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

Percentage Accurate: 70.0% → 98.8%

Time: 5.0s

Alternatives: 21

Speedup: 2.4×

• could not determine a ground truth

  1. z0 = -2.8790634347881104e-290
  2. z1 = -3.711389174709193e-110

Specification

Math

\[\begin{array}{l} t_0 := -1 - e^{\frac{-3.1415927410125732}{z0}}\\ \frac{t\_0}{t\_0 \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := -1 - e^{\frac{-3.1415927410125732}{z0}}\\ \frac{t\_0}{t\_0 \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{\pi}{z0}}\\ t_1 := t\_0 - -1\\ t_2 := \frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\\ t_3 := e^{\frac{-3.1415927410125732}{z0}}\\ t_4 := -1 - t\_3\\ t_5 := \frac{1 - z1}{t\_1}\\ t_6 := \frac{t\_4}{t\_4 \cdot t\_5 - z1}\\ \mathbf{if}\;t\_6 \leq -\infty:\\ \;\;\;\;\frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ \mathbf{elif}\;t\_6 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{t\_4}{-1 \cdot \frac{1 + t\_3}{1 + t\_0} + z1 \cdot \left(\frac{1}{t\_1} - \left(\frac{t\_3}{-1 - t\_0} - -1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{t\_2 \cdot t\_5 - z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ PI z0)))
       (t_1 (- t_0 -1.0))
       (t_2
        (-
         (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
         2.0))
       (t_3 (exp (/ -3.1415927410125732 z0)))
       (t_4 (- -1.0 t_3))
       (t_5 (/ (- 1.0 z1) t_1))
       (t_6 (/ t_4 (- (* t_4 t_5) z1))))
  (if (<= t_6 (- INFINITY))
    (/
     -2.0
     (-
      (*
       -1.0
       (/
        (-
         (* 1.5707963705062866 (- z1 1.0))
         (* -0.5 (* PI (- z1 1.0))))
        z0))
      1.0))
    (if (<= t_6 5e+292)
      (/
       t_4
       (+
        (* -1.0 (/ (+ 1.0 t_3) (+ 1.0 t_0)))
        (* z1 (- (/ 1.0 t_1) (- (/ t_3 (- -1.0 t_0)) -1.0)))))
      (/ t_2 (- (* t_2 t_5) z1))))))

C

double code(double z0, double z1) {
	double t_0 = exp((((double) M_PI) / z0));
	double t_1 = t_0 - -1.0;
	double t_2 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double t_3 = exp((-3.1415927410125732 / z0));
	double t_4 = -1.0 - t_3;
	double t_5 = (1.0 - z1) / t_1;
	double t_6 = t_4 / ((t_4 * t_5) - z1);
	double tmp;
	if (t_6 <= -((double) INFINITY)) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (t_6 <= 5e+292) {
		tmp = t_4 / ((-1.0 * ((1.0 + t_3) / (1.0 + t_0))) + (z1 * ((1.0 / t_1) - ((t_3 / (-1.0 - t_0)) - -1.0))));
	} else {
		tmp = t_2 / ((t_2 * t_5) - z1);
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((Math.PI / z0));
	double t_1 = t_0 - -1.0;
	double t_2 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double t_3 = Math.exp((-3.1415927410125732 / z0));
	double t_4 = -1.0 - t_3;
	double t_5 = (1.0 - z1) / t_1;
	double t_6 = t_4 / ((t_4 * t_5) - z1);
	double tmp;
	if (t_6 <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (t_6 <= 5e+292) {
		tmp = t_4 / ((-1.0 * ((1.0 + t_3) / (1.0 + t_0))) + (z1 * ((1.0 / t_1) - ((t_3 / (-1.0 - t_0)) - -1.0))));
	} else {
		tmp = t_2 / ((t_2 * t_5) - z1);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((math.pi / z0))
	t_1 = t_0 - -1.0
	t_2 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0
	t_3 = math.exp((-3.1415927410125732 / z0))
	t_4 = -1.0 - t_3
	t_5 = (1.0 - z1) / t_1
	t_6 = t_4 / ((t_4 * t_5) - z1)
	tmp = 0
	if t_6 <= -math.inf:
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	elif t_6 <= 5e+292:
		tmp = t_4 / ((-1.0 * ((1.0 + t_3) / (1.0 + t_0))) + (z1 * ((1.0 / t_1) - ((t_3 / (-1.0 - t_0)) - -1.0))))
	else:
		tmp = t_2 / ((t_2 * t_5) - z1)
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(pi / z0))
	t_1 = Float64(t_0 - -1.0)
	t_2 = Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0)
	t_3 = exp(Float64(-3.1415927410125732 / z0))
	t_4 = Float64(-1.0 - t_3)
	t_5 = Float64(Float64(1.0 - z1) / t_1)
	t_6 = Float64(t_4 / Float64(Float64(t_4 * t_5) - z1))
	tmp = 0.0
	if (t_6 <= Float64(-Inf))
		tmp = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0));
	elseif (t_6 <= 5e+292)
		tmp = Float64(t_4 / Float64(Float64(-1.0 * Float64(Float64(1.0 + t_3) / Float64(1.0 + t_0))) + Float64(z1 * Float64(Float64(1.0 / t_1) - Float64(Float64(t_3 / Float64(-1.0 - t_0)) - -1.0)))));
	else
		tmp = Float64(t_2 / Float64(Float64(t_2 * t_5) - z1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((pi / z0));
	t_1 = t_0 - -1.0;
	t_2 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	t_3 = exp((-3.1415927410125732 / z0));
	t_4 = -1.0 - t_3;
	t_5 = (1.0 - z1) / t_1;
	t_6 = t_4 / ((t_4 * t_5) - z1);
	tmp = 0.0;
	if (t_6 <= -Inf)
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	elseif (t_6 <= 5e+292)
		tmp = t_4 / ((-1.0 * ((1.0 + t_3) / (1.0 + t_0))) + (z1 * ((1.0 / t_1) - ((t_3 / (-1.0 - t_0)) - -1.0))));
	else
		tmp = t_2 / ((t_2 * t_5) - z1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(1.0 - z1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 / N[(N[(t$95$4 * t$95$5), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$6, (-Infinity)], N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$6, 5e+292], N[(t$95$4 / N[(N[(-1.0 * N[(N[(1.0 + t$95$3), $MachinePrecision] / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z1 * N[(N[(1.0 / t$95$1), $MachinePrecision] - N[(N[(t$95$3 / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 / N[(N[(t$95$2 * t$95$5), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < -inf.0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -inf.0 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < 4.9999999999999996e292

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around 0

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

      1. lower-+.f64 N/A

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

   4. Applied rewrites 83.8%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-+.f64 N/A

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

      4. add-flip N/A

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

      5. metadata-eval N/A

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

      6. associate-+l- N/A

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

      7. lower--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. metadata-eval N/A

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

      11. sub-flip N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

   6. Applied rewrites 83.8%

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

   if 4.9999999999999996e292 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1))

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{-3.1415927410125732}{z0}}\\ t_1 := -1 - t\_0\\ t_2 := e^{\frac{\pi}{z0}}\\ t_3 := 1 + t\_2\\ t_4 := \frac{1 - z1}{t\_2 - -1}\\ t_5 := \frac{t\_1}{t\_1 \cdot t\_4 - z1}\\ t_6 := \frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;\frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ \mathbf{elif}\;t\_5 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{t\_1}{-1 \cdot \frac{1 + t\_0}{t\_3} + z1 \cdot \left(\left(\frac{1}{t\_3} + \frac{t\_0}{t\_3}\right) - 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_6}{t\_6 \cdot t\_4 - z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ -3.1415927410125732 z0)))
       (t_1 (- -1.0 t_0))
       (t_2 (exp (/ PI z0)))
       (t_3 (+ 1.0 t_2))
       (t_4 (/ (- 1.0 z1) (- t_2 -1.0)))
       (t_5 (/ t_1 (- (* t_1 t_4) z1)))
       (t_6
        (-
         (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
         2.0)))
  (if (<= t_5 (- INFINITY))
    (/
     -2.0
     (-
      (*
       -1.0
       (/
        (-
         (* 1.5707963705062866 (- z1 1.0))
         (* -0.5 (* PI (- z1 1.0))))
        z0))
      1.0))
    (if (<= t_5 5e+292)
      (/
       t_1
       (+
        (* -1.0 (/ (+ 1.0 t_0) t_3))
        (* z1 (- (+ (/ 1.0 t_3) (/ t_0 t_3)) 1.0))))
      (/ t_6 (- (* t_6 t_4) z1))))))

C

double code(double z0, double z1) {
	double t_0 = exp((-3.1415927410125732 / z0));
	double t_1 = -1.0 - t_0;
	double t_2 = exp((((double) M_PI) / z0));
	double t_3 = 1.0 + t_2;
	double t_4 = (1.0 - z1) / (t_2 - -1.0);
	double t_5 = t_1 / ((t_1 * t_4) - z1);
	double t_6 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (t_5 <= 5e+292) {
		tmp = t_1 / ((-1.0 * ((1.0 + t_0) / t_3)) + (z1 * (((1.0 / t_3) + (t_0 / t_3)) - 1.0)));
	} else {
		tmp = t_6 / ((t_6 * t_4) - z1);
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((-3.1415927410125732 / z0));
	double t_1 = -1.0 - t_0;
	double t_2 = Math.exp((Math.PI / z0));
	double t_3 = 1.0 + t_2;
	double t_4 = (1.0 - z1) / (t_2 - -1.0);
	double t_5 = t_1 / ((t_1 * t_4) - z1);
	double t_6 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (t_5 <= 5e+292) {
		tmp = t_1 / ((-1.0 * ((1.0 + t_0) / t_3)) + (z1 * (((1.0 / t_3) + (t_0 / t_3)) - 1.0)));
	} else {
		tmp = t_6 / ((t_6 * t_4) - z1);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((-3.1415927410125732 / z0))
	t_1 = -1.0 - t_0
	t_2 = math.exp((math.pi / z0))
	t_3 = 1.0 + t_2
	t_4 = (1.0 - z1) / (t_2 - -1.0)
	t_5 = t_1 / ((t_1 * t_4) - z1)
	t_6 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0
	tmp = 0
	if t_5 <= -math.inf:
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	elif t_5 <= 5e+292:
		tmp = t_1 / ((-1.0 * ((1.0 + t_0) / t_3)) + (z1 * (((1.0 / t_3) + (t_0 / t_3)) - 1.0)))
	else:
		tmp = t_6 / ((t_6 * t_4) - z1)
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(-3.1415927410125732 / z0))
	t_1 = Float64(-1.0 - t_0)
	t_2 = exp(Float64(pi / z0))
	t_3 = Float64(1.0 + t_2)
	t_4 = Float64(Float64(1.0 - z1) / Float64(t_2 - -1.0))
	t_5 = Float64(t_1 / Float64(Float64(t_1 * t_4) - z1))
	t_6 = Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0));
	elseif (t_5 <= 5e+292)
		tmp = Float64(t_1 / Float64(Float64(-1.0 * Float64(Float64(1.0 + t_0) / t_3)) + Float64(z1 * Float64(Float64(Float64(1.0 / t_3) + Float64(t_0 / t_3)) - 1.0))));
	else
		tmp = Float64(t_6 / Float64(Float64(t_6 * t_4) - z1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((-3.1415927410125732 / z0));
	t_1 = -1.0 - t_0;
	t_2 = exp((pi / z0));
	t_3 = 1.0 + t_2;
	t_4 = (1.0 - z1) / (t_2 - -1.0);
	t_5 = t_1 / ((t_1 * t_4) - z1);
	t_6 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	elseif (t_5 <= 5e+292)
		tmp = t_1 / ((-1.0 * ((1.0 + t_0) / t_3)) + (z1 * (((1.0 / t_3) + (t_0 / t_3)) - 1.0)));
	else
		tmp = t_6 / ((t_6 * t_4) - z1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(1.0 - z1), $MachinePrecision] / N[(t$95$2 - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$1 / N[(N[(t$95$1 * t$95$4), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 5e+292], N[(t$95$1 / N[(N[(-1.0 * N[(N[(1.0 + t$95$0), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(z1 * N[(N[(N[(1.0 / t$95$3), $MachinePrecision] + N[(t$95$0 / t$95$3), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$6 / N[(N[(t$95$6 * t$95$4), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < -inf.0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -inf.0 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < 4.9999999999999996e292

