6} \cdot {\pi}^{6}\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot \color{blue}{{\mathsf{PI}\left(\right)}^{6}}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{\color{blue}{6}}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

       3. lower-pow.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

       4. lower-pow.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

       5. lower-PI.f64 79.5%

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \left({z2}^{6} \cdot {\pi}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   11. Applied rewrites 79.5%

       \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \color{blue}{\left({z2}^{6} \cdot {\pi}^{6}\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   if 4.9999999999999997e-30 < z0 < 3.5000000000000002e154

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 70.4%

      \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -0.6666666666666666 \cdot {\pi}^{4}\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-z0}{\sin \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z3}\right) \cdot 2\right)\right)}} \]

   9. Evaluated real constant 70.4%

      \[\leadsto z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -64.9393940226683\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-z0}{\sin \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z3}\right) \cdot 2\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \sin \left(\left(z2 + z2\right) \cdot \pi\right)\\ t_1 := \left|z0\right| \cdot \left|z0\right|\\ \mathbf{if}\;\left|z0\right| \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{z1 \cdot t\_1}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \left({z2}^{6} \cdot {\pi}^{6}\right)\right) \cdot \left|z0\right|}{\left(-t\_0\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{elif}\;\left|z0\right| \leq 2.65 \cdot 10^{+152}:\\ \;\;\;\;z1 \cdot \frac{t\_1}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -64.9393940226683\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-\left|z0\right|}{t\_0 \cdot z3}\right) \cdot 2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|z0\right| \cdot z1}{1 - z1} \cdot \frac{\left|z0\right|}{1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{\left|z0\right|}{z3}\right) \cdot 2\right)}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0 (sin (* (+ z2 z2) PI))) (t_1 (* (fabs z0) (fabs z0))))
  (if (<= (fabs z0) 5e-30)
    (/
     (* z1 t_1)
     (*
      (-
       1.0
       (cos
        (*
         -2.0
         (atan
          (/
           (*
            (+
             1.0
             (* -0.08888888888888889 (* (pow z2 6.0) (pow PI 6.0))))
            (fabs z0))
           (* (- t_0) z3))))))
      (- 1.0 z1)))
    (if (<= (fabs z0) 2.65e+152)
      (*
       z1
       (/
        t_1
        (*
         (- 1.0 z1)
         (-
          1.0
          (cos
           (*
            (atan
             (*
              (-
               (*
                (-
                 (*
                  (-
                   (* (* -0.08888888888888889 (* z2 z2)) (pow PI 6.0))
                   -64.9393940226683)
                  (* z2 z2))
                 (* 2.0 (* PI PI)))
                (* z2 z2))
               -1.0)
              (/ (- (fabs z0)) (* t_0 z3))))
            2.0))))))
      (*
       (/ (* (fabs z0) z1) (- 1.0 z1))
       (/
        (fabs z0)
        (-
         1.0
         (cos
          (* (atan (* (tan (* 0.5 PI)) (/ (fabs z0) z3))) 2.0)))))))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = sin(((z2 + z2) * ((double) M_PI)));
	double t_1 = fabs(z0) * fabs(z0);
	double tmp;
	if (fabs(z0) <= 5e-30) {
		tmp = (z1 * t_1) / ((1.0 - cos((-2.0 * atan((((1.0 + (-0.08888888888888889 * (pow(z2, 6.0) * pow(((double) M_PI), 6.0)))) * fabs(z0)) / (-t_0 * z3)))))) * (1.0 - z1));
	} else if (fabs(z0) <= 2.65e+152) {
		tmp = z1 * (t_1 / ((1.0 - z1) * (1.0 - cos((atan(((((((((-0.08888888888888889 * (z2 * z2)) * pow(((double) M_PI), 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (((double) M_PI) * ((double) M_PI)))) * (z2 * z2)) - -1.0) * (-fabs(z0) / (t_0 * z3)))) * 2.0)))));
	} else {
		tmp = ((fabs(z0) * z1) / (1.0 - z1)) * (fabs(z0) / (1.0 - cos((atan((tan((0.5 * ((double) M_PI))) * (fabs(z0) / z3))) * 2.0))));
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = Math.sin(((z2 + z2) * Math.PI));
	double t_1 = Math.abs(z0) * Math.abs(z0);
	double tmp;
	if (Math.abs(z0) <= 5e-30) {
		tmp = (z1 * t_1) / ((1.0 - Math.cos((-2.0 * Math.atan((((1.0 + (-0.08888888888888889 * (Math.pow(z2, 6.0) * Math.pow(Math.PI, 6.0)))) * Math.abs(z0)) / (-t_0 * z3)))))) * (1.0 - z1));
	} else if (Math.abs(z0) <= 2.65e+152) {
		tmp = z1 * (t_1 / ((1.0 - z1) * (1.0 - Math.cos((Math.atan(((((((((-0.08888888888888889 * (z2 * z2)) * Math.pow(Math.PI, 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (Math.PI * Math.PI))) * (z2 * z2)) - -1.0) * (-Math.abs(z0) / (t_0 * z3)))) * 2.0)))));
	} else {
		tmp = ((Math.abs(z0) * z1) / (1.0 - z1)) * (Math.abs(z0) / (1.0 - Math.cos((Math.atan((Math.tan((0.5 * Math.PI)) * (Math.abs(z0) / z3))) * 2.0))));
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = math.sin(((z2 + z2) * math.pi))
	t_1 = math.fabs(z0) * math.fabs(z0)
	tmp = 0
	if math.fabs(z0) <= 5e-30:
		tmp = (z1 * t_1) / ((1.0 - math.cos((-2.0 * math.atan((((1.0 + (-0.08888888888888889 * (math.pow(z2, 6.0) * math.pow(math.pi, 6.0)))) * math.fabs(z0)) / (-t_0 * z3)))))) * (1.0 - z1))
	elif math.fabs(z0) <= 2.65e+152:
		tmp = z1 * (t_1 / ((1.0 - z1) * (1.0 - math.cos((math.atan(((((((((-0.08888888888888889 * (z2 * z2)) * math.pow(math.pi, 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (math.pi * math.pi))) * (z2 * z2)) - -1.0) * (-math.fabs(z0) / (t_0 * z3)))) * 2.0)))))
	else:
		tmp = ((math.fabs(z0) * z1) / (1.0 - z1)) * (math.fabs(z0) / (1.0 - math.cos((math.atan((math.tan((0.5 * math.pi)) * (math.fabs(z0) / z3))) * 2.0))))
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = sin(Float64(Float64(z2 + z2) * pi))
	t_1 = Float64(abs(z0) * abs(z0))
	tmp = 0.0
	if (abs(z0) <= 5e-30)
		tmp = Float64(Float64(z1 * t_1) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(Float64(1.0 + Float64(-0.08888888888888889 * Float64((z2 ^ 6.0) * (pi ^ 6.0)))) * abs(z0)) / Float64(Float64(-t_0) * z3)))))) * Float64(1.0 - z1)));
	elseif (abs(z0) <= 2.65e+152)
		tmp = Float64(z1 * Float64(t_1 / Float64(Float64(1.0 - z1) * Float64(1.0 - cos(Float64(atan(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(-0.08888888888888889 * Float64(z2 * z2)) * (pi ^ 6.0)) - -64.9393940226683) * Float64(z2 * z2)) - Float64(2.0 * Float64(pi * pi))) * Float64(z2 * z2)) - -1.0) * Float64(Float64(-abs(z0)) / Float64(t_0 * z3)))) * 2.0))))));
	else
		tmp = Float64(Float64(Float64(abs(z0) * z1) / Float64(1.0 - z1)) * Float64(abs(z0) / Float64(1.0 - cos(Float64(atan(Float64(tan(Float64(0.5 * pi)) * Float64(abs(z0) / z3))) * 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = sin(((z2 + z2) * pi));
	t_1 = abs(z0) * abs(z0);
	tmp = 0.0;
	if (abs(z0) <= 5e-30)
		tmp = (z1 * t_1) / ((1.0 - cos((-2.0 * atan((((1.0 + (-0.08888888888888889 * ((z2 ^ 6.0) * (pi ^ 6.0)))) * abs(z0)) / (-t_0 * z3)))))) * (1.0 - z1));
	elseif (abs(z0) <= 2.65e+152)
		tmp = z1 * (t_1 / ((1.0 - z1) * (1.0 - cos((atan(((((((((-0.08888888888888889 * (z2 * z2)) * (pi ^ 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (pi * pi))) * (z2 * z2)) - -1.0) * (-abs(z0) / (t_0 * z3)))) * 2.0)))));
	else
		tmp = ((abs(z0) * z1) / (1.0 - z1)) * (abs(z0) / (1.0 - cos((atan((tan((0.5 * pi)) * (abs(z0) / z3))) * 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[Sin[N[(N[(z2 + z2), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[z0], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Abs[z0], $MachinePrecision], 5e-30], N[(N[(z1 * t$95$1), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(N[(1.0 + N[(-0.08888888888888889 * N[(N[Power[z2, 6.0], $MachinePrecision] * N[Power[Pi, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[((-t$95$0) * z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[z0], $MachinePrecision], 2.65e+152], N[(z1 * N[(t$95$1 / N[(N[(1.0 - z1), $MachinePrecision] * N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(N[(N[(N[(N[(N[(N[(-0.08888888888888889 * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] * N[Power[Pi, 6.0], $MachinePrecision]), $MachinePrecision] - -64.9393940226683), $MachinePrecision] * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(Pi * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision] * N[((-N[Abs[z0], $MachinePrecision]) / N[(t$95$0 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Abs[z0], $MachinePrecision] * z1), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(N[Abs[z0], $MachinePrecision] / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[Tan[N[(0.5 * Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Abs[z0], $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < 4.9999999999999997e-30

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   7. Taylor expanded in z2 around inf

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \color{blue}{\left({z2}^{6} \cdot {\pi}^{6}\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot \color{blue}{{\mathsf{PI}\left(\right)}^{6}}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{\color{blue}{6}}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \frac{-4}{45} \cdot \left({z2}^{6} \cdot {\mathsf{PI}\left(\right)}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 73.5%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \left({z2}^{6} \cdot {\pi}^{6}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   9. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + -0.08888888888888889 \cdot \color{blue}{\left({z2}^{6} \cdot {\pi}^{6}\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   if 4.9999999999999997e-30 < z0 < 2.6499999999999999e152

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 70.4%

      \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -0.6666666666666666 \cdot {\pi}^{4}\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-z0}{\sin \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z3}\right) \cdot 2\right)\right)}} \]

   9. Evaluated real constant 70.4%

      \[\leadsto z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -64.9393940226683\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-z0}{\sin \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z3}\right) \cdot 2\right)\right)} \]

   if 2.6499999999999999e152 < z0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.2%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{0.5}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z1\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z1\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 \cdot z1\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      8. *-commutative N/A

         \[\leadsto \frac{\left(z0 \cdot z1\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right)}} \]

