(/ (- (- 1 (/ z0 (- (exp (/ -7853981852531433/2500000000000000 z1)) -1))) (/ (- 1 z0) (+ 1 (exp (/ PI z1))))) (+ (/ (- 1 z0) (+ 1 (exp (/ PI z1)))) (/ z0 (- (exp (/ -7853981852531433/2500000000000000 z1)) -1))))

Percentage Accurate: 66.4% → 92.8%

Time: 4.1s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} t_0 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_1 := \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}\\ \frac{\left(1 - t\_0\right) - t\_1}{t\_1 + t\_0} \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_1 (/ (- 1.0 z0) (+ 1.0 (exp (/ PI z1))))))
  (/ (- (- 1.0 t_0) t_1) (+ t_1 t_0))))

C

double code(double z0, double z1) {
	double t_0 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_1 = (1.0 - z0) / (1.0 + exp((((double) M_PI) / z1)));
	return ((1.0 - t_0) - t_1) / (t_1 + t_0);
}

Java

public static double code(double z0, double z1) {
	double t_0 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_1 = (1.0 - z0) / (1.0 + Math.exp((Math.PI / z1)));
	return ((1.0 - t_0) - t_1) / (t_1 + t_0);
}

Python

def code(z0, z1):
	t_0 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_1 = (1.0 - z0) / (1.0 + math.exp((math.pi / z1)))
	return ((1.0 - t_0) - t_1) / (t_1 + t_0)

Julia

function code(z0, z1)
	t_0 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_1 = Float64(Float64(1.0 - z0) / Float64(1.0 + exp(Float64(pi / z1))))
	return Float64(Float64(Float64(1.0 - t_0) - t_1) / Float64(t_1 + t_0))
end

MATLAB

function tmp = code(z0, z1)
	t_0 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_1 = (1.0 - z0) / (1.0 + exp((pi / z1)));
	tmp = ((1.0 - t_0) - t_1) / (t_1 + t_0);
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 - t$95$0), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(t$95$1 + t$95$0), $MachinePrecision]), $MachinePrecision]]]

Initial Program: 66.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_1 := \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}\\ \frac{\left(1 - t\_0\right) - t\_1}{t\_1 + t\_0} \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_1 (/ (- 1.0 z0) (+ 1.0 (exp (/ PI z1))))))
  (/ (- (- 1.0 t_0) t_1) (+ t_1 t_0))))

C

double code(double z0, double z1) {
	double t_0 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_1 = (1.0 - z0) / (1.0 + exp((((double) M_PI) / z1)));
	return ((1.0 - t_0) - t_1) / (t_1 + t_0);
}

Java

public static double code(double z0, double z1) {
	double t_0 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_1 = (1.0 - z0) / (1.0 + Math.exp((Math.PI / z1)));
	return ((1.0 - t_0) - t_1) / (t_1 + t_0);
}

Python

def code(z0, z1):
	t_0 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_1 = (1.0 - z0) / (1.0 + math.exp((math.pi / z1)))
	return ((1.0 - t_0) - t_1) / (t_1 + t_0)

Julia

function code(z0, z1)
	t_0 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_1 = Float64(Float64(1.0 - z0) / Float64(1.0 + exp(Float64(pi / z1))))
	return Float64(Float64(Float64(1.0 - t_0) - t_1) / Float64(t_1 + t_0))
end

MATLAB

function tmp = code(z0, z1)
	t_0 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_1 = (1.0 - z0) / (1.0 + exp((pi / z1)));
	tmp = ((1.0 - t_0) - t_1) / (t_1 + t_0);
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 - t$95$0), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(t$95$1 + t$95$0), $MachinePrecision]), $MachinePrecision]]]

Alternative 1: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{1}{1 + e^{\frac{\pi}{z1}}}\\ t_1 := e^{\frac{-3.1415927410125732}{z1}}\\ t_2 := \frac{z0}{t\_1 - -1}\\ t_3 := \frac{\left(1 - t\_2\right) - t\_0}{t\_0 + t\_2}\\ \mathbf{if}\;z1 \leq -2.4 \cdot 10^{+176}:\\ \;\;\;\;1 - 2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)\\ \mathbf{elif}\;z1 \leq -0.2:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z1 \leq 0.6:\\ \;\;\;\;\frac{-1 \cdot \left(z0 \cdot \left(\left(-1 \cdot \frac{1 - t\_0}{z0} + \frac{1}{1 + t\_1}\right) - t\_0\right)\right)}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + t\_2}\\ \mathbf{elif}\;z1 \leq 3.3 \cdot 10^{+99}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (/ 1.0 (+ 1.0 (exp (/ PI z1)))))
       (t_1 (exp (/ -3.1415927410125732 z1)))
       (t_2 (/ z0 (- t_1 -1.0)))
       (t_3 (/ (- (- 1.0 t_2) t_0) (+ t_0 t_2))))
  (if (<= z1 -2.4e+176)
    (-
     1.0
     (*
      2.0
      (*
       (- (* 0.7853981852531433 z0) (* -0.25 (- (* PI z0) PI)))
       (/ 2.0 z1))))
    (if (<= z1 -0.2)
      t_3
      (if (<= z1 0.6)
        (/
         (*
          -1.0
          (*
           z0
           (-
            (+ (* -1.0 (/ (- 1.0 t_0) z0)) (/ 1.0 (+ 1.0 t_1)))
            t_0)))
         (+ (/ (- 1.0 z0) (+ 1.0 (pow (exp PI) (/ 1.0 z1)))) t_2))
        (if (<= z1 3.3e+99)
          t_3
          (+
           1.0
           (*
            -1.0
            (/
             (-
              (* 2.0 (- (* -0.25 PI) (* -0.25 (* z0 PI))))
              (* 0.5 PI))
             z1)))))))))

C

double code(double z0, double z1) {
	double t_0 = 1.0 / (1.0 + exp((((double) M_PI) / z1)));
	double t_1 = exp((-3.1415927410125732 / z1));
	double t_2 = z0 / (t_1 - -1.0);
	double t_3 = ((1.0 - t_2) - t_0) / (t_0 + t_2);
	double tmp;
	if (z1 <= -2.4e+176) {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((((double) M_PI) * z0) - ((double) M_PI)))) * (2.0 / z1)));
	} else if (z1 <= -0.2) {
		tmp = t_3;
	} else if (z1 <= 0.6) {
		tmp = (-1.0 * (z0 * (((-1.0 * ((1.0 - t_0) / z0)) + (1.0 / (1.0 + t_1))) - t_0))) / (((1.0 - z0) / (1.0 + pow(exp(((double) M_PI)), (1.0 / z1)))) + t_2);
	} else if (z1 <= 3.3e+99) {
		tmp = t_3;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * ((double) M_PI)) - (-0.25 * (z0 * ((double) M_PI))))) - (0.5 * ((double) M_PI))) / z1));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = 1.0 / (1.0 + Math.exp((Math.PI / z1)));
	double t_1 = Math.exp((-3.1415927410125732 / z1));
	double t_2 = z0 / (t_1 - -1.0);
	double t_3 = ((1.0 - t_2) - t_0) / (t_0 + t_2);
	double tmp;
	if (z1 <= -2.4e+176) {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((Math.PI * z0) - Math.PI))) * (2.0 / z1)));
	} else if (z1 <= -0.2) {
		tmp = t_3;
	} else if (z1 <= 0.6) {
		tmp = (-1.0 * (z0 * (((-1.0 * ((1.0 - t_0) / z0)) + (1.0 / (1.0 + t_1))) - t_0))) / (((1.0 - z0) / (1.0 + Math.pow(Math.exp(Math.PI), (1.0 / z1)))) + t_2);
	} else if (z1 <= 3.3e+99) {
		tmp = t_3;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * Math.PI) - (-0.25 * (z0 * Math.PI)))) - (0.5 * Math.PI)) / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = 1.0 / (1.0 + math.exp((math.pi / z1)))
	t_1 = math.exp((-3.1415927410125732 / z1))
	t_2 = z0 / (t_1 - -1.0)
	t_3 = ((1.0 - t_2) - t_0) / (t_0 + t_2)
	tmp = 0
	if z1 <= -2.4e+176:
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((math.pi * z0) - math.pi))) * (2.0 / z1)))
	elif z1 <= -0.2:
		tmp = t_3
	elif z1 <= 0.6:
		tmp = (-1.0 * (z0 * (((-1.0 * ((1.0 - t_0) / z0)) + (1.0 / (1.0 + t_1))) - t_0))) / (((1.0 - z0) / (1.0 + math.pow(math.exp(math.pi), (1.0 / z1)))) + t_2)
	elif z1 <= 3.3e+99:
		tmp = t_3
	else:
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * math.pi) - (-0.25 * (z0 * math.pi)))) - (0.5 * math.pi)) / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(1.0 / Float64(1.0 + exp(Float64(pi / z1))))
	t_1 = exp(Float64(-3.1415927410125732 / z1))
	t_2 = Float64(z0 / Float64(t_1 - -1.0))
	t_3 = Float64(Float64(Float64(1.0 - t_2) - t_0) / Float64(t_0 + t_2))
	tmp = 0.0
	if (z1 <= -2.4e+176)
		tmp = Float64(1.0 - Float64(2.0 * Float64(Float64(Float64(0.7853981852531433 * z0) - Float64(-0.25 * Float64(Float64(pi * z0) - pi))) * Float64(2.0 / z1))));
	elseif (z1 <= -0.2)
		tmp = t_3;
	elseif (z1 <= 0.6)
		tmp = Float64(Float64(-1.0 * Float64(z0 * Float64(Float64(Float64(-1.0 * Float64(Float64(1.0 - t_0) / z0)) + Float64(1.0 / Float64(1.0 + t_1))) - t_0))) / Float64(Float64(Float64(1.0 - z0) / Float64(1.0 + (exp(pi) ^ Float64(1.0 / z1)))) + t_2));
	elseif (z1 <= 3.3e+99)
		tmp = t_3;
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(Float64(Float64(2.0 * Float64(Float64(-0.25 * pi) - Float64(-0.25 * Float64(z0 * pi)))) - Float64(0.5 * pi)) / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = 1.0 / (1.0 + exp((pi / z1)));
	t_1 = exp((-3.1415927410125732 / z1));
	t_2 = z0 / (t_1 - -1.0);
	t_3 = ((1.0 - t_2) - t_0) / (t_0 + t_2);
	tmp = 0.0;
	if (z1 <= -2.4e+176)
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((pi * z0) - pi))) * (2.0 / z1)));
	elseif (z1 <= -0.2)
		tmp = t_3;
	elseif (z1 <= 0.6)
		tmp = (-1.0 * (z0 * (((-1.0 * ((1.0 - t_0) / z0)) + (1.0 / (1.0 + t_1))) - t_0))) / (((1.0 - z0) / (1.0 + (exp(pi) ^ (1.0 / z1)))) + t_2);
	elseif (z1 <= 3.3e+99)
		tmp = t_3;
	else
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * pi) - (-0.25 * (z0 * pi)))) - (0.5 * pi)) / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(1.0 / N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(z0 / N[(t$95$1 - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(1.0 - t$95$2), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(t$95$0 + t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z1, -2.4e+176], N[(1.0 - N[(2.0 * N[(N[(N[(0.7853981852531433 * z0), $MachinePrecision] - N[(-0.25 * N[(N[(Pi * z0), $MachinePrecision] - Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, -0.2], t$95$3, If[LessEqual[z1, 0.6], N[(N[(-1.0 * N[(z0 * N[(N[(N[(-1.0 * N[(N[(1.0 - t$95$0), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[Power[N[Exp[Pi], $MachinePrecision], N[(1.0 / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 3.3e+99], t$95$3, N[(1.0 + N[(-1.0 * N[(N[(N[(2.0 * N[(N[(-0.25 * Pi), $MachinePrecision] - N[(-0.25 * N[(z0 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.5 * Pi), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z1 < -2.4000000000000001e176

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. add-flip N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)\right)\right) \]

   6. Applied rewrites 39.1%

      \[\leadsto 1 - \color{blue}{2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)} \]

   if -2.4000000000000001e176 < z1 < -0.20000000000000001 or 0.59999999999999998 < z1 < 3.2999999999999999e99

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-PI.f64 51.6%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-PI.f64 62.6%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   7. Applied rewrites 62.6%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   if -0.20000000000000001 < z1 < 0.59999999999999998

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   2. Step-by-step derivation

      1. lift-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + \color{blue}{e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\color{blue}{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. mult-flip N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\color{blue}{\pi \cdot \frac{1}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. exp-prod N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + \color{blue}{{\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lift-PI.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\color{blue}{\mathsf{PI}\left(\right)}}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + \color{blue}{{\left(e^{\mathsf{PI}\left(\right)}\right)}^{\left(\frac{1}{z1}\right)}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      7. lift-PI.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\color{blue}{\pi}}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\color{blue}{\left(e^{\pi}\right)}}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      9. lower-/.f64 66.4%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\color{blue}{\left(\frac{1}{z1}\right)}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   3. Applied rewrites 66.4%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + \color{blue}{{\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   4. Step-by-step derivation

      1. lift-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + \color{blue}{e^{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\color{blue}{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. mult-flip N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\color{blue}{\pi \cdot \frac{1}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. exp-prod N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + \color{blue}{{\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lift-PI.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + {\left(e^{\color{blue}{\mathsf{PI}\left(\right)}}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + \color{blue}{{\left(e^{\mathsf{PI}\left(\right)}\right)}^{\left(\frac{1}{z1}\right)}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      7. lift-PI.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + {\left(e^{\color{blue}{\pi}}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + {\color{blue}{\left(e^{\pi}\right)}}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      9. lower-/.f64 66.4%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\color{blue}{\left(\frac{1}{z1}\right)}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Applied rewrites 66.4%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + \color{blue}{{\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   6. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(z0 \cdot \left(\left(-1 \cdot \frac{1 - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{z0} + \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}\right)\right)}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(z0 \cdot \left(\left(-1 \cdot \frac{1 - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{z0} + \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right) - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}\right)\right)}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \left(z0 \cdot \color{blue}{\left(\left(-1 \cdot \frac{1 - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{z0} + \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right) - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}\right)}\right)}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \left(z0 \cdot \left(\left(-1 \cdot \frac{1 - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{z0} + \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right) - \color{blue}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}\right)\right)}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

