(/ (* (* z1 z0) (exp (* z4 (/ (- z2) z3)))) (* (* (+ z3 z3) z3) (sinh (/ 1 z3))))

Percentage Accurate: 58.4% → 99.1%

Time: 7.5s

Alternatives: 16

Speedup: 0.5×

• could not determine a ground truth

  1. z1 = 7.83417168527421e-92
  2. z0 = -2.05617681403011e+148
  3. z4 = 3.839485969835657e+102
  4. z2 = -8.48677286673519e-40
  5. z3 = 3.051569210253541e-72

Specification

Math

\[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (/
 (* (* z1 z0) (exp (* z4 (/ (- z2) z3))))
 (* (* (+ z3 z3) z3) (sinh (/ 1.0 z3)))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	return ((z1 * z0) * exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * sinh((1.0 / z3)));
}

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(z1, z0, z4, z2, z3)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8), intent (in) :: z4
    real(8), intent (in) :: z2
    real(8), intent (in) :: z3
    code = ((z1 * z0) * exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * sinh((1.0d0 / z3)))
end function

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	return ((z1 * z0) * Math.exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * Math.sinh((1.0 / z3)));
}

Python

def code(z1, z0, z4, z2, z3):
	return ((z1 * z0) * math.exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * math.sinh((1.0 / z3)))

Julia

function code(z1, z0, z4, z2, z3)
	return Float64(Float64(Float64(z1 * z0) * exp(Float64(z4 * Float64(Float64(-z2) / z3)))) / Float64(Float64(Float64(z3 + z3) * z3) * sinh(Float64(1.0 / z3))))
end

MATLAB

function tmp = code(z1, z0, z4, z2, z3)
	tmp = ((z1 * z0) * exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * sinh((1.0 / z3)));
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := N[(N[(N[(z1 * z0), $MachinePrecision] * N[Exp[N[(z4 * N[((-z2) / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z3 + z3), $MachinePrecision] * z3), $MachinePrecision] * N[Sinh[N[(1.0 / z3), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 58.4% accurate, 1.0× speedup

Math

\[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (/
 (* (* z1 z0) (exp (* z4 (/ (- z2) z3))))
 (* (* (+ z3 z3) z3) (sinh (/ 1.0 z3)))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	return ((z1 * z0) * exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * sinh((1.0 / z3)));
}

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(z1, z0, z4, z2, z3)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8), intent (in) :: z4
    real(8), intent (in) :: z2
    real(8), intent (in) :: z3
    code = ((z1 * z0) * exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * sinh((1.0d0 / z3)))
end function

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	return ((z1 * z0) * Math.exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * Math.sinh((1.0 / z3)));
}

Python

def code(z1, z0, z4, z2, z3):
	return ((z1 * z0) * math.exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * math.sinh((1.0 / z3)))

Julia

function code(z1, z0, z4, z2, z3)
	return Float64(Float64(Float64(z1 * z0) * exp(Float64(z4 * Float64(Float64(-z2) / z3)))) / Float64(Float64(Float64(z3 + z3) * z3) * sinh(Float64(1.0 / z3))))
end

MATLAB

function tmp = code(z1, z0, z4, z2, z3)
	tmp = ((z1 * z0) * exp((z4 * (-z2 / z3)))) / (((z3 + z3) * z3) * sinh((1.0 / z3)));
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := N[(N[(N[(z1 * z0), $MachinePrecision] * N[Exp[N[(z4 * N[((-z2) / z3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z3 + z3), $MachinePrecision] * z3), $MachinePrecision] * N[Sinh[N[(1.0 / z3), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 0.4× speedup

Math

\[\mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \left(\left(-\mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}\right)\right) \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (*
 (copysign 1.0 z1)
 (*
  (copysign 1.0 z0)
  (*
   (- (fmin (fabs z1) (fabs z0)))
   (/
    (* (exp (* (/ (- z2) z3) z4)) (fmax (fabs z1) (fabs z0)))
    (* (* (sinh (/ -1.0 z3)) (+ z3 z3)) z3))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	return copysign(1.0, z1) * (copysign(1.0, z0) * (-fmin(fabs(z1), fabs(z0)) * ((exp(((-z2 / z3) * z4)) * fmax(fabs(z1), fabs(z0))) / ((sinh((-1.0 / z3)) * (z3 + z3)) * z3))));
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * (-fmin(Math.abs(z1), Math.abs(z0)) * ((Math.exp(((-z2 / z3) * z4)) * fmax(Math.abs(z1), Math.abs(z0))) / ((Math.sinh((-1.0 / z3)) * (z3 + z3)) * z3))));
}

Python

def code(z1, z0, z4, z2, z3):
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * (-fmin(math.fabs(z1), math.fabs(z0)) * ((math.exp(((-z2 / z3) * z4)) * fmax(math.fabs(z1), math.fabs(z0))) / ((math.sinh((-1.0 / z3)) * (z3 + z3)) * z3))))

Julia

function code(z1, z0, z4, z2, z3)
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * Float64(Float64(-fmin(abs(z1), abs(z0))) * Float64(Float64(exp(Float64(Float64(Float64(-z2) / z3) * z4)) * fmax(abs(z1), abs(z0))) / Float64(Float64(sinh(Float64(-1.0 / z3)) * Float64(z3 + z3)) * z3)))))
end

MATLAB

function tmp = code(z1, z0, z4, z2, z3)
	tmp = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * (-min(abs(z1), abs(z0)) * ((exp(((-z2 / z3) * z4)) * max(abs(z1), abs(z0))) / ((sinh((-1.0 / z3)) * (z3 + z3)) * z3))));
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[((-N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]) * N[(N[(N[Exp[N[(N[((-z2) / z3), $MachinePrecision] * z4), $MachinePrecision]], $MachinePrecision] * N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(N[Sinh[N[(-1.0 / z3), $MachinePrecision]], $MachinePrecision] * N[(z3 + z3), $MachinePrecision]), $MachinePrecision] * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.4%

   \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

   2. frac-2neg N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

   5. associate-*l* N/A

      \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

   6. distribute-lft-neg-in N/A

      \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

   7. associate-/l* N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   8. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   9. lower-neg.f64 N/A

      \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

   10. lower-/.f64 N/A

       \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

3. Applied rewrites 95.5%

   \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]
4. Add Preprocessing

Alternative 2: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := -\mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ t_2 := t\_0 \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot t\_1}{-2 \cdot z3}\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -11500:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z3 \leq 4000000:\\ \;\;\;\;t\_0 \cdot \frac{1 \cdot t\_1}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (- (fmin (fabs z1) (fabs z0))))
       (t_1 (fmax (fabs z1) (fabs z0)))
       (t_2
        (* t_0 (/ (* (exp (* (/ (- z2) z3) z4)) t_1) (* -2.0 z3)))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -11500.0)
      t_2
      (if (<= z3 4000000.0)
        (*
         t_0
         (/ (* 1.0 t_1) (* (* (sinh (/ -1.0 z3)) (+ z3 z3)) z3)))
        t_2))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = -fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double t_2 = t_0 * ((exp(((-z2 / z3) * z4)) * t_1) / (-2.0 * z3));
	double tmp;
	if (z3 <= -11500.0) {
		tmp = t_2;
	} else if (z3 <= 4000000.0) {
		tmp = t_0 * ((1.0 * t_1) / ((sinh((-1.0 / z3)) * (z3 + z3)) * z3));
	} else {
		tmp = t_2;
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = -fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double t_2 = t_0 * ((Math.exp(((-z2 / z3) * z4)) * t_1) / (-2.0 * z3));
	double tmp;
	if (z3 <= -11500.0) {
		tmp = t_2;
	} else if (z3 <= 4000000.0) {
		tmp = t_0 * ((1.0 * t_1) / ((Math.sinh((-1.0 / z3)) * (z3 + z3)) * z3));
	} else {
		tmp = t_2;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = -fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	t_2 = t_0 * ((math.exp(((-z2 / z3) * z4)) * t_1) / (-2.0 * z3))
	tmp = 0
	if z3 <= -11500.0:
		tmp = t_2
	elif z3 <= 4000000.0:
		tmp = t_0 * ((1.0 * t_1) / ((math.sinh((-1.0 / z3)) * (z3 + z3)) * z3))
	else:
		tmp = t_2
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = Float64(-fmin(abs(z1), abs(z0)))
	t_1 = fmax(abs(z1), abs(z0))
	t_2 = Float64(t_0 * Float64(Float64(exp(Float64(Float64(Float64(-z2) / z3) * z4)) * t_1) / Float64(-2.0 * z3)))
	tmp = 0.0
	if (z3 <= -11500.0)
		tmp = t_2;
	elseif (z3 <= 4000000.0)
		tmp = Float64(t_0 * Float64(Float64(1.0 * t_1) / Float64(Float64(sinh(Float64(-1.0 / z3)) * Float64(z3 + z3)) * z3)));
	else
		tmp = t_2;
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = -min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	t_2 = t_0 * ((exp(((-z2 / z3) * z4)) * t_1) / (-2.0 * z3));
	tmp = 0.0;
	if (z3 <= -11500.0)
		tmp = t_2;
	elseif (z3 <= 4000000.0)
		tmp = t_0 * ((1.0 * t_1) / ((sinh((-1.0 / z3)) * (z3 + z3)) * z3));
	else
		tmp = t_2;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = (-N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision])}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * N[(N[(N[Exp[N[(N[((-z2) / z3), $MachinePrecision] * z4), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision] / N[(-2.0 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -11500.0], t$95$2, If[LessEqual[z3, 4000000.0], N[(t$95$0 * N[(N[(1.0 * t$95$1), $MachinePrecision] / N[(N[(N[Sinh[N[(-1.0 / z3), $MachinePrecision]], $MachinePrecision] * N[(z3 + z3), $MachinePrecision]), $MachinePrecision] * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z3 < -11500 or 4e6 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto \left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\color{blue}{-2} \cdot z3} \]
   5. Step-by-step derivation

   6. Applied rewrites 79.2%

      \[\leadsto \left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\color{blue}{-2} \cdot z3} \]

   if -11500 < z3 < 4e6

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

   4. Taylor expanded in z4 around 0

      \[\leadsto \left(-z1\right) \cdot \frac{\color{blue}{1} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3} \]
   5. Step-by-step derivation