      9. times-frac N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)}} \]

      10. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1}} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)} \]

      12. lower-/.f64 55.5%

          \[\leadsto \frac{z0 \cdot z1}{1 - z1} \cdot \color{blue}{\frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)}} \]

   6. Applied rewrites 55.5%

      \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left|z0\right| \cdot \pi}{z3}\\ \mathbf{if}\;\left|z0\right| \leq 2.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{\left(z1 \cdot \left|z0\right|\right) \cdot \left|z0\right|}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot t\_0 - -0.3333333333333333 \cdot t\_0\right)\right) + -0.5 \cdot \frac{\left|z0\right|}{z3 \cdot \pi}}{z2}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{elif}\;\left|z0\right| \leq 2.65 \cdot 10^{+152}:\\ \;\;\;\;z1 \cdot \frac{\left|z0\right| \cdot \left|z0\right|}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -64.9393940226683\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-\left|z0\right|}{\sin \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z3}\right) \cdot 2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|z0\right| \cdot z1}{1 - z1} \cdot \frac{\left|z0\right|}{1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{\left|z0\right|}{z3}\right) \cdot 2\right)}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0 (/ (* (fabs z0) PI) z3)))
  (if (<= (fabs z0) 2.7e-30)
    (/
     (* (* z1 (fabs z0)) (fabs z0))
     (*
      (-
       1.0
       (cos
        (*
         -2.0
         (atan
          (/
           (+
            (*
             -1.0
             (*
              (pow z2 2.0)
              (- (* -1.0 t_0) (* -0.3333333333333333 t_0))))
            (* -0.5 (/ (fabs z0) (* z3 PI))))
           z2)))))
      (- 1.0 z1)))
    (if (<= (fabs z0) 2.65e+152)
      (*
       z1
       (/
        (* (fabs z0) (fabs z0))
        (*
         (- 1.0 z1)
         (-
          1.0
          (cos
           (*
            (atan
             (*
              (-
               (*
                (-
                 (*
                  (-
                   (* (* -0.08888888888888889 (* z2 z2)) (pow PI 6.0))
                   -64.9393940226683)
                  (* z2 z2))
                 (* 2.0 (* PI PI)))
                (* z2 z2))
               -1.0)
              (/ (- (fabs z0)) (* (sin (* (+ z2 z2) PI)) z3))))
            2.0))))))
      (*
       (/ (* (fabs z0) z1) (- 1.0 z1))
       (/
        (fabs z0)
        (-
         1.0
         (cos
          (* (atan (* (tan (* 0.5 PI)) (/ (fabs z0) z3))) 2.0)))))))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = (fabs(z0) * ((double) M_PI)) / z3;
	double tmp;
	if (fabs(z0) <= 2.7e-30) {
		tmp = ((z1 * fabs(z0)) * fabs(z0)) / ((1.0 - cos((-2.0 * atan((((-1.0 * (pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (fabs(z0) / (z3 * ((double) M_PI))))) / z2))))) * (1.0 - z1));
	} else if (fabs(z0) <= 2.65e+152) {
		tmp = z1 * ((fabs(z0) * fabs(z0)) / ((1.0 - z1) * (1.0 - cos((atan(((((((((-0.08888888888888889 * (z2 * z2)) * pow(((double) M_PI), 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (((double) M_PI) * ((double) M_PI)))) * (z2 * z2)) - -1.0) * (-fabs(z0) / (sin(((z2 + z2) * ((double) M_PI))) * z3)))) * 2.0)))));
	} else {
		tmp = ((fabs(z0) * z1) / (1.0 - z1)) * (fabs(z0) / (1.0 - cos((atan((tan((0.5 * ((double) M_PI))) * (fabs(z0) / z3))) * 2.0))));
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = (Math.abs(z0) * Math.PI) / z3;
	double tmp;
	if (Math.abs(z0) <= 2.7e-30) {
		tmp = ((z1 * Math.abs(z0)) * Math.abs(z0)) / ((1.0 - Math.cos((-2.0 * Math.atan((((-1.0 * (Math.pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (Math.abs(z0) / (z3 * Math.PI)))) / z2))))) * (1.0 - z1));
	} else if (Math.abs(z0) <= 2.65e+152) {
		tmp = z1 * ((Math.abs(z0) * Math.abs(z0)) / ((1.0 - z1) * (1.0 - Math.cos((Math.atan(((((((((-0.08888888888888889 * (z2 * z2)) * Math.pow(Math.PI, 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (Math.PI * Math.PI))) * (z2 * z2)) - -1.0) * (-Math.abs(z0) / (Math.sin(((z2 + z2) * Math.PI)) * z3)))) * 2.0)))));
	} else {
		tmp = ((Math.abs(z0) * z1) / (1.0 - z1)) * (Math.abs(z0) / (1.0 - Math.cos((Math.atan((Math.tan((0.5 * Math.PI)) * (Math.abs(z0) / z3))) * 2.0))));
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = (math.fabs(z0) * math.pi) / z3
	tmp = 0
	if math.fabs(z0) <= 2.7e-30:
		tmp = ((z1 * math.fabs(z0)) * math.fabs(z0)) / ((1.0 - math.cos((-2.0 * math.atan((((-1.0 * (math.pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (math.fabs(z0) / (z3 * math.pi)))) / z2))))) * (1.0 - z1))
	elif math.fabs(z0) <= 2.65e+152:
		tmp = z1 * ((math.fabs(z0) * math.fabs(z0)) / ((1.0 - z1) * (1.0 - math.cos((math.atan(((((((((-0.08888888888888889 * (z2 * z2)) * math.pow(math.pi, 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (math.pi * math.pi))) * (z2 * z2)) - -1.0) * (-math.fabs(z0) / (math.sin(((z2 + z2) * math.pi)) * z3)))) * 2.0)))))
	else:
		tmp = ((math.fabs(z0) * z1) / (1.0 - z1)) * (math.fabs(z0) / (1.0 - math.cos((math.atan((math.tan((0.5 * math.pi)) * (math.fabs(z0) / z3))) * 2.0))))
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(Float64(abs(z0) * pi) / z3)
	tmp = 0.0
	if (abs(z0) <= 2.7e-30)
		tmp = Float64(Float64(Float64(z1 * abs(z0)) * abs(z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(Float64(-1.0 * Float64((z2 ^ 2.0) * Float64(Float64(-1.0 * t_0) - Float64(-0.3333333333333333 * t_0)))) + Float64(-0.5 * Float64(abs(z0) / Float64(z3 * pi)))) / z2))))) * Float64(1.0 - z1)));
	elseif (abs(z0) <= 2.65e+152)
		tmp = Float64(z1 * Float64(Float64(abs(z0) * abs(z0)) / Float64(Float64(1.0 - z1) * Float64(1.0 - cos(Float64(atan(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(-0.08888888888888889 * Float64(z2 * z2)) * (pi ^ 6.0)) - -64.9393940226683) * Float64(z2 * z2)) - Float64(2.0 * Float64(pi * pi))) * Float64(z2 * z2)) - -1.0) * Float64(Float64(-abs(z0)) / Float64(sin(Float64(Float64(z2 + z2) * pi)) * z3)))) * 2.0))))));
	else
		tmp = Float64(Float64(Float64(abs(z0) * z1) / Float64(1.0 - z1)) * Float64(abs(z0) / Float64(1.0 - cos(Float64(atan(Float64(tan(Float64(0.5 * pi)) * Float64(abs(z0) / z3))) * 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = (abs(z0) * pi) / z3;
	tmp = 0.0;
	if (abs(z0) <= 2.7e-30)
		tmp = ((z1 * abs(z0)) * abs(z0)) / ((1.0 - cos((-2.0 * atan((((-1.0 * ((z2 ^ 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (abs(z0) / (z3 * pi)))) / z2))))) * (1.0 - z1));
	elseif (abs(z0) <= 2.65e+152)
		tmp = z1 * ((abs(z0) * abs(z0)) / ((1.0 - z1) * (1.0 - cos((atan(((((((((-0.08888888888888889 * (z2 * z2)) * (pi ^ 6.0)) - -64.9393940226683) * (z2 * z2)) - (2.0 * (pi * pi))) * (z2 * z2)) - -1.0) * (-abs(z0) / (sin(((z2 + z2) * pi)) * z3)))) * 2.0)))));
	else
		tmp = ((abs(z0) * z1) / (1.0 - z1)) * (abs(z0) / (1.0 - cos((atan((tan((0.5 * pi)) * (abs(z0) / z3))) * 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(N[(N[Abs[z0], $MachinePrecision] * Pi), $MachinePrecision] / z3), $MachinePrecision]}, If[LessEqual[N[Abs[z0], $MachinePrecision], 2.7e-30], N[(N[(N[(z1 * N[Abs[z0], $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(N[(-1.0 * N[(N[Power[z2, 2.0], $MachinePrecision] * N[(N[(-1.0 * t$95$0), $MachinePrecision] - N[(-0.3333333333333333 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(N[Abs[z0], $MachinePrecision] / N[(z3 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[z0], $MachinePrecision], 2.65e+152], N[(z1 * N[(N[(N[Abs[z0], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - z1), $MachinePrecision] * N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(N[(N[(N[(N[(N[(N[(-0.08888888888888889 * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] * N[Power[Pi, 6.0], $MachinePrecision]), $MachinePrecision] - -64.9393940226683), $MachinePrecision] * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(Pi * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z2 * z2), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision] * N[((-N[Abs[z0], $MachinePrecision]) / N[(N[Sin[N[(N[(z2 + z2), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Abs[z0], $MachinePrecision] * z1), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(N[Abs[z0], $MachinePrecision] / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[Tan[N[(0.5 * Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Abs[z0], $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < 2.6999999999999999e-30

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 79.5%

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 79.5%

      \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \pi}{z3} - \frac{-1}{3} \cdot \frac{z0 \cdot \pi}{z3}\right)\right) + \frac{-1}{2} \cdot \frac{z0}{z3 \cdot \pi}}{z2}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \mathsf{PI}\left(\right)}{z3} - \frac{-1}{3} \cdot \frac{z0 \cdot \mathsf{PI}\left(\right)}{z3}\right)\right) + \frac{-1}{2} \cdot \frac{z0}{z3 \cdot \mathsf{PI}\left(\right)}}{\color{blue}{z2}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   11. Applied rewrites 58.6%

       \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \pi}{z3} - -0.3333333333333333 \cdot \frac{z0 \cdot \pi}{z3}\right)\right) + -0.5 \cdot \frac{z0}{z3 \cdot \pi}}{z2}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   if 2.6999999999999999e-30 < z0 < 2.6499999999999999e152

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 70.4%

      \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -0.6666666666666666 \cdot {\pi}^{4}\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-z0}{\sin \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z3}\right) \cdot 2\right)\right)}} \]