   8. Applied rewrites 76.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(z0 \cdot \left(\left(-1 \cdot \frac{1 - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{z0} + \frac{1}{1 + e^{\frac{-3.1415927410125732}{z1}}}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}\right)\right)}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   if 3.2999999999999999e99 < z1

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \pi}{z1} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \mathsf{PI}\left(\right)}{z1} \]

      2. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   7. Applied rewrites 38.9%

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   8. Taylor expanded in z0 around 0

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\frac{-1}{4} \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \pi}{z1} \]

      2. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   10. Applied rewrites 38.9%

       \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 2: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := 1 + e^{\frac{\pi}{z1}}\\ t_1 := \frac{1}{t\_0}\\ t_2 := e^{\frac{-3.1415927410125732}{z1}}\\ t_3 := \frac{z0}{t\_2 - -1}\\ t_4 := \frac{\left(1 - t\_3\right) - t\_1}{t\_1 + t\_3}\\ \mathbf{if}\;z1 \leq -2.4 \cdot 10^{+176}:\\ \;\;\;\;1 - 2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)\\ \mathbf{elif}\;z1 \leq -1.6:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z1 \leq 1.95 \cdot 10^{-305}:\\ \;\;\;\;\frac{z0 \cdot \left(t\_1 - \frac{1}{1 + t\_2}\right)}{\frac{1 - z0}{t\_0} + t\_3}\\ \mathbf{elif}\;z1 \leq 3.3 \cdot 10^{+99}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (+ 1.0 (exp (/ PI z1))))
       (t_1 (/ 1.0 t_0))
       (t_2 (exp (/ -3.1415927410125732 z1)))
       (t_3 (/ z0 (- t_2 -1.0)))
       (t_4 (/ (- (- 1.0 t_3) t_1) (+ t_1 t_3))))
  (if (<= z1 -2.4e+176)
    (-
     1.0
     (*
      2.0
      (*
       (- (* 0.7853981852531433 z0) (* -0.25 (- (* PI z0) PI)))
       (/ 2.0 z1))))
    (if (<= z1 -1.6)
      t_4
      (if (<= z1 1.95e-305)
        (/
         (* z0 (- t_1 (/ 1.0 (+ 1.0 t_2))))
         (+ (/ (- 1.0 z0) t_0) t_3))
        (if (<= z1 3.3e+99)
          t_4
          (+
           1.0
           (*
            -1.0
            (/
             (-
              (* 2.0 (- (* -0.25 PI) (* -0.25 (* z0 PI))))
              (* 0.5 PI))
             z1)))))))))

C

double code(double z0, double z1) {
	double t_0 = 1.0 + exp((((double) M_PI) / z1));
	double t_1 = 1.0 / t_0;
	double t_2 = exp((-3.1415927410125732 / z1));
	double t_3 = z0 / (t_2 - -1.0);
	double t_4 = ((1.0 - t_3) - t_1) / (t_1 + t_3);
	double tmp;
	if (z1 <= -2.4e+176) {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((((double) M_PI) * z0) - ((double) M_PI)))) * (2.0 / z1)));
	} else if (z1 <= -1.6) {
		tmp = t_4;
	} else if (z1 <= 1.95e-305) {
		tmp = (z0 * (t_1 - (1.0 / (1.0 + t_2)))) / (((1.0 - z0) / t_0) + t_3);
	} else if (z1 <= 3.3e+99) {
		tmp = t_4;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * ((double) M_PI)) - (-0.25 * (z0 * ((double) M_PI))))) - (0.5 * ((double) M_PI))) / z1));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = 1.0 + Math.exp((Math.PI / z1));
	double t_1 = 1.0 / t_0;
	double t_2 = Math.exp((-3.1415927410125732 / z1));
	double t_3 = z0 / (t_2 - -1.0);
	double t_4 = ((1.0 - t_3) - t_1) / (t_1 + t_3);
	double tmp;
	if (z1 <= -2.4e+176) {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((Math.PI * z0) - Math.PI))) * (2.0 / z1)));
	} else if (z1 <= -1.6) {
		tmp = t_4;
	} else if (z1 <= 1.95e-305) {
		tmp = (z0 * (t_1 - (1.0 / (1.0 + t_2)))) / (((1.0 - z0) / t_0) + t_3);
	} else if (z1 <= 3.3e+99) {
		tmp = t_4;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * Math.PI) - (-0.25 * (z0 * Math.PI)))) - (0.5 * Math.PI)) / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = 1.0 + math.exp((math.pi / z1))
	t_1 = 1.0 / t_0
	t_2 = math.exp((-3.1415927410125732 / z1))
	t_3 = z0 / (t_2 - -1.0)
	t_4 = ((1.0 - t_3) - t_1) / (t_1 + t_3)
	tmp = 0
	if z1 <= -2.4e+176:
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((math.pi * z0) - math.pi))) * (2.0 / z1)))
	elif z1 <= -1.6:
		tmp = t_4
	elif z1 <= 1.95e-305:
		tmp = (z0 * (t_1 - (1.0 / (1.0 + t_2)))) / (((1.0 - z0) / t_0) + t_3)
	elif z1 <= 3.3e+99:
		tmp = t_4
	else:
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * math.pi) - (-0.25 * (z0 * math.pi)))) - (0.5 * math.pi)) / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(1.0 + exp(Float64(pi / z1)))
	t_1 = Float64(1.0 / t_0)
	t_2 = exp(Float64(-3.1415927410125732 / z1))
	t_3 = Float64(z0 / Float64(t_2 - -1.0))
	t_4 = Float64(Float64(Float64(1.0 - t_3) - t_1) / Float64(t_1 + t_3))
	tmp = 0.0
	if (z1 <= -2.4e+176)
		tmp = Float64(1.0 - Float64(2.0 * Float64(Float64(Float64(0.7853981852531433 * z0) - Float64(-0.25 * Float64(Float64(pi * z0) - pi))) * Float64(2.0 / z1))));
	elseif (z1 <= -1.6)
		tmp = t_4;
	elseif (z1 <= 1.95e-305)
		tmp = Float64(Float64(z0 * Float64(t_1 - Float64(1.0 / Float64(1.0 + t_2)))) / Float64(Float64(Float64(1.0 - z0) / t_0) + t_3));
	elseif (z1 <= 3.3e+99)
		tmp = t_4;
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(Float64(Float64(2.0 * Float64(Float64(-0.25 * pi) - Float64(-0.25 * Float64(z0 * pi)))) - Float64(0.5 * pi)) / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = 1.0 + exp((pi / z1));
	t_1 = 1.0 / t_0;
	t_2 = exp((-3.1415927410125732 / z1));
	t_3 = z0 / (t_2 - -1.0);
	t_4 = ((1.0 - t_3) - t_1) / (t_1 + t_3);
	tmp = 0.0;
	if (z1 <= -2.4e+176)
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((pi * z0) - pi))) * (2.0 / z1)));
	elseif (z1 <= -1.6)
		tmp = t_4;
	elseif (z1 <= 1.95e-305)
		tmp = (z0 * (t_1 - (1.0 / (1.0 + t_2)))) / (((1.0 - z0) / t_0) + t_3);
	elseif (z1 <= 3.3e+99)
		tmp = t_4;
	else
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * pi) - (-0.25 * (z0 * pi)))) - (0.5 * pi)) / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(z0 / N[(t$95$2 - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(1.0 - t$95$3), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z1, -2.4e+176], N[(1.0 - N[(2.0 * N[(N[(N[(0.7853981852531433 * z0), $MachinePrecision] - N[(-0.25 * N[(N[(Pi * z0), $MachinePrecision] - Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, -1.6], t$95$4, If[LessEqual[z1, 1.95e-305], N[(N[(z0 * N[(t$95$1 - N[(1.0 / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(1.0 - z0), $MachinePrecision] / t$95$0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 3.3e+99], t$95$4, N[(1.0 + N[(-1.0 * N[(N[(N[(2.0 * N[(N[(-0.25 * Pi), $MachinePrecision] - N[(-0.25 * N[(z0 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.5 * Pi), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z1 < -2.4000000000000001e176

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. add-flip N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)\right)\right) \]

   6. Applied rewrites 39.1%

      \[\leadsto 1 - \color{blue}{2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)} \]

   if -2.4000000000000001e176 < z1 < -1.6000000000000001 or 1.9500000000000001e-305 < z1 < 3.2999999999999999e99

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-PI.f64 51.6%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-PI.f64 62.6%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   7. Applied rewrites 62.6%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   if -1.6000000000000001 < z1 < 1.9500000000000001e-305

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{z0 \cdot \left(\frac{1}{1 + e^{\frac{\pi}{z1}}} - \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right)}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{z0 \cdot \color{blue}{\left(\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} - \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right)}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} - \color{blue}{\frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} - \frac{\color{blue}{1}}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} - \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-exp.f64 N/A

         \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} - \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} - \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      7. lower-PI.f64 N/A

         \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\pi}{z1}}} - \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\pi}{z1}}} - \frac{1}{\color{blue}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      9. lower-+.f64 N/A

         \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\pi}{z1}}} - \frac{1}{1 + \color{blue}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      10. lower-exp.f64 N/A

          \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\pi}{z1}}} - \frac{1}{1 + e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      11. lower-/.f64 39.1%

          \[\leadsto \frac{z0 \cdot \left(\frac{1}{1 + e^{\frac{\pi}{z1}}} - \frac{1}{1 + e^{\frac{-3.1415927410125732}{z1}}}\right)}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \frac{\color{blue}{z0 \cdot \left(\frac{1}{1 + e^{\frac{\pi}{z1}}} - \frac{1}{1 + e^{\frac{-3.1415927410125732}{z1}}}\right)}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   if 3.2999999999999999e99 < z1

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \pi}{z1} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \mathsf{PI}\left(\right)}{z1} \]

      2. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   7. Applied rewrites 38.9%

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   8. Taylor expanded in z0 around 0

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\frac{-1}{4} \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \pi}{z1} \]

      2. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   10. Applied rewrites 38.9%

       \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 92.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{\pi}{z1}}\\ t_1 := t\_0 - -1\\ t_2 := 1 + t\_0\\ t_3 := \frac{1}{t\_2}\\ t_4 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_5 := \frac{\left(1 - t\_4\right) - t\_3}{t\_3 + t\_4}\\ \mathbf{if}\;z1 \leq -2.4 \cdot 10^{+176}:\\ \;\;\;\;1 - 2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)\\ \mathbf{elif}\;z1 \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;z1 \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{\left(\left(1 - 0.5 \cdot z0\right) - \frac{1}{t\_1}\right) + \frac{z0}{t\_1}}{\frac{1 - z0}{t\_2} + 0.5 \cdot z0}\\ \mathbf{elif}\;z1 \leq 3.3 \cdot 10^{+99}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ PI z1)))
       (t_1 (- t_0 -1.0))
       (t_2 (+ 1.0 t_0))
       (t_3 (/ 1.0 t_2))
       (t_4 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_5 (/ (- (- 1.0 t_4) t_3) (+ t_3 t_4))))
  (if (<= z1 -2.4e+176)
    (-
     1.0
     (*
      2.0
      (*
       (- (* 0.7853981852531433 z0) (* -0.25 (- (* PI z0) PI)))
       (/ 2.0 z1))))
    (if (<= z1 -1.3e+20)
      t_5
      (if (<= z1 -5e-310)
        (/
         (+ (- (- 1.0 (* 0.5 z0)) (/ 1.0 t_1)) (/ z0 t_1))
         (+ (/ (- 1.0 z0) t_2) (* 0.5 z0)))
        (if (<= z1 3.3e+99)
          t_5
          (+
           1.0
           (*
            -1.0
            (/
             (-
              (* 2.0 (- (* -0.25 PI) (* -0.25 (* z0 PI))))
              (* 0.5 PI))
             z1)))))))))