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around 0

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

      1. lower-+.f64 N/A

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

   4. Applied rewrites 83.8%

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

   if 4.9999999999999996e292 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1))

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{\pi}{z0}}\\ t_1 := -1 - e^{\frac{-3.1415927410125732}{z0}}\\ t_2 := \frac{1 - z1}{t\_0 - -1}\\ t_3 := \frac{t\_1}{t\_1 \cdot t\_2 - z1}\\ t_4 := \frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{t\_1}{\left(z1 - 1\right) \cdot \left(\frac{1}{-1 - t\_0} \cdot t\_1\right) - z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_4}{t\_4 \cdot t\_2 - z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ PI z0)))
       (t_1 (- -1.0 (exp (/ -3.1415927410125732 z0))))
       (t_2 (/ (- 1.0 z1) (- t_0 -1.0)))
       (t_3 (/ t_1 (- (* t_1 t_2) z1)))
       (t_4
        (-
         (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
         2.0)))
  (if (<= t_3 (- INFINITY))
    (/
     -2.0
     (-
      (*
       -1.0
       (/
        (-
         (* 1.5707963705062866 (- z1 1.0))
         (* -0.5 (* PI (- z1 1.0))))
        z0))
      1.0))
    (if (<= t_3 5e+292)
      (/ t_1 (- (* (- z1 1.0) (* (/ 1.0 (- -1.0 t_0)) t_1)) z1))
      (/ t_4 (- (* t_4 t_2) z1))))))

C

double code(double z0, double z1) {
	double t_0 = exp((((double) M_PI) / z0));
	double t_1 = -1.0 - exp((-3.1415927410125732 / z0));
	double t_2 = (1.0 - z1) / (t_0 - -1.0);
	double t_3 = t_1 / ((t_1 * t_2) - z1);
	double t_4 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (t_3 <= 5e+292) {
		tmp = t_1 / (((z1 - 1.0) * ((1.0 / (-1.0 - t_0)) * t_1)) - z1);
	} else {
		tmp = t_4 / ((t_4 * t_2) - z1);
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((Math.PI / z0));
	double t_1 = -1.0 - Math.exp((-3.1415927410125732 / z0));
	double t_2 = (1.0 - z1) / (t_0 - -1.0);
	double t_3 = t_1 / ((t_1 * t_2) - z1);
	double t_4 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (t_3 <= 5e+292) {
		tmp = t_1 / (((z1 - 1.0) * ((1.0 / (-1.0 - t_0)) * t_1)) - z1);
	} else {
		tmp = t_4 / ((t_4 * t_2) - z1);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((math.pi / z0))
	t_1 = -1.0 - math.exp((-3.1415927410125732 / z0))
	t_2 = (1.0 - z1) / (t_0 - -1.0)
	t_3 = t_1 / ((t_1 * t_2) - z1)
	t_4 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0
	tmp = 0
	if t_3 <= -math.inf:
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	elif t_3 <= 5e+292:
		tmp = t_1 / (((z1 - 1.0) * ((1.0 / (-1.0 - t_0)) * t_1)) - z1)
	else:
		tmp = t_4 / ((t_4 * t_2) - z1)
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(pi / z0))
	t_1 = Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0)))
	t_2 = Float64(Float64(1.0 - z1) / Float64(t_0 - -1.0))
	t_3 = Float64(t_1 / Float64(Float64(t_1 * t_2) - z1))
	t_4 = Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0));
	elseif (t_3 <= 5e+292)
		tmp = Float64(t_1 / Float64(Float64(Float64(z1 - 1.0) * Float64(Float64(1.0 / Float64(-1.0 - t_0)) * t_1)) - z1));
	else
		tmp = Float64(t_4 / Float64(Float64(t_4 * t_2) - z1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((pi / z0));
	t_1 = -1.0 - exp((-3.1415927410125732 / z0));
	t_2 = (1.0 - z1) / (t_0 - -1.0);
	t_3 = t_1 / ((t_1 * t_2) - z1);
	t_4 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	elseif (t_3 <= 5e+292)
		tmp = t_1 / (((z1 - 1.0) * ((1.0 / (-1.0 - t_0)) * t_1)) - z1);
	else
		tmp = t_4 / ((t_4 * t_2) - z1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - z1), $MachinePrecision] / N[(t$95$0 - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(N[(t$95$1 * t$95$2), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+292], N[(t$95$1 / N[(N[(N[(z1 - 1.0), $MachinePrecision] * N[(N[(1.0 / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], N[(t$95$4 / N[(N[(t$95$4 * t$95$2), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < -inf.0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -inf.0 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < 4.9999999999999996e292

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   if 4.9999999999999996e292 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1))

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := -1 - e^{\frac{-3.1415927410125732}{z0}}\\ t_1 := \frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\\ t_2 := \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1}\\ t_3 := \frac{t\_0}{t\_0 \cdot t\_2 - z1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{t\_1 \cdot t\_2 - z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (- -1.0 (exp (/ -3.1415927410125732 z0))))
       (t_1
        (-
         (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
         2.0))
       (t_2 (/ (- 1.0 z1) (- (exp (/ PI z0)) -1.0)))
       (t_3 (/ t_0 (- (* t_0 t_2) z1))))
  (if (<= t_3 (- INFINITY))
    (/
     -2.0
     (-
      (*
       -1.0
       (/
        (-
         (* 1.5707963705062866 (- z1 1.0))
         (* -0.5 (* PI (- z1 1.0))))
        z0))
      1.0))
    (if (<= t_3 5e+292) t_3 (/ t_1 (- (* t_1 t_2) z1))))))

C

double code(double z0, double z1) {
	double t_0 = -1.0 - exp((-3.1415927410125732 / z0));
	double t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double t_2 = (1.0 - z1) / (exp((((double) M_PI) / z0)) - -1.0);
	double t_3 = t_0 / ((t_0 * t_2) - z1);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (t_3 <= 5e+292) {
		tmp = t_3;
	} else {
		tmp = t_1 / ((t_1 * t_2) - z1);
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = -1.0 - Math.exp((-3.1415927410125732 / z0));
	double t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double t_2 = (1.0 - z1) / (Math.exp((Math.PI / z0)) - -1.0);
	double t_3 = t_0 / ((t_0 * t_2) - z1);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (t_3 <= 5e+292) {
		tmp = t_3;
	} else {
		tmp = t_1 / ((t_1 * t_2) - z1);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -1.0 - math.exp((-3.1415927410125732 / z0))
	t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0
	t_2 = (1.0 - z1) / (math.exp((math.pi / z0)) - -1.0)
	t_3 = t_0 / ((t_0 * t_2) - z1)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	elif t_3 <= 5e+292:
		tmp = t_3
	else:
		tmp = t_1 / ((t_1 * t_2) - z1)
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0)))
	t_1 = Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0)
	t_2 = Float64(Float64(1.0 - z1) / Float64(exp(Float64(pi / z0)) - -1.0))
	t_3 = Float64(t_0 / Float64(Float64(t_0 * t_2) - z1))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0));
	elseif (t_3 <= 5e+292)
		tmp = t_3;
	else
		tmp = Float64(t_1 / Float64(Float64(t_1 * t_2) - z1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -1.0 - exp((-3.1415927410125732 / z0));
	t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	t_2 = (1.0 - z1) / (exp((pi / z0)) - -1.0);
	t_3 = t_0 / ((t_0 * t_2) - z1);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	elseif (t_3 <= 5e+292)
		tmp = t_3;
	else
		tmp = t_1 / ((t_1 * t_2) - z1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - z1), $MachinePrecision] / N[(N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 / N[(N[(t$95$0 * t$95$2), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+292], t$95$3, N[(t$95$1 / N[(N[(t$95$1 * t$95$2), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < -inf.0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -inf.0 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < 4.9999999999999996e292

   1. Initial program 70.0%

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

   if 4.9999999999999996e292 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1))

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)\\ t_1 := e^{\frac{-3.1415927410125732}{z0}}\\ t_2 := -1 - t\_1\\ t_3 := \frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\\ t_4 := -1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2\\ t_5 := e^{\frac{\pi}{z0}}\\ t_6 := 1.5707963705062866 \cdot \left(z1 - 1\right)\\ \mathbf{if}\;z0 \leq -1950000:\\ \;\;\;\;\frac{t\_2}{-1 \cdot \frac{\left(-1 \cdot \frac{2.4674012375957233 \cdot \left(z1 - 1\right) - \left(-0.5 \cdot \left(\pi \cdot \left(t\_6 - t\_0\right)\right) + 0.25 \cdot \left({\pi}^{2} \cdot \left(z1 - 1\right)\right)\right)}{z0} + t\_6\right) - t\_0}{z0} - 1}\\ \mathbf{elif}\;z0 \leq -3 \cdot 10^{-103}:\\ \;\;\;\;\frac{t\_4}{t\_4 \cdot \frac{1 - z1}{t\_5 - -1} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{t\_2}{\frac{z1 \cdot 2}{1 + t\_5} - z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1 \cdot t\_3 - t\_3 \cdot t\_1}{t\_3 \cdot t\_3}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (* -0.5 (* PI (- z1 1.0))))
       (t_1 (exp (/ -3.1415927410125732 z0)))
       (t_2 (- -1.0 t_1))
       (t_3
        (-
         (/ (* (- z1 1.0) (- (* -0.5 PI) 1.5707963705062866)) z0)
         1.0))
       (t_4
        (-
         (*
          -1.0
          (/
           (-
            (*
             -1.0
             (/
              (- (* 5.167713211464109 (/ 1.0 z0)) 4.9348024751914465)
              z0))
            3.1415927410125732)
           z0))
         2.0))
       (t_5 (exp (/ PI z0)))
       (t_6 (* 1.5707963705062866 (- z1 1.0))))
  (if (<= z0 -1950000.0)
    (/
     t_2
     (-
      (*
       -1.0
       (/
        (-
         (+
          (*
           -1.0
           (/
            (-
             (* 2.4674012375957233 (- z1 1.0))
             (+
              (* -0.5 (* PI (- t_6 t_0)))
              (* 0.25 (* (pow PI 2.0) (- z1 1.0)))))
            z0))
          t_6)
         t_0)
        z0))
      1.0))
    (if (<= z0 -3e-103)
      (/ t_4 (- (* t_4 (/ (- 1.0 z1) (- t_5 -1.0))) z1))
      (if (<= z0 3.1)
        (/ t_2 (- (/ (* z1 2.0) (+ 1.0 t_5)) z1))
        (/ (- (* -1.0 t_3) (* t_3 t_1)) (* t_3 t_3)))))))