   6. Applied rewrites 81.0%

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

Alternative 3: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{-z2}{z3}\\ t_1 := \left|z1\right| \cdot \left|z0\right|\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 10^{+262}:\\ \;\;\;\;\frac{t\_1 \cdot e^{z4 \cdot t\_0}}{\left(z3 + z3\right) \cdot \left(\sinh \left(\frac{1}{z3}\right) \cdot z3\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-\left|z1\right|\right) \cdot \frac{e^{t\_0 \cdot z4} \cdot \left|z0\right|}{-2 \cdot z3}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (/ (- z2) z3)) (t_1 (* (fabs z1) (fabs z0))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= t_1 1e+262)
      (/
       (* t_1 (exp (* z4 t_0)))
       (* (+ z3 z3) (* (sinh (/ 1.0 z3)) z3)))
      (*
       (- (fabs z1))
       (/ (* (exp (* t_0 z4)) (fabs z0)) (* -2.0 z3))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = -z2 / z3;
	double t_1 = fabs(z1) * fabs(z0);
	double tmp;
	if (t_1 <= 1e+262) {
		tmp = (t_1 * exp((z4 * t_0))) / ((z3 + z3) * (sinh((1.0 / z3)) * z3));
	} else {
		tmp = -fabs(z1) * ((exp((t_0 * z4)) * fabs(z0)) / (-2.0 * z3));
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = -z2 / z3;
	double t_1 = Math.abs(z1) * Math.abs(z0);
	double tmp;
	if (t_1 <= 1e+262) {
		tmp = (t_1 * Math.exp((z4 * t_0))) / ((z3 + z3) * (Math.sinh((1.0 / z3)) * z3));
	} else {
		tmp = -Math.abs(z1) * ((Math.exp((t_0 * z4)) * Math.abs(z0)) / (-2.0 * z3));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = -z2 / z3
	t_1 = math.fabs(z1) * math.fabs(z0)
	tmp = 0
	if t_1 <= 1e+262:
		tmp = (t_1 * math.exp((z4 * t_0))) / ((z3 + z3) * (math.sinh((1.0 / z3)) * z3))
	else:
		tmp = -math.fabs(z1) * ((math.exp((t_0 * z4)) * math.fabs(z0)) / (-2.0 * z3))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = Float64(Float64(-z2) / z3)
	t_1 = Float64(abs(z1) * abs(z0))
	tmp = 0.0
	if (t_1 <= 1e+262)
		tmp = Float64(Float64(t_1 * exp(Float64(z4 * t_0))) / Float64(Float64(z3 + z3) * Float64(sinh(Float64(1.0 / z3)) * z3)));
	else
		tmp = Float64(Float64(-abs(z1)) * Float64(Float64(exp(Float64(t_0 * z4)) * abs(z0)) / Float64(-2.0 * z3)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = -z2 / z3;
	t_1 = abs(z1) * abs(z0);
	tmp = 0.0;
	if (t_1 <= 1e+262)
		tmp = (t_1 * exp((z4 * t_0))) / ((z3 + z3) * (sinh((1.0 / z3)) * z3));
	else
		tmp = -abs(z1) * ((exp((t_0 * z4)) * abs(z0)) / (-2.0 * z3));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[((-z2) / z3), $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[z1], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, 1e+262], N[(N[(t$95$1 * N[Exp[N[(z4 * t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(z3 + z3), $MachinePrecision] * N[(N[Sinh[N[(1.0 / z3), $MachinePrecision]], $MachinePrecision] * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-N[Abs[z1], $MachinePrecision]) * N[(N[(N[Exp[N[(t$95$0 * z4), $MachinePrecision]], $MachinePrecision] * N[Abs[z0], $MachinePrecision]), $MachinePrecision] / N[(-2.0 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z1 z0) < 1e262

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right)} \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. associate-*l* N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(z3 + z3\right) \cdot \left(z3 \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(z3 + z3\right) \cdot \left(z3 \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(z3 + z3\right) \cdot \color{blue}{\left(\sinh \left(\frac{1}{z3}\right) \cdot z3\right)}} \]

      6. lower-*.f64 88.9%

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(z3 + z3\right) \cdot \color{blue}{\left(\sinh \left(\frac{1}{z3}\right) \cdot z3\right)}} \]

   3. Applied rewrites 88.9%

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(z3 + z3\right) \cdot \left(\sinh \left(\frac{1}{z3}\right) \cdot z3\right)}} \]

   if 1e262 < (*.f64 z1 z0)

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto \left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\color{blue}{-2} \cdot z3} \]
   5. Step-by-step derivation

   6. Applied rewrites 79.2%

      \[\leadsto \left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\color{blue}{-2} \cdot z3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ t_2 := \left(-t\_0\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot t\_1}{-2 \cdot z3}\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq 1.1 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z3 \leq 4000000:\\ \;\;\;\;\frac{\left(t\_0 \cdot t\_1\right) \cdot 1}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0)))
       (t_2
        (*
         (- t_0)
         (/ (* (exp (* (/ (- z2) z3) z4)) t_1) (* -2.0 z3)))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 1.1e-162)
      t_2
      (if (<= z3 4000000.0)
        (/ (* (* t_0 t_1) 1.0) (* (* (+ z3 z3) z3) (sinh (/ 1.0 z3))))
        t_2))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double t_2 = -t_0 * ((exp(((-z2 / z3) * z4)) * t_1) / (-2.0 * z3));
	double tmp;
	if (z3 <= 1.1e-162) {
		tmp = t_2;
	} else if (z3 <= 4000000.0) {
		tmp = ((t_0 * t_1) * 1.0) / (((z3 + z3) * z3) * sinh((1.0 / z3)));
	} else {
		tmp = t_2;
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double t_2 = -t_0 * ((Math.exp(((-z2 / z3) * z4)) * t_1) / (-2.0 * z3));
	double tmp;
	if (z3 <= 1.1e-162) {
		tmp = t_2;
	} else if (z3 <= 4000000.0) {
		tmp = ((t_0 * t_1) * 1.0) / (((z3 + z3) * z3) * Math.sinh((1.0 / z3)));
	} else {
		tmp = t_2;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	t_2 = -t_0 * ((math.exp(((-z2 / z3) * z4)) * t_1) / (-2.0 * z3))
	tmp = 0
	if z3 <= 1.1e-162:
		tmp = t_2
	elif z3 <= 4000000.0:
		tmp = ((t_0 * t_1) * 1.0) / (((z3 + z3) * z3) * math.sinh((1.0 / z3)))
	else:
		tmp = t_2
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	t_2 = Float64(Float64(-t_0) * Float64(Float64(exp(Float64(Float64(Float64(-z2) / z3) * z4)) * t_1) / Float64(-2.0 * z3)))
	tmp = 0.0
	if (z3 <= 1.1e-162)
		tmp = t_2;
	elseif (z3 <= 4000000.0)
		tmp = Float64(Float64(Float64(t_0 * t_1) * 1.0) / Float64(Float64(Float64(z3 + z3) * z3) * sinh(Float64(1.0 / z3))));
	else
		tmp = t_2;
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	t_2 = -t_0 * ((exp(((-z2 / z3) * z4)) * t_1) / (-2.0 * z3));
	tmp = 0.0;
	if (z3 <= 1.1e-162)
		tmp = t_2;
	elseif (z3 <= 4000000.0)
		tmp = ((t_0 * t_1) * 1.0) / (((z3 + z3) * z3) * sinh((1.0 / z3)));
	else
		tmp = t_2;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[((-t$95$0) * N[(N[(N[Exp[N[(N[((-z2) / z3), $MachinePrecision] * z4), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision] / N[(-2.0 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, 1.1e-162], t$95$2, If[LessEqual[z3, 4000000.0], N[(N[(N[(t$95$0 * t$95$1), $MachinePrecision] * 1.0), $MachinePrecision] / N[(N[(N[(z3 + z3), $MachinePrecision] * z3), $MachinePrecision] * N[Sinh[N[(1.0 / z3), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z3 < 1.1e-162 or 4e6 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto \left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\color{blue}{-2} \cdot z3} \]
   5. Step-by-step derivation

   6. Applied rewrites 79.2%

      \[\leadsto \left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\color{blue}{-2} \cdot z3} \]

   if 1.1e-162 < z3 < 4e6

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \color{blue}{1}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \color{blue}{1}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := -t\_0\\ t_2 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ t_3 := \frac{\left(t\_0 \cdot t\_2\right) \cdot 1}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -11500:\\ \;\;\;\;t\_1 \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{t\_2 \cdot z3} - 2 \cdot \frac{1}{t\_2}\right)}\\ \mathbf{elif}\;z3 \leq -8 \cdot 10^{-150}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z3 \leq 1.1 \cdot 10^{-162}:\\ \;\;\;\;t\_2 \cdot \frac{\frac{z3 \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{elif}\;z3 \leq 1.25 \cdot 10^{+48}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \frac{-0.5 \cdot t\_2 + 0.5 \cdot \frac{t\_2 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (- t_0))
       (t_2 (fmax (fabs z1) (fabs z0)))
       (t_3
        (/
         (* (* t_0 t_2) 1.0)
         (* (* (+ z3 z3) z3) (sinh (/ 1.0 z3))))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -11500.0)
      (*
       t_1
       (/
        1.0
        (*
         z3
         (- (* -2.0 (/ (* z2 z4) (* t_2 z3))) (* 2.0 (/ 1.0 t_2))))))
      (if (<= z3 -8e-150)
        t_3
        (if (<= z3 1.1e-162)
          (* t_2 (/ (/ (* z3 t_0) (+ z3 z3)) z3))
          (if (<= z3 1.25e+48)
            t_3
            (*
             t_1
             (/
              (+ (* -0.5 t_2) (* 0.5 (/ (* t_2 (* z2 z4)) z3)))
              z3))))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = -t_0;
	double t_2 = fmax(fabs(z1), fabs(z0));
	double t_3 = ((t_0 * t_2) * 1.0) / (((z3 + z3) * z3) * sinh((1.0 / z3)));
	double tmp;
	if (z3 <= -11500.0) {
		tmp = t_1 * (1.0 / (z3 * ((-2.0 * ((z2 * z4) / (t_2 * z3))) - (2.0 * (1.0 / t_2)))));
	} else if (z3 <= -8e-150) {
		tmp = t_3;
	} else if (z3 <= 1.1e-162) {
		tmp = t_2 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 1.25e+48) {
		tmp = t_3;
	} else {
		tmp = t_1 * (((-0.5 * t_2) + (0.5 * ((t_2 * (z2 * z4)) / z3))) / z3);
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = -t_0;
	double t_2 = fmax(Math.abs(z1), Math.abs(z0));
	double t_3 = ((t_0 * t_2) * 1.0) / (((z3 + z3) * z3) * Math.sinh((1.0 / z3)));
	double tmp;
	if (z3 <= -11500.0) {
		tmp = t_1 * (1.0 / (z3 * ((-2.0 * ((z2 * z4) / (t_2 * z3))) - (2.0 * (1.0 / t_2)))));
	} else if (z3 <= -8e-150) {
		tmp = t_3;
	} else if (z3 <= 1.1e-162) {
		tmp = t_2 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 1.25e+48) {
		tmp = t_3;
	} else {
		tmp = t_1 * (((-0.5 * t_2) + (0.5 * ((t_2 * (z2 * z4)) / z3))) / z3);
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = -t_0
	t_2 = fmax(math.fabs(z1), math.fabs(z0))
	t_3 = ((t_0 * t_2) * 1.0) / (((z3 + z3) * z3) * math.sinh((1.0 / z3)))
	tmp = 0
	if z3 <= -11500.0:
		tmp = t_1 * (1.0 / (z3 * ((-2.0 * ((z2 * z4) / (t_2 * z3))) - (2.0 * (1.0 / t_2)))))
	elif z3 <= -8e-150:
		tmp = t_3
	elif z3 <= 1.1e-162:
		tmp = t_2 * (((z3 * t_0) / (z3 + z3)) / z3)
	elif z3 <= 1.25e+48:
		tmp = t_3
	else:
		tmp = t_1 * (((-0.5 * t_2) + (0.5 * ((t_2 * (z2 * z4)) / z3))) / z3)
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = Float64(-t_0)
	t_2 = fmax(abs(z1), abs(z0))
	t_3 = Float64(Float64(Float64(t_0 * t_2) * 1.0) / Float64(Float64(Float64(z3 + z3) * z3) * sinh(Float64(1.0 / z3))))
	tmp = 0.0
	if (z3 <= -11500.0)
		tmp = Float64(t_1 * Float64(1.0 / Float64(z3 * Float64(Float64(-2.0 * Float64(Float64(z2 * z4) / Float64(t_2 * z3))) - Float64(2.0 * Float64(1.0 / t_2))))));
	elseif (z3 <= -8e-150)
		tmp = t_3;
	elseif (z3 <= 1.1e-162)
		tmp = Float64(t_2 * Float64(Float64(Float64(z3 * t_0) / Float64(z3 + z3)) / z3));
	elseif (z3 <= 1.25e+48)
		tmp = t_3;
	else
		tmp = Float64(t_1 * Float64(Float64(Float64(-0.5 * t_2) + Float64(0.5 * Float64(Float64(t_2 * Float64(z2 * z4)) / z3))) / z3));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = -t_0;
	t_2 = max(abs(z1), abs(z0));
	t_3 = ((t_0 * t_2) * 1.0) / (((z3 + z3) * z3) * sinh((1.0 / z3)));
	tmp = 0.0;
	if (z3 <= -11500.0)
		tmp = t_1 * (1.0 / (z3 * ((-2.0 * ((z2 * z4) / (t_2 * z3))) - (2.0 * (1.0 / t_2)))));
	elseif (z3 <= -8e-150)
		tmp = t_3;
	elseif (z3 <= 1.1e-162)
		tmp = t_2 * (((z3 * t_0) / (z3 + z3)) / z3);
	elseif (z3 <= 1.25e+48)
		tmp = t_3;
	else
		tmp = t_1 * (((-0.5 * t_2) + (0.5 * ((t_2 * (z2 * z4)) / z3))) / z3);
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = (-t$95$0)}, Block[{t$95$2 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 * t$95$2), $MachinePrecision] * 1.0), $MachinePrecision] / N[(N[(N[(z3 + z3), $MachinePrecision] * z3), $MachinePrecision] * N[Sinh[N[(1.0 / z3), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -11500.0], N[(t$95$1 * N[(1.0 / N[(z3 * N[(N[(-2.0 * N[(N[(z2 * z4), $MachinePrecision] / N[(t$95$2 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, -8e-150], t$95$3, If[LessEqual[z3, 1.1e-162], N[(t$95$2 * N[(N[(N[(z3 * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.25e+48], t$95$3, N[(t$95$1 * N[(N[(N[(-0.5 * t$95$2), $MachinePrecision] + N[(0.5 * N[(N[(t$95$2 * N[(z2 * z4), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z3 < -11500