   9. Evaluated real constant 70.4%

      \[\leadsto z1 \cdot \frac{z0 \cdot z0}{\left(1 - z1\right) \cdot \left(1 - \cos \left(\tan^{-1} \left(\left(\left(\left(\left(-0.08888888888888889 \cdot \left(z2 \cdot z2\right)\right) \cdot {\pi}^{6} - -64.9393940226683\right) \cdot \left(z2 \cdot z2\right) - 2 \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(z2 \cdot z2\right) - -1\right) \cdot \frac{-z0}{\sin \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z3}\right) \cdot 2\right)\right)} \]

   if 2.6499999999999999e152 < z0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.2%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{0.5}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z1\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z1\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 \cdot z1\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      8. *-commutative N/A

         \[\leadsto \frac{\left(z0 \cdot z1\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right)}} \]

      9. times-frac N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)}} \]

      10. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1}} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)} \]

      12. lower-/.f64 55.5%

          \[\leadsto \frac{z0 \cdot z1}{1 - z1} \cdot \color{blue}{\frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)}} \]

   6. Applied rewrites 55.5%

      \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left|z0\right| \cdot \pi}{z3}\\ \mathbf{if}\;\left|z0\right| \leq 2.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{\left(z1 \cdot \left|z0\right|\right) \cdot \left|z0\right|}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot t\_0 - -0.3333333333333333 \cdot t\_0\right)\right) + -0.5 \cdot \frac{\left|z0\right|}{z3 \cdot \pi}}{z2}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|z0\right| \cdot z1}{1 - z1} \cdot \frac{\left|z0\right|}{1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{\left|z0\right|}{z3}\right) \cdot 2\right)}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0 (/ (* (fabs z0) PI) z3)))
  (if (<= (fabs z0) 2.2e+113)
    (/
     (* (* z1 (fabs z0)) (fabs z0))
     (*
      (-
       1.0
       (cos
        (*
         -2.0
         (atan
          (/
           (+
            (*
             -1.0
             (*
              (pow z2 2.0)
              (- (* -1.0 t_0) (* -0.3333333333333333 t_0))))
            (* -0.5 (/ (fabs z0) (* z3 PI))))
           z2)))))
      (- 1.0 z1)))
    (*
     (/ (* (fabs z0) z1) (- 1.0 z1))
     (/
      (fabs z0)
      (-
       1.0
       (cos (* (atan (* (tan (* 0.5 PI)) (/ (fabs z0) z3))) 2.0))))))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = (fabs(z0) * ((double) M_PI)) / z3;
	double tmp;
	if (fabs(z0) <= 2.2e+113) {
		tmp = ((z1 * fabs(z0)) * fabs(z0)) / ((1.0 - cos((-2.0 * atan((((-1.0 * (pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (fabs(z0) / (z3 * ((double) M_PI))))) / z2))))) * (1.0 - z1));
	} else {
		tmp = ((fabs(z0) * z1) / (1.0 - z1)) * (fabs(z0) / (1.0 - cos((atan((tan((0.5 * ((double) M_PI))) * (fabs(z0) / z3))) * 2.0))));
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = (Math.abs(z0) * Math.PI) / z3;
	double tmp;
	if (Math.abs(z0) <= 2.2e+113) {
		tmp = ((z1 * Math.abs(z0)) * Math.abs(z0)) / ((1.0 - Math.cos((-2.0 * Math.atan((((-1.0 * (Math.pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (Math.abs(z0) / (z3 * Math.PI)))) / z2))))) * (1.0 - z1));
	} else {
		tmp = ((Math.abs(z0) * z1) / (1.0 - z1)) * (Math.abs(z0) / (1.0 - Math.cos((Math.atan((Math.tan((0.5 * Math.PI)) * (Math.abs(z0) / z3))) * 2.0))));
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = (math.fabs(z0) * math.pi) / z3
	tmp = 0
	if math.fabs(z0) <= 2.2e+113:
		tmp = ((z1 * math.fabs(z0)) * math.fabs(z0)) / ((1.0 - math.cos((-2.0 * math.atan((((-1.0 * (math.pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (math.fabs(z0) / (z3 * math.pi)))) / z2))))) * (1.0 - z1))
	else:
		tmp = ((math.fabs(z0) * z1) / (1.0 - z1)) * (math.fabs(z0) / (1.0 - math.cos((math.atan((math.tan((0.5 * math.pi)) * (math.fabs(z0) / z3))) * 2.0))))
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(Float64(abs(z0) * pi) / z3)
	tmp = 0.0
	if (abs(z0) <= 2.2e+113)
		tmp = Float64(Float64(Float64(z1 * abs(z0)) * abs(z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(Float64(-1.0 * Float64((z2 ^ 2.0) * Float64(Float64(-1.0 * t_0) - Float64(-0.3333333333333333 * t_0)))) + Float64(-0.5 * Float64(abs(z0) / Float64(z3 * pi)))) / z2))))) * Float64(1.0 - z1)));
	else
		tmp = Float64(Float64(Float64(abs(z0) * z1) / Float64(1.0 - z1)) * Float64(abs(z0) / Float64(1.0 - cos(Float64(atan(Float64(tan(Float64(0.5 * pi)) * Float64(abs(z0) / z3))) * 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = (abs(z0) * pi) / z3;
	tmp = 0.0;
	if (abs(z0) <= 2.2e+113)
		tmp = ((z1 * abs(z0)) * abs(z0)) / ((1.0 - cos((-2.0 * atan((((-1.0 * ((z2 ^ 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (abs(z0) / (z3 * pi)))) / z2))))) * (1.0 - z1));
	else
		tmp = ((abs(z0) * z1) / (1.0 - z1)) * (abs(z0) / (1.0 - cos((atan((tan((0.5 * pi)) * (abs(z0) / z3))) * 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(N[(N[Abs[z0], $MachinePrecision] * Pi), $MachinePrecision] / z3), $MachinePrecision]}, If[LessEqual[N[Abs[z0], $MachinePrecision], 2.2e+113], N[(N[(N[(z1 * N[Abs[z0], $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(N[(-1.0 * N[(N[Power[z2, 2.0], $MachinePrecision] * N[(N[(-1.0 * t$95$0), $MachinePrecision] - N[(-0.3333333333333333 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(N[Abs[z0], $MachinePrecision] / N[(z3 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Abs[z0], $MachinePrecision] * z1), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(N[Abs[z0], $MachinePrecision] / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[Tan[N[(0.5 * Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Abs[z0], $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z0 < 2.2000000000000001e113

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 79.5%

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 79.5%

      \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \pi}{z3} - \frac{-1}{3} \cdot \frac{z0 \cdot \pi}{z3}\right)\right) + \frac{-1}{2} \cdot \frac{z0}{z3 \cdot \pi}}{z2}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \mathsf{PI}\left(\right)}{z3} - \frac{-1}{3} \cdot \frac{z0 \cdot \mathsf{PI}\left(\right)}{z3}\right)\right) + \frac{-1}{2} \cdot \frac{z0}{z3 \cdot \mathsf{PI}\left(\right)}}{\color{blue}{z2}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   11. Applied rewrites 58.6%

       \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \pi}{z3} - -0.3333333333333333 \cdot \frac{z0 \cdot \pi}{z3}\right)\right) + -0.5 \cdot \frac{z0}{z3 \cdot \pi}}{z2}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   if 2.2000000000000001e113 < z0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.2%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{0.5}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z1\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z1\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 \cdot z1\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      8. *-commutative N/A

         \[\leadsto \frac{\left(z0 \cdot z1\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right)}} \]

      9. times-frac N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)}} \]

      10. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1}} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)} \]

      12. lower-/.f64 55.5%

          \[\leadsto \frac{z0 \cdot z1}{1 - z1} \cdot \color{blue}{\frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)}} \]

   6. Applied rewrites 55.5%

      \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left|z0\right| \cdot \pi}{z3}\\ \mathbf{if}\;\left|z0\right| \leq 2.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{z1 \cdot \left(\left|z0\right| \cdot \left|z0\right|\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot t\_0 - -0.3333333333333333 \cdot t\_0\right)\right) + -0.5 \cdot \frac{\left|z0\right|}{z3 \cdot \pi}}{z2}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|z0\right| \cdot z1}{1 - z1} \cdot \frac{\left|z0\right|}{1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{\left|z0\right|}{z3}\right) \cdot 2\right)}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0 (/ (* (fabs z0) PI) z3)))
  (if (<= (fabs z0) 2.2e+113)
    (/
     (* z1 (* (fabs z0) (fabs z0)))
     (*
      (-
       1.0
       (cos
        (*
         -2.0
         (atan
          (/
           (+
            (*
             -1.0
             (*
              (pow z2 2.0)
              (- (* -1.0 t_0) (* -0.3333333333333333 t_0))))
            (* -0.5 (/ (fabs z0) (* z3 PI))))
           z2)))))
      (- 1.0 z1)))
    (*
     (/ (* (fabs z0) z1) (- 1.0 z1))
     (/
      (fabs z0)
      (-
       1.0
       (cos (* (atan (* (tan (* 0.5 PI)) (/ (fabs z0) z3))) 2.0))))))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = (fabs(z0) * ((double) M_PI)) / z3;
	double tmp;
	if (fabs(z0) <= 2.2e+113) {
		tmp = (z1 * (fabs(z0) * fabs(z0))) / ((1.0 - cos((-2.0 * atan((((-1.0 * (pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (fabs(z0) / (z3 * ((double) M_PI))))) / z2))))) * (1.0 - z1));
	} else {
		tmp = ((fabs(z0) * z1) / (1.0 - z1)) * (fabs(z0) / (1.0 - cos((atan((tan((0.5 * ((double) M_PI))) * (fabs(z0) / z3))) * 2.0))));
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = (Math.abs(z0) * Math.PI) / z3;
	double tmp;
	if (Math.abs(z0) <= 2.2e+113) {
		tmp = (z1 * (Math.abs(z0) * Math.abs(z0))) / ((1.0 - Math.cos((-2.0 * Math.atan((((-1.0 * (Math.pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (Math.abs(z0) / (z3 * Math.PI)))) / z2))))) * (1.0 - z1));
	} else {
		tmp = ((Math.abs(z0) * z1) / (1.0 - z1)) * (Math.abs(z0) / (1.0 - Math.cos((Math.atan((Math.tan((0.5 * Math.PI)) * (Math.abs(z0) / z3))) * 2.0))));
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = (math.fabs(z0) * math.pi) / z3
	tmp = 0
	if math.fabs(z0) <= 2.2e+113:
		tmp = (z1 * (math.fabs(z0) * math.fabs(z0))) / ((1.0 - math.cos((-2.0 * math.atan((((-1.0 * (math.pow(z2, 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (math.fabs(z0) / (z3 * math.pi)))) / z2))))) * (1.0 - z1))
	else:
		tmp = ((math.fabs(z0) * z1) / (1.0 - z1)) * (math.fabs(z0) / (1.0 - math.cos((math.atan((math.tan((0.5 * math.pi)) * (math.fabs(z0) / z3))) * 2.0))))
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(Float64(abs(z0) * pi) / z3)
	tmp = 0.0
	if (abs(z0) <= 2.2e+113)
		tmp = Float64(Float64(z1 * Float64(abs(z0) * abs(z0))) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(Float64(-1.0 * Float64((z2 ^ 2.0) * Float64(Float64(-1.0 * t_0) - Float64(-0.3333333333333333 * t_0)))) + Float64(-0.5 * Float64(abs(z0) / Float64(z3 * pi)))) / z2))))) * Float64(1.0 - z1)));
	else
		tmp = Float64(Float64(Float64(abs(z0) * z1) / Float64(1.0 - z1)) * Float64(abs(z0) / Float64(1.0 - cos(Float64(atan(Float64(tan(Float64(0.5 * pi)) * Float64(abs(z0) / z3))) * 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = (abs(z0) * pi) / z3;
	tmp = 0.0;
	if (abs(z0) <= 2.2e+113)
		tmp = (z1 * (abs(z0) * abs(z0))) / ((1.0 - cos((-2.0 * atan((((-1.0 * ((z2 ^ 2.0) * ((-1.0 * t_0) - (-0.3333333333333333 * t_0)))) + (-0.5 * (abs(z0) / (z3 * pi)))) / z2))))) * (1.0 - z1));
	else
		tmp = ((abs(z0) * z1) / (1.0 - z1)) * (abs(z0) / (1.0 - cos((atan((tan((0.5 * pi)) * (abs(z0) / z3))) * 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(N[(N[Abs[z0], $MachinePrecision] * Pi), $MachinePrecision] / z3), $MachinePrecision]}, If[LessEqual[N[Abs[z0], $MachinePrecision], 2.2e+113], N[(N[(z1 * N[(N[Abs[z0], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(N[(-1.0 * N[(N[Power[z2, 2.0], $MachinePrecision] * N[(N[(-1.0 * t$95$0), $MachinePrecision] - N[(-0.3333333333333333 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(N[Abs[z0], $MachinePrecision] / N[(z3 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Abs[z0], $MachinePrecision] * z1), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(N[Abs[z0], $MachinePrecision] / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[Tan[N[(0.5 * Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Abs[z0], $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z0 < 2.2000000000000001e113