C

double code(double z0, double z1) {
	double t_0 = -0.5 * (((double) M_PI) * (z1 - 1.0));
	double t_1 = exp((-3.1415927410125732 / z0));
	double t_2 = -1.0 - t_1;
	double t_3 = (((z1 - 1.0) * ((-0.5 * ((double) M_PI)) - 1.5707963705062866)) / z0) - 1.0;
	double t_4 = (-1.0 * (((-1.0 * (((5.167713211464109 * (1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0;
	double t_5 = exp((((double) M_PI) / z0));
	double t_6 = 1.5707963705062866 * (z1 - 1.0);
	double tmp;
	if (z0 <= -1950000.0) {
		tmp = t_2 / ((-1.0 * ((((-1.0 * (((2.4674012375957233 * (z1 - 1.0)) - ((-0.5 * (((double) M_PI) * (t_6 - t_0))) + (0.25 * (pow(((double) M_PI), 2.0) * (z1 - 1.0))))) / z0)) + t_6) - t_0) / z0)) - 1.0);
	} else if (z0 <= -3e-103) {
		tmp = t_4 / ((t_4 * ((1.0 - z1) / (t_5 - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = t_2 / (((z1 * 2.0) / (1.0 + t_5)) - z1);
	} else {
		tmp = ((-1.0 * t_3) - (t_3 * t_1)) / (t_3 * t_3);
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = -0.5 * (Math.PI * (z1 - 1.0));
	double t_1 = Math.exp((-3.1415927410125732 / z0));
	double t_2 = -1.0 - t_1;
	double t_3 = (((z1 - 1.0) * ((-0.5 * Math.PI) - 1.5707963705062866)) / z0) - 1.0;
	double t_4 = (-1.0 * (((-1.0 * (((5.167713211464109 * (1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0;
	double t_5 = Math.exp((Math.PI / z0));
	double t_6 = 1.5707963705062866 * (z1 - 1.0);
	double tmp;
	if (z0 <= -1950000.0) {
		tmp = t_2 / ((-1.0 * ((((-1.0 * (((2.4674012375957233 * (z1 - 1.0)) - ((-0.5 * (Math.PI * (t_6 - t_0))) + (0.25 * (Math.pow(Math.PI, 2.0) * (z1 - 1.0))))) / z0)) + t_6) - t_0) / z0)) - 1.0);
	} else if (z0 <= -3e-103) {
		tmp = t_4 / ((t_4 * ((1.0 - z1) / (t_5 - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = t_2 / (((z1 * 2.0) / (1.0 + t_5)) - z1);
	} else {
		tmp = ((-1.0 * t_3) - (t_3 * t_1)) / (t_3 * t_3);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -0.5 * (math.pi * (z1 - 1.0))
	t_1 = math.exp((-3.1415927410125732 / z0))
	t_2 = -1.0 - t_1
	t_3 = (((z1 - 1.0) * ((-0.5 * math.pi) - 1.5707963705062866)) / z0) - 1.0
	t_4 = (-1.0 * (((-1.0 * (((5.167713211464109 * (1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0
	t_5 = math.exp((math.pi / z0))
	t_6 = 1.5707963705062866 * (z1 - 1.0)
	tmp = 0
	if z0 <= -1950000.0:
		tmp = t_2 / ((-1.0 * ((((-1.0 * (((2.4674012375957233 * (z1 - 1.0)) - ((-0.5 * (math.pi * (t_6 - t_0))) + (0.25 * (math.pow(math.pi, 2.0) * (z1 - 1.0))))) / z0)) + t_6) - t_0) / z0)) - 1.0)
	elif z0 <= -3e-103:
		tmp = t_4 / ((t_4 * ((1.0 - z1) / (t_5 - -1.0))) - z1)
	elif z0 <= 3.1:
		tmp = t_2 / (((z1 * 2.0) / (1.0 + t_5)) - z1)
	else:
		tmp = ((-1.0 * t_3) - (t_3 * t_1)) / (t_3 * t_3)
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))
	t_1 = exp(Float64(-3.1415927410125732 / z0))
	t_2 = Float64(-1.0 - t_1)
	t_3 = Float64(Float64(Float64(Float64(z1 - 1.0) * Float64(Float64(-0.5 * pi) - 1.5707963705062866)) / z0) - 1.0)
	t_4 = Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(5.167713211464109 * Float64(1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0)
	t_5 = exp(Float64(pi / z0))
	t_6 = Float64(1.5707963705062866 * Float64(z1 - 1.0))
	tmp = 0.0
	if (z0 <= -1950000.0)
		tmp = Float64(t_2 / Float64(Float64(-1.0 * Float64(Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(2.4674012375957233 * Float64(z1 - 1.0)) - Float64(Float64(-0.5 * Float64(pi * Float64(t_6 - t_0))) + Float64(0.25 * Float64((pi ^ 2.0) * Float64(z1 - 1.0))))) / z0)) + t_6) - t_0) / z0)) - 1.0));
	elseif (z0 <= -3e-103)
		tmp = Float64(t_4 / Float64(Float64(t_4 * Float64(Float64(1.0 - z1) / Float64(t_5 - -1.0))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(t_2 / Float64(Float64(Float64(z1 * 2.0) / Float64(1.0 + t_5)) - z1));
	else
		tmp = Float64(Float64(Float64(-1.0 * t_3) - Float64(t_3 * t_1)) / Float64(t_3 * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -0.5 * (pi * (z1 - 1.0));
	t_1 = exp((-3.1415927410125732 / z0));
	t_2 = -1.0 - t_1;
	t_3 = (((z1 - 1.0) * ((-0.5 * pi) - 1.5707963705062866)) / z0) - 1.0;
	t_4 = (-1.0 * (((-1.0 * (((5.167713211464109 * (1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0;
	t_5 = exp((pi / z0));
	t_6 = 1.5707963705062866 * (z1 - 1.0);
	tmp = 0.0;
	if (z0 <= -1950000.0)
		tmp = t_2 / ((-1.0 * ((((-1.0 * (((2.4674012375957233 * (z1 - 1.0)) - ((-0.5 * (pi * (t_6 - t_0))) + (0.25 * ((pi ^ 2.0) * (z1 - 1.0))))) / z0)) + t_6) - t_0) / z0)) - 1.0);
	elseif (z0 <= -3e-103)
		tmp = t_4 / ((t_4 * ((1.0 - z1) / (t_5 - -1.0))) - z1);
	elseif (z0 <= 3.1)
		tmp = t_2 / (((z1 * 2.0) / (1.0 + t_5)) - z1);
	else
		tmp = ((-1.0 * t_3) - (t_3 * t_1)) / (t_3 * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z1 - 1.0), $MachinePrecision] * N[(N[(-0.5 * Pi), $MachinePrecision] - 1.5707963705062866), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(5.167713211464109 * N[(1.0 / z0), $MachinePrecision]), $MachinePrecision] - 4.9348024751914465), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 3.1415927410125732), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$5 = N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$6 = N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z0, -1950000.0], N[(t$95$2 / N[(N[(-1.0 * N[(N[(N[(N[(-1.0 * N[(N[(N[(2.4674012375957233 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(-0.5 * N[(Pi * N[(t$95$6 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.25 * N[(N[Power[Pi, 2.0], $MachinePrecision] * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] - t$95$0), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, -3e-103], N[(t$95$4 / N[(N[(t$95$4 * N[(N[(1.0 - z1), $MachinePrecision] / N[(t$95$5 - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(t$95$2 / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(1.0 + t$95$5), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-1.0 * t$95$3), $MachinePrecision] - N[(t$95$3 * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(t$95$3 * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z0 < -1.95e6

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{25000000000000000000000000000000} \cdot \left(z1 - 1\right) - \left(\frac{-1}{2} \cdot \left(\pi \cdot \left(\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)\right)\right) + \frac{1}{4} \cdot \left({\pi}^{2} \cdot \left(z1 - 1\right)\right)\right)}{z0} + \frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right)\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   6. Applied rewrites 66.1%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\left(-1 \cdot \frac{2.4674012375957233 \cdot \left(z1 - 1\right) - \left(-0.5 \cdot \left(\pi \cdot \left(1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)\right)\right) + 0.25 \cdot \left({\pi}^{2} \cdot \left(z1 - 1\right)\right)\right)}{z0} + 1.5707963705062866 \cdot \left(z1 - 1\right)\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   if -1.95e6 < z0 < -3e-103

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lower-/.f64 36.4%

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 36.4%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lower-/.f64 37.3%

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.3%

      \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   if -3e-103 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   if 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   8. Applied rewrites 62.0%

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) - \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) \cdot e^{\frac{-3.1415927410125732}{z0}}}{\left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) \cdot \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right)}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 98.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{-3.1415927410125732}{z0}}\\ t_1 := -1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2\\ t_2 := e^{\frac{\pi}{z0}}\\ t_3 := \frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\\ \mathbf{if}\;z0 \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;\frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ \mathbf{elif}\;z0 \leq -3 \cdot 10^{-103}:\\ \;\;\;\;\frac{t\_1}{t\_1 \cdot \frac{1 - z1}{t\_2 - -1} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - t\_0}{\frac{z1 \cdot 2}{1 + t\_2} - z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1 \cdot t\_3 - t\_3 \cdot t\_0}{t\_3 \cdot t\_3}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ -3.1415927410125732 z0)))
       (t_1
        (-
         (*
          -1.0
          (/
           (-
            (*
             -1.0
             (/
              (- (* 5.167713211464109 (/ 1.0 z0)) 4.9348024751914465)
              z0))
            3.1415927410125732)
           z0))
         2.0))
       (t_2 (exp (/ PI z0)))
       (t_3
        (-
         (/ (* (- z1 1.0) (- (* -0.5 PI) 1.5707963705062866)) z0)
         1.0)))
  (if (<= z0 -1.25e+16)
    (/
     -2.0
     (-
      (*
       -1.0
       (/
        (-
         (* 1.5707963705062866 (- z1 1.0))
         (* -0.5 (* PI (- z1 1.0))))
        z0))
      1.0))
    (if (<= z0 -3e-103)
      (/ t_1 (- (* t_1 (/ (- 1.0 z1) (- t_2 -1.0))) z1))
      (if (<= z0 3.1)
        (/ (- -1.0 t_0) (- (/ (* z1 2.0) (+ 1.0 t_2)) z1))
        (/ (- (* -1.0 t_3) (* t_3 t_0)) (* t_3 t_3)))))))