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\color{blue}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

      3. associate-/r* N/A

         \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}{z3}} \]

      4. div-flip N/A

         \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{1}{\frac{z3}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

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

         \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{1}{\frac{z3}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

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

         \[\leadsto \left(-z1\right) \cdot \frac{1}{\color{blue}{\frac{z3}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

      7. lower-/.f64 95.2%

         \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\color{blue}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{\color{blue}{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      9. *-commutative N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{\color{blue}{z0 \cdot e^{\frac{-z2}{z3} \cdot z4}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      10. lower-*.f64 95.2%

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{\color{blue}{z0 \cdot e^{\frac{-z2}{z3} \cdot z4}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{\color{blue}{\frac{-z2}{z3} \cdot z4}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      12. *-commutative N/A

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{\color{blue}{z4 \cdot \frac{-z2}{z3}}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      13. lift-*.f64 95.2%

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{\color{blue}{z4 \cdot \frac{-z2}{z3}}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      14. lift-*.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

      15. *-commutative N/A

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(z3 + z3\right) \cdot \sinh \left(\frac{-1}{z3}\right)}}}} \]

   5. Applied rewrites 95.2%

      \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{1}{\frac{z3}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(z3 + z3\right) \cdot \sinh \left(\frac{-1}{z3}\right)}}}} \]

   6. Taylor expanded in z3 around inf

      \[\leadsto \left(-z1\right) \cdot \frac{1}{\color{blue}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)}} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \color{blue}{\left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)}} \]

      2. lower--.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - \color{blue}{2 \cdot \frac{1}{z0}}\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - \color{blue}{2} \cdot \frac{1}{z0}\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \color{blue}{\frac{1}{z0}}\right)} \]

      8. lower-/.f64 57.8%

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{\color{blue}{z0}}\right)} \]

   8. Applied rewrites 57.8%

      \[\leadsto \left(-z1\right) \cdot \frac{1}{\color{blue}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)}} \]

   if -11500 < z3 < -8.0000000000000001e-150 or 1.1e-162 < z3 < 1.2499999999999999e48

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \color{blue}{1}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \color{blue}{1}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   if -8.0000000000000001e-150 < z3 < 1.1e-162

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around 0

      \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]

   if 1.2499999999999999e48 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{\color{blue}{z3}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      7. lower-*.f64 45.0%

         \[\leadsto \left(-z1\right) \cdot \frac{-0.5 \cdot z0 + 0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

   6. Applied rewrites 45.0%

      \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{-0.5 \cdot z0 + 0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 63.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := -t\_0\\ t_2 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -1.42 \cdot 10^{-148}:\\ \;\;\;\;t\_1 \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{t\_2 \cdot z3} - 2 \cdot \frac{1}{t\_2}\right)}\\ \mathbf{elif}\;z3 \leq 1.05 \cdot 10^{-144}:\\ \;\;\;\;t\_2 \cdot \frac{\frac{z3 \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{elif}\;z3 \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;t\_2 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \frac{-0.5 \cdot t\_2 + 0.5 \cdot \frac{t\_2 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (- t_0))
       (t_2 (fmax (fabs z1) (fabs z0))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -1.42e-148)
      (*
       t_1
       (/
        1.0
        (*
         z3
         (- (* -2.0 (/ (* z2 z4) (* t_2 z3))) (* 2.0 (/ 1.0 t_2))))))
      (if (<= z3 1.05e-144)
        (* t_2 (/ (/ (* z3 t_0) (+ z3 z3)) z3))
        (if (<= z3 6.8e-6)
          (* t_2 (/ (/ (* (* -1.0 (* z2 z4)) t_0) (+ z3 z3)) z3))
          (*
           t_1
           (/
            (+ (* -0.5 t_2) (* 0.5 (/ (* t_2 (* z2 z4)) z3)))
            z3)))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = -t_0;
	double t_2 = fmax(fabs(z1), fabs(z0));
	double tmp;
	if (z3 <= -1.42e-148) {
		tmp = t_1 * (1.0 / (z3 * ((-2.0 * ((z2 * z4) / (t_2 * z3))) - (2.0 * (1.0 / t_2)))));
	} else if (z3 <= 1.05e-144) {
		tmp = t_2 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 6.8e-6) {
		tmp = t_2 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = t_1 * (((-0.5 * t_2) + (0.5 * ((t_2 * (z2 * z4)) / z3))) / z3);
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = -t_0;
	double t_2 = fmax(Math.abs(z1), Math.abs(z0));
	double tmp;
	if (z3 <= -1.42e-148) {
		tmp = t_1 * (1.0 / (z3 * ((-2.0 * ((z2 * z4) / (t_2 * z3))) - (2.0 * (1.0 / t_2)))));
	} else if (z3 <= 1.05e-144) {
		tmp = t_2 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 6.8e-6) {
		tmp = t_2 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = t_1 * (((-0.5 * t_2) + (0.5 * ((t_2 * (z2 * z4)) / z3))) / z3);
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = -t_0
	t_2 = fmax(math.fabs(z1), math.fabs(z0))
	tmp = 0
	if z3 <= -1.42e-148:
		tmp = t_1 * (1.0 / (z3 * ((-2.0 * ((z2 * z4) / (t_2 * z3))) - (2.0 * (1.0 / t_2)))))
	elif z3 <= 1.05e-144:
		tmp = t_2 * (((z3 * t_0) / (z3 + z3)) / z3)
	elif z3 <= 6.8e-6:
		tmp = t_2 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3)
	else:
		tmp = t_1 * (((-0.5 * t_2) + (0.5 * ((t_2 * (z2 * z4)) / z3))) / z3)
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = Float64(-t_0)
	t_2 = fmax(abs(z1), abs(z0))
	tmp = 0.0
	if (z3 <= -1.42e-148)
		tmp = Float64(t_1 * Float64(1.0 / Float64(z3 * Float64(Float64(-2.0 * Float64(Float64(z2 * z4) / Float64(t_2 * z3))) - Float64(2.0 * Float64(1.0 / t_2))))));
	elseif (z3 <= 1.05e-144)
		tmp = Float64(t_2 * Float64(Float64(Float64(z3 * t_0) / Float64(z3 + z3)) / z3));
	elseif (z3 <= 6.8e-6)
		tmp = Float64(t_2 * Float64(Float64(Float64(Float64(-1.0 * Float64(z2 * z4)) * t_0) / Float64(z3 + z3)) / z3));
	else
		tmp = Float64(t_1 * Float64(Float64(Float64(-0.5 * t_2) + Float64(0.5 * Float64(Float64(t_2 * Float64(z2 * z4)) / z3))) / z3));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = -t_0;
	t_2 = max(abs(z1), abs(z0));
	tmp = 0.0;
	if (z3 <= -1.42e-148)
		tmp = t_1 * (1.0 / (z3 * ((-2.0 * ((z2 * z4) / (t_2 * z3))) - (2.0 * (1.0 / t_2)))));
	elseif (z3 <= 1.05e-144)
		tmp = t_2 * (((z3 * t_0) / (z3 + z3)) / z3);
	elseif (z3 <= 6.8e-6)
		tmp = t_2 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	else
		tmp = t_1 * (((-0.5 * t_2) + (0.5 * ((t_2 * (z2 * z4)) / z3))) / z3);
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = (-t$95$0)}, Block[{t$95$2 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -1.42e-148], N[(t$95$1 * N[(1.0 / N[(z3 * N[(N[(-2.0 * N[(N[(z2 * z4), $MachinePrecision] / N[(t$95$2 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.05e-144], N[(t$95$2 * N[(N[(N[(z3 * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 6.8e-6], N[(t$95$2 * N[(N[(N[(N[(-1.0 * N[(z2 * z4), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(N[(N[(-0.5 * t$95$2), $MachinePrecision] + N[(0.5 * N[(N[(t$95$2 * N[(z2 * z4), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z3 < -1.42e-148

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\color{blue}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

      3. associate-/r* N/A

         \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}{z3}} \]

      4. div-flip N/A

         \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{1}{\frac{z3}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

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

         \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{1}{\frac{z3}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

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

         \[\leadsto \left(-z1\right) \cdot \frac{1}{\color{blue}{\frac{z3}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

      7. lower-/.f64 95.2%

         \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\color{blue}{\frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{\color{blue}{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      9. *-commutative N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{\color{blue}{z0 \cdot e^{\frac{-z2}{z3} \cdot z4}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      10. lower-*.f64 95.2%

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{\color{blue}{z0 \cdot e^{\frac{-z2}{z3} \cdot z4}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{\color{blue}{\frac{-z2}{z3} \cdot z4}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      12. *-commutative N/A

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{\color{blue}{z4 \cdot \frac{-z2}{z3}}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      13. lift-*.f64 95.2%

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{\color{blue}{z4 \cdot \frac{-z2}{z3}}}}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}} \]

      14. lift-*.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)}}}} \]

      15. *-commutative N/A

          \[\leadsto \left(-z1\right) \cdot \frac{1}{\frac{z3}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(z3 + z3\right) \cdot \sinh \left(\frac{-1}{z3}\right)}}}} \]

   5. Applied rewrites 95.2%

      \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{1}{\frac{z3}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(z3 + z3\right) \cdot \sinh \left(\frac{-1}{z3}\right)}}}} \]

   6. Taylor expanded in z3 around inf

      \[\leadsto \left(-z1\right) \cdot \frac{1}{\color{blue}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)}} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \color{blue}{\left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)}} \]