C

double code(double z0, double z1) {
	double t_0 = exp((((double) M_PI) / z1));
	double t_1 = t_0 - -1.0;
	double t_2 = 1.0 + t_0;
	double t_3 = 1.0 / t_2;
	double t_4 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_5 = ((1.0 - t_4) - t_3) / (t_3 + t_4);
	double tmp;
	if (z1 <= -2.4e+176) {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((((double) M_PI) * z0) - ((double) M_PI)))) * (2.0 / z1)));
	} else if (z1 <= -1.3e+20) {
		tmp = t_5;
	} else if (z1 <= -5e-310) {
		tmp = (((1.0 - (0.5 * z0)) - (1.0 / t_1)) + (z0 / t_1)) / (((1.0 - z0) / t_2) + (0.5 * z0));
	} else if (z1 <= 3.3e+99) {
		tmp = t_5;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * ((double) M_PI)) - (-0.25 * (z0 * ((double) M_PI))))) - (0.5 * ((double) M_PI))) / z1));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((Math.PI / z1));
	double t_1 = t_0 - -1.0;
	double t_2 = 1.0 + t_0;
	double t_3 = 1.0 / t_2;
	double t_4 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_5 = ((1.0 - t_4) - t_3) / (t_3 + t_4);
	double tmp;
	if (z1 <= -2.4e+176) {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((Math.PI * z0) - Math.PI))) * (2.0 / z1)));
	} else if (z1 <= -1.3e+20) {
		tmp = t_5;
	} else if (z1 <= -5e-310) {
		tmp = (((1.0 - (0.5 * z0)) - (1.0 / t_1)) + (z0 / t_1)) / (((1.0 - z0) / t_2) + (0.5 * z0));
	} else if (z1 <= 3.3e+99) {
		tmp = t_5;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * Math.PI) - (-0.25 * (z0 * Math.PI)))) - (0.5 * Math.PI)) / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((math.pi / z1))
	t_1 = t_0 - -1.0
	t_2 = 1.0 + t_0
	t_3 = 1.0 / t_2
	t_4 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_5 = ((1.0 - t_4) - t_3) / (t_3 + t_4)
	tmp = 0
	if z1 <= -2.4e+176:
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((math.pi * z0) - math.pi))) * (2.0 / z1)))
	elif z1 <= -1.3e+20:
		tmp = t_5
	elif z1 <= -5e-310:
		tmp = (((1.0 - (0.5 * z0)) - (1.0 / t_1)) + (z0 / t_1)) / (((1.0 - z0) / t_2) + (0.5 * z0))
	elif z1 <= 3.3e+99:
		tmp = t_5
	else:
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * math.pi) - (-0.25 * (z0 * math.pi)))) - (0.5 * math.pi)) / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(pi / z1))
	t_1 = Float64(t_0 - -1.0)
	t_2 = Float64(1.0 + t_0)
	t_3 = Float64(1.0 / t_2)
	t_4 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_5 = Float64(Float64(Float64(1.0 - t_4) - t_3) / Float64(t_3 + t_4))
	tmp = 0.0
	if (z1 <= -2.4e+176)
		tmp = Float64(1.0 - Float64(2.0 * Float64(Float64(Float64(0.7853981852531433 * z0) - Float64(-0.25 * Float64(Float64(pi * z0) - pi))) * Float64(2.0 / z1))));
	elseif (z1 <= -1.3e+20)
		tmp = t_5;
	elseif (z1 <= -5e-310)
		tmp = Float64(Float64(Float64(Float64(1.0 - Float64(0.5 * z0)) - Float64(1.0 / t_1)) + Float64(z0 / t_1)) / Float64(Float64(Float64(1.0 - z0) / t_2) + Float64(0.5 * z0)));
	elseif (z1 <= 3.3e+99)
		tmp = t_5;
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(Float64(Float64(2.0 * Float64(Float64(-0.25 * pi) - Float64(-0.25 * Float64(z0 * pi)))) - Float64(0.5 * pi)) / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((pi / z1));
	t_1 = t_0 - -1.0;
	t_2 = 1.0 + t_0;
	t_3 = 1.0 / t_2;
	t_4 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_5 = ((1.0 - t_4) - t_3) / (t_3 + t_4);
	tmp = 0.0;
	if (z1 <= -2.4e+176)
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((pi * z0) - pi))) * (2.0 / z1)));
	elseif (z1 <= -1.3e+20)
		tmp = t_5;
	elseif (z1 <= -5e-310)
		tmp = (((1.0 - (0.5 * z0)) - (1.0 / t_1)) + (z0 / t_1)) / (((1.0 - z0) / t_2) + (0.5 * z0));
	elseif (z1 <= 3.3e+99)
		tmp = t_5;
	else
		tmp = 1.0 + (-1.0 * (((2.0 * ((-0.25 * pi) - (-0.25 * (z0 * pi)))) - (0.5 * pi)) / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(1.0 - t$95$4), $MachinePrecision] - t$95$3), $MachinePrecision] / N[(t$95$3 + t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z1, -2.4e+176], N[(1.0 - N[(2.0 * N[(N[(N[(0.7853981852531433 * z0), $MachinePrecision] - N[(-0.25 * N[(N[(Pi * z0), $MachinePrecision] - Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, -1.3e+20], t$95$5, If[LessEqual[z1, -5e-310], N[(N[(N[(N[(1.0 - N[(0.5 * z0), $MachinePrecision]), $MachinePrecision] - N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z0 / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(1.0 - z0), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 3.3e+99], t$95$5, N[(1.0 + N[(-1.0 * N[(N[(N[(2.0 * N[(N[(-0.25 * Pi), $MachinePrecision] - N[(-0.25 * N[(z0 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.5 * Pi), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z1 < -2.4000000000000001e176

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. add-flip N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)\right)\right) \]

   6. Applied rewrites 39.1%

      \[\leadsto 1 - \color{blue}{2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)} \]

   if -2.4000000000000001e176 < z1 < -1.3e20 or -4.9999999999999847e-310 < z1 < 3.2999999999999999e99

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-PI.f64 51.6%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-PI.f64 62.6%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   7. Applied rewrites 62.6%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   if -1.3e20 < z1 < -4.9999999999999847e-310

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \color{blue}{\frac{1}{2} \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 44.6%

         \[\leadsto \frac{\left(1 - 0.5 \cdot \color{blue}{z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 44.6%

      \[\leadsto \frac{\left(1 - \color{blue}{0.5 \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

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

      1. lower-*.f64 55.5%

         \[\leadsto \frac{\left(1 - 0.5 \cdot z0\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 55.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-sub N/A

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

      5. lift-/.f64 N/A

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

      6. associate--r- N/A

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

      7. lower-+.f64 N/A

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

   9. Applied rewrites 66.8%

      \[\leadsto \frac{\color{blue}{\left(\left(1 - 0.5 \cdot z0\right) - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   if 3.2999999999999999e99 < z1

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \pi}{z1} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \mathsf{PI}\left(\right)}{z1} \]

      2. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   7. Applied rewrites 38.9%

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   8. Taylor expanded in z0 around 0

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\frac{-1}{4} \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - \frac{1}{2} \cdot \pi}{z1} \]

      2. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]

   10. Applied rewrites 38.9%

       \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(-0.25 \cdot \pi - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 0.5 \cdot \pi}{z1} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{\pi}{z1}}\\ t_1 := 1 + t\_0\\ t_2 := \frac{1 - z0}{t\_1}\\ t_3 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_4 := \frac{\left(1 - t\_3\right) - t\_2}{t\_2 + t\_3}\\ t_5 := t\_0 - -1\\ t_6 := \frac{z0}{t\_5}\\ t_7 := t\_2 + 0.5 \cdot z0\\ \mathbf{if}\;t\_4 \leq -0.5:\\ \;\;\;\;\frac{\left(0.5 - 0.5 \cdot z0\right) + t\_6}{t\_7}\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-10}:\\ \;\;\;\;\frac{\left(1 - \frac{1}{t\_5}\right) + t\_6}{t\_7}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{1 - \frac{1}{t\_1}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + t\_3}\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ PI z1)))
       (t_1 (+ 1.0 t_0))
       (t_2 (/ (- 1.0 z0) t_1))
       (t_3 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_4 (/ (- (- 1.0 t_3) t_2) (+ t_2 t_3)))
       (t_5 (- t_0 -1.0))
       (t_6 (/ z0 t_5))
       (t_7 (+ t_2 (* 0.5 z0))))
  (if (<= t_4 -0.5)
    (/ (+ (- 0.5 (* 0.5 z0)) t_6) t_7)
    (if (<= t_4 4e-10)
      (/ (+ (- 1.0 (/ 1.0 t_5)) t_6) t_7)
      (if (<= t_4 2e+282)
        (/
         (- 1.0 (/ 1.0 t_1))
         (+ (/ (- 1.0 z0) (+ 1.0 (pow (exp PI) (/ 1.0 z1)))) t_3))
        (+
         1.0
         (*
          -1.0
          (/
           (-
            (*
             2.0
             (-
              (+ (* -0.25 PI) (* 0.7853981852531433 z0))
              (* -0.25 (* z0 PI))))
            (* 2.0 (* z0 (- (* -0.25 PI) 0.7853981852531433))))
           z1))))))))

C

double code(double z0, double z1) {
	double t_0 = exp((((double) M_PI) / z1));
	double t_1 = 1.0 + t_0;
	double t_2 = (1.0 - z0) / t_1;
	double t_3 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_4 = ((1.0 - t_3) - t_2) / (t_2 + t_3);
	double t_5 = t_0 - -1.0;
	double t_6 = z0 / t_5;
	double t_7 = t_2 + (0.5 * z0);
	double tmp;
	if (t_4 <= -0.5) {
		tmp = ((0.5 - (0.5 * z0)) + t_6) / t_7;
	} else if (t_4 <= 4e-10) {
		tmp = ((1.0 - (1.0 / t_5)) + t_6) / t_7;
	} else if (t_4 <= 2e+282) {
		tmp = (1.0 - (1.0 / t_1)) / (((1.0 - z0) / (1.0 + pow(exp(((double) M_PI)), (1.0 / z1)))) + t_3);
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * ((double) M_PI)) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * ((double) M_PI))))) - (2.0 * (z0 * ((-0.25 * ((double) M_PI)) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((Math.PI / z1));
	double t_1 = 1.0 + t_0;
	double t_2 = (1.0 - z0) / t_1;
	double t_3 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_4 = ((1.0 - t_3) - t_2) / (t_2 + t_3);
	double t_5 = t_0 - -1.0;
	double t_6 = z0 / t_5;
	double t_7 = t_2 + (0.5 * z0);
	double tmp;
	if (t_4 <= -0.5) {
		tmp = ((0.5 - (0.5 * z0)) + t_6) / t_7;
	} else if (t_4 <= 4e-10) {
		tmp = ((1.0 - (1.0 / t_5)) + t_6) / t_7;
	} else if (t_4 <= 2e+282) {
		tmp = (1.0 - (1.0 / t_1)) / (((1.0 - z0) / (1.0 + Math.pow(Math.exp(Math.PI), (1.0 / z1)))) + t_3);
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * Math.PI) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * Math.PI)))) - (2.0 * (z0 * ((-0.25 * Math.PI) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((math.pi / z1))
	t_1 = 1.0 + t_0
	t_2 = (1.0 - z0) / t_1
	t_3 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_4 = ((1.0 - t_3) - t_2) / (t_2 + t_3)
	t_5 = t_0 - -1.0
	t_6 = z0 / t_5
	t_7 = t_2 + (0.5 * z0)
	tmp = 0
	if t_4 <= -0.5:
		tmp = ((0.5 - (0.5 * z0)) + t_6) / t_7
	elif t_4 <= 4e-10:
		tmp = ((1.0 - (1.0 / t_5)) + t_6) / t_7
	elif t_4 <= 2e+282:
		tmp = (1.0 - (1.0 / t_1)) / (((1.0 - z0) / (1.0 + math.pow(math.exp(math.pi), (1.0 / z1)))) + t_3)
	else:
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * math.pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * math.pi)))) - (2.0 * (z0 * ((-0.25 * math.pi) - 0.7853981852531433)))) / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(pi / z1))
	t_1 = Float64(1.0 + t_0)
	t_2 = Float64(Float64(1.0 - z0) / t_1)
	t_3 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_4 = Float64(Float64(Float64(1.0 - t_3) - t_2) / Float64(t_2 + t_3))
	t_5 = Float64(t_0 - -1.0)
	t_6 = Float64(z0 / t_5)
	t_7 = Float64(t_2 + Float64(0.5 * z0))
	tmp = 0.0
	if (t_4 <= -0.5)
		tmp = Float64(Float64(Float64(0.5 - Float64(0.5 * z0)) + t_6) / t_7);
	elseif (t_4 <= 4e-10)
		tmp = Float64(Float64(Float64(1.0 - Float64(1.0 / t_5)) + t_6) / t_7);
	elseif (t_4 <= 2e+282)
		tmp = Float64(Float64(1.0 - Float64(1.0 / t_1)) / Float64(Float64(Float64(1.0 - z0) / Float64(1.0 + (exp(pi) ^ Float64(1.0 / z1)))) + t_3));
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(Float64(Float64(2.0 * Float64(Float64(Float64(-0.25 * pi) + Float64(0.7853981852531433 * z0)) - Float64(-0.25 * Float64(z0 * pi)))) - Float64(2.0 * Float64(z0 * Float64(Float64(-0.25 * pi) - 0.7853981852531433)))) / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((pi / z1));
	t_1 = 1.0 + t_0;
	t_2 = (1.0 - z0) / t_1;
	t_3 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_4 = ((1.0 - t_3) - t_2) / (t_2 + t_3);
	t_5 = t_0 - -1.0;
	t_6 = z0 / t_5;
	t_7 = t_2 + (0.5 * z0);
	tmp = 0.0;
	if (t_4 <= -0.5)
		tmp = ((0.5 - (0.5 * z0)) + t_6) / t_7;
	elseif (t_4 <= 4e-10)
		tmp = ((1.0 - (1.0 / t_5)) + t_6) / t_7;
	elseif (t_4 <= 2e+282)
		tmp = (1.0 - (1.0 / t_1)) / (((1.0 - z0) / (1.0 + (exp(pi) ^ (1.0 / z1)))) + t_3);
	else
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * pi)))) - (2.0 * (z0 * ((-0.25 * pi) - 0.7853981852531433)))) / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - z0), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(1.0 - t$95$3), $MachinePrecision] - t$95$2), $MachinePrecision] / N[(t$95$2 + t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$0 - -1.0), $MachinePrecision]}, Block[{t$95$6 = N[(z0 / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$2 + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -0.5], N[(N[(N[(0.5 - N[(0.5 * z0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] / t$95$7), $MachinePrecision], If[LessEqual[t$95$4, 4e-10], N[(N[(N[(1.0 - N[(1.0 / t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] / t$95$7), $MachinePrecision], If[LessEqual[t$95$4, 2e+282], N[(N[(1.0 - N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[Power[N[Exp[Pi], $MachinePrecision], N[(1.0 / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 * N[(N[(N[(2.0 * N[(N[(N[(-0.25 * Pi), $MachinePrecision] + N[(0.7853981852531433 * z0), $MachinePrecision]), $MachinePrecision] - N[(-0.25 * N[(z0 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(z0 * N[(N[(-0.25 * Pi), $MachinePrecision] - 0.7853981852531433), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < -0.5

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \color{blue}{\frac{1}{2} \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 44.6%

         \[\leadsto \frac{\left(1 - 0.5 \cdot \color{blue}{z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 44.6%

      \[\leadsto \frac{\left(1 - \color{blue}{0.5 \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

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

      1. lower-*.f64 55.5%

         \[\leadsto \frac{\left(1 - 0.5 \cdot z0\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 55.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-sub N/A

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

      5. lift-/.f64 N/A

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

      6. associate--r- N/A

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

      7. lower-+.f64 N/A

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

   9. Applied rewrites 66.8%

      \[\leadsto \frac{\color{blue}{\left(\left(1 - 0.5 \cdot z0\right) - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   10. Taylor expanded in z1 around inf

       \[\leadsto \frac{\color{blue}{\left(\frac{1}{2} - \frac{1}{2} \cdot z0\right)} + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]
   11. Step-by-step derivation

       1. lower--.f64 N/A

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

       2. lower-*.f64 65.1%

          \[\leadsto \frac{\left(0.5 - 0.5 \cdot \color{blue}{z0}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   12. Applied rewrites 65.1%

       \[\leadsto \frac{\color{blue}{\left(0.5 - 0.5 \cdot z0\right)} + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   if -0.5 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 4.0000000000000001e-10

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \color{blue}{\frac{1}{2} \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 44.6%

         \[\leadsto \frac{\left(1 - 0.5 \cdot \color{blue}{z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 44.6%

      \[\leadsto \frac{\left(1 - \color{blue}{0.5 \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