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + \frac{2}{3} \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + \color{blue}{{z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \color{blue}{\left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)}\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(\color{blue}{-2 \cdot {\mathsf{PI}\left(\right)}^{2}} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + \color{blue}{{z2}^{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\mathsf{PI}\left(\right)}^{2} + {z2}^{\color{blue}{2}} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \color{blue}{\left(\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right) + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)}\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      9. lower-pow.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(\color{blue}{\frac{-4}{45} \cdot \left({z2}^{2} \cdot {\mathsf{PI}\left(\right)}^{6}\right)} + \frac{2}{3} \cdot {\mathsf{PI}\left(\right)}^{4}\right)\right)\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 73.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(1 + {z2}^{2} \cdot \left(-2 \cdot {\pi}^{2} + {z2}^{2} \cdot \left(-0.08888888888888889 \cdot \left({z2}^{2} \cdot {\pi}^{6}\right) + 0.6666666666666666 \cdot {\pi}^{4}\right)\right)\right)} \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   7. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \pi}{z3} - \frac{-1}{3} \cdot \frac{z0 \cdot \pi}{z3}\right)\right) + \frac{-1}{2} \cdot \frac{z0}{z3 \cdot \pi}}{z2}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \mathsf{PI}\left(\right)}{z3} - \frac{-1}{3} \cdot \frac{z0 \cdot \mathsf{PI}\left(\right)}{z3}\right)\right) + \frac{-1}{2} \cdot \frac{z0}{z3 \cdot \mathsf{PI}\left(\right)}}{\color{blue}{z2}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   9. Applied rewrites 54.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left({z2}^{2} \cdot \left(-1 \cdot \frac{z0 \cdot \pi}{z3} - -0.3333333333333333 \cdot \frac{z0 \cdot \pi}{z3}\right)\right) + -0.5 \cdot \frac{z0}{z3 \cdot \pi}}{z2}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   if 2.2000000000000001e113 < z0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.2%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{0.5}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z1\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z1\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 \cdot z1\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      8. *-commutative N/A

         \[\leadsto \frac{\left(z0 \cdot z1\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right)}} \]

      9. times-frac N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)}} \]

      10. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1}} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)} \]

      12. lower-/.f64 55.5%

          \[\leadsto \frac{z0 \cdot z1}{1 - z1} \cdot \color{blue}{\frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)}} \]

   6. Applied rewrites 55.5%

      \[\leadsto \color{blue}{\frac{z0 \cdot z1}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right) \leq 400:\\ \;\;\;\;z0 \cdot \frac{z0 \cdot z1}{\left(1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (if (<= (tan (* PI (- (+ z2 z2) -0.5))) 400.0)
  (*
   z0
   (/
    (* z0 z1)
    (*
     (- 1.0 (cos (* (atan (* (tan (* 0.5 PI)) (/ z0 z3))) 2.0)))
     (- 1.0 z1))))
  (*
   (/ (* z1 z0) (- 1.0 z1))
   (/
    z0
    (- 1.0 (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0)))))))

C

double code(double z1, double z0, double z3, double z2) {
	double tmp;
	if (tan((((double) M_PI) * ((z2 + z2) - -0.5))) <= 400.0) {
		tmp = z0 * ((z0 * z1) / ((1.0 - cos((atan((tan((0.5 * ((double) M_PI))) * (z0 / z3))) * 2.0))) * (1.0 - z1)));
	} else {
		tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0))));
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double tmp;
	if (Math.tan((Math.PI * ((z2 + z2) - -0.5))) <= 400.0) {
		tmp = z0 * ((z0 * z1) / ((1.0 - Math.cos((Math.atan((Math.tan((0.5 * Math.PI)) * (z0 / z3))) * 2.0))) * (1.0 - z1)));
	} else {
		tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0))));
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	tmp = 0
	if math.tan((math.pi * ((z2 + z2) - -0.5))) <= 400.0:
		tmp = z0 * ((z0 * z1) / ((1.0 - math.cos((math.atan((math.tan((0.5 * math.pi)) * (z0 / z3))) * 2.0))) * (1.0 - z1)))
	else:
		tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))))
	return tmp

Julia

function code(z1, z0, z3, z2)
	tmp = 0.0
	if (tan(Float64(pi * Float64(Float64(z2 + z2) - -0.5))) <= 400.0)
		tmp = Float64(z0 * Float64(Float64(z0 * z1) / Float64(Float64(1.0 - cos(Float64(atan(Float64(tan(Float64(0.5 * pi)) * Float64(z0 / z3))) * 2.0))) * Float64(1.0 - z1))));
	else
		tmp = Float64(Float64(Float64(z1 * z0) / Float64(1.0 - z1)) * Float64(z0 / Float64(1.0 - cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	tmp = 0.0;
	if (tan((pi * ((z2 + z2) - -0.5))) <= 400.0)
		tmp = z0 * ((z0 * z1) / ((1.0 - cos((atan((tan((0.5 * pi)) * (z0 / z3))) * 2.0))) * (1.0 - z1)));
	else
		tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := If[LessEqual[N[Tan[N[(Pi * N[(N[(z2 + z2), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 400.0], N[(z0 * N[(N[(z0 * z1), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[Tan[N[(0.5 * Pi), $MachinePrecision]], $MachinePrecision] * N[(z0 / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z1 * z0), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(z0 / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64)))) < 400

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.2%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{0.5}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z0\right) \cdot z1}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z0\right)} \cdot z1}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot \left(z0 \cdot z1\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot \color{blue}{\left(z0 \cdot z1\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{z0 \cdot \frac{z0 \cdot z1}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \frac{z0 \cdot z1}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      9. lower-/.f64 55.4%

         \[\leadsto z0 \cdot \color{blue}{\frac{z0 \cdot z1}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)\right) \cdot \left(1 - z1\right)}} \]

   6. Applied rewrites 55.4%

      \[\leadsto \color{blue}{z0 \cdot \frac{z0 \cdot z1}{\left(1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)\right) \cdot \left(1 - z1\right)}} \]

   if 400 < (tan.f64 (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64))))

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right)}} \]

      7. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)}} \]

   8. Applied rewrites 54.6%

      \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 57.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)}\\ t_1 := \frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-312}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{-136}:\\ \;\;\;\;\frac{z0 \cdot z0}{\left(1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)\right) \cdot 1} \cdot z1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0
        (/
         (* z1 (* z0 z0))
         (*
          (-
           1.0
           (cos
            (*
             -2.0
             (atan (* (/ z0 z3) (tan (* PI (- (+ z2 z2) -0.5))))))))
          (- 1.0 z1))))
       (t_1
        (*
         (/ (* z1 z0) (- 1.0 z1))
         (/
          z0
          (-
           1.0
           (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0)))))))
  (if (<= t_0 -2e-312)
    t_1
    (if (<= t_0 1e-136)
      (*
       (/
        (* z0 z0)
        (*
         (- 1.0 (cos (* (atan (* (tan (* 0.5 PI)) (/ z0 z3))) 2.0)))
         1.0))
       z1)
      t_1))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan(((z0 / z3) * tan((((double) M_PI) * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
	double t_1 = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0))));
	double tmp;
	if (t_0 <= -2e-312) {
		tmp = t_1;
	} else if (t_0 <= 1e-136) {
		tmp = ((z0 * z0) / ((1.0 - cos((atan((tan((0.5 * ((double) M_PI))) * (z0 / z3))) * 2.0))) * 1.0)) * z1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = (z1 * (z0 * z0)) / ((1.0 - Math.cos((-2.0 * Math.atan(((z0 / z3) * Math.tan((Math.PI * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
	double t_1 = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0))));
	double tmp;
	if (t_0 <= -2e-312) {
		tmp = t_1;
	} else if (t_0 <= 1e-136) {
		tmp = ((z0 * z0) / ((1.0 - Math.cos((Math.atan((Math.tan((0.5 * Math.PI)) * (z0 / z3))) * 2.0))) * 1.0)) * z1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = (z1 * (z0 * z0)) / ((1.0 - math.cos((-2.0 * math.atan(((z0 / z3) * math.tan((math.pi * ((z2 + z2) - -0.5)))))))) * (1.0 - z1))
	t_1 = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))))
	tmp = 0
	if t_0 <= -2e-312:
		tmp = t_1
	elif t_0 <= 1e-136:
		tmp = ((z0 * z0) / ((1.0 - math.cos((math.atan((math.tan((0.5 * math.pi)) * (z0 / z3))) * 2.0))) * 1.0)) * z1
	else:
		tmp = t_1
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(Float64(z1 * Float64(z0 * z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(z0 / z3) * tan(Float64(pi * Float64(Float64(z2 + z2) - -0.5)))))))) * Float64(1.0 - z1)))
	t_1 = Float64(Float64(Float64(z1 * z0) / Float64(1.0 - z1)) * Float64(z0 / Float64(1.0 - cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0)))))
	tmp = 0.0
	if (t_0 <= -2e-312)
		tmp = t_1;
	elseif (t_0 <= 1e-136)
		tmp = Float64(Float64(Float64(z0 * z0) / Float64(Float64(1.0 - cos(Float64(atan(Float64(tan(Float64(0.5 * pi)) * Float64(z0 / z3))) * 2.0))) * 1.0)) * z1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan(((z0 / z3) * tan((pi * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
	t_1 = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0))));
	tmp = 0.0;
	if (t_0 <= -2e-312)
		tmp = t_1;
	elseif (t_0 <= 1e-136)
		tmp = ((z0 * z0) / ((1.0 - cos((atan((tan((0.5 * pi)) * (z0 / z3))) * 2.0))) * 1.0)) * z1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(N[(z1 * N[(z0 * z0), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(z0 / z3), $MachinePrecision] * N[Tan[N[(Pi * N[(N[(z2 + z2), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(z1 * z0), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(z0 / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e-312], t$95$1, If[LessEqual[t$95$0, 1e-136], N[(N[(N[(z0 * z0), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[Tan[N[(0.5 * Pi), $MachinePrecision]], $MachinePrecision] * N[(z0 / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z1 (*.f64 z0 z0)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) (atan.f64 (*.f64 (/.f64 z0 z3) (tan.f64 (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64))))))))) (-.f64 #s(literal 1 binary64) z1))) < -2.0000000000018713e-312 or 1e-136 < (/.f64 (*.f64 z1 (*.f64 z0 z0)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) (atan.f64 (*.f64 (/.f64 z0 z3) (tan.f64 (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64))))))))) (-.f64 #s(literal 1 binary64) z1)))