      2. lower--.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - \color{blue}{2 \cdot \frac{1}{z0}}\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - \color{blue}{2} \cdot \frac{1}{z0}\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \color{blue}{\frac{1}{z0}}\right)} \]

      8. lower-/.f64 57.8%

         \[\leadsto \left(-z1\right) \cdot \frac{1}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{\color{blue}{z0}}\right)} \]

   8. Applied rewrites 57.8%

      \[\leadsto \left(-z1\right) \cdot \frac{1}{\color{blue}{z3 \cdot \left(-2 \cdot \frac{z2 \cdot z4}{z0 \cdot z3} - 2 \cdot \frac{1}{z0}\right)}} \]

   if -1.42e-148 < z3 < 1.0500000000000001e-144

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around 0

      \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]

   if 1.0500000000000001e-144 < z3 < 6.8000000000000001e-6

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around inf

      \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot \color{blue}{z4}\right)\right) \cdot z1}{z3 + z3}}{z3} \]

       2. lower-*.f64 32.4%

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot z1}{z3 + z3}}{z3} \]

   11. Applied rewrites 32.4%

       \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]

   if 6.8000000000000001e-6 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{\color{blue}{z3}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      7. lower-*.f64 45.0%

         \[\leadsto \left(-z1\right) \cdot \frac{-0.5 \cdot z0 + 0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

   6. Applied rewrites 45.0%

      \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{-0.5 \cdot z0 + 0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ t_2 := z3 \cdot t\_0\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -2.1:\\ \;\;\;\;\frac{t\_0}{\frac{z3 + z3}{t\_1}}\\ \mathbf{elif}\;z3 \leq -5.6 \cdot 10^{-111}:\\ \;\;\;\;\frac{1}{\frac{\left(t\_2 + t\_2\right) \cdot 1}{\left(t\_0 \cdot t\_0\right) \cdot t\_1}}\\ \mathbf{elif}\;z3 \leq 1.05 \cdot 10^{-144}:\\ \;\;\;\;t\_1 \cdot \frac{\frac{t\_2}{z3 + z3}}{z3}\\ \mathbf{elif}\;z3 \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;t\_1 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\_0\right) \cdot \frac{-0.5 \cdot t\_1 + 0.5 \cdot \frac{t\_1 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0)))
       (t_2 (* z3 t_0)))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -2.1)
      (/ t_0 (/ (+ z3 z3) t_1))
      (if (<= z3 -5.6e-111)
        (/ 1.0 (/ (* (+ t_2 t_2) 1.0) (* (* t_0 t_0) t_1)))
        (if (<= z3 1.05e-144)
          (* t_1 (/ (/ t_2 (+ z3 z3)) z3))
          (if (<= z3 6.8e-6)
            (* t_1 (/ (/ (* (* -1.0 (* z2 z4)) t_0) (+ z3 z3)) z3))
            (*
             (- t_0)
             (/
              (+ (* -0.5 t_1) (* 0.5 (/ (* t_1 (* z2 z4)) z3)))
              z3))))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double t_2 = z3 * t_0;
	double tmp;
	if (z3 <= -2.1) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= -5.6e-111) {
		tmp = 1.0 / (((t_2 + t_2) * 1.0) / ((t_0 * t_0) * t_1));
	} else if (z3 <= 1.05e-144) {
		tmp = t_1 * ((t_2 / (z3 + z3)) / z3);
	} else if (z3 <= 6.8e-6) {
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = -t_0 * (((-0.5 * t_1) + (0.5 * ((t_1 * (z2 * z4)) / z3))) / z3);
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double t_2 = z3 * t_0;
	double tmp;
	if (z3 <= -2.1) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= -5.6e-111) {
		tmp = 1.0 / (((t_2 + t_2) * 1.0) / ((t_0 * t_0) * t_1));
	} else if (z3 <= 1.05e-144) {
		tmp = t_1 * ((t_2 / (z3 + z3)) / z3);
	} else if (z3 <= 6.8e-6) {
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = -t_0 * (((-0.5 * t_1) + (0.5 * ((t_1 * (z2 * z4)) / z3))) / z3);
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	t_2 = z3 * t_0
	tmp = 0
	if z3 <= -2.1:
		tmp = t_0 / ((z3 + z3) / t_1)
	elif z3 <= -5.6e-111:
		tmp = 1.0 / (((t_2 + t_2) * 1.0) / ((t_0 * t_0) * t_1))
	elif z3 <= 1.05e-144:
		tmp = t_1 * ((t_2 / (z3 + z3)) / z3)
	elif z3 <= 6.8e-6:
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3)
	else:
		tmp = -t_0 * (((-0.5 * t_1) + (0.5 * ((t_1 * (z2 * z4)) / z3))) / z3)
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	t_2 = Float64(z3 * t_0)
	tmp = 0.0
	if (z3 <= -2.1)
		tmp = Float64(t_0 / Float64(Float64(z3 + z3) / t_1));
	elseif (z3 <= -5.6e-111)
		tmp = Float64(1.0 / Float64(Float64(Float64(t_2 + t_2) * 1.0) / Float64(Float64(t_0 * t_0) * t_1)));
	elseif (z3 <= 1.05e-144)
		tmp = Float64(t_1 * Float64(Float64(t_2 / Float64(z3 + z3)) / z3));
	elseif (z3 <= 6.8e-6)
		tmp = Float64(t_1 * Float64(Float64(Float64(Float64(-1.0 * Float64(z2 * z4)) * t_0) / Float64(z3 + z3)) / z3));
	else
		tmp = Float64(Float64(-t_0) * Float64(Float64(Float64(-0.5 * t_1) + Float64(0.5 * Float64(Float64(t_1 * Float64(z2 * z4)) / z3))) / z3));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	t_2 = z3 * t_0;
	tmp = 0.0;
	if (z3 <= -2.1)
		tmp = t_0 / ((z3 + z3) / t_1);
	elseif (z3 <= -5.6e-111)
		tmp = 1.0 / (((t_2 + t_2) * 1.0) / ((t_0 * t_0) * t_1));
	elseif (z3 <= 1.05e-144)
		tmp = t_1 * ((t_2 / (z3 + z3)) / z3);
	elseif (z3 <= 6.8e-6)
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	else
		tmp = -t_0 * (((-0.5 * t_1) + (0.5 * ((t_1 * (z2 * z4)) / z3))) / z3);
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(z3 * t$95$0), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -2.1], N[(t$95$0 / N[(N[(z3 + z3), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, -5.6e-111], N[(1.0 / N[(N[(N[(t$95$2 + t$95$2), $MachinePrecision] * 1.0), $MachinePrecision] / N[(N[(t$95$0 * t$95$0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.05e-144], N[(t$95$1 * N[(N[(t$95$2 / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 6.8e-6], N[(t$95$1 * N[(N[(N[(N[(-1.0 * N[(z2 * z4), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], N[((-t$95$0) * N[(N[(N[(-0.5 * t$95$1), $MachinePrecision] + N[(0.5 * N[(N[(t$95$1 * N[(z2 * z4), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 5 regimes

2. if z3 < -2.1000000000000001

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. div-flip-rev N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      10. lower-/.f64 43.9%

          \[\leadsto \frac{z1}{\frac{z3 + z3}{\color{blue}{z0}}} \]

   8. Applied rewrites 43.9%

      \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

   if -2.1000000000000001 < z3 < -5.5999999999999999e-111

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. div-flip N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z1 \cdot z0}}} \]

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

          \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z1 \cdot z0}}} \]

      20. lower-unsound-/.f64 46.9%

          \[\leadsto \frac{1}{\frac{z3 + z3}{\color{blue}{z1 \cdot z0}}} \]

      21. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z1 \cdot \color{blue}{z0}}} \]

      22. *-commutative N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      23. lift-*.f64 46.9%

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

   6. Applied rewrites 46.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{\color{blue}{z0 \cdot z1}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      3. *-commutative N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z1 \cdot \color{blue}{z0}}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{\color{blue}{z0}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{\color{blue}{z0}}} \]

      6. lower-/.f64 43.8%

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{z0}} \]

   8. Applied rewrites 43.8%

      \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{\color{blue}{z0}}} \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{\color{blue}{z0}}} \]

      2. mult-flip N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z1} \cdot \color{blue}{\frac{1}{z0}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z1} \cdot \frac{\color{blue}{1}}{z0}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z1} \cdot \frac{1}{z0}} \]

      5. div-add N/A

         \[\leadsto \frac{1}{\left(\frac{z3}{z1} + \frac{z3}{z1}\right) \cdot \frac{\color{blue}{1}}{z0}} \]

      6. common-denominator N/A

         \[\leadsto \frac{1}{\frac{z3 \cdot z1 + z3 \cdot z1}{z1 \cdot z1} \cdot \frac{\color{blue}{1}}{z0}} \]

      7. frac-times N/A

         \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}}} \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}}} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0}} \]

      10. lower-+.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(\color{blue}{z1} \cdot z1\right) \cdot z0}} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(z1 \cdot z1\right) \cdot z0}} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(z1 \cdot z1\right) \cdot z0}} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(z1 \cdot z1\right) \cdot \color{blue}{z0}}} \]

      14. lower-*.f64 33.7%

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(z1 \cdot z1\right) \cdot z0}} \]

   10. Applied rewrites 33.7%

       \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}}} \]

   if -5.5999999999999999e-111 < z3 < 1.0500000000000001e-144

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around 0

      \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]

   if 1.0500000000000001e-144 < z3 < 6.8000000000000001e-6

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around inf

      \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot \color{blue}{z4}\right)\right) \cdot z1}{z3 + z3}}{z3} \]

       2. lower-*.f64 32.4%

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot z1}{z3 + z3}}{z3} \]

   11. Applied rewrites 32.4%

       \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]

   if 6.8000000000000001e-6 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(z1 \cdot z0\right)} \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{z1 \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}\right)}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \left(z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}\right)}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z1\right)\right) \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

      9. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z1\right)} \cdot \frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{z0 \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\mathsf{neg}\left(\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)\right)}} \]

   3. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(-z1\right) \cdot \frac{e^{\frac{-z2}{z3} \cdot z4} \cdot z0}{\left(\sinh \left(\frac{-1}{z3}\right) \cdot \left(z3 + z3\right)\right) \cdot z3}} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{\color{blue}{z3}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(-z1\right) \cdot \frac{\frac{-1}{2} \cdot z0 + \frac{1}{2} \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

      7. lower-*.f64 45.0%

         \[\leadsto \left(-z1\right) \cdot \frac{-0.5 \cdot z0 + 0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3} \]