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

      1. lower-*.f64 55.5%

         \[\leadsto \frac{\left(1 - 0.5 \cdot z0\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 55.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-sub N/A

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

      5. lift-/.f64 N/A

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

      6. associate--r- N/A

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

      7. lower-+.f64 N/A

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

   9. Applied rewrites 66.8%

      \[\leadsto \frac{\color{blue}{\left(\left(1 - 0.5 \cdot z0\right) - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   10. Taylor expanded in z0 around 0

       \[\leadsto \frac{\left(\color{blue}{1} - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]
   11. Step-by-step derivation

   12. Applied rewrites 42.8%

       \[\leadsto \frac{\left(\color{blue}{1} - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   if 4.0000000000000001e-10 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 2.0000000000000001e282

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   2. Step-by-step derivation

      1. lift-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + \color{blue}{e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\color{blue}{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. mult-flip N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\color{blue}{\pi \cdot \frac{1}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. exp-prod N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + \color{blue}{{\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lift-PI.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\color{blue}{\mathsf{PI}\left(\right)}}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + \color{blue}{{\left(e^{\mathsf{PI}\left(\right)}\right)}^{\left(\frac{1}{z1}\right)}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      7. lift-PI.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\color{blue}{\pi}}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\color{blue}{\left(e^{\pi}\right)}}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      9. lower-/.f64 66.4%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\color{blue}{\left(\frac{1}{z1}\right)}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   3. Applied rewrites 66.4%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + \color{blue}{{\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   4. Step-by-step derivation

      1. lift-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + \color{blue}{e^{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\color{blue}{\frac{\pi}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. mult-flip N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + e^{\color{blue}{\pi \cdot \frac{1}{z1}}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. exp-prod N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + \color{blue}{{\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lift-PI.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + {\left(e^{\color{blue}{\mathsf{PI}\left(\right)}}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + \color{blue}{{\left(e^{\mathsf{PI}\left(\right)}\right)}^{\left(\frac{1}{z1}\right)}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      7. lift-PI.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + {\left(e^{\color{blue}{\pi}}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + {\color{blue}{\left(e^{\pi}\right)}}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      9. lower-/.f64 66.4%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\color{blue}{\left(\frac{1}{z1}\right)}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Applied rewrites 66.4%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}}{\frac{1 - z0}{1 + \color{blue}{{\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   6. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{1 - \frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{1 - \color{blue}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1 - \frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{1 - \frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-exp.f64 N/A

         \[\leadsto \frac{1 - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1 - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      6. lower-PI.f64 41.0%

         \[\leadsto \frac{1 - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   8. Applied rewrites 41.0%

      \[\leadsto \frac{\color{blue}{1 - \frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + {\left(e^{\pi}\right)}^{\left(\frac{1}{z1}\right)}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   if 2.0000000000000001e282 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))))

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \pi - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      2. lower--.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      4. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]

   7. Applied rewrites 38.9%

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{\pi}{z1}}\\ t_1 := 1 + t\_0\\ t_2 := \frac{1 - z0}{t\_1}\\ t_3 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_4 := t\_2 + t\_3\\ t_5 := \frac{\left(1 - t\_3\right) - t\_2}{t\_4}\\ t_6 := t\_0 - -1\\ t_7 := \frac{z0}{t\_6}\\ t_8 := t\_2 + 0.5 \cdot z0\\ \mathbf{if}\;t\_5 \leq -0.5:\\ \;\;\;\;\frac{\left(0.5 - 0.5 \cdot z0\right) + t\_7}{t\_8}\\ \mathbf{elif}\;t\_5 \leq 4 \cdot 10^{-10}:\\ \;\;\;\;\frac{\left(1 - \frac{1}{t\_6}\right) + t\_7}{t\_8}\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{1 - \frac{1}{t\_1}}{t\_4}\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ PI z1)))
       (t_1 (+ 1.0 t_0))
       (t_2 (/ (- 1.0 z0) t_1))
       (t_3 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_4 (+ t_2 t_3))
       (t_5 (/ (- (- 1.0 t_3) t_2) t_4))
       (t_6 (- t_0 -1.0))
       (t_7 (/ z0 t_6))
       (t_8 (+ t_2 (* 0.5 z0))))
  (if (<= t_5 -0.5)
    (/ (+ (- 0.5 (* 0.5 z0)) t_7) t_8)
    (if (<= t_5 4e-10)
      (/ (+ (- 1.0 (/ 1.0 t_6)) t_7) t_8)
      (if (<= t_5 2e+282)
        (/ (- 1.0 (/ 1.0 t_1)) t_4)
        (+
         1.0
         (*
          -1.0
          (/
           (-
            (*
             2.0
             (-
              (+ (* -0.25 PI) (* 0.7853981852531433 z0))
              (* -0.25 (* z0 PI))))
            (* 2.0 (* z0 (- (* -0.25 PI) 0.7853981852531433))))
           z1))))))))

C

double code(double z0, double z1) {
	double t_0 = exp((((double) M_PI) / z1));
	double t_1 = 1.0 + t_0;
	double t_2 = (1.0 - z0) / t_1;
	double t_3 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_4 = t_2 + t_3;
	double t_5 = ((1.0 - t_3) - t_2) / t_4;
	double t_6 = t_0 - -1.0;
	double t_7 = z0 / t_6;
	double t_8 = t_2 + (0.5 * z0);
	double tmp;
	if (t_5 <= -0.5) {
		tmp = ((0.5 - (0.5 * z0)) + t_7) / t_8;
	} else if (t_5 <= 4e-10) {
		tmp = ((1.0 - (1.0 / t_6)) + t_7) / t_8;
	} else if (t_5 <= 2e+282) {
		tmp = (1.0 - (1.0 / t_1)) / t_4;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * ((double) M_PI)) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * ((double) M_PI))))) - (2.0 * (z0 * ((-0.25 * ((double) M_PI)) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((Math.PI / z1));
	double t_1 = 1.0 + t_0;
	double t_2 = (1.0 - z0) / t_1;
	double t_3 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_4 = t_2 + t_3;
	double t_5 = ((1.0 - t_3) - t_2) / t_4;
	double t_6 = t_0 - -1.0;
	double t_7 = z0 / t_6;
	double t_8 = t_2 + (0.5 * z0);
	double tmp;
	if (t_5 <= -0.5) {
		tmp = ((0.5 - (0.5 * z0)) + t_7) / t_8;
	} else if (t_5 <= 4e-10) {
		tmp = ((1.0 - (1.0 / t_6)) + t_7) / t_8;
	} else if (t_5 <= 2e+282) {
		tmp = (1.0 - (1.0 / t_1)) / t_4;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * Math.PI) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * Math.PI)))) - (2.0 * (z0 * ((-0.25 * Math.PI) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((math.pi / z1))
	t_1 = 1.0 + t_0
	t_2 = (1.0 - z0) / t_1
	t_3 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_4 = t_2 + t_3
	t_5 = ((1.0 - t_3) - t_2) / t_4
	t_6 = t_0 - -1.0
	t_7 = z0 / t_6
	t_8 = t_2 + (0.5 * z0)
	tmp = 0
	if t_5 <= -0.5:
		tmp = ((0.5 - (0.5 * z0)) + t_7) / t_8
	elif t_5 <= 4e-10:
		tmp = ((1.0 - (1.0 / t_6)) + t_7) / t_8
	elif t_5 <= 2e+282:
		tmp = (1.0 - (1.0 / t_1)) / t_4
	else:
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * math.pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * math.pi)))) - (2.0 * (z0 * ((-0.25 * math.pi) - 0.7853981852531433)))) / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(pi / z1))
	t_1 = Float64(1.0 + t_0)
	t_2 = Float64(Float64(1.0 - z0) / t_1)
	t_3 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_4 = Float64(t_2 + t_3)
	t_5 = Float64(Float64(Float64(1.0 - t_3) - t_2) / t_4)
	t_6 = Float64(t_0 - -1.0)
	t_7 = Float64(z0 / t_6)
	t_8 = Float64(t_2 + Float64(0.5 * z0))
	tmp = 0.0
	if (t_5 <= -0.5)
		tmp = Float64(Float64(Float64(0.5 - Float64(0.5 * z0)) + t_7) / t_8);
	elseif (t_5 <= 4e-10)
		tmp = Float64(Float64(Float64(1.0 - Float64(1.0 / t_6)) + t_7) / t_8);
	elseif (t_5 <= 2e+282)
		tmp = Float64(Float64(1.0 - Float64(1.0 / t_1)) / t_4);
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(Float64(Float64(2.0 * Float64(Float64(Float64(-0.25 * pi) + Float64(0.7853981852531433 * z0)) - Float64(-0.25 * Float64(z0 * pi)))) - Float64(2.0 * Float64(z0 * Float64(Float64(-0.25 * pi) - 0.7853981852531433)))) / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((pi / z1));
	t_1 = 1.0 + t_0;
	t_2 = (1.0 - z0) / t_1;
	t_3 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_4 = t_2 + t_3;
	t_5 = ((1.0 - t_3) - t_2) / t_4;
	t_6 = t_0 - -1.0;
	t_7 = z0 / t_6;
	t_8 = t_2 + (0.5 * z0);
	tmp = 0.0;
	if (t_5 <= -0.5)
		tmp = ((0.5 - (0.5 * z0)) + t_7) / t_8;
	elseif (t_5 <= 4e-10)
		tmp = ((1.0 - (1.0 / t_6)) + t_7) / t_8;
	elseif (t_5 <= 2e+282)
		tmp = (1.0 - (1.0 / t_1)) / t_4;
	else
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * pi)))) - (2.0 * (z0 * ((-0.25 * pi) - 0.7853981852531433)))) / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - z0), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(1.0 - t$95$3), $MachinePrecision] - t$95$2), $MachinePrecision] / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$0 - -1.0), $MachinePrecision]}, Block[{t$95$7 = N[(z0 / t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$2 + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, -0.5], N[(N[(N[(0.5 - N[(0.5 * z0), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] / t$95$8), $MachinePrecision], If[LessEqual[t$95$5, 4e-10], N[(N[(N[(1.0 - N[(1.0 / t$95$6), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] / t$95$8), $MachinePrecision], If[LessEqual[t$95$5, 2e+282], N[(N[(1.0 - N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision], N[(1.0 + N[(-1.0 * N[(N[(N[(2.0 * N[(N[(N[(-0.25 * Pi), $MachinePrecision] + N[(0.7853981852531433 * z0), $MachinePrecision]), $MachinePrecision] - N[(-0.25 * N[(z0 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(z0 * N[(N[(-0.25 * Pi), $MachinePrecision] - 0.7853981852531433), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < -0.5

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \color{blue}{\frac{1}{2} \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 44.6%

         \[\leadsto \frac{\left(1 - 0.5 \cdot \color{blue}{z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 44.6%

      \[\leadsto \frac{\left(1 - \color{blue}{0.5 \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

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

      1. lower-*.f64 55.5%

         \[\leadsto \frac{\left(1 - 0.5 \cdot z0\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 55.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-sub N/A

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

      5. lift-/.f64 N/A

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

      6. associate--r- N/A

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

      7. lower-+.f64 N/A

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

   9. Applied rewrites 66.8%

      \[\leadsto \frac{\color{blue}{\left(\left(1 - 0.5 \cdot z0\right) - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   10. Taylor expanded in z1 around inf

       \[\leadsto \frac{\color{blue}{\left(\frac{1}{2} - \frac{1}{2} \cdot z0\right)} + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]
   11. Step-by-step derivation

       1. lower--.f64 N/A

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

       2. lower-*.f64 65.1%

          \[\leadsto \frac{\left(0.5 - 0.5 \cdot \color{blue}{z0}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   12. Applied rewrites 65.1%

       \[\leadsto \frac{\color{blue}{\left(0.5 - 0.5 \cdot z0\right)} + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   if -0.5 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 4.0000000000000001e-10

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \color{blue}{\frac{1}{2} \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 44.6%

         \[\leadsto \frac{\left(1 - 0.5 \cdot \color{blue}{z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 44.6%

      \[\leadsto \frac{\left(1 - \color{blue}{0.5 \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

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

      1. lower-*.f64 55.5%

         \[\leadsto \frac{\left(1 - 0.5 \cdot z0\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 55.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-sub N/A

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

      5. lift-/.f64 N/A

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

      6. associate--r- N/A

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

      7. lower-+.f64 N/A

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

   9. Applied rewrites 66.8%

      \[\leadsto \frac{\color{blue}{\left(\left(1 - 0.5 \cdot z0\right) - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   10. Taylor expanded in z0 around 0

       \[\leadsto \frac{\left(\color{blue}{1} - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]
   11. Step-by-step derivation

   12. Applied rewrites 42.8%

       \[\leadsto \frac{\left(\color{blue}{1} - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   if 4.0000000000000001e-10 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 2.0000000000000001e282

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{1 - \frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{1 - \color{blue}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1 - \frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{1 - \frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      4. lower-exp.f64 N/A

         \[\leadsto \frac{1 - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1 - \frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      6. lower-PI.f64 41.0%

         \[\leadsto \frac{1 - \frac{1}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 41.0%

      \[\leadsto \frac{\color{blue}{1 - \frac{1}{1 + e^{\frac{\pi}{z1}}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   if 2.0000000000000001e282 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))))

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \pi - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      2. lower--.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      4. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]

   7. Applied rewrites 38.9%

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 75.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := 1 + e^{\frac{\pi}{z1}}\\ t_1 := \frac{1 - z0}{t\_0}\\ t_2 := \frac{1 - z0}{2 + \frac{\pi}{z1}}\\ t_3 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_4 := \frac{\left(1 - t\_3\right) - t\_1}{t\_1 + t\_3}\\ t_5 := \frac{0.5}{\frac{1}{t\_0} + 0.5 \cdot z0}\\ \mathbf{if}\;t\_4 \leq -5 \cdot 10^{+49}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{\left(1 - \frac{z0}{2}\right) - t\_2}{t\_2 + \frac{z0}{2}}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (+ 1.0 (exp (/ PI z1))))
       (t_1 (/ (- 1.0 z0) t_0))
       (t_2 (/ (- 1.0 z0) (+ 2.0 (/ PI z1))))
       (t_3 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_4 (/ (- (- 1.0 t_3) t_1) (+ t_1 t_3)))
       (t_5 (/ 0.5 (+ (/ 1.0 t_0) (* 0.5 z0)))))
  (if (<= t_4 -5e+49)
    t_5
    (if (<= t_4 2.0)
      (/ (- (- 1.0 (/ z0 2.0)) t_2) (+ t_2 (/ z0 2.0)))
      (if (<= t_4 2e+282)
        t_5
        (+
         1.0
         (*
          -1.0
          (/
           (-
            (*
             2.0
             (-
              (+ (* -0.25 PI) (* 0.7853981852531433 z0))
              (* -0.25 (* z0 PI))))
            (* 2.0 (* z0 (- (* -0.25 PI) 0.7853981852531433))))
           z1))))))))