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right)}} \]

      7. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)}} \]

   8. Applied rewrites 54.6%

      \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}} \]

   if -2.0000000000018713e-312 < (/.f64 (*.f64 z1 (*.f64 z0 z0)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) (atan.f64 (*.f64 (/.f64 z0 z3) (tan.f64 (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64))))))))) (-.f64 #s(literal 1 binary64) z1))) < 1e-136

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.2%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{0.5}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)\right) \cdot \color{blue}{1}} \]
   6. Step-by-step derivation

   7. Applied rewrites 31.7%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)\right) \cdot \color{blue}{1}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \cdot z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \cdot z1} \]

   9. Applied rewrites 31.8%

      \[\leadsto \color{blue}{\frac{z0 \cdot z0}{\left(1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)\right) \cdot 1} \cdot z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 55.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)}\\ t_1 := \frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-312}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq \infty:\\ \;\;\;\;\left(z0 \cdot z1\right) \cdot \frac{z0}{\left(1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)\right) \cdot 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0
        (/
         (* z1 (* z0 z0))
         (*
          (-
           1.0
           (cos
            (*
             -2.0
             (atan (* (/ z0 z3) (tan (* PI (- (+ z2 z2) -0.5))))))))
          (- 1.0 z1))))
       (t_1
        (*
         (/ (* z1 z0) (- 1.0 z1))
         (/
          z0
          (-
           1.0
           (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0)))))))
  (if (<= t_0 -2e-312)
    t_1
    (if (<= t_0 INFINITY)
      (*
       (* z0 z1)
       (/
        z0
        (*
         (- 1.0 (cos (* (atan (* (tan (* 0.5 PI)) (/ z0 z3))) 2.0)))
         1.0)))
      t_1))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan(((z0 / z3) * tan((((double) M_PI) * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
	double t_1 = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0))));
	double tmp;
	if (t_0 <= -2e-312) {
		tmp = t_1;
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = (z0 * z1) * (z0 / ((1.0 - cos((atan((tan((0.5 * ((double) M_PI))) * (z0 / z3))) * 2.0))) * 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = (z1 * (z0 * z0)) / ((1.0 - Math.cos((-2.0 * Math.atan(((z0 / z3) * Math.tan((Math.PI * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
	double t_1 = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0))));
	double tmp;
	if (t_0 <= -2e-312) {
		tmp = t_1;
	} else if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = (z0 * z1) * (z0 / ((1.0 - Math.cos((Math.atan((Math.tan((0.5 * Math.PI)) * (z0 / z3))) * 2.0))) * 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = (z1 * (z0 * z0)) / ((1.0 - math.cos((-2.0 * math.atan(((z0 / z3) * math.tan((math.pi * ((z2 + z2) - -0.5)))))))) * (1.0 - z1))
	t_1 = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))))
	tmp = 0
	if t_0 <= -2e-312:
		tmp = t_1
	elif t_0 <= math.inf:
		tmp = (z0 * z1) * (z0 / ((1.0 - math.cos((math.atan((math.tan((0.5 * math.pi)) * (z0 / z3))) * 2.0))) * 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(Float64(z1 * Float64(z0 * z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(Float64(z0 / z3) * tan(Float64(pi * Float64(Float64(z2 + z2) - -0.5)))))))) * Float64(1.0 - z1)))
	t_1 = Float64(Float64(Float64(z1 * z0) / Float64(1.0 - z1)) * Float64(z0 / Float64(1.0 - cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0)))))
	tmp = 0.0
	if (t_0 <= -2e-312)
		tmp = t_1;
	elseif (t_0 <= Inf)
		tmp = Float64(Float64(z0 * z1) * Float64(z0 / Float64(Float64(1.0 - cos(Float64(atan(Float64(tan(Float64(0.5 * pi)) * Float64(z0 / z3))) * 2.0))) * 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan(((z0 / z3) * tan((pi * ((z2 + z2) - -0.5)))))))) * (1.0 - z1));
	t_1 = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0))));
	tmp = 0.0;
	if (t_0 <= -2e-312)
		tmp = t_1;
	elseif (t_0 <= Inf)
		tmp = (z0 * z1) * (z0 / ((1.0 - cos((atan((tan((0.5 * pi)) * (z0 / z3))) * 2.0))) * 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(N[(z1 * N[(z0 * z0), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(N[(z0 / z3), $MachinePrecision] * N[Tan[N[(Pi * N[(N[(z2 + z2), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(z1 * z0), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(z0 / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e-312], t$95$1, If[LessEqual[t$95$0, Infinity], N[(N[(z0 * z1), $MachinePrecision] * N[(z0 / N[(N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[Tan[N[(0.5 * Pi), $MachinePrecision]], $MachinePrecision] * N[(z0 / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z1 (*.f64 z0 z0)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) (atan.f64 (*.f64 (/.f64 z0 z3) (tan.f64 (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64))))))))) (-.f64 #s(literal 1 binary64) z1))) < -2.0000000000018713e-312 or +inf.0 < (/.f64 (*.f64 z1 (*.f64 z0 z0)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) (atan.f64 (*.f64 (/.f64 z0 z3) (tan.f64 (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64))))))))) (-.f64 #s(literal 1 binary64) z1)))

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right)}} \]

      7. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)}} \]

   8. Applied rewrites 54.6%

      \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}} \]

   if -2.0000000000018713e-312 < (/.f64 (*.f64 z1 (*.f64 z0 z0)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) (atan.f64 (*.f64 (/.f64 z0 z3) (tan.f64 (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64))))))))) (-.f64 #s(literal 1 binary64) z1))) < +inf.0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.2%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \color{blue}{0.5}\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)\right) \cdot \color{blue}{1}} \]
   6. Step-by-step derivation

   7. Applied rewrites 31.7%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)\right) \cdot \color{blue}{1}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \]

      6. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z1 \cdot z0\right) \cdot \frac{z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1}} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z1 \cdot z0\right) \cdot \frac{z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1}} \]

      8. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(z1 \cdot z0\right)} \cdot \frac{z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{\left(z0 \cdot z1\right)} \cdot \frac{z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \]

      10. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(z0 \cdot z1\right)} \cdot \frac{z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \frac{1}{2}\right)\right)\right)\right) \cdot 1} \]

      11. lower-/.f64 36.4%

          \[\leadsto \left(z0 \cdot z1\right) \cdot \color{blue}{\frac{z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot 0.5\right)\right)\right)\right) \cdot 1}} \]

   9. Applied rewrites 36.4%

      \[\leadsto \color{blue}{\left(z0 \cdot z1\right) \cdot \frac{z0}{\left(1 - \cos \left(\tan^{-1} \left(\tan \left(0.5 \cdot \pi\right) \cdot \frac{z0}{z3}\right) \cdot 2\right)\right) \cdot 1}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(z2 + z2\right) - -0.5\\ \mathbf{if}\;\pi \cdot t\_0 \leq 5 \cdot 10^{+206}:\\ \;\;\;\;\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0 \cdot z0}{\cos \left(\tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(t\_0 \cdot \pi\right)\right) \cdot -2\right) - 1}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0 (- (+ z2 z2) -0.5)))
  (if (<= (* PI t_0) 5e+206)
    (*
     (/ (* z1 z0) (- 1.0 z1))
     (/
      z0
      (- 1.0 (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0)))))
    (/
     (* z0 z0)
     (- (cos (* (atan (* (/ z0 z3) (tan (* t_0 PI)))) -2.0)) 1.0)))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = (z2 + z2) - -0.5;
	double tmp;
	if ((((double) M_PI) * t_0) <= 5e+206) {
		tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0))));
	} else {
		tmp = (z0 * z0) / (cos((atan(((z0 / z3) * tan((t_0 * ((double) M_PI))))) * -2.0)) - 1.0);
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = (z2 + z2) - -0.5;
	double tmp;
	if ((Math.PI * t_0) <= 5e+206) {
		tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0))));
	} else {
		tmp = (z0 * z0) / (Math.cos((Math.atan(((z0 / z3) * Math.tan((t_0 * Math.PI)))) * -2.0)) - 1.0);
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = (z2 + z2) - -0.5
	tmp = 0
	if (math.pi * t_0) <= 5e+206:
		tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))))
	else:
		tmp = (z0 * z0) / (math.cos((math.atan(((z0 / z3) * math.tan((t_0 * math.pi)))) * -2.0)) - 1.0)
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(Float64(z2 + z2) - -0.5)
	tmp = 0.0
	if (Float64(pi * t_0) <= 5e+206)
		tmp = Float64(Float64(Float64(z1 * z0) / Float64(1.0 - z1)) * Float64(z0 / Float64(1.0 - cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0)))));
	else
		tmp = Float64(Float64(z0 * z0) / Float64(cos(Float64(atan(Float64(Float64(z0 / z3) * tan(Float64(t_0 * pi)))) * -2.0)) - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = (z2 + z2) - -0.5;
	tmp = 0.0;
	if ((pi * t_0) <= 5e+206)
		tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0))));
	else
		tmp = (z0 * z0) / (cos((atan(((z0 / z3) * tan((t_0 * pi)))) * -2.0)) - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(N[(z2 + z2), $MachinePrecision] - -0.5), $MachinePrecision]}, If[LessEqual[N[(Pi * t$95$0), $MachinePrecision], 5e+206], N[(N[(N[(z1 * z0), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(z0 / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z0 * z0), $MachinePrecision] / N[(N[Cos[N[(N[ArcTan[N[(N[(z0 / z3), $MachinePrecision] * N[Tan[N[(t$95$0 * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64))) < 5.0000000000000002e206