   6. Applied rewrites 45.0%

      \[\leadsto \left(-z1\right) \cdot \color{blue}{\frac{-0.5 \cdot z0 + 0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z4\right)}{z3}}{z3}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 62.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ t_2 := z3 \cdot t\_0\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -2.1:\\ \;\;\;\;\frac{t\_0}{\frac{z3 + z3}{t\_1}}\\ \mathbf{elif}\;z3 \leq -5.6 \cdot 10^{-111}:\\ \;\;\;\;\frac{1}{\frac{\left(t\_2 + t\_2\right) \cdot 1}{\left(t\_0 \cdot t\_0\right) \cdot t\_1}}\\ \mathbf{elif}\;z3 \leq 1.05 \cdot 10^{-144}:\\ \;\;\;\;t\_1 \cdot \frac{\frac{t\_2}{z3 + z3}}{z3}\\ \mathbf{elif}\;z3 \leq 0.00019:\\ \;\;\;\;t\_1 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 + -0.5 \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(t\_1 \cdot t\_0\right)\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0)))
       (t_2 (* z3 t_0)))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -2.1)
      (/ t_0 (/ (+ z3 z3) t_1))
      (if (<= z3 -5.6e-111)
        (/ 1.0 (/ (* (+ t_2 t_2) 1.0) (* (* t_0 t_0) t_1)))
        (if (<= z3 1.05e-144)
          (* t_1 (/ (/ t_2 (+ z3 z3)) z3))
          (if (<= z3 0.00019)
            (* t_1 (/ (/ (* (* -1.0 (* z2 z4)) t_0) (+ z3 z3)) z3))
            (*
             (/ (+ 0.5 (* -0.5 (/ (* z2 z4) z3))) z3)
             (* t_1 t_0))))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double t_2 = z3 * t_0;
	double tmp;
	if (z3 <= -2.1) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= -5.6e-111) {
		tmp = 1.0 / (((t_2 + t_2) * 1.0) / ((t_0 * t_0) * t_1));
	} else if (z3 <= 1.05e-144) {
		tmp = t_1 * ((t_2 / (z3 + z3)) / z3);
	} else if (z3 <= 0.00019) {
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = ((0.5 + (-0.5 * ((z2 * z4) / z3))) / z3) * (t_1 * t_0);
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double t_2 = z3 * t_0;
	double tmp;
	if (z3 <= -2.1) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= -5.6e-111) {
		tmp = 1.0 / (((t_2 + t_2) * 1.0) / ((t_0 * t_0) * t_1));
	} else if (z3 <= 1.05e-144) {
		tmp = t_1 * ((t_2 / (z3 + z3)) / z3);
	} else if (z3 <= 0.00019) {
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = ((0.5 + (-0.5 * ((z2 * z4) / z3))) / z3) * (t_1 * t_0);
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	t_2 = z3 * t_0
	tmp = 0
	if z3 <= -2.1:
		tmp = t_0 / ((z3 + z3) / t_1)
	elif z3 <= -5.6e-111:
		tmp = 1.0 / (((t_2 + t_2) * 1.0) / ((t_0 * t_0) * t_1))
	elif z3 <= 1.05e-144:
		tmp = t_1 * ((t_2 / (z3 + z3)) / z3)
	elif z3 <= 0.00019:
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3)
	else:
		tmp = ((0.5 + (-0.5 * ((z2 * z4) / z3))) / z3) * (t_1 * t_0)
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	t_2 = Float64(z3 * t_0)
	tmp = 0.0
	if (z3 <= -2.1)
		tmp = Float64(t_0 / Float64(Float64(z3 + z3) / t_1));
	elseif (z3 <= -5.6e-111)
		tmp = Float64(1.0 / Float64(Float64(Float64(t_2 + t_2) * 1.0) / Float64(Float64(t_0 * t_0) * t_1)));
	elseif (z3 <= 1.05e-144)
		tmp = Float64(t_1 * Float64(Float64(t_2 / Float64(z3 + z3)) / z3));
	elseif (z3 <= 0.00019)
		tmp = Float64(t_1 * Float64(Float64(Float64(Float64(-1.0 * Float64(z2 * z4)) * t_0) / Float64(z3 + z3)) / z3));
	else
		tmp = Float64(Float64(Float64(0.5 + Float64(-0.5 * Float64(Float64(z2 * z4) / z3))) / z3) * Float64(t_1 * t_0));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	t_2 = z3 * t_0;
	tmp = 0.0;
	if (z3 <= -2.1)
		tmp = t_0 / ((z3 + z3) / t_1);
	elseif (z3 <= -5.6e-111)
		tmp = 1.0 / (((t_2 + t_2) * 1.0) / ((t_0 * t_0) * t_1));
	elseif (z3 <= 1.05e-144)
		tmp = t_1 * ((t_2 / (z3 + z3)) / z3);
	elseif (z3 <= 0.00019)
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	else
		tmp = ((0.5 + (-0.5 * ((z2 * z4) / z3))) / z3) * (t_1 * t_0);
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(z3 * t$95$0), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -2.1], N[(t$95$0 / N[(N[(z3 + z3), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, -5.6e-111], N[(1.0 / N[(N[(N[(t$95$2 + t$95$2), $MachinePrecision] * 1.0), $MachinePrecision] / N[(N[(t$95$0 * t$95$0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.05e-144], N[(t$95$1 * N[(N[(t$95$2 / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 0.00019], N[(t$95$1 * N[(N[(N[(N[(-1.0 * N[(z2 * z4), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.5 + N[(-0.5 * N[(N[(z2 * z4), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision] * N[(t$95$1 * t$95$0), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 5 regimes

2. if z3 < -2.1000000000000001

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. div-flip-rev N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      10. lower-/.f64 43.9%

          \[\leadsto \frac{z1}{\frac{z3 + z3}{\color{blue}{z0}}} \]

   8. Applied rewrites 43.9%

      \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

   if -2.1000000000000001 < z3 < -5.5999999999999999e-111

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. div-flip N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z1 \cdot z0}}} \]

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

          \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z1 \cdot z0}}} \]

      20. lower-unsound-/.f64 46.9%

          \[\leadsto \frac{1}{\frac{z3 + z3}{\color{blue}{z1 \cdot z0}}} \]

      21. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z1 \cdot \color{blue}{z0}}} \]

      22. *-commutative N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      23. lift-*.f64 46.9%

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

   6. Applied rewrites 46.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{\color{blue}{z0 \cdot z1}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      3. *-commutative N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z1 \cdot \color{blue}{z0}}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{\color{blue}{z0}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{\color{blue}{z0}}} \]

      6. lower-/.f64 43.8%

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{z0}} \]

   8. Applied rewrites 43.8%

      \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{\color{blue}{z0}}} \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{\color{blue}{z0}}} \]

      2. mult-flip N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z1} \cdot \color{blue}{\frac{1}{z0}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z1} \cdot \frac{\color{blue}{1}}{z0}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z1} \cdot \frac{1}{z0}} \]

      5. div-add N/A

         \[\leadsto \frac{1}{\left(\frac{z3}{z1} + \frac{z3}{z1}\right) \cdot \frac{\color{blue}{1}}{z0}} \]

      6. common-denominator N/A

         \[\leadsto \frac{1}{\frac{z3 \cdot z1 + z3 \cdot z1}{z1 \cdot z1} \cdot \frac{\color{blue}{1}}{z0}} \]

      7. frac-times N/A

         \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}}} \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}}} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0}} \]

      10. lower-+.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(\color{blue}{z1} \cdot z1\right) \cdot z0}} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(z1 \cdot z1\right) \cdot z0}} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(z1 \cdot z1\right) \cdot z0}} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(z1 \cdot z1\right) \cdot \color{blue}{z0}}} \]

      14. lower-*.f64 33.7%

          \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\left(z1 \cdot z1\right) \cdot z0}} \]

   10. Applied rewrites 33.7%

       \[\leadsto \frac{1}{\frac{\left(z3 \cdot z1 + z3 \cdot z1\right) \cdot 1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}}} \]

   if -5.5999999999999999e-111 < z3 < 1.0500000000000001e-144

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around 0

      \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]

   if 1.0500000000000001e-144 < z3 < 1.9000000000000001e-4

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around inf

      \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot \color{blue}{z4}\right)\right) \cdot z1}{z3 + z3}}{z3} \]

       2. lower-*.f64 32.4%

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot z1}{z3 + z3}}{z3} \]

   11. Applied rewrites 32.4%

       \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]

   if 1.9000000000000001e-4 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      4. lower-*.f64 45.5%

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   4. Applied rewrites 45.5%

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z1 \cdot z0\right) \cdot \frac{1 + -1 \cdot \frac{z2 \cdot z4}{z3}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1 + -1 \cdot \frac{z2 \cdot z4}{z3}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \cdot \left(z1 \cdot z0\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1 + -1 \cdot \frac{z2 \cdot z4}{z3}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \cdot \left(z1 \cdot z0\right)} \]

   6. Applied rewrites 46.3%

      \[\leadsto \color{blue}{\frac{1 - \frac{z4 \cdot z2}{z3}}{\sinh \left(\frac{1}{z3}\right) \cdot \left(\left(z3 + z3\right) \cdot z3\right)} \cdot \left(z0 \cdot z1\right)} \]

   7. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{z3}} \cdot \left(z0 \cdot z1\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{\color{blue}{z3}} \cdot \left(z0 \cdot z1\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(z0 \cdot z1\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(z0 \cdot z1\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(z0 \cdot z1\right) \]

      5. lower-*.f64 47.2%

         \[\leadsto \frac{0.5 + -0.5 \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(z0 \cdot z1\right) \]

   9. Applied rewrites 47.2%

      \[\leadsto \color{blue}{\frac{0.5 + -0.5 \cdot \frac{z2 \cdot z4}{z3}}{z3}} \cdot \left(z0 \cdot z1\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{t\_0}{\frac{z3 + z3}{t\_1}}\\ \mathbf{elif}\;z3 \leq 1.05 \cdot 10^{-144}:\\ \;\;\;\;t\_1 \cdot \frac{\frac{z3 \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{elif}\;z3 \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;t\_1 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 + -0.5 \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(t\_1 \cdot t\_0\right)\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -2e+44)
      (/ t_0 (/ (+ z3 z3) t_1))
      (if (<= z3 1.05e-144)
        (* t_1 (/ (/ (* z3 t_0) (+ z3 z3)) z3))
        (if (<= z3 6.8e-6)
          (* t_1 (/ (/ (* (* -1.0 (* z2 z4)) t_0) (+ z3 z3)) z3))
          (*
           (/ (+ 0.5 (* -0.5 (/ (* z2 z4) z3))) z3)
           (* t_1 t_0)))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double tmp;
	if (z3 <= -2e+44) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1.05e-144) {
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 6.8e-6) {
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = ((0.5 + (-0.5 * ((z2 * z4) / z3))) / z3) * (t_1 * t_0);
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double tmp;
	if (z3 <= -2e+44) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1.05e-144) {
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 6.8e-6) {
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = ((0.5 + (-0.5 * ((z2 * z4) / z3))) / z3) * (t_1 * t_0);
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	tmp = 0
	if z3 <= -2e+44:
		tmp = t_0 / ((z3 + z3) / t_1)
	elif z3 <= 1.05e-144:
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3)
	elif z3 <= 6.8e-6:
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3)
	else:
		tmp = ((0.5 + (-0.5 * ((z2 * z4) / z3))) / z3) * (t_1 * t_0)
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	tmp = 0.0
	if (z3 <= -2e+44)
		tmp = Float64(t_0 / Float64(Float64(z3 + z3) / t_1));
	elseif (z3 <= 1.05e-144)
		tmp = Float64(t_1 * Float64(Float64(Float64(z3 * t_0) / Float64(z3 + z3)) / z3));
	elseif (z3 <= 6.8e-6)
		tmp = Float64(t_1 * Float64(Float64(Float64(Float64(-1.0 * Float64(z2 * z4)) * t_0) / Float64(z3 + z3)) / z3));
	else
		tmp = Float64(Float64(Float64(0.5 + Float64(-0.5 * Float64(Float64(z2 * z4) / z3))) / z3) * Float64(t_1 * t_0));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	tmp = 0.0;
	if (z3 <= -2e+44)
		tmp = t_0 / ((z3 + z3) / t_1);
	elseif (z3 <= 1.05e-144)
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	elseif (z3 <= 6.8e-6)
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	else
		tmp = ((0.5 + (-0.5 * ((z2 * z4) / z3))) / z3) * (t_1 * t_0);
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -2e+44], N[(t$95$0 / N[(N[(z3 + z3), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.05e-144], N[(t$95$1 * N[(N[(N[(z3 * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 6.8e-6], N[(t$95$1 * N[(N[(N[(N[(-1.0 * N[(z2 * z4), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.5 + N[(-0.5 * N[(N[(z2 * z4), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision] * N[(t$95$1 * t$95$0), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if z3 < -2.0000000000000002e44