C

double code(double z0, double z1) {
	double t_0 = 1.0 + exp((((double) M_PI) / z1));
	double t_1 = (1.0 - z0) / t_0;
	double t_2 = (1.0 - z0) / (2.0 + (((double) M_PI) / z1));
	double t_3 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_4 = ((1.0 - t_3) - t_1) / (t_1 + t_3);
	double t_5 = 0.5 / ((1.0 / t_0) + (0.5 * z0));
	double tmp;
	if (t_4 <= -5e+49) {
		tmp = t_5;
	} else if (t_4 <= 2.0) {
		tmp = ((1.0 - (z0 / 2.0)) - t_2) / (t_2 + (z0 / 2.0));
	} else if (t_4 <= 2e+282) {
		tmp = t_5;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * ((double) M_PI)) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * ((double) M_PI))))) - (2.0 * (z0 * ((-0.25 * ((double) M_PI)) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = 1.0 + Math.exp((Math.PI / z1));
	double t_1 = (1.0 - z0) / t_0;
	double t_2 = (1.0 - z0) / (2.0 + (Math.PI / z1));
	double t_3 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_4 = ((1.0 - t_3) - t_1) / (t_1 + t_3);
	double t_5 = 0.5 / ((1.0 / t_0) + (0.5 * z0));
	double tmp;
	if (t_4 <= -5e+49) {
		tmp = t_5;
	} else if (t_4 <= 2.0) {
		tmp = ((1.0 - (z0 / 2.0)) - t_2) / (t_2 + (z0 / 2.0));
	} else if (t_4 <= 2e+282) {
		tmp = t_5;
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * Math.PI) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * Math.PI)))) - (2.0 * (z0 * ((-0.25 * Math.PI) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = 1.0 + math.exp((math.pi / z1))
	t_1 = (1.0 - z0) / t_0
	t_2 = (1.0 - z0) / (2.0 + (math.pi / z1))
	t_3 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_4 = ((1.0 - t_3) - t_1) / (t_1 + t_3)
	t_5 = 0.5 / ((1.0 / t_0) + (0.5 * z0))
	tmp = 0
	if t_4 <= -5e+49:
		tmp = t_5
	elif t_4 <= 2.0:
		tmp = ((1.0 - (z0 / 2.0)) - t_2) / (t_2 + (z0 / 2.0))
	elif t_4 <= 2e+282:
		tmp = t_5
	else:
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * math.pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * math.pi)))) - (2.0 * (z0 * ((-0.25 * math.pi) - 0.7853981852531433)))) / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(1.0 + exp(Float64(pi / z1)))
	t_1 = Float64(Float64(1.0 - z0) / t_0)
	t_2 = Float64(Float64(1.0 - z0) / Float64(2.0 + Float64(pi / z1)))
	t_3 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_4 = Float64(Float64(Float64(1.0 - t_3) - t_1) / Float64(t_1 + t_3))
	t_5 = Float64(0.5 / Float64(Float64(1.0 / t_0) + Float64(0.5 * z0)))
	tmp = 0.0
	if (t_4 <= -5e+49)
		tmp = t_5;
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(Float64(1.0 - Float64(z0 / 2.0)) - t_2) / Float64(t_2 + Float64(z0 / 2.0)));
	elseif (t_4 <= 2e+282)
		tmp = t_5;
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(Float64(Float64(2.0 * Float64(Float64(Float64(-0.25 * pi) + Float64(0.7853981852531433 * z0)) - Float64(-0.25 * Float64(z0 * pi)))) - Float64(2.0 * Float64(z0 * Float64(Float64(-0.25 * pi) - 0.7853981852531433)))) / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = 1.0 + exp((pi / z1));
	t_1 = (1.0 - z0) / t_0;
	t_2 = (1.0 - z0) / (2.0 + (pi / z1));
	t_3 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_4 = ((1.0 - t_3) - t_1) / (t_1 + t_3);
	t_5 = 0.5 / ((1.0 / t_0) + (0.5 * z0));
	tmp = 0.0;
	if (t_4 <= -5e+49)
		tmp = t_5;
	elseif (t_4 <= 2.0)
		tmp = ((1.0 - (z0 / 2.0)) - t_2) / (t_2 + (z0 / 2.0));
	elseif (t_4 <= 2e+282)
		tmp = t_5;
	else
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * pi)))) - (2.0 * (z0 * ((-0.25 * pi) - 0.7853981852531433)))) / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - z0), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - z0), $MachinePrecision] / N[(2.0 + N[(Pi / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(1.0 - t$95$3), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(0.5 / N[(N[(1.0 / t$95$0), $MachinePrecision] + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -5e+49], t$95$5, If[LessEqual[t$95$4, 2.0], N[(N[(N[(1.0 - N[(z0 / 2.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] / N[(t$95$2 + N[(z0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+282], t$95$5, N[(1.0 + N[(-1.0 * N[(N[(N[(2.0 * N[(N[(N[(-0.25 * Pi), $MachinePrecision] + N[(0.7853981852531433 * z0), $MachinePrecision]), $MachinePrecision] - N[(-0.25 * N[(z0 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(z0 * N[(N[(-0.25 * Pi), $MachinePrecision] - 0.7853981852531433), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < -5.0000000000000004e49 or 2 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 2.0000000000000001e282

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

   4. Applied rewrites 30.4%

      \[\leadsto \frac{\color{blue}{0.5}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{\frac{1}{2} \cdot z0}} \]
   6. Step-by-step derivation

      1. lower-*.f64 40.2%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 40.2%

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{0.5 \cdot z0}} \]

   8. Taylor expanded in z0 around 0

      \[\leadsto \frac{0.5}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + 0.5 \cdot z0} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{1}{2} \cdot z0} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{1}{2} \cdot z0} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{1}{2} \cdot z0} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{1}{2} \cdot z0} \]

      5. lower-PI.f64 38.9%

         \[\leadsto \frac{0.5}{\frac{1}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   10. Applied rewrites 38.9%

       \[\leadsto \frac{0.5}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + 0.5 \cdot z0} \]

   if -5.0000000000000004e49 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 2

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-PI.f64 52.5%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 52.5%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-PI.f64 53.7%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   7. Applied rewrites 53.7%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{\color{blue}{2}}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   9. Step-by-step derivation

   10. Applied rewrites 36.4%

       \[\leadsto \frac{\left(1 - \frac{z0}{\color{blue}{2}}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   11. Taylor expanded in z1 around inf

       \[\leadsto \frac{\left(1 - \frac{z0}{2}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{\color{blue}{2}}} \]
   12. Step-by-step derivation

   13. Applied rewrites 53.9%

       \[\leadsto \frac{\left(1 - \frac{z0}{2}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{\color{blue}{2}}} \]

   if 2.0000000000000001e282 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))))

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \pi - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      2. lower--.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      4. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]

   7. Applied rewrites 38.9%

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := 1 + e^{\frac{\pi}{z1}}\\ t_1 := \frac{1 - z0}{t\_0}\\ t_2 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_3 := \frac{\left(1 - t\_2\right) - t\_1}{t\_1 + t\_2}\\ t_4 := \frac{1 - z0}{2 + \frac{\pi}{z1}}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+49}:\\ \;\;\;\;\frac{0.5}{\frac{1}{t\_0} + 0.5 \cdot z0}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{\left(1 - \frac{z0}{2}\right) - t\_4}{t\_4 + \frac{z0}{2}}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{0.5}{t\_1 + 0.5 \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (+ 1.0 (exp (/ PI z1))))
       (t_1 (/ (- 1.0 z0) t_0))
       (t_2 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_3 (/ (- (- 1.0 t_2) t_1) (+ t_1 t_2)))
       (t_4 (/ (- 1.0 z0) (+ 2.0 (/ PI z1)))))
  (if (<= t_3 -5e+49)
    (/ 0.5 (+ (/ 1.0 t_0) (* 0.5 z0)))
    (if (<= t_3 2.0)
      (/ (- (- 1.0 (/ z0 2.0)) t_4) (+ t_4 (/ z0 2.0)))
      (if (<= t_3 2e+282)
        (/ 0.5 (+ t_1 (* 0.5 z0)))
        (+
         1.0
         (*
          -1.0
          (/
           (-
            (*
             2.0
             (-
              (+ (* -0.25 PI) (* 0.7853981852531433 z0))
              (* -0.25 (* z0 PI))))
            (* 2.0 (* z0 (- (* -0.25 PI) 0.7853981852531433))))
           z1))))))))

C

double code(double z0, double z1) {
	double t_0 = 1.0 + exp((((double) M_PI) / z1));
	double t_1 = (1.0 - z0) / t_0;
	double t_2 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_3 = ((1.0 - t_2) - t_1) / (t_1 + t_2);
	double t_4 = (1.0 - z0) / (2.0 + (((double) M_PI) / z1));
	double tmp;
	if (t_3 <= -5e+49) {
		tmp = 0.5 / ((1.0 / t_0) + (0.5 * z0));
	} else if (t_3 <= 2.0) {
		tmp = ((1.0 - (z0 / 2.0)) - t_4) / (t_4 + (z0 / 2.0));
	} else if (t_3 <= 2e+282) {
		tmp = 0.5 / (t_1 + (0.5 * z0));
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * ((double) M_PI)) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * ((double) M_PI))))) - (2.0 * (z0 * ((-0.25 * ((double) M_PI)) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = 1.0 + Math.exp((Math.PI / z1));
	double t_1 = (1.0 - z0) / t_0;
	double t_2 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_3 = ((1.0 - t_2) - t_1) / (t_1 + t_2);
	double t_4 = (1.0 - z0) / (2.0 + (Math.PI / z1));
	double tmp;
	if (t_3 <= -5e+49) {
		tmp = 0.5 / ((1.0 / t_0) + (0.5 * z0));
	} else if (t_3 <= 2.0) {
		tmp = ((1.0 - (z0 / 2.0)) - t_4) / (t_4 + (z0 / 2.0));
	} else if (t_3 <= 2e+282) {
		tmp = 0.5 / (t_1 + (0.5 * z0));
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * Math.PI) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * Math.PI)))) - (2.0 * (z0 * ((-0.25 * Math.PI) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = 1.0 + math.exp((math.pi / z1))
	t_1 = (1.0 - z0) / t_0
	t_2 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_3 = ((1.0 - t_2) - t_1) / (t_1 + t_2)
	t_4 = (1.0 - z0) / (2.0 + (math.pi / z1))
	tmp = 0
	if t_3 <= -5e+49:
		tmp = 0.5 / ((1.0 / t_0) + (0.5 * z0))
	elif t_3 <= 2.0:
		tmp = ((1.0 - (z0 / 2.0)) - t_4) / (t_4 + (z0 / 2.0))
	elif t_3 <= 2e+282:
		tmp = 0.5 / (t_1 + (0.5 * z0))
	else:
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * math.pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * math.pi)))) - (2.0 * (z0 * ((-0.25 * math.pi) - 0.7853981852531433)))) / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(1.0 + exp(Float64(pi / z1)))
	t_1 = Float64(Float64(1.0 - z0) / t_0)
	t_2 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_3 = Float64(Float64(Float64(1.0 - t_2) - t_1) / Float64(t_1 + t_2))
	t_4 = Float64(Float64(1.0 - z0) / Float64(2.0 + Float64(pi / z1)))
	tmp = 0.0
	if (t_3 <= -5e+49)
		tmp = Float64(0.5 / Float64(Float64(1.0 / t_0) + Float64(0.5 * z0)));
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(Float64(1.0 - Float64(z0 / 2.0)) - t_4) / Float64(t_4 + Float64(z0 / 2.0)));
	elseif (t_3 <= 2e+282)
		tmp = Float64(0.5 / Float64(t_1 + Float64(0.5 * z0)));
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(Float64(Float64(2.0 * Float64(Float64(Float64(-0.25 * pi) + Float64(0.7853981852531433 * z0)) - Float64(-0.25 * Float64(z0 * pi)))) - Float64(2.0 * Float64(z0 * Float64(Float64(-0.25 * pi) - 0.7853981852531433)))) / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = 1.0 + exp((pi / z1));
	t_1 = (1.0 - z0) / t_0;
	t_2 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_3 = ((1.0 - t_2) - t_1) / (t_1 + t_2);
	t_4 = (1.0 - z0) / (2.0 + (pi / z1));
	tmp = 0.0;
	if (t_3 <= -5e+49)
		tmp = 0.5 / ((1.0 / t_0) + (0.5 * z0));
	elseif (t_3 <= 2.0)
		tmp = ((1.0 - (z0 / 2.0)) - t_4) / (t_4 + (z0 / 2.0));
	elseif (t_3 <= 2e+282)
		tmp = 0.5 / (t_1 + (0.5 * z0));
	else
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * pi)))) - (2.0 * (z0 * ((-0.25 * pi) - 0.7853981852531433)))) / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - z0), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(1.0 - t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(1.0 - z0), $MachinePrecision] / N[(2.0 + N[(Pi / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+49], N[(0.5 / N[(N[(1.0 / t$95$0), $MachinePrecision] + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(N[(1.0 - N[(z0 / 2.0), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision] / N[(t$95$4 + N[(z0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+282], N[(0.5 / N[(t$95$1 + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 * N[(N[(N[(2.0 * N[(N[(N[(-0.25 * Pi), $MachinePrecision] + N[(0.7853981852531433 * z0), $MachinePrecision]), $MachinePrecision] - N[(-0.25 * N[(z0 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(z0 * N[(N[(-0.25 * Pi), $MachinePrecision] - 0.7853981852531433), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < -5.0000000000000004e49