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right)}} \]

      7. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)}} \]

   8. Applied rewrites 54.6%

      \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}} \]

   if 5.0000000000000002e206 < (*.f64 (PI.f64) (-.f64 (+.f64 z2 z2) #s(literal -1/2 binary64)))

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z1 around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{{z0}^{2}}{1 - \cos \left(-2 \cdot \tan^{-1} \left(-1 \cdot \frac{z0 \cdot \cos \left(2 \cdot \left(z2 \cdot \pi\right)\right)}{z3 \cdot \sin \left(2 \cdot \left(z2 \cdot \pi\right)\right)}\right)\right)}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\frac{{z0}^{2}}{1 - \cos \left(-2 \cdot \tan^{-1} \left(-1 \cdot \frac{z0 \cdot \cos \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}{z3 \cdot \sin \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}\right)\right)}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{{z0}^{2}}{\color{blue}{1 - \cos \left(-2 \cdot \tan^{-1} \left(-1 \cdot \frac{z0 \cdot \cos \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}{z3 \cdot \sin \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}\right)\right)}} \]

      3. lower-pow.f64 N/A

         \[\leadsto -1 \cdot \frac{{z0}^{2}}{\color{blue}{1} - \cos \left(-2 \cdot \tan^{-1} \left(-1 \cdot \frac{z0 \cdot \cos \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}{z3 \cdot \sin \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot \frac{{z0}^{2}}{1 - \color{blue}{\cos \left(-2 \cdot \tan^{-1} \left(-1 \cdot \frac{z0 \cdot \cos \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}{z3 \cdot \sin \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}\right)\right)}} \]

      5. lower-cos.f64 N/A

         \[\leadsto -1 \cdot \frac{{z0}^{2}}{1 - \cos \left(-2 \cdot \tan^{-1} \left(-1 \cdot \frac{z0 \cdot \cos \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}{z3 \cdot \sin \left(2 \cdot \left(z2 \cdot \mathsf{PI}\left(\right)\right)\right)}\right)\right)} \]

   6. Applied rewrites 38.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{{z0}^{2}}{1 - \cos \left(-2 \cdot \tan^{-1} \left(-1 \cdot \frac{z0 \cdot \cos \left(2 \cdot \left(z2 \cdot \pi\right)\right)}{z3 \cdot \sin \left(2 \cdot \left(z2 \cdot \pi\right)\right)}\right)\right)}} \]

   8. Applied rewrites 31.5%

      \[\leadsto \frac{z0 \cdot z0}{\color{blue}{\cos \left(\tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\left(\left(z2 + z2\right) - -0.5\right) \cdot \pi\right)\right) \cdot -2\right) - 1}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 55.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left(z1 \cdot \left|z0\right|\right) \cdot \left|z0\right|}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{\left|z0\right|}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{if}\;\left|z0\right| \leq 5 \cdot 10^{-30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\left|z0\right| \leq 3.7 \cdot 10^{+153}:\\ \;\;\;\;z1 \cdot \frac{\left|z0\right| \cdot \left|z0\right|}{\left(1 - \cos \left(\tan^{-1} \left(\frac{\left|z0\right|}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right) \cdot \left(1 - z1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0
        (/
         (* (* z1 (fabs z0)) (fabs z0))
         (*
          (-
           1.0
           (cos
            (* -2.0 (atan (* -0.5 (/ (fabs z0) (* z2 (* z3 PI))))))))
          (- 1.0 z1)))))
  (if (<= (fabs z0) 5e-30)
    t_0
    (if (<= (fabs z0) 3.7e+153)
      (*
       z1
       (/
        (* (fabs z0) (fabs z0))
        (*
         (-
          1.0
          (cos
           (* (atan (* (/ (fabs z0) (* (* z3 PI) z2)) -0.5)) 2.0)))
         (- 1.0 z1))))
      t_0))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = ((z1 * fabs(z0)) * fabs(z0)) / ((1.0 - cos((-2.0 * atan((-0.5 * (fabs(z0) / (z2 * (z3 * ((double) M_PI))))))))) * (1.0 - z1));
	double tmp;
	if (fabs(z0) <= 5e-30) {
		tmp = t_0;
	} else if (fabs(z0) <= 3.7e+153) {
		tmp = z1 * ((fabs(z0) * fabs(z0)) / ((1.0 - cos((atan(((fabs(z0) / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0))) * (1.0 - z1)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = ((z1 * Math.abs(z0)) * Math.abs(z0)) / ((1.0 - Math.cos((-2.0 * Math.atan((-0.5 * (Math.abs(z0) / (z2 * (z3 * Math.PI)))))))) * (1.0 - z1));
	double tmp;
	if (Math.abs(z0) <= 5e-30) {
		tmp = t_0;
	} else if (Math.abs(z0) <= 3.7e+153) {
		tmp = z1 * ((Math.abs(z0) * Math.abs(z0)) / ((1.0 - Math.cos((Math.atan(((Math.abs(z0) / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0))) * (1.0 - z1)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = ((z1 * math.fabs(z0)) * math.fabs(z0)) / ((1.0 - math.cos((-2.0 * math.atan((-0.5 * (math.fabs(z0) / (z2 * (z3 * math.pi)))))))) * (1.0 - z1))
	tmp = 0
	if math.fabs(z0) <= 5e-30:
		tmp = t_0
	elif math.fabs(z0) <= 3.7e+153:
		tmp = z1 * ((math.fabs(z0) * math.fabs(z0)) / ((1.0 - math.cos((math.atan(((math.fabs(z0) / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))) * (1.0 - z1)))
	else:
		tmp = t_0
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(Float64(Float64(z1 * abs(z0)) * abs(z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(-0.5 * Float64(abs(z0) / Float64(z2 * Float64(z3 * pi)))))))) * Float64(1.0 - z1)))
	tmp = 0.0
	if (abs(z0) <= 5e-30)
		tmp = t_0;
	elseif (abs(z0) <= 3.7e+153)
		tmp = Float64(z1 * Float64(Float64(abs(z0) * abs(z0)) / Float64(Float64(1.0 - cos(Float64(atan(Float64(Float64(abs(z0) / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0))) * Float64(1.0 - z1))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = ((z1 * abs(z0)) * abs(z0)) / ((1.0 - cos((-2.0 * atan((-0.5 * (abs(z0) / (z2 * (z3 * pi)))))))) * (1.0 - z1));
	tmp = 0.0;
	if (abs(z0) <= 5e-30)
		tmp = t_0;
	elseif (abs(z0) <= 3.7e+153)
		tmp = z1 * ((abs(z0) * abs(z0)) / ((1.0 - cos((atan(((abs(z0) / ((z3 * pi) * z2)) * -0.5)) * 2.0))) * (1.0 - z1)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(N[(N[(z1 * N[Abs[z0], $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(-0.5 * N[(N[Abs[z0], $MachinePrecision] / N[(z2 * N[(z3 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Abs[z0], $MachinePrecision], 5e-30], t$95$0, If[LessEqual[N[Abs[z0], $MachinePrecision], 3.7e+153], N[(z1 * N[(N[(N[Abs[z0], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(N[Abs[z0], $MachinePrecision] / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z0 < 4.9999999999999997e-30 or 3.7000000000000002e153 < z0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 52.0%

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 52.0%

      \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   if 4.9999999999999997e-30 < z0 < 3.7000000000000002e153

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      5. lower-/.f64 48.9%

         \[\leadsto z1 \cdot \color{blue}{\frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

   8. Applied rewrites 48.9%

      \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right) \cdot \left(1 - z1\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 54.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left|z0\right| \leq 3.7 \cdot 10^{+153}:\\ \;\;\;\;\frac{\left|z0\right| \cdot \left|z0\right|}{1 - \cos \left(\tan^{-1} \left(\frac{\left|z0\right|}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)} \cdot \frac{z1}{1 - z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z1 \cdot \left|z0\right|\right) \cdot \left|z0\right|}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{\left|z0\right|}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (if (<= (fabs z0) 3.7e+153)
  (*
   (/
    (* (fabs z0) (fabs z0))
    (-
     1.0
     (cos (* (atan (* (/ (fabs z0) (* (* z3 PI) z2)) -0.5)) 2.0))))
   (/ z1 (- 1.0 z1)))
  (/
   (* (* z1 (fabs z0)) (fabs z0))
   (*
    (-
     1.0
     (cos (* -2.0 (atan (* -0.5 (/ (fabs z0) (* z2 (* z3 PI))))))))
    (- 1.0 z1)))))

C

double code(double z1, double z0, double z3, double z2) {
	double tmp;
	if (fabs(z0) <= 3.7e+153) {
		tmp = ((fabs(z0) * fabs(z0)) / (1.0 - cos((atan(((fabs(z0) / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0)))) * (z1 / (1.0 - z1));
	} else {
		tmp = ((z1 * fabs(z0)) * fabs(z0)) / ((1.0 - cos((-2.0 * atan((-0.5 * (fabs(z0) / (z2 * (z3 * ((double) M_PI))))))))) * (1.0 - z1));
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double tmp;
	if (Math.abs(z0) <= 3.7e+153) {
		tmp = ((Math.abs(z0) * Math.abs(z0)) / (1.0 - Math.cos((Math.atan(((Math.abs(z0) / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0)))) * (z1 / (1.0 - z1));
	} else {
		tmp = ((z1 * Math.abs(z0)) * Math.abs(z0)) / ((1.0 - Math.cos((-2.0 * Math.atan((-0.5 * (Math.abs(z0) / (z2 * (z3 * Math.PI)))))))) * (1.0 - z1));
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	tmp = 0
	if math.fabs(z0) <= 3.7e+153:
		tmp = ((math.fabs(z0) * math.fabs(z0)) / (1.0 - math.cos((math.atan(((math.fabs(z0) / ((z3 * math.pi) * z2)) * -0.5)) * 2.0)))) * (z1 / (1.0 - z1))
	else:
		tmp = ((z1 * math.fabs(z0)) * math.fabs(z0)) / ((1.0 - math.cos((-2.0 * math.atan((-0.5 * (math.fabs(z0) / (z2 * (z3 * math.pi)))))))) * (1.0 - z1))
	return tmp