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. div-flip-rev N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      10. lower-/.f64 43.9%

          \[\leadsto \frac{z1}{\frac{z3 + z3}{\color{blue}{z0}}} \]

   8. Applied rewrites 43.9%

      \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

   if -2.0000000000000002e44 < z3 < 1.0500000000000001e-144

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around 0

      \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]

   if 1.0500000000000001e-144 < z3 < 6.8000000000000001e-6

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around inf

      \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot \color{blue}{z4}\right)\right) \cdot z1}{z3 + z3}}{z3} \]

       2. lower-*.f64 32.4%

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot z1}{z3 + z3}}{z3} \]

   11. Applied rewrites 32.4%

       \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]

   if 6.8000000000000001e-6 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      4. lower-*.f64 45.5%

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   4. Applied rewrites 45.5%

      \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z1 \cdot z0\right) \cdot \frac{1 + -1 \cdot \frac{z2 \cdot z4}{z3}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1 + -1 \cdot \frac{z2 \cdot z4}{z3}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \cdot \left(z1 \cdot z0\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1 + -1 \cdot \frac{z2 \cdot z4}{z3}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \cdot \left(z1 \cdot z0\right)} \]

   6. Applied rewrites 46.3%

      \[\leadsto \color{blue}{\frac{1 - \frac{z4 \cdot z2}{z3}}{\sinh \left(\frac{1}{z3}\right) \cdot \left(\left(z3 + z3\right) \cdot z3\right)} \cdot \left(z0 \cdot z1\right)} \]

   7. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{z3}} \cdot \left(z0 \cdot z1\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{\color{blue}{z3}} \cdot \left(z0 \cdot z1\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(z0 \cdot z1\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(z0 \cdot z1\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{2} + \frac{-1}{2} \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(z0 \cdot z1\right) \]

      5. lower-*.f64 47.2%

         \[\leadsto \frac{0.5 + -0.5 \cdot \frac{z2 \cdot z4}{z3}}{z3} \cdot \left(z0 \cdot z1\right) \]

   9. Applied rewrites 47.2%

      \[\leadsto \color{blue}{\frac{0.5 + -0.5 \cdot \frac{z2 \cdot z4}{z3}}{z3}} \cdot \left(z0 \cdot z1\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{t\_0}{\frac{z3 + z3}{t\_1}}\\ \mathbf{elif}\;z3 \leq 1.05 \cdot 10^{-144}:\\ \;\;\;\;t\_1 \cdot \frac{\frac{z3 \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{elif}\;z3 \leq 0.00018:\\ \;\;\;\;t\_1 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z3 + z3}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -2e+44)
      (/ t_0 (/ (+ z3 z3) t_1))
      (if (<= z3 1.05e-144)
        (* t_1 (/ (/ (* z3 t_0) (+ z3 z3)) z3))
        (if (<= z3 0.00018)
          (* t_1 (/ (/ (* (* -1.0 (* z2 z4)) t_0) (+ z3 z3)) z3))
          (* t_0 (/ t_1 (+ z3 z3))))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double tmp;
	if (z3 <= -2e+44) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1.05e-144) {
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 0.00018) {
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = t_0 * (t_1 / (z3 + z3));
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double tmp;
	if (z3 <= -2e+44) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1.05e-144) {
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 0.00018) {
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	} else {
		tmp = t_0 * (t_1 / (z3 + z3));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	tmp = 0
	if z3 <= -2e+44:
		tmp = t_0 / ((z3 + z3) / t_1)
	elif z3 <= 1.05e-144:
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3)
	elif z3 <= 0.00018:
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3)
	else:
		tmp = t_0 * (t_1 / (z3 + z3))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	tmp = 0.0
	if (z3 <= -2e+44)
		tmp = Float64(t_0 / Float64(Float64(z3 + z3) / t_1));
	elseif (z3 <= 1.05e-144)
		tmp = Float64(t_1 * Float64(Float64(Float64(z3 * t_0) / Float64(z3 + z3)) / z3));
	elseif (z3 <= 0.00018)
		tmp = Float64(t_1 * Float64(Float64(Float64(Float64(-1.0 * Float64(z2 * z4)) * t_0) / Float64(z3 + z3)) / z3));
	else
		tmp = Float64(t_0 * Float64(t_1 / Float64(z3 + z3)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	tmp = 0.0;
	if (z3 <= -2e+44)
		tmp = t_0 / ((z3 + z3) / t_1);
	elseif (z3 <= 1.05e-144)
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	elseif (z3 <= 0.00018)
		tmp = t_1 * ((((-1.0 * (z2 * z4)) * t_0) / (z3 + z3)) / z3);
	else
		tmp = t_0 * (t_1 / (z3 + z3));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -2e+44], N[(t$95$0 / N[(N[(z3 + z3), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.05e-144], N[(t$95$1 * N[(N[(N[(z3 * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 0.00018], N[(t$95$1 * N[(N[(N[(N[(-1.0 * N[(z2 * z4), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$1 / N[(z3 + z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if z3 < -2.0000000000000002e44

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. div-flip-rev N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      10. lower-/.f64 43.9%

          \[\leadsto \frac{z1}{\frac{z3 + z3}{\color{blue}{z0}}} \]

   8. Applied rewrites 43.9%

      \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

   if -2.0000000000000002e44 < z3 < 1.0500000000000001e-144

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around 0

      \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]

   if 1.0500000000000001e-144 < z3 < 1.8000000000000001e-4

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around inf

      \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot \color{blue}{z4}\right)\right) \cdot z1}{z3 + z3}}{z3} \]

       2. lower-*.f64 32.4%

          \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \left(z2 \cdot z4\right)\right) \cdot z1}{z3 + z3}}{z3} \]

   11. Applied rewrites 32.4%

       \[\leadsto z0 \cdot \frac{\frac{\left(-1 \cdot \color{blue}{\left(z2 \cdot z4\right)}\right) \cdot z1}{z3 + z3}}{z3} \]

   if 1.8000000000000001e-4 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

      20. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

      21. lower-/.f64 44.1%

          \[\leadsto z1 \cdot \frac{z0}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{t\_0}{\frac{z3 + z3}{t\_1}}\\ \mathbf{elif}\;z3 \leq 1.15 \cdot 10^{-81}:\\ \;\;\;\;t\_1 \cdot \frac{\frac{z3 \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{elif}\;z3 \leq 1.18 \cdot 10^{+82}:\\ \;\;\;\;\left(\frac{1}{t\_1 \cdot \frac{z3 + z3}{t\_0}} \cdot t\_1\right) \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z3 + z3}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -2e+44)
      (/ t_0 (/ (+ z3 z3) t_1))
      (if (<= z3 1.15e-81)
        (* t_1 (/ (/ (* z3 t_0) (+ z3 z3)) z3))
        (if (<= z3 1.18e+82)
          (* (* (/ 1.0 (* t_1 (/ (+ z3 z3) t_0))) t_1) t_1)
          (* t_0 (/ t_1 (+ z3 z3))))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double tmp;
	if (z3 <= -2e+44) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1.15e-81) {
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 1.18e+82) {
		tmp = ((1.0 / (t_1 * ((z3 + z3) / t_0))) * t_1) * t_1;
	} else {
		tmp = t_0 * (t_1 / (z3 + z3));
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double tmp;
	if (z3 <= -2e+44) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1.15e-81) {
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 1.18e+82) {
		tmp = ((1.0 / (t_1 * ((z3 + z3) / t_0))) * t_1) * t_1;
	} else {
		tmp = t_0 * (t_1 / (z3 + z3));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	tmp = 0
	if z3 <= -2e+44:
		tmp = t_0 / ((z3 + z3) / t_1)
	elif z3 <= 1.15e-81:
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3)
	elif z3 <= 1.18e+82:
		tmp = ((1.0 / (t_1 * ((z3 + z3) / t_0))) * t_1) * t_1
	else:
		tmp = t_0 * (t_1 / (z3 + z3))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	tmp = 0.0
	if (z3 <= -2e+44)
		tmp = Float64(t_0 / Float64(Float64(z3 + z3) / t_1));
	elseif (z3 <= 1.15e-81)
		tmp = Float64(t_1 * Float64(Float64(Float64(z3 * t_0) / Float64(z3 + z3)) / z3));
	elseif (z3 <= 1.18e+82)
		tmp = Float64(Float64(Float64(1.0 / Float64(t_1 * Float64(Float64(z3 + z3) / t_0))) * t_1) * t_1);
	else
		tmp = Float64(t_0 * Float64(t_1 / Float64(z3 + z3)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	tmp = 0.0;
	if (z3 <= -2e+44)
		tmp = t_0 / ((z3 + z3) / t_1);
	elseif (z3 <= 1.15e-81)
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	elseif (z3 <= 1.18e+82)
		tmp = ((1.0 / (t_1 * ((z3 + z3) / t_0))) * t_1) * t_1;
	else
		tmp = t_0 * (t_1 / (z3 + z3));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -2e+44], N[(t$95$0 / N[(N[(z3 + z3), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.15e-81], N[(t$95$1 * N[(N[(N[(z3 * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.18e+82], N[(N[(N[(1.0 / N[(t$95$1 * N[(N[(z3 + z3), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] * t$95$1), $MachinePrecision], N[(t$95$0 * N[(t$95$1 / N[(z3 + z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if z3 < -2.0000000000000002e44

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. div-flip-rev N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      10. lower-/.f64 43.9%

          \[\leadsto \frac{z1}{\frac{z3 + z3}{\color{blue}{z0}}} \]

   8. Applied rewrites 43.9%

      \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

   if -2.0000000000000002e44 < z3 < 1.15e-81

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around 0

      \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]

   if 1.15e-81 < z3 < 1.1800000000000001e82

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. associate-/r/ N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot \color{blue}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot \color{blue}{z1} \]

      10. lower-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      11. lower-unsound-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      12. lower-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      13. lower-unsound-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      14. div-flip N/A

          \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

      15. lower-/.f64 44.1%

          \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

   8. Applied rewrites 44.1%

      \[\leadsto \frac{z0}{z3 + z3} \cdot \color{blue}{z1} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z0}{z3 + z3} \cdot \color{blue}{z1} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

      3. associate-/r/ N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 + z3}{z1}}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3 + z3}{\color{blue}{z1}}} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z3 + z3}{z1}}{z0}}} \]

      6. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{z0}} \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{z0}} \]

      8. div-add N/A

         \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      11. div-add N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1}}{z0} + \color{blue}{\frac{\frac{z3}{z1}}{z0}}} \]

      12. frac-add N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{\color{blue}{z0 \cdot z0}}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot z0}} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot z0}} \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{\color{blue}{z0} \cdot z0}} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot \color{blue}{z0}}} \]

      17. associate-/r/ N/A

          \[\leadsto \frac{1}{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}} \cdot \color{blue}{\left(z0 \cdot z0\right)} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}} \cdot \left(z0 \cdot \color{blue}{z0}\right) \]

      19. associate-*r* N/A

          \[\leadsto \left(\frac{1}{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}} \cdot z0\right) \cdot \color{blue}{z0} \]

      20. lower-*.f64 N/A

          \[\leadsto \left(\frac{1}{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}} \cdot z0\right) \cdot \color{blue}{z0} \]