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

   4. Applied rewrites 30.4%

      \[\leadsto \frac{\color{blue}{0.5}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{\frac{1}{2} \cdot z0}} \]
   6. Step-by-step derivation

      1. lower-*.f64 40.2%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 40.2%

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{0.5 \cdot z0}} \]

   8. Taylor expanded in z0 around 0

      \[\leadsto \frac{0.5}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + 0.5 \cdot z0} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1}{\color{blue}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{1}{2} \cdot z0} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1}{1 + \color{blue}{e^{\frac{\mathsf{PI}\left(\right)}{z1}}}} + \frac{1}{2} \cdot z0} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{1}{2} \cdot z0} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{1}{2} \cdot z0} \]

      5. lower-PI.f64 38.9%

         \[\leadsto \frac{0.5}{\frac{1}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   10. Applied rewrites 38.9%

       \[\leadsto \frac{0.5}{\color{blue}{\frac{1}{1 + e^{\frac{\pi}{z1}}}} + 0.5 \cdot z0} \]

   if -5.0000000000000004e49 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 2

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-PI.f64 52.5%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 52.5%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-PI.f64 53.7%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   7. Applied rewrites 53.7%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{\color{blue}{2}}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   9. Step-by-step derivation

   10. Applied rewrites 36.4%

       \[\leadsto \frac{\left(1 - \frac{z0}{\color{blue}{2}}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   11. Taylor expanded in z1 around inf

       \[\leadsto \frac{\left(1 - \frac{z0}{2}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{\color{blue}{2}}} \]
   12. Step-by-step derivation

   13. Applied rewrites 53.9%

       \[\leadsto \frac{\left(1 - \frac{z0}{2}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{\color{blue}{2}}} \]

   if 2 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 2.0000000000000001e282

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

   4. Applied rewrites 30.4%

      \[\leadsto \frac{\color{blue}{0.5}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{\frac{1}{2} \cdot z0}} \]
   6. Step-by-step derivation

      1. lower-*.f64 40.2%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 40.2%

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{0.5 \cdot z0}} \]

   if 2.0000000000000001e282 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))))

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \pi - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      2. lower--.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      4. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]

   7. Applied rewrites 38.9%

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{\pi}{z1}}\\ t_1 := \frac{1 - z0}{1 + t\_0}\\ t_2 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ \mathbf{if}\;\frac{\left(1 - t\_2\right) - t\_1}{t\_1 + t\_2} \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{\left(0.5 - 0.5 \cdot z0\right) + \frac{z0}{t\_0 - -1}}{t\_1 + 0.5 \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ PI z1)))
       (t_1 (/ (- 1.0 z0) (+ 1.0 t_0)))
       (t_2 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0))))
  (if (<= (/ (- (- 1.0 t_2) t_1) (+ t_1 t_2)) 2e+282)
    (/ (+ (- 0.5 (* 0.5 z0)) (/ z0 (- t_0 -1.0))) (+ t_1 (* 0.5 z0)))
    (+
     1.0
     (*
      -1.0
      (/
       (-
        (*
         2.0
         (-
          (+ (* -0.25 PI) (* 0.7853981852531433 z0))
          (* -0.25 (* z0 PI))))
        (* 2.0 (* z0 (- (* -0.25 PI) 0.7853981852531433))))
       z1))))))

C

double code(double z0, double z1) {
	double t_0 = exp((((double) M_PI) / z1));
	double t_1 = (1.0 - z0) / (1.0 + t_0);
	double t_2 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double tmp;
	if ((((1.0 - t_2) - t_1) / (t_1 + t_2)) <= 2e+282) {
		tmp = ((0.5 - (0.5 * z0)) + (z0 / (t_0 - -1.0))) / (t_1 + (0.5 * z0));
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * ((double) M_PI)) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * ((double) M_PI))))) - (2.0 * (z0 * ((-0.25 * ((double) M_PI)) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((Math.PI / z1));
	double t_1 = (1.0 - z0) / (1.0 + t_0);
	double t_2 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double tmp;
	if ((((1.0 - t_2) - t_1) / (t_1 + t_2)) <= 2e+282) {
		tmp = ((0.5 - (0.5 * z0)) + (z0 / (t_0 - -1.0))) / (t_1 + (0.5 * z0));
	} else {
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * Math.PI) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * Math.PI)))) - (2.0 * (z0 * ((-0.25 * Math.PI) - 0.7853981852531433)))) / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((math.pi / z1))
	t_1 = (1.0 - z0) / (1.0 + t_0)
	t_2 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	tmp = 0
	if (((1.0 - t_2) - t_1) / (t_1 + t_2)) <= 2e+282:
		tmp = ((0.5 - (0.5 * z0)) + (z0 / (t_0 - -1.0))) / (t_1 + (0.5 * z0))
	else:
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * math.pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * math.pi)))) - (2.0 * (z0 * ((-0.25 * math.pi) - 0.7853981852531433)))) / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(pi / z1))
	t_1 = Float64(Float64(1.0 - z0) / Float64(1.0 + t_0))
	t_2 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	tmp = 0.0
	if (Float64(Float64(Float64(1.0 - t_2) - t_1) / Float64(t_1 + t_2)) <= 2e+282)
		tmp = Float64(Float64(Float64(0.5 - Float64(0.5 * z0)) + Float64(z0 / Float64(t_0 - -1.0))) / Float64(t_1 + Float64(0.5 * z0)));
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(Float64(Float64(2.0 * Float64(Float64(Float64(-0.25 * pi) + Float64(0.7853981852531433 * z0)) - Float64(-0.25 * Float64(z0 * pi)))) - Float64(2.0 * Float64(z0 * Float64(Float64(-0.25 * pi) - 0.7853981852531433)))) / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((pi / z1));
	t_1 = (1.0 - z0) / (1.0 + t_0);
	t_2 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	tmp = 0.0;
	if ((((1.0 - t_2) - t_1) / (t_1 + t_2)) <= 2e+282)
		tmp = ((0.5 - (0.5 * z0)) + (z0 / (t_0 - -1.0))) / (t_1 + (0.5 * z0));
	else
		tmp = 1.0 + (-1.0 * (((2.0 * (((-0.25 * pi) + (0.7853981852531433 * z0)) - (-0.25 * (z0 * pi)))) - (2.0 * (z0 * ((-0.25 * pi) - 0.7853981852531433)))) / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(1.0 - t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision], 2e+282], N[(N[(N[(0.5 - N[(0.5 * z0), $MachinePrecision]), $MachinePrecision] + N[(z0 / N[(t$95$0 - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 * N[(N[(N[(2.0 * N[(N[(N[(-0.25 * Pi), $MachinePrecision] + N[(0.7853981852531433 * z0), $MachinePrecision]), $MachinePrecision] - N[(-0.25 * N[(z0 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(z0 * N[(N[(-0.25 * Pi), $MachinePrecision] - 0.7853981852531433), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 2.0000000000000001e282

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \color{blue}{\frac{1}{2} \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 44.6%

         \[\leadsto \frac{\left(1 - 0.5 \cdot \color{blue}{z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 44.6%

      \[\leadsto \frac{\left(1 - \color{blue}{0.5 \cdot z0}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

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

      1. lower-*.f64 55.5%

         \[\leadsto \frac{\left(1 - 0.5 \cdot z0\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 55.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-sub N/A

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

      5. lift-/.f64 N/A

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

      6. associate--r- N/A

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

      7. lower-+.f64 N/A

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

   9. Applied rewrites 66.8%

      \[\leadsto \frac{\color{blue}{\left(\left(1 - 0.5 \cdot z0\right) - \frac{1}{e^{\frac{\pi}{z1}} - -1}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   10. Taylor expanded in z1 around inf

       \[\leadsto \frac{\color{blue}{\left(\frac{1}{2} - \frac{1}{2} \cdot z0\right)} + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]
   11. Step-by-step derivation

       1. lower--.f64 N/A

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

       2. lower-*.f64 65.1%

          \[\leadsto \frac{\left(0.5 - 0.5 \cdot \color{blue}{z0}\right) + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   12. Applied rewrites 65.1%

       \[\leadsto \frac{\color{blue}{\left(0.5 - 0.5 \cdot z0\right)} + \frac{z0}{e^{\frac{\pi}{z1}} - -1}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot z0} \]

   if 2.0000000000000001e282 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))))

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \pi - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      2. lower--.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) - \frac{7853981852531433}{10000000000000000}\right)\right)}{z1} \]

      4. lower-PI.f64 38.9%

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]

   7. Applied rewrites 38.9%

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(z0 \cdot \left(-0.25 \cdot \pi - 0.7853981852531433\right)\right)}{z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}\\ t_1 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_2 := \frac{\pi}{z0 \cdot z1}\\ t_3 := \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}\\ t_4 := \frac{\left(1 - t\_1\right) - t\_0}{t\_0 + t\_1}\\ t_5 := 0.7853981852531433 + 0.25 \cdot \pi\\ \mathbf{if}\;t\_4 \leq 0:\\ \;\;\;\;\frac{\left(1 - 0.5 \cdot z0\right) - t\_3}{t\_3 + 0.5 \cdot z0}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+218}:\\ \;\;\;\;\frac{0.5}{\frac{1 - z0}{1 + \left(1 + \frac{\pi}{z1}\right)} + 0.5 \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;1 + -1 \cdot \left(z0 \cdot \left(\left(-1 \cdot \frac{-2 \cdot t\_5 - 2 \cdot t\_5}{z1} + -0.5 \cdot t\_2\right) - 0.5 \cdot t\_2\right)\right)\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (/ (- 1.0 z0) (+ 1.0 (exp (/ PI z1)))))
       (t_1 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_2 (/ PI (* z0 z1)))
       (t_3 (/ (* -1.0 z0) (+ 2.0 (/ PI z1))))
       (t_4 (/ (- (- 1.0 t_1) t_0) (+ t_0 t_1)))
       (t_5 (+ 0.7853981852531433 (* 0.25 PI))))
  (if (<= t_4 0.0)
    (/ (- (- 1.0 (* 0.5 z0)) t_3) (+ t_3 (* 0.5 z0)))
    (if (<= t_4 5e+218)
      (/ 0.5 (+ (/ (- 1.0 z0) (+ 1.0 (+ 1.0 (/ PI z1)))) (* 0.5 z0)))
      (+
       1.0
       (*
        -1.0
        (*
         z0
         (-
          (+
           (* -1.0 (/ (- (* -2.0 t_5) (* 2.0 t_5)) z1))
           (* -0.5 t_2))
          (* 0.5 t_2)))))))))

C

double code(double z0, double z1) {
	double t_0 = (1.0 - z0) / (1.0 + exp((((double) M_PI) / z1)));
	double t_1 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_2 = ((double) M_PI) / (z0 * z1);
	double t_3 = (-1.0 * z0) / (2.0 + (((double) M_PI) / z1));
	double t_4 = ((1.0 - t_1) - t_0) / (t_0 + t_1);
	double t_5 = 0.7853981852531433 + (0.25 * ((double) M_PI));
	double tmp;
	if (t_4 <= 0.0) {
		tmp = ((1.0 - (0.5 * z0)) - t_3) / (t_3 + (0.5 * z0));
	} else if (t_4 <= 5e+218) {
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (((double) M_PI) / z1)))) + (0.5 * z0));
	} else {
		tmp = 1.0 + (-1.0 * (z0 * (((-1.0 * (((-2.0 * t_5) - (2.0 * t_5)) / z1)) + (-0.5 * t_2)) - (0.5 * t_2))));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = (1.0 - z0) / (1.0 + Math.exp((Math.PI / z1)));
	double t_1 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_2 = Math.PI / (z0 * z1);
	double t_3 = (-1.0 * z0) / (2.0 + (Math.PI / z1));
	double t_4 = ((1.0 - t_1) - t_0) / (t_0 + t_1);
	double t_5 = 0.7853981852531433 + (0.25 * Math.PI);
	double tmp;
	if (t_4 <= 0.0) {
		tmp = ((1.0 - (0.5 * z0)) - t_3) / (t_3 + (0.5 * z0));
	} else if (t_4 <= 5e+218) {
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (Math.PI / z1)))) + (0.5 * z0));
	} else {
		tmp = 1.0 + (-1.0 * (z0 * (((-1.0 * (((-2.0 * t_5) - (2.0 * t_5)) / z1)) + (-0.5 * t_2)) - (0.5 * t_2))));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (1.0 - z0) / (1.0 + math.exp((math.pi / z1)))
	t_1 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_2 = math.pi / (z0 * z1)
	t_3 = (-1.0 * z0) / (2.0 + (math.pi / z1))
	t_4 = ((1.0 - t_1) - t_0) / (t_0 + t_1)
	t_5 = 0.7853981852531433 + (0.25 * math.pi)
	tmp = 0
	if t_4 <= 0.0:
		tmp = ((1.0 - (0.5 * z0)) - t_3) / (t_3 + (0.5 * z0))
	elif t_4 <= 5e+218:
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (math.pi / z1)))) + (0.5 * z0))
	else:
		tmp = 1.0 + (-1.0 * (z0 * (((-1.0 * (((-2.0 * t_5) - (2.0 * t_5)) / z1)) + (-0.5 * t_2)) - (0.5 * t_2))))
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(1.0 - z0) / Float64(1.0 + exp(Float64(pi / z1))))
	t_1 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_2 = Float64(pi / Float64(z0 * z1))
	t_3 = Float64(Float64(-1.0 * z0) / Float64(2.0 + Float64(pi / z1)))
	t_4 = Float64(Float64(Float64(1.0 - t_1) - t_0) / Float64(t_0 + t_1))
	t_5 = Float64(0.7853981852531433 + Float64(0.25 * pi))
	tmp = 0.0
	if (t_4 <= 0.0)
		tmp = Float64(Float64(Float64(1.0 - Float64(0.5 * z0)) - t_3) / Float64(t_3 + Float64(0.5 * z0)));
	elseif (t_4 <= 5e+218)
		tmp = Float64(0.5 / Float64(Float64(Float64(1.0 - z0) / Float64(1.0 + Float64(1.0 + Float64(pi / z1)))) + Float64(0.5 * z0)));
	else
		tmp = Float64(1.0 + Float64(-1.0 * Float64(z0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(-2.0 * t_5) - Float64(2.0 * t_5)) / z1)) + Float64(-0.5 * t_2)) - Float64(0.5 * t_2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (1.0 - z0) / (1.0 + exp((pi / z1)));
	t_1 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_2 = pi / (z0 * z1);
	t_3 = (-1.0 * z0) / (2.0 + (pi / z1));
	t_4 = ((1.0 - t_1) - t_0) / (t_0 + t_1);
	t_5 = 0.7853981852531433 + (0.25 * pi);
	tmp = 0.0;
	if (t_4 <= 0.0)
		tmp = ((1.0 - (0.5 * z0)) - t_3) / (t_3 + (0.5 * z0));
	elseif (t_4 <= 5e+218)
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (pi / z1)))) + (0.5 * z0));
	else
		tmp = 1.0 + (-1.0 * (z0 * (((-1.0 * (((-2.0 * t_5) - (2.0 * t_5)) / z1)) + (-0.5 * t_2)) - (0.5 * t_2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(Pi / N[(z0 * z1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(-1.0 * z0), $MachinePrecision] / N[(2.0 + N[(Pi / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(1.0 - t$95$1), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(t$95$0 + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(0.7853981852531433 + N[(0.25 * Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, 0.0], N[(N[(N[(1.0 - N[(0.5 * z0), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] / N[(t$95$3 + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+218], N[(0.5 / N[(N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[(1.0 + N[(Pi / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 * N[(z0 * N[(N[(N[(-1.0 * N[(N[(N[(-2.0 * t$95$5), $MachinePrecision] - N[(2.0 * t$95$5), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(0.5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 0.0