Julia

function code(z1, z0, z3, z2)
	tmp = 0.0
	if (abs(z0) <= 3.7e+153)
		tmp = Float64(Float64(Float64(abs(z0) * abs(z0)) / Float64(1.0 - cos(Float64(atan(Float64(Float64(abs(z0) / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0)))) * Float64(z1 / Float64(1.0 - z1)));
	else
		tmp = Float64(Float64(Float64(z1 * abs(z0)) * abs(z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(-0.5 * Float64(abs(z0) / Float64(z2 * Float64(z3 * pi)))))))) * Float64(1.0 - z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	tmp = 0.0;
	if (abs(z0) <= 3.7e+153)
		tmp = ((abs(z0) * abs(z0)) / (1.0 - cos((atan(((abs(z0) / ((z3 * pi) * z2)) * -0.5)) * 2.0)))) * (z1 / (1.0 - z1));
	else
		tmp = ((z1 * abs(z0)) * abs(z0)) / ((1.0 - cos((-2.0 * atan((-0.5 * (abs(z0) / (z2 * (z3 * pi)))))))) * (1.0 - z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := If[LessEqual[N[Abs[z0], $MachinePrecision], 3.7e+153], N[(N[(N[(N[Abs[z0], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(N[Abs[z0], $MachinePrecision] / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z1 / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z1 * N[Abs[z0], $MachinePrecision]), $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(-0.5 * N[(N[Abs[z0], $MachinePrecision] / N[(z2 * N[(z3 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z0 < 3.7000000000000002e153

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(z0 \cdot z0\right) \cdot z1}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 \cdot z0\right) \cdot z1}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      5. times-frac N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)} \cdot \frac{z1}{1 - z1}} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)} \cdot \frac{z1}{1 - z1}} \]

   8. Applied rewrites 51.0%

      \[\leadsto \color{blue}{\frac{z0 \cdot z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)} \cdot \frac{z1}{1 - z1}} \]

   if 3.7000000000000002e153 < z0

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-*.f64 52.0%

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   8. Applied rewrites 52.0%

      \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 54.6% accurate, 1.4× speedup

Math

\[\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (*
 (/ (* z1 z0) (- 1.0 z1))
 (/ z0 (- 1.0 (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0))))))

C

double code(double z1, double z0, double z3, double z2) {
	return ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0))));
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	return ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0))));
}

Python

def code(z1, z0, z3, z2):
	return ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))))

Julia

function code(z1, z0, z3, z2)
	return Float64(Float64(Float64(z1 * z0) / Float64(1.0 - z1)) * Float64(z0 / Float64(1.0 - cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0)))))
end

MATLAB

function tmp = code(z1, z0, z3, z2)
	tmp = ((z1 * z0) / (1.0 - z1)) * (z0 / (1.0 - cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0))));
end

Wolfram

code[z1_, z0_, z3_, z2_] := N[(N[(N[(z1 * z0), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision] * N[(z0 / N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 46.2%

   \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   3. lift-tan.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   4. tan-quot N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   5. frac-times N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   6. *-commutative N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   7. lower-/.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

3. Applied rewrites 53.5%

   \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

4. Taylor expanded in z2 around 0

   \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
5. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   3. lower-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   4. lower-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   5. lower-PI.f64 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

6. Applied rewrites 47.0%

   \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
7. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   4. associate-*r* N/A

      \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

   6. *-commutative N/A

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot z0}{\color{blue}{\left(1 - z1\right) \cdot \left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right)}} \]

   7. times-frac N/A

      \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)}} \]

8. Applied rewrites 54.6%

   \[\leadsto \color{blue}{\frac{z1 \cdot z0}{1 - z1} \cdot \frac{z0}{1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)}} \]
9. Add Preprocessing

Alternative 14: 52.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := 1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\\ \mathbf{if}\;z1 \leq -6.8 \cdot 10^{-29}:\\ \;\;\;\;z1 \cdot \frac{z0 \cdot z0}{t\_0 \cdot \left(1 - z1\right)}\\ \mathbf{elif}\;z1 \leq 2.15 \cdot 10^{+17}:\\ \;\;\;\;z0 \cdot \frac{z0 \cdot z1}{1 \cdot t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0
        (-
         1.0
         (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0)))))
  (if (<= z1 -6.8e-29)
    (* z1 (/ (* z0 z0) (* t_0 (- 1.0 z1))))
    (if (<= z1 2.15e+17)
      (* z0 (/ (* z0 z1) (* 1.0 t_0)))
      (/
       (* z1 (* z0 z0))
       (*
        (- 1.0 (cos (* -2.0 (atan (* -0.5 (/ z0 (* z2 (* z3 PI))))))))
        (- 1.0 z1)))))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = 1.0 - cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0));
	double tmp;
	if (z1 <= -6.8e-29) {
		tmp = z1 * ((z0 * z0) / (t_0 * (1.0 - z1)));
	} else if (z1 <= 2.15e+17) {
		tmp = z0 * ((z0 * z1) / (1.0 * t_0));
	} else {
		tmp = (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan((-0.5 * (z0 / (z2 * (z3 * ((double) M_PI))))))))) * (1.0 - z1));
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = 1.0 - Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0));
	double tmp;
	if (z1 <= -6.8e-29) {
		tmp = z1 * ((z0 * z0) / (t_0 * (1.0 - z1)));
	} else if (z1 <= 2.15e+17) {
		tmp = z0 * ((z0 * z1) / (1.0 * t_0));
	} else {
		tmp = (z1 * (z0 * z0)) / ((1.0 - Math.cos((-2.0 * Math.atan((-0.5 * (z0 / (z2 * (z3 * Math.PI)))))))) * (1.0 - z1));
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = 1.0 - math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))
	tmp = 0
	if z1 <= -6.8e-29:
		tmp = z1 * ((z0 * z0) / (t_0 * (1.0 - z1)))
	elif z1 <= 2.15e+17:
		tmp = z0 * ((z0 * z1) / (1.0 * t_0))
	else:
		tmp = (z1 * (z0 * z0)) / ((1.0 - math.cos((-2.0 * math.atan((-0.5 * (z0 / (z2 * (z3 * math.pi)))))))) * (1.0 - z1))
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(1.0 - cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0)))
	tmp = 0.0
	if (z1 <= -6.8e-29)
		tmp = Float64(z1 * Float64(Float64(z0 * z0) / Float64(t_0 * Float64(1.0 - z1))));
	elseif (z1 <= 2.15e+17)
		tmp = Float64(z0 * Float64(Float64(z0 * z1) / Float64(1.0 * t_0)));
	else
		tmp = Float64(Float64(z1 * Float64(z0 * z0)) / Float64(Float64(1.0 - cos(Float64(-2.0 * atan(Float64(-0.5 * Float64(z0 / Float64(z2 * Float64(z3 * pi)))))))) * Float64(1.0 - z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = 1.0 - cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0));
	tmp = 0.0;
	if (z1 <= -6.8e-29)
		tmp = z1 * ((z0 * z0) / (t_0 * (1.0 - z1)));
	elseif (z1 <= 2.15e+17)
		tmp = z0 * ((z0 * z1) / (1.0 * t_0));
	else
		tmp = (z1 * (z0 * z0)) / ((1.0 - cos((-2.0 * atan((-0.5 * (z0 / (z2 * (z3 * pi)))))))) * (1.0 - z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z1, -6.8e-29], N[(z1 * N[(N[(z0 * z0), $MachinePrecision] / N[(t$95$0 * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 2.15e+17], N[(z0 * N[(N[(z0 * z1), $MachinePrecision] / N[(1.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z1 * N[(z0 * z0), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - N[Cos[N[(-2.0 * N[ArcTan[N[(-0.5 * N[(z0 / N[(z2 * N[(z3 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z1 < -6.7999999999999994e-29

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      5. lower-/.f64 48.9%

         \[\leadsto z1 \cdot \color{blue}{\frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

   8. Applied rewrites 48.9%

      \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right) \cdot \left(1 - z1\right)}} \]

   if -6.7999999999999994e-29 < z1 < 2.15e17

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   7. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
   8. Step-by-step derivation

   9. Applied rewrites 32.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
   10. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       4. associate-*l* N/A

          \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       5. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       6. *-commutative N/A

          \[\leadsto \frac{\color{blue}{z0 \cdot \left(z1 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       7. associate-/l* N/A

          \[\leadsto \color{blue}{z0 \cdot \frac{z1 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

       8. lower-*.f64 N/A

          \[\leadsto \color{blue}{z0 \cdot \frac{z1 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

   11. Applied rewrites 36.2%

       \[\leadsto \color{blue}{z0 \cdot \frac{z0 \cdot z1}{1 \cdot \left(1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right)}} \]

   if 2.15e17 < z1

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 51.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := 1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\\ t_1 := z1 \cdot \frac{z0 \cdot z0}{t\_0 \cdot \left(1 - z1\right)}\\ \mathbf{if}\;z1 \leq -6.8 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z1 \leq 2.15 \cdot 10^{+17}:\\ \;\;\;\;z0 \cdot \frac{z0 \cdot z1}{1 \cdot t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0
        (- 1.0 (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0))))
       (t_1 (* z1 (/ (* z0 z0) (* t_0 (- 1.0 z1))))))
  (if (<= z1 -6.8e-29)
    t_1
    (if (<= z1 2.15e+17) (* z0 (/ (* z0 z1) (* 1.0 t_0))) t_1))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = 1.0 - cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0));
	double t_1 = z1 * ((z0 * z0) / (t_0 * (1.0 - z1)));
	double tmp;
	if (z1 <= -6.8e-29) {
		tmp = t_1;
	} else if (z1 <= 2.15e+17) {
		tmp = z0 * ((z0 * z1) / (1.0 * t_0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = 1.0 - Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0));
	double t_1 = z1 * ((z0 * z0) / (t_0 * (1.0 - z1)));
	double tmp;
	if (z1 <= -6.8e-29) {
		tmp = t_1;
	} else if (z1 <= 2.15e+17) {
		tmp = z0 * ((z0 * z1) / (1.0 * t_0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = 1.0 - math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))
	t_1 = z1 * ((z0 * z0) / (t_0 * (1.0 - z1)))
	tmp = 0
	if z1 <= -6.8e-29:
		tmp = t_1
	elif z1 <= 2.15e+17:
		tmp = z0 * ((z0 * z1) / (1.0 * t_0))
	else:
		tmp = t_1
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = Float64(1.0 - cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0)))
	t_1 = Float64(z1 * Float64(Float64(z0 * z0) / Float64(t_0 * Float64(1.0 - z1))))
	tmp = 0.0
	if (z1 <= -6.8e-29)
		tmp = t_1;
	elseif (z1 <= 2.15e+17)
		tmp = Float64(z0 * Float64(Float64(z0 * z1) / Float64(1.0 * t_0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = 1.0 - cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0));
	t_1 = z1 * ((z0 * z0) / (t_0 * (1.0 - z1)));
	tmp = 0.0;
	if (z1 <= -6.8e-29)
		tmp = t_1;
	elseif (z1 <= 2.15e+17)
		tmp = z0 * ((z0 * z1) / (1.0 * t_0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z1 * N[(N[(z0 * z0), $MachinePrecision] / N[(t$95$0 * N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z1, -6.8e-29], t$95$1, If[LessEqual[z1, 2.15e+17], N[(z0 * N[(N[(z0 * z1), $MachinePrecision] / N[(1.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z1 < -6.7999999999999994e-29 or 2.15e17 < z1