C

double code(double z0, double z1) {
	double t_0 = exp((-3.1415927410125732 / z0));
	double t_1 = (-1.0 * (((-1.0 * (((5.167713211464109 * (1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0;
	double t_2 = exp((((double) M_PI) / z0));
	double t_3 = (((z1 - 1.0) * ((-0.5 * ((double) M_PI)) - 1.5707963705062866)) / z0) - 1.0;
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (z0 <= -3e-103) {
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (t_2 - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - t_0) / (((z1 * 2.0) / (1.0 + t_2)) - z1);
	} else {
		tmp = ((-1.0 * t_3) - (t_3 * t_0)) / (t_3 * t_3);
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((-3.1415927410125732 / z0));
	double t_1 = (-1.0 * (((-1.0 * (((5.167713211464109 * (1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0;
	double t_2 = Math.exp((Math.PI / z0));
	double t_3 = (((z1 - 1.0) * ((-0.5 * Math.PI) - 1.5707963705062866)) / z0) - 1.0;
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (z0 <= -3e-103) {
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (t_2 - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - t_0) / (((z1 * 2.0) / (1.0 + t_2)) - z1);
	} else {
		tmp = ((-1.0 * t_3) - (t_3 * t_0)) / (t_3 * t_3);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((-3.1415927410125732 / z0))
	t_1 = (-1.0 * (((-1.0 * (((5.167713211464109 * (1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0
	t_2 = math.exp((math.pi / z0))
	t_3 = (((z1 - 1.0) * ((-0.5 * math.pi) - 1.5707963705062866)) / z0) - 1.0
	tmp = 0
	if z0 <= -1.25e+16:
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	elif z0 <= -3e-103:
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (t_2 - -1.0))) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - t_0) / (((z1 * 2.0) / (1.0 + t_2)) - z1)
	else:
		tmp = ((-1.0 * t_3) - (t_3 * t_0)) / (t_3 * t_3)
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(-3.1415927410125732 / z0))
	t_1 = Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(5.167713211464109 * Float64(1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0)
	t_2 = exp(Float64(pi / z0))
	t_3 = Float64(Float64(Float64(Float64(z1 - 1.0) * Float64(Float64(-0.5 * pi) - 1.5707963705062866)) / z0) - 1.0)
	tmp = 0.0
	if (z0 <= -1.25e+16)
		tmp = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0));
	elseif (z0 <= -3e-103)
		tmp = Float64(t_1 / Float64(Float64(t_1 * Float64(Float64(1.0 - z1) / Float64(t_2 - -1.0))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - t_0) / Float64(Float64(Float64(z1 * 2.0) / Float64(1.0 + t_2)) - z1));
	else
		tmp = Float64(Float64(Float64(-1.0 * t_3) - Float64(t_3 * t_0)) / Float64(t_3 * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((-3.1415927410125732 / z0));
	t_1 = (-1.0 * (((-1.0 * (((5.167713211464109 * (1.0 / z0)) - 4.9348024751914465) / z0)) - 3.1415927410125732) / z0)) - 2.0;
	t_2 = exp((pi / z0));
	t_3 = (((z1 - 1.0) * ((-0.5 * pi) - 1.5707963705062866)) / z0) - 1.0;
	tmp = 0.0;
	if (z0 <= -1.25e+16)
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	elseif (z0 <= -3e-103)
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (t_2 - -1.0))) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - t_0) / (((z1 * 2.0) / (1.0 + t_2)) - z1);
	else
		tmp = ((-1.0 * t_3) - (t_3 * t_0)) / (t_3 * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(5.167713211464109 * N[(1.0 / z0), $MachinePrecision]), $MachinePrecision] - 4.9348024751914465), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 3.1415927410125732), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z1 - 1.0), $MachinePrecision] * N[(N[(-0.5 * Pi), $MachinePrecision] - 1.5707963705062866), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 1.0), $MachinePrecision]}, If[LessEqual[z0, -1.25e+16], N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, -3e-103], N[(t$95$1 / N[(N[(t$95$1 * N[(N[(1.0 - z1), $MachinePrecision] / N[(t$95$2 - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - t$95$0), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-1.0 * t$95$3), $MachinePrecision] - N[(t$95$3 * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(t$95$3 * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z0 < -1.25e16

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -1.25e16 < z0 < -3e-103

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lower-/.f64 36.4%

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 36.4%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{\frac{161491037858253405198930717009894818193991386579}{31250000000000000000000000000000000000000000000} \cdot \frac{1}{z0} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lower-/.f64 37.3%

         \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.3%

      \[\leadsto \frac{-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{5.167713211464109 \cdot \frac{1}{z0} - 4.9348024751914465}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   if -3e-103 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   if 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   8. Applied rewrites 62.0%

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) - \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) \cdot e^{\frac{-3.1415927410125732}{z0}}}{\left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) \cdot \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right)}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 97.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := e^{\frac{\pi}{z0}}\\ t_1 := \frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\\ t_2 := \frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\\ t_3 := e^{\frac{-3.1415927410125732}{z0}}\\ \mathbf{if}\;z0 \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;\frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ \mathbf{elif}\;z0 \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{t\_2}{t\_2 \cdot \frac{1}{\frac{t\_0 - -1}{1 - z1}} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - t\_3}{\frac{z1 \cdot 2}{1 + t\_0} - z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1 \cdot t\_1 - t\_1 \cdot t\_3}{t\_1 \cdot t\_1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (exp (/ PI z0)))
       (t_1
        (-
         (/ (* (- z1 1.0) (- (* -0.5 PI) 1.5707963705062866)) z0)
         1.0))
       (t_2
        (-
         (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
         2.0))
       (t_3 (exp (/ -3.1415927410125732 z0))))
  (if (<= z0 -1.25e+16)
    (/
     -2.0
     (-
      (*
       -1.0
       (/
        (-
         (* 1.5707963705062866 (- z1 1.0))
         (* -0.5 (* PI (- z1 1.0))))
        z0))
      1.0))
    (if (<= z0 -1.7e-154)
      (/ t_2 (- (* t_2 (/ 1.0 (/ (- t_0 -1.0) (- 1.0 z1)))) z1))
      (if (<= z0 3.1)
        (/ (- -1.0 t_3) (- (/ (* z1 2.0) (+ 1.0 t_0)) z1))
        (/ (- (* -1.0 t_1) (* t_1 t_3)) (* t_1 t_1)))))))

C

double code(double z0, double z1) {
	double t_0 = exp((((double) M_PI) / z0));
	double t_1 = (((z1 - 1.0) * ((-0.5 * ((double) M_PI)) - 1.5707963705062866)) / z0) - 1.0;
	double t_2 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double t_3 = exp((-3.1415927410125732 / z0));
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (z0 <= -1.7e-154) {
		tmp = t_2 / ((t_2 * (1.0 / ((t_0 - -1.0) / (1.0 - z1)))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - t_3) / (((z1 * 2.0) / (1.0 + t_0)) - z1);
	} else {
		tmp = ((-1.0 * t_1) - (t_1 * t_3)) / (t_1 * t_1);
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = Math.exp((Math.PI / z0));
	double t_1 = (((z1 - 1.0) * ((-0.5 * Math.PI) - 1.5707963705062866)) / z0) - 1.0;
	double t_2 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double t_3 = Math.exp((-3.1415927410125732 / z0));
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	} else if (z0 <= -1.7e-154) {
		tmp = t_2 / ((t_2 * (1.0 / ((t_0 - -1.0) / (1.0 - z1)))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - t_3) / (((z1 * 2.0) / (1.0 + t_0)) - z1);
	} else {
		tmp = ((-1.0 * t_1) - (t_1 * t_3)) / (t_1 * t_1);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.exp((math.pi / z0))
	t_1 = (((z1 - 1.0) * ((-0.5 * math.pi) - 1.5707963705062866)) / z0) - 1.0
	t_2 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0
	t_3 = math.exp((-3.1415927410125732 / z0))
	tmp = 0
	if z0 <= -1.25e+16:
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	elif z0 <= -1.7e-154:
		tmp = t_2 / ((t_2 * (1.0 / ((t_0 - -1.0) / (1.0 - z1)))) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - t_3) / (((z1 * 2.0) / (1.0 + t_0)) - z1)
	else:
		tmp = ((-1.0 * t_1) - (t_1 * t_3)) / (t_1 * t_1)
	return tmp

Julia

function code(z0, z1)
	t_0 = exp(Float64(pi / z0))
	t_1 = Float64(Float64(Float64(Float64(z1 - 1.0) * Float64(Float64(-0.5 * pi) - 1.5707963705062866)) / z0) - 1.0)
	t_2 = Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0)
	t_3 = exp(Float64(-3.1415927410125732 / z0))
	tmp = 0.0
	if (z0 <= -1.25e+16)
		tmp = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0));
	elseif (z0 <= -1.7e-154)
		tmp = Float64(t_2 / Float64(Float64(t_2 * Float64(1.0 / Float64(Float64(t_0 - -1.0) / Float64(1.0 - z1)))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - t_3) / Float64(Float64(Float64(z1 * 2.0) / Float64(1.0 + t_0)) - z1));
	else
		tmp = Float64(Float64(Float64(-1.0 * t_1) - Float64(t_1 * t_3)) / Float64(t_1 * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = exp((pi / z0));
	t_1 = (((z1 - 1.0) * ((-0.5 * pi) - 1.5707963705062866)) / z0) - 1.0;
	t_2 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	t_3 = exp((-3.1415927410125732 / z0));
	tmp = 0.0;
	if (z0 <= -1.25e+16)
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	elseif (z0 <= -1.7e-154)
		tmp = t_2 / ((t_2 * (1.0 / ((t_0 - -1.0) / (1.0 - z1)))) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - t_3) / (((z1 * 2.0) / (1.0 + t_0)) - z1);
	else
		tmp = ((-1.0 * t_1) - (t_1 * t_3)) / (t_1 * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(z1 - 1.0), $MachinePrecision] * N[(N[(-0.5 * Pi), $MachinePrecision] - 1.5707963705062866), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z0, -1.25e+16], N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, -1.7e-154], N[(t$95$2 / N[(N[(t$95$2 * N[(1.0 / N[(N[(t$95$0 - -1.0), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - t$95$3), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-1.0 * t$95$1), $MachinePrecision] - N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z0 < -1.25e16

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -1.25e16 < z0 < -1.6999999999999999e-154

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   12. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1 - z1}{e^{\frac{\pi}{z0}} - -1}} - z1} \]

       2. div-flip N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

       3. lower-unsound-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

       4. lower-unsound-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1}{\color{blue}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

   13. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

   if -1.6999999999999999e-154 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   if 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   8. Applied rewrites 62.0%

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) - \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) \cdot e^{\frac{-3.1415927410125732}{z0}}}{\left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right) \cdot \left(\frac{\left(z1 - 1\right) \cdot \left(-0.5 \cdot \pi - 1.5707963705062866\right)}{z0} - 1\right)}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 97.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_0 := \frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\\ t_1 := \frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ t_2 := e^{\frac{\pi}{z0}}\\ \mathbf{if}\;z0 \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z0 \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{t\_0}{t\_0 \cdot \frac{1}{\frac{t\_2 - -1}{1 - z1}} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + t\_2} - z1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (-
         (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
         2.0))
       (t_1
        (/
         -2.0
         (-
          (*
           -1.0
           (/
            (-
             (* 1.5707963705062866 (- z1 1.0))
             (* -0.5 (* PI (- z1 1.0))))
            z0))
          1.0)))
       (t_2 (exp (/ PI z0))))
  (if (<= z0 -1.25e+16)
    t_1
    (if (<= z0 -1.7e-154)
      (/ t_0 (- (* t_0 (/ 1.0 (/ (- t_2 -1.0) (- 1.0 z1)))) z1))
      (if (<= z0 3.1)
        (/
         (- -1.0 (exp (/ -3.1415927410125732 z0)))
         (- (/ (* z1 2.0) (+ 1.0 t_2)) z1))
        t_1)))))

C

double code(double z0, double z1) {
	double t_0 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double t_1 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	double t_2 = exp((((double) M_PI) / z0));
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_1;
	} else if (z0 <= -1.7e-154) {
		tmp = t_0 / ((t_0 * (1.0 / ((t_2 - -1.0) / (1.0 - z1)))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (1.0 + t_2)) - z1);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double t_1 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	double t_2 = Math.exp((Math.PI / z0));
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_1;
	} else if (z0 <= -1.7e-154) {
		tmp = t_0 / ((t_0 * (1.0 / ((t_2 - -1.0) / (1.0 - z1)))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - Math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (1.0 + t_2)) - z1);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0
	t_1 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	t_2 = math.exp((math.pi / z0))
	tmp = 0
	if z0 <= -1.25e+16:
		tmp = t_1
	elif z0 <= -1.7e-154:
		tmp = t_0 / ((t_0 * (1.0 / ((t_2 - -1.0) / (1.0 - z1)))) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (1.0 + t_2)) - z1)
	else:
		tmp = t_1
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0)
	t_1 = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
	t_2 = exp(Float64(pi / z0))
	tmp = 0.0
	if (z0 <= -1.25e+16)
		tmp = t_1;
	elseif (z0 <= -1.7e-154)
		tmp = Float64(t_0 / Float64(Float64(t_0 * Float64(1.0 / Float64(Float64(t_2 - -1.0) / Float64(1.0 - z1)))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0))) / Float64(Float64(Float64(z1 * 2.0) / Float64(1.0 + t_2)) - z1));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	t_1 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	t_2 = exp((pi / z0));
	tmp = 0.0;
	if (z0 <= -1.25e+16)
		tmp = t_1;
	elseif (z0 <= -1.7e-154)
		tmp = t_0 / ((t_0 * (1.0 / ((t_2 - -1.0) / (1.0 - z1)))) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (1.0 + t_2)) - z1);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$1 = N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z0, -1.25e+16], t$95$1, If[LessEqual[z0, -1.7e-154], N[(t$95$0 / N[(N[(t$95$0 * N[(1.0 / N[(N[(t$95$2 - -1.0), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -1.25e16 or 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -1.25e16 < z0 < -1.6999999999999999e-154