   10. Applied rewrites 40.3%

       \[\leadsto \left(\frac{1}{z0 \cdot \frac{z3 + z3}{z1}} \cdot z0\right) \cdot \color{blue}{z0} \]

   if 1.1800000000000001e82 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

      20. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

      21. lower-/.f64 44.1%

          \[\leadsto z1 \cdot \frac{z0}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 60.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{t\_0}{\frac{z3 + z3}{t\_1}}\\ \mathbf{elif}\;z3 \leq 10^{-75}:\\ \;\;\;\;t\_1 \cdot \frac{\frac{z3 \cdot t\_0}{z3 + z3}}{z3}\\ \mathbf{elif}\;z3 \leq 1.18 \cdot 10^{+82}:\\ \;\;\;\;t\_1 \cdot \frac{t\_1}{t\_1 \cdot \frac{z3 + z3}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z3 + z3}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -2e+44)
      (/ t_0 (/ (+ z3 z3) t_1))
      (if (<= z3 1e-75)
        (* t_1 (/ (/ (* z3 t_0) (+ z3 z3)) z3))
        (if (<= z3 1.18e+82)
          (* t_1 (/ t_1 (* t_1 (/ (+ z3 z3) t_0))))
          (* t_0 (/ t_1 (+ z3 z3))))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double tmp;
	if (z3 <= -2e+44) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1e-75) {
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 1.18e+82) {
		tmp = t_1 * (t_1 / (t_1 * ((z3 + z3) / t_0)));
	} else {
		tmp = t_0 * (t_1 / (z3 + z3));
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double tmp;
	if (z3 <= -2e+44) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1e-75) {
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	} else if (z3 <= 1.18e+82) {
		tmp = t_1 * (t_1 / (t_1 * ((z3 + z3) / t_0)));
	} else {
		tmp = t_0 * (t_1 / (z3 + z3));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	tmp = 0
	if z3 <= -2e+44:
		tmp = t_0 / ((z3 + z3) / t_1)
	elif z3 <= 1e-75:
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3)
	elif z3 <= 1.18e+82:
		tmp = t_1 * (t_1 / (t_1 * ((z3 + z3) / t_0)))
	else:
		tmp = t_0 * (t_1 / (z3 + z3))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	tmp = 0.0
	if (z3 <= -2e+44)
		tmp = Float64(t_0 / Float64(Float64(z3 + z3) / t_1));
	elseif (z3 <= 1e-75)
		tmp = Float64(t_1 * Float64(Float64(Float64(z3 * t_0) / Float64(z3 + z3)) / z3));
	elseif (z3 <= 1.18e+82)
		tmp = Float64(t_1 * Float64(t_1 / Float64(t_1 * Float64(Float64(z3 + z3) / t_0))));
	else
		tmp = Float64(t_0 * Float64(t_1 / Float64(z3 + z3)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	tmp = 0.0;
	if (z3 <= -2e+44)
		tmp = t_0 / ((z3 + z3) / t_1);
	elseif (z3 <= 1e-75)
		tmp = t_1 * (((z3 * t_0) / (z3 + z3)) / z3);
	elseif (z3 <= 1.18e+82)
		tmp = t_1 * (t_1 / (t_1 * ((z3 + z3) / t_0)));
	else
		tmp = t_0 * (t_1 / (z3 + z3));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -2e+44], N[(t$95$0 / N[(N[(z3 + z3), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1e-75], N[(t$95$1 * N[(N[(N[(z3 * t$95$0), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision] / z3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.18e+82], N[(t$95$1 * N[(t$95$1 / N[(t$95$1 * N[(N[(z3 + z3), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$1 / N[(z3 + z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if z3 < -2.0000000000000002e44

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. div-flip-rev N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      10. lower-/.f64 43.9%

          \[\leadsto \frac{z1}{\frac{z3 + z3}{\color{blue}{z0}}} \]

   8. Applied rewrites 43.9%

      \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

   if -2.0000000000000002e44 < z3 < 9.9999999999999996e-76

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\color{blue}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{z1 \cdot z0}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z1 \cdot z0}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z0 \cdot z1}}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{z1}{\left(z3 + z3\right) \cdot z3}\right)} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)} \]

      8. associate-*l* N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}\right) \]

      12. lower-/.f64 54.5%

          \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\frac{e^{z4 \cdot \frac{-z2}{z3}}}{\sinh \left(\frac{1}{z3}\right)}}\right) \]

   3. Applied rewrites 54.5%

      \[\leadsto \color{blue}{z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \frac{e^{\frac{-z2}{z3} \cdot z4}}{\sinh \left(\frac{1}{z3}\right)}\right)} \]

   4. Taylor expanded in z3 around inf

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \color{blue}{\left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)}\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + \color{blue}{-1 \cdot \frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \color{blue}{\frac{z2 \cdot z4}{z3}}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{\color{blue}{z3}}\right)\right)\right) \]

      5. lower-*.f64 30.6%

         \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

   6. Applied rewrites 30.6%

      \[\leadsto z0 \cdot \left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \color{blue}{\left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(\frac{z1}{\left(z3 + z3\right) \cdot z3} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\color{blue}{\frac{z1}{\left(z3 + z3\right) \cdot z3}} \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\left(z3 + z3\right) \cdot z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{\color{blue}{\left(z3 + z3\right) \cdot z3}} \]

      5. associate-/r* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

      6. lower-/.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{\frac{z1 \cdot \left(z3 \cdot \left(1 + -1 \cdot \frac{z2 \cdot z4}{z3}\right)\right)}{z3 + z3}}{z3}} \]

   8. Applied rewrites 40.5%

      \[\leadsto z0 \cdot \color{blue}{\frac{\frac{\left(z3 - z2 \cdot z4\right) \cdot z1}{z3 + z3}}{z3}} \]

   9. Taylor expanded in z4 around 0

      \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto z0 \cdot \frac{\frac{z3 \cdot z1}{z3 + z3}}{z3} \]

   if 9.9999999999999996e-76 < z3 < 1.1800000000000001e82

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. associate-/r/ N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot \color{blue}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot \color{blue}{z1} \]

      10. lower-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      11. lower-unsound-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      12. lower-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      13. lower-unsound-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      14. div-flip N/A

          \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

      15. lower-/.f64 44.1%

          \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

   8. Applied rewrites 44.1%

      \[\leadsto \frac{z0}{z3 + z3} \cdot \color{blue}{z1} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z0}{z3 + z3} \cdot \color{blue}{z1} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

      3. associate-/r/ N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 + z3}{z1}}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3 + z3}{\color{blue}{z1}}} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z3 + z3}{z1}}{z0}}} \]

      6. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{z0}} \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{z0}} \]

      8. div-add N/A

         \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      11. div-add N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1}}{z0} + \color{blue}{\frac{\frac{z3}{z1}}{z0}}} \]

      12. frac-add N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{\color{blue}{z0 \cdot z0}}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot z0}} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot z0}} \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{\color{blue}{z0} \cdot z0}} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot \color{blue}{z0}}} \]

      17. frac-2neg N/A

          \[\leadsto \frac{1}{\frac{\mathsf{neg}\left(\left(\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}\right)\right)}{\color{blue}{\mathsf{neg}\left(z0 \cdot z0\right)}}} \]

      18. div-flip-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(z0 \cdot z0\right)}{\color{blue}{\mathsf{neg}\left(\left(\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}\right)\right)}} \]

      19. frac-2neg N/A

          \[\leadsto \frac{z0 \cdot z0}{\color{blue}{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{z0 \cdot z0}{\color{blue}{\frac{z3}{z1} \cdot z0} + z0 \cdot \frac{z3}{z1}} \]

      21. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z0}{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}} \]

   10. Applied rewrites 40.4%

       \[\leadsto z0 \cdot \color{blue}{\frac{z0}{z0 \cdot \frac{z3 + z3}{z1}}} \]

   if 1.1800000000000001e82 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

      20. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

      21. lower-/.f64 44.1%

          \[\leadsto z1 \cdot \frac{z0}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;z3 \leq -2.1:\\ \;\;\;\;\frac{t\_0}{\frac{z3 + z3}{t\_1}}\\ \mathbf{elif}\;z3 \leq 1.18 \cdot 10^{+82}:\\ \;\;\;\;t\_1 \cdot \frac{t\_1}{t\_1 \cdot \frac{z3 + z3}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z3 + z3}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (if (<= z3 -2.1)
      (/ t_0 (/ (+ z3 z3) t_1))
      (if (<= z3 1.18e+82)
        (* t_1 (/ t_1 (* t_1 (/ (+ z3 z3) t_0))))
        (* t_0 (/ t_1 (+ z3 z3)))))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double tmp;
	if (z3 <= -2.1) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1.18e+82) {
		tmp = t_1 * (t_1 / (t_1 * ((z3 + z3) / t_0)));
	} else {
		tmp = t_0 * (t_1 / (z3 + z3));
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double tmp;
	if (z3 <= -2.1) {
		tmp = t_0 / ((z3 + z3) / t_1);
	} else if (z3 <= 1.18e+82) {
		tmp = t_1 * (t_1 / (t_1 * ((z3 + z3) / t_0)));
	} else {
		tmp = t_0 * (t_1 / (z3 + z3));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0, z4, z2, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	tmp = 0
	if z3 <= -2.1:
		tmp = t_0 / ((z3 + z3) / t_1)
	elif z3 <= 1.18e+82:
		tmp = t_1 * (t_1 / (t_1 * ((z3 + z3) / t_0)))
	else:
		tmp = t_0 * (t_1 / (z3 + z3))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0, z4, z2, z3)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	tmp = 0.0
	if (z3 <= -2.1)
		tmp = Float64(t_0 / Float64(Float64(z3 + z3) / t_1));
	elseif (z3 <= 1.18e+82)
		tmp = Float64(t_1 * Float64(t_1 / Float64(t_1 * Float64(Float64(z3 + z3) / t_0))));
	else
		tmp = Float64(t_0 * Float64(t_1 / Float64(z3 + z3)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0, z4, z2, z3)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	tmp = 0.0;
	if (z3 <= -2.1)
		tmp = t_0 / ((z3 + z3) / t_1);
	elseif (z3 <= 1.18e+82)
		tmp = t_1 * (t_1 / (t_1 * ((z3 + z3) / t_0)));
	else
		tmp = t_0 * (t_1 / (z3 + z3));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z3, -2.1], N[(t$95$0 / N[(N[(z3 + z3), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z3, 1.18e+82], N[(t$95$1 * N[(t$95$1 / N[(t$95$1 * N[(N[(z3 + z3), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$1 / N[(z3 + z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z3 < -2.1000000000000001

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. div-flip-rev N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

      10. lower-/.f64 43.9%

          \[\leadsto \frac{z1}{\frac{z3 + z3}{\color{blue}{z0}}} \]

   8. Applied rewrites 43.9%

      \[\leadsto \frac{z1}{\color{blue}{\frac{z3 + z3}{z0}}} \]

   if -2.1000000000000001 < z3 < 1.1800000000000001e82

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. *-commutative N/A

          \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      20. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      21. lower-*.f64 N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      22. lower-/.f64 44.1%

          \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

      2. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z3 + z3}{z0 \cdot z1}}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0 \cdot \color{blue}{z1}}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z0}}{\color{blue}{z1}}} \]

      8. associate-/r/ N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot \color{blue}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot \color{blue}{z1} \]

      10. lower-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      11. lower-unsound-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      12. lower-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      13. lower-unsound-/.f32 N/A

          \[\leadsto \frac{1}{\frac{z3 + z3}{z0}} \cdot z1 \]