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

      5. lower-/.f64 48.9%

         \[\leadsto z1 \cdot \color{blue}{\frac{z0 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)}} \]

   8. Applied rewrites 48.9%

      \[\leadsto \color{blue}{z1 \cdot \frac{z0 \cdot z0}{\left(1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right) \cdot \left(1 - z1\right)}} \]

   if -6.7999999999999994e-29 < z1 < 2.15e17

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   7. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
   8. Step-by-step derivation

   9. Applied rewrites 32.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
   10. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       4. associate-*l* N/A

          \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       5. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       6. *-commutative N/A

          \[\leadsto \frac{\color{blue}{z0 \cdot \left(z1 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       7. associate-/l* N/A

          \[\leadsto \color{blue}{z0 \cdot \frac{z1 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

       8. lower-*.f64 N/A

          \[\leadsto \color{blue}{z0 \cdot \frac{z1 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

   11. Applied rewrites 36.2%

       \[\leadsto \color{blue}{z0 \cdot \frac{z0 \cdot z1}{1 \cdot \left(1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 38.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_0 := \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\\ \mathbf{if}\;z1 \leq 2.45 \cdot 10^{+17}:\\ \;\;\;\;z0 \cdot \frac{z0 \cdot z1}{1 \cdot \left(1 - t\_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(-z0\right) \cdot z0\right) \cdot z1}{\left(t\_0 - 1\right) \cdot 1}\\ \end{array} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (let* ((t_0 (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0))))
  (if (<= z1 2.45e+17)
    (* z0 (/ (* z0 z1) (* 1.0 (- 1.0 t_0))))
    (/ (* (* (- z0) z0) z1) (* (- t_0 1.0) 1.0)))))

C

double code(double z1, double z0, double z3, double z2) {
	double t_0 = cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0));
	double tmp;
	if (z1 <= 2.45e+17) {
		tmp = z0 * ((z0 * z1) / (1.0 * (1.0 - t_0)));
	} else {
		tmp = ((-z0 * z0) * z1) / ((t_0 - 1.0) * 1.0);
	}
	return tmp;
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	double t_0 = Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0));
	double tmp;
	if (z1 <= 2.45e+17) {
		tmp = z0 * ((z0 * z1) / (1.0 * (1.0 - t_0)));
	} else {
		tmp = ((-z0 * z0) * z1) / ((t_0 - 1.0) * 1.0);
	}
	return tmp;
}

Python

def code(z1, z0, z3, z2):
	t_0 = math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0))
	tmp = 0
	if z1 <= 2.45e+17:
		tmp = z0 * ((z0 * z1) / (1.0 * (1.0 - t_0)))
	else:
		tmp = ((-z0 * z0) * z1) / ((t_0 - 1.0) * 1.0)
	return tmp

Julia

function code(z1, z0, z3, z2)
	t_0 = cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0))
	tmp = 0.0
	if (z1 <= 2.45e+17)
		tmp = Float64(z0 * Float64(Float64(z0 * z1) / Float64(1.0 * Float64(1.0 - t_0))));
	else
		tmp = Float64(Float64(Float64(Float64(-z0) * z0) * z1) / Float64(Float64(t_0 - 1.0) * 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0, z3, z2)
	t_0 = cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0));
	tmp = 0.0;
	if (z1 <= 2.45e+17)
		tmp = z0 * ((z0 * z1) / (1.0 * (1.0 - t_0)));
	else
		tmp = ((-z0 * z0) * z1) / ((t_0 - 1.0) * 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_, z3_, z2_] := Block[{t$95$0 = N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z1, 2.45e+17], N[(z0 * N[(N[(z0 * z1), $MachinePrecision] / N[(1.0 * N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[((-z0) * z0), $MachinePrecision] * z1), $MachinePrecision] / N[(N[(t$95$0 - 1.0), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z1 < 2.45e17

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   7. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
   8. Step-by-step derivation

   9. Applied rewrites 32.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
   10. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       4. associate-*l* N/A

          \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       5. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       6. *-commutative N/A

          \[\leadsto \frac{\color{blue}{z0 \cdot \left(z1 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

       7. associate-/l* N/A

          \[\leadsto \color{blue}{z0 \cdot \frac{z1 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

       8. lower-*.f64 N/A

          \[\leadsto \color{blue}{z0 \cdot \frac{z1 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

   11. Applied rewrites 36.2%

       \[\leadsto \color{blue}{z0 \cdot \frac{z0 \cdot z1}{1 \cdot \left(1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right)}} \]

   if 2.45e17 < z1

   1. Initial program 46.2%

      \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lift-tan.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. tan-quot N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. frac-times N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   3. Applied rewrites 53.5%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

      5. lower-PI.f64 47.0%

         \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   6. Applied rewrites 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   7. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
   8. Step-by-step derivation

   9. Applied rewrites 32.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
   10. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

       2. frac-2neg N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z1 \cdot \left(z0 \cdot z0\right)\right)}{\mathsf{neg}\left(\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1\right)}} \]

       3. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(z1 \cdot \left(z0 \cdot z0\right)\right)}{\mathsf{neg}\left(\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1\right)}} \]

   11. Applied rewrites 30.3%

       \[\leadsto \color{blue}{\frac{\left(\left(-z0\right) \cdot z0\right) \cdot z1}{\left(\cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right) - 1\right) \cdot 1}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 36.2% accurate, 1.4× speedup

Math

\[z0 \cdot \frac{z0 \cdot z1}{1 \cdot \left(1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right)} \]

FPCore

(FPCore (z1 z0 z3 z2)
  :precision binary64
  (*
 z0
 (/
  (* z0 z1)
  (*
   1.0
   (- 1.0 (cos (* (atan (* (/ z0 (* (* z3 PI) z2)) -0.5)) 2.0)))))))

C

double code(double z1, double z0, double z3, double z2) {
	return z0 * ((z0 * z1) / (1.0 * (1.0 - cos((atan(((z0 / ((z3 * ((double) M_PI)) * z2)) * -0.5)) * 2.0)))));
}

Java

public static double code(double z1, double z0, double z3, double z2) {
	return z0 * ((z0 * z1) / (1.0 * (1.0 - Math.cos((Math.atan(((z0 / ((z3 * Math.PI) * z2)) * -0.5)) * 2.0)))));
}

Python

def code(z1, z0, z3, z2):
	return z0 * ((z0 * z1) / (1.0 * (1.0 - math.cos((math.atan(((z0 / ((z3 * math.pi) * z2)) * -0.5)) * 2.0)))))

Julia

function code(z1, z0, z3, z2)
	return Float64(z0 * Float64(Float64(z0 * z1) / Float64(1.0 * Float64(1.0 - cos(Float64(atan(Float64(Float64(z0 / Float64(Float64(z3 * pi) * z2)) * -0.5)) * 2.0))))))
end

MATLAB

function tmp = code(z1, z0, z3, z2)
	tmp = z0 * ((z0 * z1) / (1.0 * (1.0 - cos((atan(((z0 / ((z3 * pi) * z2)) * -0.5)) * 2.0)))));
end

Wolfram

code[z1_, z0_, z3_, z2_] := N[(z0 * N[(N[(z0 * z1), $MachinePrecision] / N[(1.0 * N[(1.0 - N[Cos[N[(N[ArcTan[N[(N[(z0 / N[(N[(z3 * Pi), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 46.2%

   \[\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - -0.5\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0}{z3} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\color{blue}{\frac{z0}{z3}} \cdot \tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)\right)\right)\right) \cdot \left(1 - z1\right)} \]

   3. lift-tan.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\tan \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   4. tan-quot N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0}{z3} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   5. frac-times N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{z3 \cdot \cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

   6. *-commutative N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\color{blue}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   7. lower-/.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{z0 \cdot \sin \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right)}{\cos \left(\pi \cdot \left(\left(z2 + z2\right) - \frac{-1}{2}\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

3. Applied rewrites 53.5%

   \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(z2 + z2\right) \cdot \pi\right) \cdot z0}{\left(-\sin \left(\left(z2 + z2\right) \cdot \pi\right)\right) \cdot z3}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

4. Taylor expanded in z2 around 0

   \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]
5. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{z0}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{\color{blue}{z2 \cdot \left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   3. lower-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \color{blue}{\left(z3 \cdot \mathsf{PI}\left(\right)\right)}}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   4. lower-*.f64 N/A

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

   5. lower-PI.f64 47.0%

      \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \left(1 - z1\right)} \]

6. Applied rewrites 47.0%

   \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)}\right)\right) \cdot \left(1 - z1\right)} \]

7. Taylor expanded in z1 around 0

   \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
8. Step-by-step derivation

9. Applied rewrites 32.0%

   \[\leadsto \frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(-0.5 \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot \color{blue}{1}} \]
10. Step-by-step derivation

    1. lift-/.f64 N/A

       \[\leadsto \color{blue}{\frac{z1 \cdot \left(z0 \cdot z0\right)}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

    2. lift-*.f64 N/A

       \[\leadsto \frac{\color{blue}{z1 \cdot \left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

    3. lift-*.f64 N/A

       \[\leadsto \frac{z1 \cdot \color{blue}{\left(z0 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

    4. associate-*l* N/A

       \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot z0}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

    5. lift-*.f64 N/A

       \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right)} \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

    6. *-commutative N/A

       \[\leadsto \frac{\color{blue}{z0 \cdot \left(z1 \cdot z0\right)}}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1} \]

    7. associate-/l* N/A

       \[\leadsto \color{blue}{z0 \cdot \frac{z1 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

    8. lower-*.f64 N/A

       \[\leadsto \color{blue}{z0 \cdot \frac{z1 \cdot z0}{\left(1 - \cos \left(-2 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \frac{z0}{z2 \cdot \left(z3 \cdot \pi\right)}\right)\right)\right) \cdot 1}} \]

11. Applied rewrites 36.2%

    \[\leadsto \color{blue}{z0 \cdot \frac{z0 \cdot z1}{1 \cdot \left(1 - \cos \left(\tan^{-1} \left(\frac{z0}{\left(z3 \cdot \pi\right) \cdot z2} \cdot -0.5\right) \cdot 2\right)\right)}} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z1 z0 z3 z2)
  :name "(/ (* z1 (* z0 z0)) (* (- 1 (cos (* -2 (atan (* (/ z0 z3) (tan (* PI (- (+ z2 z2) -1/2)))))))) (- 1 z1)))"
  :precision binary64
  (/ (* z1 (* z0 z0)) (* (- 1.0 (cos (* -2.0 (atan (* (/ z0 z3) (tan (* PI (- (+ z2 z2) -0.5)))))))) (- 1.0 z1))))