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   12. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1 - z1}{e^{\frac{\pi}{z0}} - -1}} - z1} \]

       2. div-flip N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

       3. lower-unsound-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

       4. lower-unsound-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1}{\color{blue}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

   13. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

   if -1.6999999999999999e-154 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 97.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ t_1 := \frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\\ \mathbf{if}\;z0 \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z0 \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{t\_1}{t\_1 \cdot \frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         -2.0
         (-
          (*
           -1.0
           (/
            (-
             (* 1.5707963705062866 (- z1 1.0))
             (* -0.5 (* PI (- z1 1.0))))
            z0))
          1.0)))
       (t_1
        (-
         (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
         2.0)))
  (if (<= z0 -1.25e+16)
    t_0
    (if (<= z0 -1.7e-154)
      (/
       t_1
       (- (* t_1 (/ 1.0 (/ (- (exp (/ PI z0)) -1.0) (- 1.0 z1)))) z1))
      (if (<= z0 3.1)
        (/
         (- -1.0 (exp (/ -3.1415927410125732 z0)))
         (- (/ (* z1 2.0) (+ 2.0 (/ PI z0))) z1))
        t_0)))))

C

double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	double t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((t_1 * (1.0 / ((exp((((double) M_PI) / z0)) - -1.0) / (1.0 - z1)))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (((double) M_PI) / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	double t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((t_1 * (1.0 / ((Math.exp((Math.PI / z0)) - -1.0) / (1.0 - z1)))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - Math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (Math.PI / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0
	tmp = 0
	if z0 <= -1.25e+16:
		tmp = t_0
	elif z0 <= -1.7e-154:
		tmp = t_1 / ((t_1 * (1.0 / ((math.exp((math.pi / z0)) - -1.0) / (1.0 - z1)))) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (math.pi / z0))) - z1)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
	t_1 = Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0)
	tmp = 0.0
	if (z0 <= -1.25e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = Float64(t_1 / Float64(Float64(t_1 * Float64(1.0 / Float64(Float64(exp(Float64(pi / z0)) - -1.0) / Float64(1.0 - z1)))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0))) / Float64(Float64(Float64(z1 * 2.0) / Float64(2.0 + Float64(pi / z0))) - z1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	tmp = 0.0;
	if (z0 <= -1.25e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = t_1 / ((t_1 * (1.0 / ((exp((pi / z0)) - -1.0) / (1.0 - z1)))) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (pi / z0))) - z1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z0, -1.25e+16], t$95$0, If[LessEqual[z0, -1.7e-154], N[(t$95$1 / N[(N[(t$95$1 * N[(1.0 / N[(N[(N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision] / N[(1.0 - z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(2.0 + N[(Pi / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -1.25e16 or 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -1.25e16 < z0 < -1.6999999999999999e-154

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   12. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1 - z1}{e^{\frac{\pi}{z0}} - -1}} - z1} \]

       2. div-flip N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

       3. lower-unsound-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

       4. lower-unsound-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1}{\color{blue}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

   13. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \color{blue}{\frac{1}{\frac{e^{\frac{\pi}{z0}} - -1}{1 - z1}}} - z1} \]

   if -1.6999999999999999e-154 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   8. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-PI.f64 33.6%

         \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1} \]

   10. Applied rewrites 33.6%

       \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \color{blue}{\frac{\pi}{z0}}} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 97.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ t_1 := \left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - 1\\ \mathbf{if}\;z0 \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z0 \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{t\_1}{t\_1 \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         -2.0
         (-
          (*
           -1.0
           (/
            (-
             (* 1.5707963705062866 (- z1 1.0))
             (* -0.5 (* PI (- z1 1.0))))
            z0))
          1.0)))
       (t_1
        (-
         (-
          (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
          1.0)
         1.0)))
  (if (<= z0 -2.8e+16)
    t_0
    (if (<= z0 -1.7e-154)
      (/ t_1 (- (* t_1 (/ (- 1.0 z1) (- (exp (/ PI z0)) -1.0))) z1))
      (if (<= z0 3.1)
        (/
         (- -1.0 (exp (/ -3.1415927410125732 z0)))
         (- (/ (* z1 2.0) (+ 2.0 (/ PI z0))) z1))
        t_0)))))

C

double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	double t_1 = (((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 1.0) - 1.0;
	double tmp;
	if (z0 <= -2.8e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (exp((((double) M_PI) / z0)) - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (((double) M_PI) / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	double t_1 = (((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 1.0) - 1.0;
	double tmp;
	if (z0 <= -2.8e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (Math.exp((Math.PI / z0)) - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - Math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (Math.PI / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	t_1 = (((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 1.0) - 1.0
	tmp = 0
	if z0 <= -2.8e+16:
		tmp = t_0
	elif z0 <= -1.7e-154:
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (math.exp((math.pi / z0)) - -1.0))) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (math.pi / z0))) - z1)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
	t_1 = Float64(Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 1.0) - 1.0)
	tmp = 0.0
	if (z0 <= -2.8e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = Float64(t_1 / Float64(Float64(t_1 * Float64(Float64(1.0 - z1) / Float64(exp(Float64(pi / z0)) - -1.0))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0))) / Float64(Float64(Float64(z1 * 2.0) / Float64(2.0 + Float64(pi / z0))) - z1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	t_1 = (((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 1.0) - 1.0;
	tmp = 0.0;
	if (z0 <= -2.8e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (exp((pi / z0)) - -1.0))) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (pi / z0))) - z1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 1.0), $MachinePrecision] - 1.0), $MachinePrecision]}, If[LessEqual[z0, -2.8e+16], t$95$0, If[LessEqual[z0, -1.7e-154], N[(t$95$1 / N[(N[(t$95$1 * N[(N[(1.0 - z1), $MachinePrecision] / N[(N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(2.0 + N[(Pi / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -2.8e16 or 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -2.8e16 < z0 < -1.6999999999999999e-154

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \left(1 + \color{blue}{1}\right)}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. associate--r+ N/A

         \[\leadsto \frac{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 1\right) - \color{blue}{1}}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 1\right) - \color{blue}{1}}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower--.f64 37.9%

         \[\leadsto \frac{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. mul-1-neg N/A

         \[\leadsto \frac{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lift-/.f64 N/A

         \[\leadsto \frac{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. distribute-neg-frac N/A

         \[\leadsto \frac{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. sub-negate-rev N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      13. lower--.f64 37.9%

          \[\leadsto \frac{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      15. lift-/.f64 N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      16. mult-flip-rev N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      17. lower-/.f64 37.9%

          \[\leadsto \frac{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - \color{blue}{1}}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift--.f64 N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. metadata-eval N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \left(1 + \color{blue}{1}\right)\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. associate--r+ N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 1\right) - \color{blue}{1}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 1\right) - \color{blue}{1}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower--.f64 37.9%

          \[\leadsto \frac{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - 1}{\left(\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift-*.f64 N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. mul-1-neg N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lift-/.f64 N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. distribute-neg-frac N/A

          \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lower-/.f64 N/A

           \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. lift--.f64 N/A

           \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. sub-negate-rev N/A

           \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       13. lower--.f64 37.9%

           \[\leadsto \frac{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       14. lift-*.f64 N/A

           \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       15. lift-/.f64 N/A

           \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       16. mult-flip-rev N/A

           \[\leadsto \frac{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       17. lower-/.f64 37.9%

           \[\leadsto \frac{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - 1\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - 1}{\left(\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 1\right) - \color{blue}{1}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   if -1.6999999999999999e-154 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   8. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-PI.f64 33.6%

         \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1} \]

   10. Applied rewrites 33.6%

       \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \color{blue}{\frac{\pi}{z0}}} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 97.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ t_1 := \frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\\ \mathbf{if}\;z0 \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z0 \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{t\_1}{t\_1 \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         -2.0
         (-
          (*
           -1.0
           (/
            (-
             (* 1.5707963705062866 (- z1 1.0))
             (* -0.5 (* PI (- z1 1.0))))
            z0))
          1.0)))
       (t_1
        (-
         (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0)
         2.0)))
  (if (<= z0 -1.25e+16)
    t_0
    (if (<= z0 -1.7e-154)
      (/ t_1 (- (* t_1 (/ (- 1.0 z1) (- (exp (/ PI z0)) -1.0))) z1))
      (if (<= z0 3.1)
        (/
         (- -1.0 (exp (/ -3.1415927410125732 z0)))
         (- (/ (* z1 2.0) (+ 2.0 (/ PI z0))) z1))
        t_0)))))

C

double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	double t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (exp((((double) M_PI) / z0)) - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (((double) M_PI) / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	double t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (Math.exp((Math.PI / z0)) - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - Math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (Math.PI / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0
	tmp = 0
	if z0 <= -1.25e+16:
		tmp = t_0
	elif z0 <= -1.7e-154:
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (math.exp((math.pi / z0)) - -1.0))) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (math.pi / z0))) - z1)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
	t_1 = Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0)
	tmp = 0.0
	if (z0 <= -1.25e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = Float64(t_1 / Float64(Float64(t_1 * Float64(Float64(1.0 - z1) / Float64(exp(Float64(pi / z0)) - -1.0))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0))) / Float64(Float64(Float64(z1 * 2.0) / Float64(2.0 + Float64(pi / z0))) - z1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	t_1 = ((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0;
	tmp = 0.0;
	if (z0 <= -1.25e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (exp((pi / z0)) - -1.0))) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (pi / z0))) - z1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z0, -1.25e+16], t$95$0, If[LessEqual[z0, -1.7e-154], N[(t$95$1 / N[(N[(t$95$1 * N[(N[(1.0 - z1), $MachinePrecision] / N[(N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(2.0 + N[(Pi / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -1.25e16 or 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -1.25e16 < z0 < -1.6999999999999999e-154

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   if -1.6999999999999999e-154 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   8. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-PI.f64 33.6%

         \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1} \]

   10. Applied rewrites 33.6%

       \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \color{blue}{\frac{\pi}{z0}}} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 97.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ \mathbf{if}\;z0 \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z0 \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\frac{z1 - 1}{-1 - e^{\frac{\pi}{z0}}} \cdot \left(\frac{3.1415927410125732 \cdot z0 - 4.9348024751914465}{z0 \cdot z0} - 2\right) - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         -2.0
         (-
          (*
           -1.0
           (/
            (-
             (* 1.5707963705062866 (- z1 1.0))
             (* -0.5 (* PI (- z1 1.0))))
            z0))
          1.0))))
  (if (<= z0 -1.25e+16)
    t_0
    (if (<= z0 -1.7e-154)
      (/
       (- (/ (- 3.1415927410125732 (/ 4.9348024751914465 z0)) z0) 2.0)
       (-
        (*
         (/ (- z1 1.0) (- -1.0 (exp (/ PI z0))))
         (-
          (/
           (- (* 3.1415927410125732 z0) 4.9348024751914465)
           (* z0 z0))
          2.0))
        z1))
      (if (<= z0 3.1)
        (/
         (- -1.0 (exp (/ -3.1415927410125732 z0)))
         (- (/ (* z1 2.0) (+ 2.0 (/ PI z0))) z1))
        t_0)))))