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-PI.f64 52.5%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 52.5%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-PI.f64 53.7%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   7. Applied rewrites 53.7%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   8. Taylor expanded in z0 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{\color{blue}{-1 \cdot z0}}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   9. Step-by-step derivation

      1. lower-*.f64 32.3%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{-1 \cdot \color{blue}{z0}}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   10. Applied rewrites 32.3%

       \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{\color{blue}{-1 \cdot z0}}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   11. Taylor expanded in z0 around inf

       \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{\color{blue}{-1 \cdot z0}}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   12. Step-by-step derivation

       1. lower-*.f64 33.7%

          \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot \color{blue}{z0}}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   13. Applied rewrites 33.7%

       \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{\color{blue}{-1 \cdot z0}}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   14. Taylor expanded in z1 around inf

       \[\leadsto \frac{\left(1 - \color{blue}{\frac{1}{2} \cdot z0}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   15. Step-by-step derivation

       1. lower-*.f64 16.4%

          \[\leadsto \frac{\left(1 - 0.5 \cdot \color{blue}{z0}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   16. Applied rewrites 16.4%

       \[\leadsto \frac{\left(1 - \color{blue}{0.5 \cdot z0}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   17. Taylor expanded in z1 around inf

       \[\leadsto \frac{\left(1 - 0.5 \cdot z0\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot z0}{2 + \frac{\pi}{z1}} + \color{blue}{\frac{1}{2} \cdot z0}} \]
   18. Step-by-step derivation

       1. lower-*.f64 29.3%

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

   19. Applied rewrites 29.3%

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

   if 0.0 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 4.9999999999999998e218

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

   4. Applied rewrites 30.4%

      \[\leadsto \frac{\color{blue}{0.5}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{\frac{1}{2} \cdot z0}} \]
   6. Step-by-step derivation

      1. lower-*.f64 40.2%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 40.2%

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{0.5 \cdot z0}} \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \color{blue}{\left(1 + \frac{\pi}{z1}\right)}} + 0.5 \cdot z0} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1 - z0}{1 + \left(1 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}\right)} + \frac{1}{2} \cdot z0} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1 - z0}{1 + \left(1 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}\right)} + \frac{1}{2} \cdot z0} \]

      3. lower-PI.f64 34.5%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \left(1 + \frac{\pi}{z1}\right)} + 0.5 \cdot z0} \]

   10. Applied rewrites 34.5%

       \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \color{blue}{\left(1 + \frac{\pi}{z1}\right)}} + 0.5 \cdot z0} \]

   if 4.9999999999999998e218 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))))

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto 1 + -1 \cdot \color{blue}{\left(z0 \cdot \left(\left(-1 \cdot \frac{-2 \cdot \left(\frac{7853981852531433}{10000000000000000} + \frac{1}{4} \cdot \pi\right) - 2 \cdot \left(\frac{7853981852531433}{10000000000000000} + \frac{1}{4} \cdot \pi\right)}{z1} + \frac{-1}{2} \cdot \frac{\pi}{z0 \cdot z1}\right) - \frac{1}{2} \cdot \frac{\pi}{z0 \cdot z1}\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \left(z0 \cdot \color{blue}{\left(\left(-1 \cdot \frac{-2 \cdot \left(\frac{7853981852531433}{10000000000000000} + \frac{1}{4} \cdot \mathsf{PI}\left(\right)\right) - 2 \cdot \left(\frac{7853981852531433}{10000000000000000} + \frac{1}{4} \cdot \mathsf{PI}\left(\right)\right)}{z1} + \frac{-1}{2} \cdot \frac{\mathsf{PI}\left(\right)}{z0 \cdot z1}\right) - \frac{1}{2} \cdot \frac{\mathsf{PI}\left(\right)}{z0 \cdot z1}\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \left(z0 \cdot \left(\left(-1 \cdot \frac{-2 \cdot \left(\frac{7853981852531433}{10000000000000000} + \frac{1}{4} \cdot \mathsf{PI}\left(\right)\right) - 2 \cdot \left(\frac{7853981852531433}{10000000000000000} + \frac{1}{4} \cdot \mathsf{PI}\left(\right)\right)}{z1} + \frac{-1}{2} \cdot \frac{\mathsf{PI}\left(\right)}{z0 \cdot z1}\right) - \color{blue}{\frac{1}{2} \cdot \frac{\mathsf{PI}\left(\right)}{z0 \cdot z1}}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto 1 + -1 \cdot \left(z0 \cdot \left(\left(-1 \cdot \frac{-2 \cdot \left(\frac{7853981852531433}{10000000000000000} + \frac{1}{4} \cdot \mathsf{PI}\left(\right)\right) - 2 \cdot \left(\frac{7853981852531433}{10000000000000000} + \frac{1}{4} \cdot \mathsf{PI}\left(\right)\right)}{z1} + \frac{-1}{2} \cdot \frac{\mathsf{PI}\left(\right)}{z0 \cdot z1}\right) - \frac{1}{2} \cdot \color{blue}{\frac{\mathsf{PI}\left(\right)}{z0 \cdot z1}}\right)\right) \]

   7. Applied rewrites 39.1%

      \[\leadsto 1 + -1 \cdot \color{blue}{\left(z0 \cdot \left(\left(-1 \cdot \frac{-2 \cdot \left(0.7853981852531433 + 0.25 \cdot \pi\right) - 2 \cdot \left(0.7853981852531433 + 0.25 \cdot \pi\right)}{z1} + -0.5 \cdot \frac{\pi}{z0 \cdot z1}\right) - 0.5 \cdot \frac{\pi}{z0 \cdot z1}\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}\\ t_1 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ t_2 := \frac{\left(1 - t\_1\right) - t\_0}{t\_0 + t\_1}\\ t_3 := \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}\\ \mathbf{if}\;t\_2 \leq 0:\\ \;\;\;\;\frac{\left(1 - 0.5 \cdot z0\right) - t\_3}{t\_3 + 0.5 \cdot z0}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+218}:\\ \;\;\;\;\frac{0.5}{\frac{1 - z0}{1 + \left(1 + \frac{\pi}{z1}\right)} + 0.5 \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;1 - 2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (/ (- 1.0 z0) (+ 1.0 (exp (/ PI z1)))))
       (t_1 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))
       (t_2 (/ (- (- 1.0 t_1) t_0) (+ t_0 t_1)))
       (t_3 (/ (* -1.0 z0) (+ 2.0 (/ PI z1)))))
  (if (<= t_2 0.0)
    (/ (- (- 1.0 (* 0.5 z0)) t_3) (+ t_3 (* 0.5 z0)))
    (if (<= t_2 5e+218)
      (/ 0.5 (+ (/ (- 1.0 z0) (+ 1.0 (+ 1.0 (/ PI z1)))) (* 0.5 z0)))
      (-
       1.0
       (*
        2.0
        (*
         (- (* 0.7853981852531433 z0) (* -0.25 (- (* PI z0) PI)))
         (/ 2.0 z1))))))))

C

double code(double z0, double z1) {
	double t_0 = (1.0 - z0) / (1.0 + exp((((double) M_PI) / z1)));
	double t_1 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double t_2 = ((1.0 - t_1) - t_0) / (t_0 + t_1);
	double t_3 = (-1.0 * z0) / (2.0 + (((double) M_PI) / z1));
	double tmp;
	if (t_2 <= 0.0) {
		tmp = ((1.0 - (0.5 * z0)) - t_3) / (t_3 + (0.5 * z0));
	} else if (t_2 <= 5e+218) {
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (((double) M_PI) / z1)))) + (0.5 * z0));
	} else {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((((double) M_PI) * z0) - ((double) M_PI)))) * (2.0 / z1)));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = (1.0 - z0) / (1.0 + Math.exp((Math.PI / z1)));
	double t_1 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double t_2 = ((1.0 - t_1) - t_0) / (t_0 + t_1);
	double t_3 = (-1.0 * z0) / (2.0 + (Math.PI / z1));
	double tmp;
	if (t_2 <= 0.0) {
		tmp = ((1.0 - (0.5 * z0)) - t_3) / (t_3 + (0.5 * z0));
	} else if (t_2 <= 5e+218) {
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (Math.PI / z1)))) + (0.5 * z0));
	} else {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((Math.PI * z0) - Math.PI))) * (2.0 / z1)));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (1.0 - z0) / (1.0 + math.exp((math.pi / z1)))
	t_1 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	t_2 = ((1.0 - t_1) - t_0) / (t_0 + t_1)
	t_3 = (-1.0 * z0) / (2.0 + (math.pi / z1))
	tmp = 0
	if t_2 <= 0.0:
		tmp = ((1.0 - (0.5 * z0)) - t_3) / (t_3 + (0.5 * z0))
	elif t_2 <= 5e+218:
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (math.pi / z1)))) + (0.5 * z0))
	else:
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((math.pi * z0) - math.pi))) * (2.0 / z1)))
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(1.0 - z0) / Float64(1.0 + exp(Float64(pi / z1))))
	t_1 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	t_2 = Float64(Float64(Float64(1.0 - t_1) - t_0) / Float64(t_0 + t_1))
	t_3 = Float64(Float64(-1.0 * z0) / Float64(2.0 + Float64(pi / z1)))
	tmp = 0.0
	if (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(1.0 - Float64(0.5 * z0)) - t_3) / Float64(t_3 + Float64(0.5 * z0)));
	elseif (t_2 <= 5e+218)
		tmp = Float64(0.5 / Float64(Float64(Float64(1.0 - z0) / Float64(1.0 + Float64(1.0 + Float64(pi / z1)))) + Float64(0.5 * z0)));
	else
		tmp = Float64(1.0 - Float64(2.0 * Float64(Float64(Float64(0.7853981852531433 * z0) - Float64(-0.25 * Float64(Float64(pi * z0) - pi))) * Float64(2.0 / z1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (1.0 - z0) / (1.0 + exp((pi / z1)));
	t_1 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	t_2 = ((1.0 - t_1) - t_0) / (t_0 + t_1);
	t_3 = (-1.0 * z0) / (2.0 + (pi / z1));
	tmp = 0.0;
	if (t_2 <= 0.0)
		tmp = ((1.0 - (0.5 * z0)) - t_3) / (t_3 + (0.5 * z0));
	elseif (t_2 <= 5e+218)
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (pi / z1)))) + (0.5 * z0));
	else
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((pi * z0) - pi))) * (2.0 / z1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(1.0 - t$95$1), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(t$95$0 + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(-1.0 * z0), $MachinePrecision] / N[(2.0 + N[(Pi / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.0], N[(N[(N[(1.0 - N[(0.5 * z0), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] / N[(t$95$3 + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+218], N[(0.5 / N[(N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[(1.0 + N[(Pi / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(2.0 * N[(N[(N[(0.7853981852531433 * z0), $MachinePrecision] - N[(-0.25 * N[(N[(Pi * z0), $MachinePrecision] - Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 0.0

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-PI.f64 52.5%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   4. Applied rewrites 52.5%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}} + \frac{z0}{e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z1}} - -1}} \]

      3. lower-PI.f64 53.7%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   7. Applied rewrites 53.7%

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{\color{blue}{2 + \frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   8. Taylor expanded in z0 around inf

      \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{\color{blue}{-1 \cdot z0}}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   9. Step-by-step derivation

      1. lower-*.f64 32.3%

         \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{-1 \cdot \color{blue}{z0}}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   10. Applied rewrites 32.3%

       \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{\color{blue}{-1 \cdot z0}}{2 + \frac{\pi}{z1}}}{\frac{1 - z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   11. Taylor expanded in z0 around inf

       \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{\color{blue}{-1 \cdot z0}}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   12. Step-by-step derivation

       1. lower-*.f64 33.7%

          \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot \color{blue}{z0}}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   13. Applied rewrites 33.7%

       \[\leadsto \frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{\color{blue}{-1 \cdot z0}}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   14. Taylor expanded in z1 around inf

       \[\leadsto \frac{\left(1 - \color{blue}{\frac{1}{2} \cdot z0}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   15. Step-by-step derivation

       1. lower-*.f64 16.4%

          \[\leadsto \frac{\left(1 - 0.5 \cdot \color{blue}{z0}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   16. Applied rewrites 16.4%

       \[\leadsto \frac{\left(1 - \color{blue}{0.5 \cdot z0}\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot z0}{2 + \frac{\pi}{z1}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   17. Taylor expanded in z1 around inf

       \[\leadsto \frac{\left(1 - 0.5 \cdot z0\right) - \frac{-1 \cdot z0}{2 + \frac{\pi}{z1}}}{\frac{-1 \cdot z0}{2 + \frac{\pi}{z1}} + \color{blue}{\frac{1}{2} \cdot z0}} \]
   18. Step-by-step derivation

       1. lower-*.f64 29.3%

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

   19. Applied rewrites 29.3%

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

   if 0.0 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 4.9999999999999998e218