      14. div-flip N/A

          \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

      15. lower-/.f64 44.1%

          \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

   8. Applied rewrites 44.1%

      \[\leadsto \frac{z0}{z3 + z3} \cdot \color{blue}{z1} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z0}{z3 + z3} \cdot \color{blue}{z1} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z0}{z3 + z3} \cdot z1 \]

      3. associate-/r/ N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 + z3}{z1}}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3 + z3}{\color{blue}{z1}}} \]

      5. div-flip-rev N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z3 + z3}{z1}}{z0}}} \]

      6. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{z0}} \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3 + z3}{z1}}{z0}} \]

      8. div-add N/A

         \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} + \frac{z3}{z1}}{z0}} \]

      11. div-add N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1}}{z0} + \color{blue}{\frac{\frac{z3}{z1}}{z0}}} \]

      12. frac-add N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{\color{blue}{z0 \cdot z0}}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot z0}} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot z0}} \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{\color{blue}{z0} \cdot z0}} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}{z0 \cdot \color{blue}{z0}}} \]

      17. frac-2neg N/A

          \[\leadsto \frac{1}{\frac{\mathsf{neg}\left(\left(\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}\right)\right)}{\color{blue}{\mathsf{neg}\left(z0 \cdot z0\right)}}} \]

      18. div-flip-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(z0 \cdot z0\right)}{\color{blue}{\mathsf{neg}\left(\left(\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}\right)\right)}} \]

      19. frac-2neg N/A

          \[\leadsto \frac{z0 \cdot z0}{\color{blue}{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{z0 \cdot z0}{\color{blue}{\frac{z3}{z1} \cdot z0} + z0 \cdot \frac{z3}{z1}} \]

      21. associate-/l* N/A

          \[\leadsto z0 \cdot \color{blue}{\frac{z0}{\frac{z3}{z1} \cdot z0 + z0 \cdot \frac{z3}{z1}}} \]

   10. Applied rewrites 40.4%

       \[\leadsto z0 \cdot \color{blue}{\frac{z0}{z0 \cdot \frac{z3 + z3}{z1}}} \]

   if 1.1800000000000001e82 < z3

   1. Initial program 58.4%

      \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

   2. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

      3. lower-*.f64 47.2%

         \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

   4. Applied rewrites 47.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

      4. mult-flip N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      6. *-commutative N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

      9. associate-*l* N/A

         \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

      10. lift-/.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

      12. frac-times N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

      13. metadata-eval N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

      15. count-2 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      16. lift-+.f64 N/A

          \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

      17. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

      19. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

      20. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

      21. lower-/.f64 44.1%

          \[\leadsto z1 \cdot \frac{z0}{\color{blue}{z3 + z3}} \]

   6. Applied rewrites 44.1%

      \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 47.1% accurate, 13.2× speedup

Math

\[\frac{z0 \cdot z1}{z3 + z3} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (/ (* z0 z1) (+ z3 z3)))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	return (z0 * z1) / (z3 + z3);
}

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(z1, z0, z4, z2, z3)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8), intent (in) :: z4
    real(8), intent (in) :: z2
    real(8), intent (in) :: z3
    code = (z0 * z1) / (z3 + z3)
end function

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	return (z0 * z1) / (z3 + z3);
}

Python

def code(z1, z0, z4, z2, z3):
	return (z0 * z1) / (z3 + z3)

Julia

function code(z1, z0, z4, z2, z3)
	return Float64(Float64(z0 * z1) / Float64(z3 + z3))
end

MATLAB

function tmp = code(z1, z0, z4, z2, z3)
	tmp = (z0 * z1) / (z3 + z3);
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := N[(N[(z0 * z1), $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.4%

   \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

2. Taylor expanded in z3 around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

   3. lower-*.f64 47.2%

      \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

4. Applied rewrites 47.2%

   \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

   2. *-commutative N/A

      \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

   3. lift-/.f64 N/A

      \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

   4. mult-flip N/A

      \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   6. *-commutative N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   8. lift-/.f64 N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   9. associate-*l* N/A

      \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

   10. lift-/.f64 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

   11. metadata-eval N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

   12. frac-times N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

   13. metadata-eval N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

   14. *-commutative N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

   15. count-2 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

   16. lift-+.f64 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

   17. mult-flip N/A

       \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

   18. lower-/.f64 47.1%

       \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

   19. lift-*.f64 N/A

       \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

   20. *-commutative N/A

       \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

   21. lift-*.f64 47.1%

       \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

6. Applied rewrites 47.1%

   \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3 + z3}} \]
7. Add Preprocessing

Alternative 15: 47.1% accurate, 0.6× speedup

Math

\[\mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \left(\mathsf{min}\left(\left|z1\right|, \left|z0\right|\right) \cdot \frac{\mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)}{z3 + z3}\right)\right) \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (*
 (copysign 1.0 z1)
 (*
  (copysign 1.0 z0)
  (*
   (fmin (fabs z1) (fabs z0))
   (/ (fmax (fabs z1) (fabs z0)) (+ z3 z3))))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	return copysign(1.0, z1) * (copysign(1.0, z0) * (fmin(fabs(z1), fabs(z0)) * (fmax(fabs(z1), fabs(z0)) / (z3 + z3))));
}

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * (fmin(Math.abs(z1), Math.abs(z0)) * (fmax(Math.abs(z1), Math.abs(z0)) / (z3 + z3))));
}

Python

def code(z1, z0, z4, z2, z3):
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * (fmin(math.fabs(z1), math.fabs(z0)) * (fmax(math.fabs(z1), math.fabs(z0)) / (z3 + z3))))

Julia

function code(z1, z0, z4, z2, z3)
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * Float64(fmin(abs(z1), abs(z0)) * Float64(fmax(abs(z1), abs(z0)) / Float64(z3 + z3)))))
end

MATLAB

function tmp = code(z1, z0, z4, z2, z3)
	tmp = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * (min(abs(z1), abs(z0)) * (max(abs(z1), abs(z0)) / (z3 + z3))));
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision] * N[(N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.4%

   \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

2. Taylor expanded in z3 around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

   3. lower-*.f64 47.2%

      \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

4. Applied rewrites 47.2%

   \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

   2. *-commutative N/A

      \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

   3. lift-/.f64 N/A

      \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

   4. mult-flip N/A

      \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   6. *-commutative N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   8. lift-/.f64 N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   9. associate-*l* N/A

      \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

   10. lift-/.f64 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

   11. metadata-eval N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

   12. frac-times N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

   13. metadata-eval N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

   14. *-commutative N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

   15. count-2 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

   16. lift-+.f64 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

   17. mult-flip N/A

       \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

   18. lift-*.f64 N/A

       \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

   19. associate-/l* N/A

       \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

   20. lower-*.f64 N/A

       \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]

   21. lower-/.f64 44.1%

       \[\leadsto z1 \cdot \frac{z0}{\color{blue}{z3 + z3}} \]

6. Applied rewrites 44.1%

   \[\leadsto z1 \cdot \color{blue}{\frac{z0}{z3 + z3}} \]
7. Add Preprocessing

Alternative 16: 44.1% accurate, 1.2× speedup

Math

\[\mathsf{max}\left(z1, z0\right) \cdot \frac{\mathsf{min}\left(z1, z0\right)}{z3 + z3} \]

FPCore

(FPCore (z1 z0 z4 z2 z3)
  :precision binary64
  (* (fmax z1 z0) (/ (fmin z1 z0) (+ z3 z3))))

C

double code(double z1, double z0, double z4, double z2, double z3) {
	return fmax(z1, z0) * (fmin(z1, z0) / (z3 + z3));
}

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(z1, z0, z4, z2, z3)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8), intent (in) :: z4
    real(8), intent (in) :: z2
    real(8), intent (in) :: z3
    code = fmax(z1, z0) * (fmin(z1, z0) / (z3 + z3))
end function

Java

public static double code(double z1, double z0, double z4, double z2, double z3) {
	return fmax(z1, z0) * (fmin(z1, z0) / (z3 + z3));
}

Python

def code(z1, z0, z4, z2, z3):
	return fmax(z1, z0) * (fmin(z1, z0) / (z3 + z3))

Julia

function code(z1, z0, z4, z2, z3)
	return Float64(fmax(z1, z0) * Float64(fmin(z1, z0) / Float64(z3 + z3)))
end

MATLAB

function tmp = code(z1, z0, z4, z2, z3)
	tmp = max(z1, z0) * (min(z1, z0) / (z3 + z3));
end

Wolfram

code[z1_, z0_, z4_, z2_, z3_] := N[(N[Max[z1, z0], $MachinePrecision] * N[(N[Min[z1, z0], $MachinePrecision] / N[(z3 + z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.4%

   \[\frac{\left(z1 \cdot z0\right) \cdot e^{z4 \cdot \frac{-z2}{z3}}}{\left(\left(z3 + z3\right) \cdot z3\right) \cdot \sinh \left(\frac{1}{z3}\right)} \]

2. Taylor expanded in z3 around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z0 \cdot z1}{z3}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{z0 \cdot z1}{\color{blue}{z3}} \]

   3. lower-*.f64 47.2%

      \[\leadsto 0.5 \cdot \frac{z0 \cdot z1}{z3} \]

4. Applied rewrites 47.2%

   \[\leadsto \color{blue}{0.5 \cdot \frac{z0 \cdot z1}{z3}} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z0 \cdot z1}{z3}} \]

   2. *-commutative N/A

      \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \color{blue}{\frac{1}{2}} \]

   3. lift-/.f64 N/A

      \[\leadsto \frac{z0 \cdot z1}{z3} \cdot \frac{1}{2} \]

   4. mult-flip N/A

      \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\left(z0 \cdot z1\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   6. *-commutative N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   8. lift-/.f64 N/A

      \[\leadsto \left(\left(z1 \cdot z0\right) \cdot \frac{1}{z3}\right) \cdot \frac{1}{2} \]

   9. associate-*l* N/A

      \[\leadsto \left(z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{1}{z3} \cdot \frac{1}{2}\right)} \]

   10. lift-/.f64 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{2}\right) \]

   11. metadata-eval N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \left(\frac{1}{z3} \cdot \frac{1}{\color{blue}{2}}\right) \]

   12. frac-times N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1 \cdot 1}{\color{blue}{z3 \cdot 2}} \]

   13. metadata-eval N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{\color{blue}{z3} \cdot 2} \]

   14. *-commutative N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{2 \cdot \color{blue}{z3}} \]

   15. count-2 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

   16. lift-+.f64 N/A

       \[\leadsto \left(z1 \cdot z0\right) \cdot \frac{1}{z3 + \color{blue}{z3}} \]

   17. mult-flip N/A

       \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3 + z3}} \]

   18. lift-*.f64 N/A

       \[\leadsto \frac{z1 \cdot z0}{\color{blue}{z3} + z3} \]

   19. *-commutative N/A

       \[\leadsto \frac{z0 \cdot z1}{\color{blue}{z3} + z3} \]

   20. associate-/l* N/A

       \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

   21. lower-*.f64 N/A

       \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]

   22. lower-/.f64 44.1%

       \[\leadsto z0 \cdot \frac{z1}{\color{blue}{z3 + z3}} \]

6. Applied rewrites 44.1%

   \[\leadsto z0 \cdot \color{blue}{\frac{z1}{z3 + z3}} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025256 
(FPCore (z1 z0 z4 z2 z3)
  :name "(/ (* (* z1 z0) (exp (* z4 (/ (- z2) z3)))) (* (* (+ z3 z3) z3) (sinh (/ 1 z3))))"
  :precision binary64
  (/ (* (* z1 z0) (exp (* z4 (/ (- z2) z3)))) (* (* (+ z3 z3) z3) (sinh (/ 1.0 z3)))))