C

double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = (((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0) / ((((z1 - 1.0) / (-1.0 - exp((((double) M_PI) / z0)))) * ((((3.1415927410125732 * z0) - 4.9348024751914465) / (z0 * z0)) - 2.0)) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (((double) M_PI) / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = (((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0) / ((((z1 - 1.0) / (-1.0 - Math.exp((Math.PI / z0)))) * ((((3.1415927410125732 * z0) - 4.9348024751914465) / (z0 * z0)) - 2.0)) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - Math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (Math.PI / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	tmp = 0
	if z0 <= -1.25e+16:
		tmp = t_0
	elif z0 <= -1.7e-154:
		tmp = (((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0) / ((((z1 - 1.0) / (-1.0 - math.exp((math.pi / z0)))) * ((((3.1415927410125732 * z0) - 4.9348024751914465) / (z0 * z0)) - 2.0)) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (math.pi / z0))) - z1)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
	tmp = 0.0
	if (z0 <= -1.25e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = Float64(Float64(Float64(Float64(3.1415927410125732 - Float64(4.9348024751914465 / z0)) / z0) - 2.0) / Float64(Float64(Float64(Float64(z1 - 1.0) / Float64(-1.0 - exp(Float64(pi / z0)))) * Float64(Float64(Float64(Float64(3.1415927410125732 * z0) - 4.9348024751914465) / Float64(z0 * z0)) - 2.0)) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0))) / Float64(Float64(Float64(z1 * 2.0) / Float64(2.0 + Float64(pi / z0))) - z1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	tmp = 0.0;
	if (z0 <= -1.25e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = (((3.1415927410125732 - (4.9348024751914465 / z0)) / z0) - 2.0) / ((((z1 - 1.0) / (-1.0 - exp((pi / z0)))) * ((((3.1415927410125732 * z0) - 4.9348024751914465) / (z0 * z0)) - 2.0)) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (pi / z0))) - z1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z0, -1.25e+16], t$95$0, If[LessEqual[z0, -1.7e-154], N[(N[(N[(N[(3.1415927410125732 - N[(4.9348024751914465 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision] / N[(N[(N[(N[(z1 - 1.0), $MachinePrecision] / N[(-1.0 - N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(3.1415927410125732 * z0), $MachinePrecision] - 4.9348024751914465), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(2.0 + N[(Pi / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -1.25e16 or 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -1.25e16 < z0 < -1.6999999999999999e-154

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   13. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\color{blue}{\frac{z1 - 1}{-1 - e^{\frac{\pi}{z0}}} \cdot \left(\frac{3.1415927410125732 \cdot z0 - 4.9348024751914465}{z0 \cdot z0} - 2\right)} - z1} \]

   if -1.6999999999999999e-154 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   8. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-PI.f64 33.6%

         \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1} \]

   10. Applied rewrites 33.6%

       \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \color{blue}{\frac{\pi}{z0}}} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 97.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} t_0 := \frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ t_1 := \frac{3.1415927410125732 \cdot z0 - 4.9348024751914465}{z0 \cdot z0} - 2\\ \mathbf{if}\;z0 \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z0 \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{t\_1}{\frac{\left(z1 - 1\right) \cdot t\_1}{-1 - e^{\frac{\pi}{z0}}} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         -2.0
         (-
          (*
           -1.0
           (/
            (-
             (* 1.5707963705062866 (- z1 1.0))
             (* -0.5 (* PI (- z1 1.0))))
            z0))
          1.0)))
       (t_1
        (-
         (/
          (- (* 3.1415927410125732 z0) 4.9348024751914465)
          (* z0 z0))
         2.0)))
  (if (<= z0 -1.25e+16)
    t_0
    (if (<= z0 -1.7e-154)
      (/ t_1 (- (/ (* (- z1 1.0) t_1) (- -1.0 (exp (/ PI z0)))) z1))
      (if (<= z0 3.1)
        (/
         (- -1.0 (exp (/ -3.1415927410125732 z0)))
         (- (/ (* z1 2.0) (+ 2.0 (/ PI z0))) z1))
        t_0)))))

C

double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	double t_1 = (((3.1415927410125732 * z0) - 4.9348024751914465) / (z0 * z0)) - 2.0;
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((((z1 - 1.0) * t_1) / (-1.0 - exp((((double) M_PI) / z0)))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (((double) M_PI) / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	double t_1 = (((3.1415927410125732 * z0) - 4.9348024751914465) / (z0 * z0)) - 2.0;
	double tmp;
	if (z0 <= -1.25e+16) {
		tmp = t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((((z1 - 1.0) * t_1) / (-1.0 - Math.exp((Math.PI / z0)))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - Math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (Math.PI / z0))) - z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	t_1 = (((3.1415927410125732 * z0) - 4.9348024751914465) / (z0 * z0)) - 2.0
	tmp = 0
	if z0 <= -1.25e+16:
		tmp = t_0
	elif z0 <= -1.7e-154:
		tmp = t_1 / ((((z1 - 1.0) * t_1) / (-1.0 - math.exp((math.pi / z0)))) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (math.pi / z0))) - z1)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
	t_1 = Float64(Float64(Float64(Float64(3.1415927410125732 * z0) - 4.9348024751914465) / Float64(z0 * z0)) - 2.0)
	tmp = 0.0
	if (z0 <= -1.25e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = Float64(t_1 / Float64(Float64(Float64(Float64(z1 - 1.0) * t_1) / Float64(-1.0 - exp(Float64(pi / z0)))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0))) / Float64(Float64(Float64(z1 * 2.0) / Float64(2.0 + Float64(pi / z0))) - z1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	t_1 = (((3.1415927410125732 * z0) - 4.9348024751914465) / (z0 * z0)) - 2.0;
	tmp = 0.0;
	if (z0 <= -1.25e+16)
		tmp = t_0;
	elseif (z0 <= -1.7e-154)
		tmp = t_1 / ((((z1 - 1.0) * t_1) / (-1.0 - exp((pi / z0)))) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (pi / z0))) - z1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(3.1415927410125732 * z0), $MachinePrecision] - 4.9348024751914465), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z0, -1.25e+16], t$95$0, If[LessEqual[z0, -1.7e-154], N[(t$95$1 / N[(N[(N[(N[(z1 - 1.0), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(-1.0 - N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(2.0 + N[(Pi / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -1.25e16 or 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -1.25e16 < z0 < -1.6999999999999999e-154

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   13. Applied rewrites 37.7%

       \[\leadsto \color{blue}{\frac{\frac{3.1415927410125732 \cdot z0 - 4.9348024751914465}{z0 \cdot z0} - 2}{\frac{\left(z1 - 1\right) \cdot \left(\frac{3.1415927410125732 \cdot z0 - 4.9348024751914465}{z0 \cdot z0} - 2\right)}{-1 - e^{\frac{\pi}{z0}}} - z1}} \]

   if -1.6999999999999999e-154 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   8. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-PI.f64 33.6%

         \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1} \]

   10. Applied rewrites 33.6%

       \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \color{blue}{\frac{\pi}{z0}}} - z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 96.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} t_0 := -1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1\\ t_1 := \frac{\frac{-4.9348024751914465}{z0}}{z0} - 2\\ \mathbf{if}\;z0 \leq -9500000:\\ \;\;\;\;\frac{3.1415927410125732 \cdot \frac{1}{z0} - 2}{t\_0}\\ \mathbf{elif}\;z0 \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{t\_1}{t\_1 \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t\_0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (-
         (*
          -1.0
          (/
           (-
            (* 1.5707963705062866 (- z1 1.0))
            (* -0.5 (* PI (- z1 1.0))))
           z0))
         1.0))
       (t_1 (- (/ (/ -4.9348024751914465 z0) z0) 2.0)))
  (if (<= z0 -9500000.0)
    (/ (- (* 3.1415927410125732 (/ 1.0 z0)) 2.0) t_0)
    (if (<= z0 -1.7e-154)
      (/ t_1 (- (* t_1 (/ (- 1.0 z1) (- (exp (/ PI z0)) -1.0))) z1))
      (if (<= z0 3.1)
        (/
         (- -1.0 (exp (/ -3.1415927410125732 z0)))
         (- (/ (* z1 2.0) (+ 2.0 (/ PI z0))) z1))
        (/ -2.0 t_0))))))

C

double code(double z0, double z1) {
	double t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0;
	double t_1 = ((-4.9348024751914465 / z0) / z0) - 2.0;
	double tmp;
	if (z0 <= -9500000.0) {
		tmp = ((3.1415927410125732 * (1.0 / z0)) - 2.0) / t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (exp((((double) M_PI) / z0)) - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (((double) M_PI) / z0))) - z1);
	} else {
		tmp = -2.0 / t_0;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0;
	double t_1 = ((-4.9348024751914465 / z0) / z0) - 2.0;
	double tmp;
	if (z0 <= -9500000.0) {
		tmp = ((3.1415927410125732 * (1.0 / z0)) - 2.0) / t_0;
	} else if (z0 <= -1.7e-154) {
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (Math.exp((Math.PI / z0)) - -1.0))) - z1);
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - Math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (Math.PI / z0))) - z1);
	} else {
		tmp = -2.0 / t_0;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0
	t_1 = ((-4.9348024751914465 / z0) / z0) - 2.0
	tmp = 0
	if z0 <= -9500000.0:
		tmp = ((3.1415927410125732 * (1.0 / z0)) - 2.0) / t_0
	elif z0 <= -1.7e-154:
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (math.exp((math.pi / z0)) - -1.0))) - z1)
	elif z0 <= 3.1:
		tmp = (-1.0 - math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (math.pi / z0))) - z1)
	else:
		tmp = -2.0 / t_0
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0)
	t_1 = Float64(Float64(Float64(-4.9348024751914465 / z0) / z0) - 2.0)
	tmp = 0.0
	if (z0 <= -9500000.0)
		tmp = Float64(Float64(Float64(3.1415927410125732 * Float64(1.0 / z0)) - 2.0) / t_0);
	elseif (z0 <= -1.7e-154)
		tmp = Float64(t_1 / Float64(Float64(t_1 * Float64(Float64(1.0 - z1) / Float64(exp(Float64(pi / z0)) - -1.0))) - z1));
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0))) / Float64(Float64(Float64(z1 * 2.0) / Float64(2.0 + Float64(pi / z0))) - z1));
	else
		tmp = Float64(-2.0 / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0;
	t_1 = ((-4.9348024751914465 / z0) / z0) - 2.0;
	tmp = 0.0;
	if (z0 <= -9500000.0)
		tmp = ((3.1415927410125732 * (1.0 / z0)) - 2.0) / t_0;
	elseif (z0 <= -1.7e-154)
		tmp = t_1 / ((t_1 * ((1.0 - z1) / (exp((pi / z0)) - -1.0))) - z1);
	elseif (z0 <= 3.1)
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (pi / z0))) - z1);
	else
		tmp = -2.0 / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(-4.9348024751914465 / z0), $MachinePrecision] / z0), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z0, -9500000.0], N[(N[(N[(3.1415927410125732 * N[(1.0 / z0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[z0, -1.7e-154], N[(t$95$1 / N[(N[(t$95$1 * N[(N[(1.0 - z1), $MachinePrecision] / N[(N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(2.0 + N[(Pi / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], N[(-2.0 / t$95$0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z0 < -9.5e6

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0} - 2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0} - \color{blue}{2}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0} - 2}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 66.2%

         \[\leadsto \frac{3.1415927410125732 \cdot \frac{1}{z0} - 2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   9. Applied rewrites 66.2%

      \[\leadsto \frac{\color{blue}{3.1415927410125732 \cdot \frac{1}{z0} - 2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -9.5e6 < z0 < -1.6999999999999999e-154

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around -inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.6%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   4. Applied rewrites 37.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}}{\left(-1 - e^{\frac{-3.1415927410125732}{z0}}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   5. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - \color{blue}{2}\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lower-/.f64 37.9%