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

   4. Applied rewrites 30.4%

      \[\leadsto \frac{\color{blue}{0.5}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{\frac{1}{2} \cdot z0}} \]
   6. Step-by-step derivation

      1. lower-*.f64 40.2%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 40.2%

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{0.5 \cdot z0}} \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \color{blue}{\left(1 + \frac{\pi}{z1}\right)}} + 0.5 \cdot z0} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1 - z0}{1 + \left(1 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}\right)} + \frac{1}{2} \cdot z0} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1 - z0}{1 + \left(1 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}\right)} + \frac{1}{2} \cdot z0} \]

      3. lower-PI.f64 34.5%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \left(1 + \frac{\pi}{z1}\right)} + 0.5 \cdot z0} \]

   10. Applied rewrites 34.5%

       \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \color{blue}{\left(1 + \frac{\pi}{z1}\right)}} + 0.5 \cdot z0} \]

   if 4.9999999999999998e218 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))))

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. add-flip N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)\right)\right) \]

   6. Applied rewrites 39.1%

      \[\leadsto 1 - \color{blue}{2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 45.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}\\ t_1 := \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\\ \mathbf{if}\;\frac{\left(1 - t\_1\right) - t\_0}{t\_0 + t\_1} \leq 5 \cdot 10^{+218}:\\ \;\;\;\;\frac{0.5}{\frac{1 - z0}{1 + \left(1 + \frac{\pi}{z1}\right)} + 0.5 \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;1 - 2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (/ (- 1.0 z0) (+ 1.0 (exp (/ PI z1)))))
       (t_1 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0))))
  (if (<= (/ (- (- 1.0 t_1) t_0) (+ t_0 t_1)) 5e+218)
    (/ 0.5 (+ (/ (- 1.0 z0) (+ 1.0 (+ 1.0 (/ PI z1)))) (* 0.5 z0)))
    (-
     1.0
     (*
      2.0
      (*
       (- (* 0.7853981852531433 z0) (* -0.25 (- (* PI z0) PI)))
       (/ 2.0 z1)))))))

C

double code(double z0, double z1) {
	double t_0 = (1.0 - z0) / (1.0 + exp((((double) M_PI) / z1)));
	double t_1 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	double tmp;
	if ((((1.0 - t_1) - t_0) / (t_0 + t_1)) <= 5e+218) {
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (((double) M_PI) / z1)))) + (0.5 * z0));
	} else {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((((double) M_PI) * z0) - ((double) M_PI)))) * (2.0 / z1)));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = (1.0 - z0) / (1.0 + Math.exp((Math.PI / z1)));
	double t_1 = z0 / (Math.exp((-3.1415927410125732 / z1)) - -1.0);
	double tmp;
	if ((((1.0 - t_1) - t_0) / (t_0 + t_1)) <= 5e+218) {
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (Math.PI / z1)))) + (0.5 * z0));
	} else {
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((Math.PI * z0) - Math.PI))) * (2.0 / z1)));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (1.0 - z0) / (1.0 + math.exp((math.pi / z1)))
	t_1 = z0 / (math.exp((-3.1415927410125732 / z1)) - -1.0)
	tmp = 0
	if (((1.0 - t_1) - t_0) / (t_0 + t_1)) <= 5e+218:
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (math.pi / z1)))) + (0.5 * z0))
	else:
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((math.pi * z0) - math.pi))) * (2.0 / z1)))
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(1.0 - z0) / Float64(1.0 + exp(Float64(pi / z1))))
	t_1 = Float64(z0 / Float64(exp(Float64(-3.1415927410125732 / z1)) - -1.0))
	tmp = 0.0
	if (Float64(Float64(Float64(1.0 - t_1) - t_0) / Float64(t_0 + t_1)) <= 5e+218)
		tmp = Float64(0.5 / Float64(Float64(Float64(1.0 - z0) / Float64(1.0 + Float64(1.0 + Float64(pi / z1)))) + Float64(0.5 * z0)));
	else
		tmp = Float64(1.0 - Float64(2.0 * Float64(Float64(Float64(0.7853981852531433 * z0) - Float64(-0.25 * Float64(Float64(pi * z0) - pi))) * Float64(2.0 / z1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (1.0 - z0) / (1.0 + exp((pi / z1)));
	t_1 = z0 / (exp((-3.1415927410125732 / z1)) - -1.0);
	tmp = 0.0;
	if ((((1.0 - t_1) - t_0) / (t_0 + t_1)) <= 5e+218)
		tmp = 0.5 / (((1.0 - z0) / (1.0 + (1.0 + (pi / z1)))) + (0.5 * z0));
	else
		tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((pi * z0) - pi))) * (2.0 / z1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[Exp[N[(Pi / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z0 / N[(N[Exp[N[(-3.1415927410125732 / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(1.0 - t$95$1), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(t$95$0 + t$95$1), $MachinePrecision]), $MachinePrecision], 5e+218], N[(0.5 / N[(N[(N[(1.0 - z0), $MachinePrecision] / N[(1.0 + N[(1.0 + N[(Pi / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(2.0 * N[(N[(N[(0.7853981852531433 * z0), $MachinePrecision] - N[(-0.25 * N[(N[(Pi * z0), $MachinePrecision] - Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64))))) < 4.9999999999999998e218

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]
   3. Step-by-step derivation

   4. Applied rewrites 30.4%

      \[\leadsto \frac{\color{blue}{0.5}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   5. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{\frac{1}{2} \cdot z0}} \]
   6. Step-by-step derivation

      1. lower-*.f64 40.2%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + 0.5 \cdot \color{blue}{z0}} \]

   7. Applied rewrites 40.2%

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \color{blue}{0.5 \cdot z0}} \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \color{blue}{\left(1 + \frac{\pi}{z1}\right)}} + 0.5 \cdot z0} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1 - z0}{1 + \left(1 + \color{blue}{\frac{\mathsf{PI}\left(\right)}{z1}}\right)} + \frac{1}{2} \cdot z0} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2}}{\frac{1 - z0}{1 + \left(1 + \frac{\mathsf{PI}\left(\right)}{\color{blue}{z1}}\right)} + \frac{1}{2} \cdot z0} \]

      3. lower-PI.f64 34.5%

         \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \left(1 + \frac{\pi}{z1}\right)} + 0.5 \cdot z0} \]

   10. Applied rewrites 34.5%

       \[\leadsto \frac{0.5}{\frac{1 - z0}{1 + \color{blue}{\left(1 + \frac{\pi}{z1}\right)}} + 0.5 \cdot z0} \]

   if 4.9999999999999998e218 < (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) z0) (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (PI.f64) z1)))) (/.f64 z0 (-.f64 (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z1)) #s(literal -1 binary64)))))

   1. Initial program 66.4%

      \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      3. lower-/.f64 N/A

         \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

      2. add-flip N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)\right)\right) \]

   6. Applied rewrites 39.1%

      \[\leadsto 1 - \color{blue}{2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 39.1% accurate, 11.5× speedup

Math

\[1 - 2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right) \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (-
 1.0
 (*
  2.0
  (*
   (- (* 0.7853981852531433 z0) (* -0.25 (- (* PI z0) PI)))
   (/ 2.0 z1)))))

C

double code(double z0, double z1) {
	return 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((((double) M_PI) * z0) - ((double) M_PI)))) * (2.0 / z1)));
}

Java

public static double code(double z0, double z1) {
	return 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((Math.PI * z0) - Math.PI))) * (2.0 / z1)));
}

Python

def code(z0, z1):
	return 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((math.pi * z0) - math.pi))) * (2.0 / z1)))

Julia

function code(z0, z1)
	return Float64(1.0 - Float64(2.0 * Float64(Float64(Float64(0.7853981852531433 * z0) - Float64(-0.25 * Float64(Float64(pi * z0) - pi))) * Float64(2.0 / z1))))
end

MATLAB

function tmp = code(z0, z1)
	tmp = 1.0 - (2.0 * (((0.7853981852531433 * z0) - (-0.25 * ((pi * z0) - pi))) * (2.0 / z1)));
end

Wolfram

code[z0_, z1_] := N[(1.0 - N[(2.0 * N[(N[(N[(0.7853981852531433 * z0), $MachinePrecision] - N[(-0.25 * N[(N[(Pi * z0), $MachinePrecision] - Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.4%

   \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

2. Taylor expanded in z1 around -inf

   \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

   2. lower-*.f64 N/A

      \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

   3. lower-/.f64 N/A

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

4. Applied rewrites 39.1%

   \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]
5. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

   2. add-flip N/A

      \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

   3. lower--.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto 1 - \left(\mathsf{neg}\left(-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right) \]

   5. mul-1-neg N/A

      \[\leadsto 1 - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}\right)\right)\right)\right) \]

6. Applied rewrites 39.1%

   \[\leadsto 1 - \color{blue}{2 \cdot \left(\left(0.7853981852531433 \cdot z0 - -0.25 \cdot \left(\pi \cdot z0 - \pi\right)\right) \cdot \frac{2}{z1}\right)} \]
7. Add Preprocessing

Alternative 13: 38.9% accurate, 35.1× speedup

Math

\[1 - \frac{-3.141592653589793}{z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (- 1.0 (/ -3.141592653589793 z1)))

C

double code(double z0, double z1) {
	return 1.0 - (-3.141592653589793 / z1);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = 1.0d0 - ((-3.141592653589793d0) / z1)
end function

Java

public static double code(double z0, double z1) {
	return 1.0 - (-3.141592653589793 / z1);
}

Python

def code(z0, z1):
	return 1.0 - (-3.141592653589793 / z1)

Julia

function code(z0, z1)
	return Float64(1.0 - Float64(-3.141592653589793 / z1))
end

MATLAB

function tmp = code(z0, z1)
	tmp = 1.0 - (-3.141592653589793 / z1);
end

Wolfram

code[z0_, z1_] := N[(1.0 - N[(-3.141592653589793 / z1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.4%

   \[\frac{\left(1 - \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}\right) - \frac{1 - z0}{1 + e^{\frac{\pi}{z1}}}}{\frac{1 - z0}{1 + e^{\frac{\pi}{z1}}} + \frac{z0}{e^{\frac{-3.1415927410125732}{z1}} - -1}} \]

2. Taylor expanded in z1 around -inf

   \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \pi\right) - \left(\frac{-1}{4} \cdot \pi + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto 1 + \color{blue}{-1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

   2. lower-*.f64 N/A

      \[\leadsto 1 + -1 \cdot \color{blue}{\frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{z1}} \]

   3. lower-/.f64 N/A

      \[\leadsto 1 + -1 \cdot \frac{2 \cdot \left(\left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right) - \frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right)\right) - 2 \cdot \left(\frac{-1}{4} \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) - \left(\frac{-1}{4} \cdot \mathsf{PI}\left(\right) + \frac{7853981852531433}{10000000000000000} \cdot z0\right)\right)}{\color{blue}{z1}} \]

4. Applied rewrites 39.1%

   \[\leadsto \color{blue}{1 + -1 \cdot \frac{2 \cdot \left(\left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right) - -0.25 \cdot \left(z0 \cdot \pi\right)\right) - 2 \cdot \left(-0.25 \cdot \left(z0 \cdot \pi\right) - \left(-0.25 \cdot \pi + 0.7853981852531433 \cdot z0\right)\right)}{z1}} \]

5. Taylor expanded in z0 around 0

   \[\leadsto 1 + -1 \cdot \frac{\frac{-1}{2} \cdot \pi - \frac{1}{2} \cdot \pi}{z1} \]
6. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto 1 + -1 \cdot \frac{\frac{-1}{2} \cdot \mathsf{PI}\left(\right) - \frac{1}{2} \cdot \mathsf{PI}\left(\right)}{z1} \]

   2. lower-*.f64 N/A

      \[\leadsto 1 + -1 \cdot \frac{\frac{-1}{2} \cdot \mathsf{PI}\left(\right) - \frac{1}{2} \cdot \mathsf{PI}\left(\right)}{z1} \]

   3. lower-PI.f64 N/A

      \[\leadsto 1 + -1 \cdot \frac{\frac{-1}{2} \cdot \pi - \frac{1}{2} \cdot \mathsf{PI}\left(\right)}{z1} \]

   4. lower-*.f64 N/A

      \[\leadsto 1 + -1 \cdot \frac{\frac{-1}{2} \cdot \pi - \frac{1}{2} \cdot \mathsf{PI}\left(\right)}{z1} \]

   5. lower-PI.f64 38.9%

      \[\leadsto 1 + -1 \cdot \frac{-0.5 \cdot \pi - 0.5 \cdot \pi}{z1} \]

7. Applied rewrites 38.9%

   \[\leadsto 1 + -1 \cdot \frac{-0.5 \cdot \pi - 0.5 \cdot \pi}{z1} \]
8. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto 1 + \color{blue}{-1 \cdot \frac{\frac{-1}{2} \cdot \pi - \frac{1}{2} \cdot \pi}{z1}} \]

   2. add-flip N/A

      \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{\frac{-1}{2} \cdot \pi - \frac{1}{2} \cdot \pi}{z1}\right)\right)} \]

   3. lower--.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{\frac{-1}{2} \cdot \pi - \frac{1}{2} \cdot \pi}{z1}\right)\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto 1 - \left(\mathsf{neg}\left(-1 \cdot \frac{\frac{-1}{2} \cdot \pi - \frac{1}{2} \cdot \pi}{z1}\right)\right) \]

9. Applied rewrites 38.9%

   \[\leadsto 1 - \color{blue}{\frac{\pi \cdot -1}{z1}} \]

10. Evaluated real constant 38.9%

    \[\leadsto 1 - \frac{-3.141592653589793}{z1} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0 z1)
  :name "(/ (- (- 1 (/ z0 (- (exp (/ -7853981852531433/2500000000000000 z1)) -1))) (/ (- 1 z0) (+ 1 (exp (/ PI z1))))) (+ (/ (- 1 z0) (+ 1 (exp (/ PI z1)))) (/ z0 (- (exp (/ -7853981852531433/2500000000000000 z1)) -1))))"
  :precision binary64
  (/ (- (- 1.0 (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0))) (/ (- 1.0 z0) (+ 1.0 (exp (/ PI z1))))) (+ (/ (- 1.0 z0) (+ 1.0 (exp (/ PI z1)))) (/ z0 (- (exp (/ -3.1415927410125732 z1)) -1.0)))))