         \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   7. Applied rewrites 37.9%

      \[\leadsto \frac{-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2}{\color{blue}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right)} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      4. distribute-neg-frac N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      8. lower--.f64 37.9%

         \[\leadsto \frac{\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      11. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

      12. lower-/.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   9. Applied rewrites 37.9%

      \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(-1 \cdot \frac{4.9348024751914465 \cdot \frac{1}{z0} - 3.1415927410125732}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(-1 \cdot \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       2. mul-1-neg N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\left(\mathsf{neg}\left(\frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}}{z0}\right)\right) - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       4. distribute-neg-frac N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       5. lower-/.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       6. lift--.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\mathsf{neg}\left(\left(\frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0} - \frac{7853981852531433}{2500000000000000}\right)\right)}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       7. sub-negate-rev N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       8. lower--.f64 37.9%

          \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - 4.9348024751914465 \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       9. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       10. lift-/.f64 N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{61685030939893080179390253033489}{12500000000000000000000000000000} \cdot \frac{1}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       11. mult-flip-rev N/A

           \[\leadsto \frac{\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{\frac{7853981852531433}{2500000000000000} - \frac{\frac{61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

       12. lower-/.f64 37.9%

           \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   11. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   12. Taylor expanded in z0 around 0

       \[\leadsto \frac{\frac{\frac{\frac{-61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   13. Step-by-step derivation

       1. lower-/.f64 36.7%

          \[\leadsto \frac{\frac{\frac{-4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   14. Applied rewrites 36.7%

       \[\leadsto \frac{\frac{\frac{-4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{3.1415927410125732 - \frac{4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   15. Taylor expanded in z0 around 0

       \[\leadsto \frac{\frac{\frac{-4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{\frac{\frac{-61685030939893080179390253033489}{12500000000000000000000000000000}}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
   16. Step-by-step derivation

       1. lower-/.f64 37.5%

          \[\leadsto \frac{\frac{\frac{-4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{\frac{-4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   17. Applied rewrites 37.5%

       \[\leadsto \frac{\frac{\frac{-4.9348024751914465}{z0}}{z0} - 2}{\left(\frac{\frac{-4.9348024751914465}{z0}}{z0} - 2\right) \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]

   if -1.6999999999999999e-154 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   8. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-PI.f64 33.6%

         \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1} \]

   10. Applied rewrites 33.6%

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

   if 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 15: 96.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} t_0 := -1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1\\ \mathbf{if}\;z0 \leq -1.8 \cdot 10^{-308}:\\ \;\;\;\;\frac{-1 - \left(1 - 3.1415927410125732 \cdot \frac{1}{z0}\right)}{t\_0}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t\_0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (-
         (*
          -1.0
          (/
           (-
            (* 1.5707963705062866 (- z1 1.0))
            (* -0.5 (* PI (- z1 1.0))))
           z0))
         1.0)))
  (if (<= z0 -1.8e-308)
    (/ (- -1.0 (- 1.0 (* 3.1415927410125732 (/ 1.0 z0)))) t_0)
    (if (<= z0 3.1)
      (/
       (- -1.0 (exp (/ -3.1415927410125732 z0)))
       (- (/ (* z1 2.0) (+ 2.0 (/ PI z0))) z1))
      (/ -2.0 t_0)))))

C

double code(double z0, double z1) {
	double t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0;
	double tmp;
	if (z0 <= -1.8e-308) {
		tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / t_0;
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (((double) M_PI) / z0))) - z1);
	} else {
		tmp = -2.0 / t_0;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0;
	double tmp;
	if (z0 <= -1.8e-308) {
		tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / t_0;
	} else if (z0 <= 3.1) {
		tmp = (-1.0 - Math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (Math.PI / z0))) - z1);
	} else {
		tmp = -2.0 / t_0;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0
	tmp = 0
	if z0 <= -1.8e-308:
		tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / t_0
	elif z0 <= 3.1:
		tmp = (-1.0 - math.exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (math.pi / z0))) - z1)
	else:
		tmp = -2.0 / t_0
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0)
	tmp = 0.0
	if (z0 <= -1.8e-308)
		tmp = Float64(Float64(-1.0 - Float64(1.0 - Float64(3.1415927410125732 * Float64(1.0 / z0)))) / t_0);
	elseif (z0 <= 3.1)
		tmp = Float64(Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0))) / Float64(Float64(Float64(z1 * 2.0) / Float64(2.0 + Float64(pi / z0))) - z1));
	else
		tmp = Float64(-2.0 / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0;
	tmp = 0.0;
	if (z0 <= -1.8e-308)
		tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / t_0;
	elseif (z0 <= 3.1)
		tmp = (-1.0 - exp((-3.1415927410125732 / z0))) / (((z1 * 2.0) / (2.0 + (pi / z0))) - z1);
	else
		tmp = -2.0 / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]}, If[LessEqual[z0, -1.8e-308], N[(N[(-1.0 - N[(1.0 - N[(3.1415927410125732 * N[(1.0 / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[z0, 3.1], N[(N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(2.0 + N[(Pi / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], N[(-2.0 / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -1.7999999999999999e-308

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{-1 - \color{blue}{\left(1 - \frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0}\right)}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - \left(1 - \color{blue}{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0}}\right)}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - \left(1 - \frac{7853981852531433}{2500000000000000} \cdot \color{blue}{\frac{1}{z0}}\right)}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 66.2%

         \[\leadsto \frac{-1 - \left(1 - 3.1415927410125732 \cdot \frac{1}{\color{blue}{z0}}\right)}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   9. Applied rewrites 66.2%

      \[\leadsto \frac{-1 - \color{blue}{\left(1 - 3.1415927410125732 \cdot \frac{1}{z0}\right)}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -1.7999999999999999e-308 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   8. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-PI.f64 33.6%

         \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{2 + \frac{\pi}{z0}} - z1} \]

   10. Applied rewrites 33.6%

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

   if 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := -1 - e^{\frac{-3.1415927410125732}{z0}}\\ t_1 := \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1}\\ \mathbf{if}\;\frac{t\_0}{t\_0 \cdot t\_1 - z1} \leq -\infty:\\ \;\;\;\;\frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{-2 \cdot t\_1 - z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (- -1.0 (exp (/ -3.1415927410125732 z0))))
       (t_1 (/ (- 1.0 z1) (- (exp (/ PI z0)) -1.0))))
  (if (<= (/ t_0 (- (* t_0 t_1) z1)) (- INFINITY))
    (/
     -2.0
     (-
      (*
       -1.0
       (/
        (-
         (* 1.5707963705062866 (- z1 1.0))
         (* -0.5 (* PI (- z1 1.0))))
        z0))
      1.0))
    (/ -2.0 (- (* -2.0 t_1) z1)))))

C

double code(double z0, double z1) {
	double t_0 = -1.0 - exp((-3.1415927410125732 / z0));
	double t_1 = (1.0 - z1) / (exp((((double) M_PI) / z0)) - -1.0);
	double tmp;
	if ((t_0 / ((t_0 * t_1) - z1)) <= -((double) INFINITY)) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
	} else {
		tmp = -2.0 / ((-2.0 * t_1) - z1);
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = -1.0 - Math.exp((-3.1415927410125732 / z0));
	double t_1 = (1.0 - z1) / (Math.exp((Math.PI / z0)) - -1.0);
	double tmp;
	if ((t_0 / ((t_0 * t_1) - z1)) <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
	} else {
		tmp = -2.0 / ((-2.0 * t_1) - z1);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -1.0 - math.exp((-3.1415927410125732 / z0))
	t_1 = (1.0 - z1) / (math.exp((math.pi / z0)) - -1.0)
	tmp = 0
	if (t_0 / ((t_0 * t_1) - z1)) <= -math.inf:
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)
	else:
		tmp = -2.0 / ((-2.0 * t_1) - z1)
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(-1.0 - exp(Float64(-3.1415927410125732 / z0)))
	t_1 = Float64(Float64(1.0 - z1) / Float64(exp(Float64(pi / z0)) - -1.0))
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(t_0 * t_1) - z1)) <= Float64(-Inf))
		tmp = Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0));
	else
		tmp = Float64(-2.0 / Float64(Float64(-2.0 * t_1) - z1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -1.0 - exp((-3.1415927410125732 / z0));
	t_1 = (1.0 - z1) / (exp((pi / z0)) - -1.0);
	tmp = 0.0;
	if ((t_0 / ((t_0 * t_1) - z1)) <= -Inf)
		tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
	else
		tmp = -2.0 / ((-2.0 * t_1) - z1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(-1.0 - N[Exp[N[(-3.1415927410125732 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - z1), $MachinePrecision] / N[(N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 / N[(N[(t$95$0 * t$95$1), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], (-Infinity)], N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], N[(-2.0 / N[(N[(-2.0 * t$95$1), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1)) < -inf.0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if -inf.0 < (/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (-.f64 (*.f64 (-.f64 #s(literal -1 binary64) (exp.f64 (/.f64 #s(literal -7853981852531433/2500000000000000 binary64) z0))) (/.f64 (-.f64 #s(literal 1 binary64) z1) (-.f64 (exp.f64 (/.f64 (PI.f64) z0)) #s(literal -1 binary64)))) z1))

   1. Initial program 70.0%

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

   2. Taylor expanded in z0 around inf

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

   4. Applied rewrites 41.6%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 42.6%

      \[\leadsto \frac{-2}{\color{blue}{-2} \cdot \frac{1 - z1}{e^{\frac{\pi}{z0}} - -1} - z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 71.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} t_0 := -1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1\\ \mathbf{if}\;z0 \leq 1.35 \cdot 10^{-303}:\\ \;\;\;\;\frac{-1 - \left(1 - 3.1415927410125732 \cdot \frac{1}{z0}\right)}{t\_0}\\ \mathbf{elif}\;z0 \leq 3.1:\\ \;\;\;\;\frac{-2}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t\_0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (-
         (*
          -1.0
          (/
           (-
            (* 1.5707963705062866 (- z1 1.0))
            (* -0.5 (* PI (- z1 1.0))))
           z0))
         1.0)))
  (if (<= z0 1.35e-303)
    (/ (- -1.0 (- 1.0 (* 3.1415927410125732 (/ 1.0 z0)))) t_0)
    (if (<= z0 3.1)
      (/ -2.0 (- (/ (* z1 2.0) (+ 1.0 (exp (/ PI z0)))) z1))
      (/ -2.0 t_0)))))

C

double code(double z0, double z1) {
	double t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0;
	double tmp;
	if (z0 <= 1.35e-303) {
		tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / t_0;
	} else if (z0 <= 3.1) {
		tmp = -2.0 / (((z1 * 2.0) / (1.0 + exp((((double) M_PI) / z0)))) - z1);
	} else {
		tmp = -2.0 / t_0;
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0;
	double tmp;
	if (z0 <= 1.35e-303) {
		tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / t_0;
	} else if (z0 <= 3.1) {
		tmp = -2.0 / (((z1 * 2.0) / (1.0 + Math.exp((Math.PI / z0)))) - z1);
	} else {
		tmp = -2.0 / t_0;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0
	tmp = 0
	if z0 <= 1.35e-303:
		tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / t_0
	elif z0 <= 3.1:
		tmp = -2.0 / (((z1 * 2.0) / (1.0 + math.exp((math.pi / z0)))) - z1)
	else:
		tmp = -2.0 / t_0
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0)
	tmp = 0.0
	if (z0 <= 1.35e-303)
		tmp = Float64(Float64(-1.0 - Float64(1.0 - Float64(3.1415927410125732 * Float64(1.0 / z0)))) / t_0);
	elseif (z0 <= 3.1)
		tmp = Float64(-2.0 / Float64(Float64(Float64(z1 * 2.0) / Float64(1.0 + exp(Float64(pi / z0)))) - z1));
	else
		tmp = Float64(-2.0 / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0;
	tmp = 0.0;
	if (z0 <= 1.35e-303)
		tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / t_0;
	elseif (z0 <= 3.1)
		tmp = -2.0 / (((z1 * 2.0) / (1.0 + exp((pi / z0)))) - z1);
	else
		tmp = -2.0 / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]}, If[LessEqual[z0, 1.35e-303], N[(N[(-1.0 - N[(1.0 - N[(3.1415927410125732 * N[(1.0 / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[z0, 3.1], N[(-2.0 / N[(N[(N[(z1 * 2.0), $MachinePrecision] / N[(1.0 + N[Exp[N[(Pi / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z1), $MachinePrecision]), $MachinePrecision], N[(-2.0 / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < 1.3499999999999999e-303

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{-1 - \color{blue}{\left(1 - \frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0}\right)}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - \left(1 - \color{blue}{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0}}\right)}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - \left(1 - \frac{7853981852531433}{2500000000000000} \cdot \color{blue}{\frac{1}{z0}}\right)}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 66.2%

         \[\leadsto \frac{-1 - \left(1 - 3.1415927410125732 \cdot \frac{1}{\color{blue}{z0}}\right)}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   9. Applied rewrites 66.2%

      \[\leadsto \frac{-1 - \color{blue}{\left(1 - 3.1415927410125732 \cdot \frac{1}{z0}\right)}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   if 1.3499999999999999e-303 < z0 < 3.1000000000000001

   1. Initial program 70.0%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-exp.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   5. Taylor expanded in z0 around inf

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

   7. Applied rewrites 34.2%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\frac{z1 \cdot 2}{1 + e^{\frac{\pi}{z0}}} - z1} \]

   8. Taylor expanded in z0 around inf

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

   10. Applied rewrites 7.2%

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

   if 3.1000000000000001 < z0

   1. Initial program 70.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 70.0%

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

   3. Applied rewrites 70.0%

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

   4. Taylor expanded in z0 around -inf

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      9. lower-PI.f64 N/A

         \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

      10. lower--.f64 66.0%

          \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. Applied rewrites 66.0%

      \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.1%

      \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 66.2% accurate, 4.9× speedup

Math

\[\frac{-1 - \left(1 - 3.1415927410125732 \cdot \frac{1}{z0}\right)}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 (- -1.0 (- 1.0 (* 3.1415927410125732 (/ 1.0 z0))))
 (-
  (*
   -1.0
   (/
    (- (* 1.5707963705062866 (- z1 1.0)) (* -0.5 (* PI (- z1 1.0))))
    z0))
  1.0)))

C

double code(double z0, double z1) {
	return (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
}

Java

public static double code(double z0, double z1) {
	return (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
}

Python

def code(z0, z1):
	return (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)

Julia

function code(z0, z1)
	return Float64(Float64(-1.0 - Float64(1.0 - Float64(3.1415927410125732 * Float64(1.0 / z0)))) / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
end

MATLAB

function tmp = code(z0, z1)
	tmp = (-1.0 - (1.0 - (3.1415927410125732 * (1.0 / z0)))) / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
end

Wolfram

code[z0_, z1_] := N[(N[(-1.0 - N[(1.0 - N[(3.1415927410125732 * N[(1.0 / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.0%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. frac-2neg N/A

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

   5. mult-flip N/A

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

   6. associate-*l* N/A

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

   7. lower-*.f64 N/A

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

   8. lift--.f64 N/A

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

   9. sub-negate-rev N/A

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

   10. lower--.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lift--.f64 N/A

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

   14. sub-negate-rev N/A

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

   15. lower--.f64 70.0%

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

3. Applied rewrites 70.0%

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

4. Taylor expanded in z0 around -inf

   \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
5. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   3. lower-/.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   4. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   7. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   9. lower-PI.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   10. lower--.f64 66.0%

       \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

6. Applied rewrites 66.0%

   \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

7. Taylor expanded in z0 around inf

   \[\leadsto \frac{-1 - \color{blue}{\left(1 - \frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0}\right)}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
8. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto \frac{-1 - \left(1 - \color{blue}{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0}}\right)}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{-1 - \left(1 - \frac{7853981852531433}{2500000000000000} \cdot \color{blue}{\frac{1}{z0}}\right)}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   3. lower-/.f64 66.2%

      \[\leadsto \frac{-1 - \left(1 - 3.1415927410125732 \cdot \frac{1}{\color{blue}{z0}}\right)}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

9. Applied rewrites 66.2%

   \[\leadsto \frac{-1 - \color{blue}{\left(1 - 3.1415927410125732 \cdot \frac{1}{z0}\right)}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
10. Add Preprocessing

Alternative 19: 66.2% accurate, 5.1× speedup

Math

\[\frac{3.1415927410125732 \cdot \frac{1}{z0} - 2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 (- (* 3.1415927410125732 (/ 1.0 z0)) 2.0)
 (-
  (*
   -1.0
   (/
    (- (* 1.5707963705062866 (- z1 1.0)) (* -0.5 (* PI (- z1 1.0))))
    z0))
  1.0)))

C

double code(double z0, double z1) {
	return ((3.1415927410125732 * (1.0 / z0)) - 2.0) / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
}

Java

public static double code(double z0, double z1) {
	return ((3.1415927410125732 * (1.0 / z0)) - 2.0) / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
}

Python

def code(z0, z1):
	return ((3.1415927410125732 * (1.0 / z0)) - 2.0) / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)

Julia

function code(z0, z1)
	return Float64(Float64(Float64(3.1415927410125732 * Float64(1.0 / z0)) - 2.0) / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
end

MATLAB

function tmp = code(z0, z1)
	tmp = ((3.1415927410125732 * (1.0 / z0)) - 2.0) / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
end

Wolfram

code[z0_, z1_] := N[(N[(N[(3.1415927410125732 * N[(1.0 / z0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision] / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.0%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. frac-2neg N/A

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

   5. mult-flip N/A

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

   6. associate-*l* N/A

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

   7. lower-*.f64 N/A

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

   8. lift--.f64 N/A

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

   9. sub-negate-rev N/A

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

   10. lower--.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lift--.f64 N/A

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

   14. sub-negate-rev N/A

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

   15. lower--.f64 70.0%

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

3. Applied rewrites 70.0%

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

4. Taylor expanded in z0 around -inf

   \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
5. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   3. lower-/.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   4. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   7. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   9. lower-PI.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   10. lower--.f64 66.0%

       \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

6. Applied rewrites 66.0%

   \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

7. Taylor expanded in z0 around inf

   \[\leadsto \frac{\color{blue}{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0} - 2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
8. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto \frac{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0} - \color{blue}{2}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{\frac{7853981852531433}{2500000000000000} \cdot \frac{1}{z0} - 2}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   3. lower-/.f64 66.2%

      \[\leadsto \frac{3.1415927410125732 \cdot \frac{1}{z0} - 2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

9. Applied rewrites 66.2%

   \[\leadsto \frac{\color{blue}{3.1415927410125732 \cdot \frac{1}{z0} - 2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
10. Add Preprocessing

Alternative 20: 66.1% accurate, 6.8× speedup

Math

\[\frac{-2}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 -2.0
 (-
  (*
   -1.0
   (/
    (- (* 1.5707963705062866 (- z1 1.0)) (* -0.5 (* PI (- z1 1.0))))
    z0))
  1.0)))

C

double code(double z0, double z1) {
	return -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (((double) M_PI) * (z1 - 1.0)))) / z0)) - 1.0);
}

Java

public static double code(double z0, double z1) {
	return -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (Math.PI * (z1 - 1.0)))) / z0)) - 1.0);
}

Python

def code(z0, z1):
	return -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (math.pi * (z1 - 1.0)))) / z0)) - 1.0)

Julia

function code(z0, z1)
	return Float64(-2.0 / Float64(Float64(-1.0 * Float64(Float64(Float64(1.5707963705062866 * Float64(z1 - 1.0)) - Float64(-0.5 * Float64(pi * Float64(z1 - 1.0)))) / z0)) - 1.0))
end

MATLAB

function tmp = code(z0, z1)
	tmp = -2.0 / ((-1.0 * (((1.5707963705062866 * (z1 - 1.0)) - (-0.5 * (pi * (z1 - 1.0)))) / z0)) - 1.0);
end

Wolfram

code[z0_, z1_] := N[(-2.0 / N[(N[(-1.0 * N[(N[(N[(1.5707963705062866 * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 * N[(Pi * N[(z1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.0%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. frac-2neg N/A

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

   5. mult-flip N/A

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

   6. associate-*l* N/A

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

   7. lower-*.f64 N/A

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

   8. lift--.f64 N/A

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

   9. sub-negate-rev N/A

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

   10. lower--.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lift--.f64 N/A

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

   14. sub-negate-rev N/A

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

   15. lower--.f64 70.0%

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

3. Applied rewrites 70.0%

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

4. Taylor expanded in z0 around -inf

   \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]
5. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - \color{blue}{1}} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   3. lower-/.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   4. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   6. lower--.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   7. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\mathsf{PI}\left(\right) \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   9. lower-PI.f64 N/A

      \[\leadsto \frac{-1 - e^{\frac{\frac{-7853981852531433}{2500000000000000}}{z0}}}{-1 \cdot \frac{\frac{7853981852531433}{5000000000000000} \cdot \left(z1 - 1\right) - \frac{-1}{2} \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

   10. lower--.f64 66.0%

       \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]

6. Applied rewrites 66.0%

   \[\leadsto \frac{-1 - e^{\frac{-3.1415927410125732}{z0}}}{\color{blue}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1}} \]

7. Taylor expanded in z0 around inf

   \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
8. Step-by-step derivation

9. Applied rewrites 66.1%

   \[\leadsto \frac{\color{blue}{-2}}{-1 \cdot \frac{1.5707963705062866 \cdot \left(z1 - 1\right) - -0.5 \cdot \left(\pi \cdot \left(z1 - 1\right)\right)}{z0} - 1} \]
10. Add Preprocessing

Alternative 21: 50.0% accurate, 376.0× speedup

Math

\[2 \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  2.0)

C

double code(double z0, double z1) {
	return 2.0;
}

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 = 2.0d0
end function

Java

public static double code(double z0, double z1) {
	return 2.0;
}

Python

def code(z0, z1):
	return 2.0

Julia

function code(z0, z1)
	return 2.0
end

MATLAB

function tmp = code(z0, z1)
	tmp = 2.0;
end

Wolfram

code[z0_, z1_] := 2.0

Derivation

1. Initial program 70.0%

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

2. Taylor expanded in z0 around inf

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

   1. lower-/.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower--.f64 35.8%

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

4. Applied rewrites 35.8%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. mul-1-neg N/A

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

   4. lift--.f64 N/A

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

   5. sub-negate-rev N/A

      \[\leadsto \frac{-2}{\left(z1 - 1\right) - z1} \]

   6. associate--l- N/A

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

   7. lower--.f64 N/A

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

   8. lower-+.f64 35.8%

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

6. Applied rewrites 35.8%

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

   1. lift--.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. +-commutative N/A

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

   4. associate--r+ N/A

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

   5. lower--.f64 N/A

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

   6. lower--.f64 50.0%

      \[\leadsto \frac{-2}{\left(z1 - z1\right) - 1} \]

8. Applied rewrites 50.0%

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

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift--.f64 N/A

      \[\leadsto \frac{-2}{\left(z1 - z1\right) - 1} \]

   4. +-inverses N/A

      \[\leadsto \frac{-2}{0 - 1} \]

   5. metadata-eval N/A

      \[\leadsto \frac{-2}{-1} \]

   6. metadata-eval 50.0%

      \[\leadsto 2 \]

10. Applied rewrites 50.0%

    \[\leadsto \color{blue}{2} \]
11. Add Preprocessing

Reproduce

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