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

Percentage Accurate: 59.6% → 99.3%

Time: 4.9s

Alternatives: 15

Speedup: 0.6×

• could not determine a ground truth

  1. z1 = 4.935709514538582e+22
  2. z2 = -9.900398234160371e+39
  3. z0 = 2.337836512016505e-265
  4. z4 = 1.8007135480090902e-75
  5. z3 = -1.544751492297357e+29

Specification

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_2 := t\_1 \cdot \frac{0.5 \cdot t\_0}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0}\\ t_3 := t\_0 \cdot \frac{t\_1}{\left(1 \cdot \sinh \left(\frac{1}{z0}\right)\right) \cdot \left(\left(z0 + z0\right) \cdot z0\right)}\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;z0 \leq -255:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z0 \leq -2.1 \cdot 10^{-153}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z0 \leq 10^{-162}:\\ \;\;\;\;\frac{t\_1}{\left(\frac{z3 \cdot z4 + z0}{z0 \cdot z0} \cdot \left(z0 + z0\right)\right) \cdot z0} \cdot t\_0\\ \mathbf{elif}\;z0 \leq 90000000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmax (fabs z1) (fabs z2)))
       (t_1 (fmin (fabs z1) (fabs z2)))
       (t_2 (* t_1 (/ (* 0.5 t_0) (* (exp (/ (* z4 z3) z0)) z0))))
       (t_3
        (*
         t_0
         (/ t_1 (* (* 1.0 (sinh (/ 1.0 z0))) (* (+ z0 z0) z0))))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= z0 -255.0)
      t_2
      (if (<= z0 -2.1e-153)
        t_3
        (if (<= z0 1e-162)
          (*
           (/ t_1 (* (* (/ (+ (* z3 z4) z0) (* z0 z0)) (+ z0 z0)) z0))
           t_0)
          (if (<= z0 90000000.0) t_3 t_2))))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmax(fabs(z1), fabs(z2));
	double t_1 = fmin(fabs(z1), fabs(z2));
	double t_2 = t_1 * ((0.5 * t_0) / (exp(((z4 * z3) / z0)) * z0));
	double t_3 = t_0 * (t_1 / ((1.0 * sinh((1.0 / z0))) * ((z0 + z0) * z0)));
	double tmp;
	if (z0 <= -255.0) {
		tmp = t_2;
	} else if (z0 <= -2.1e-153) {
		tmp = t_3;
	} else if (z0 <= 1e-162) {
		tmp = (t_1 / (((((z3 * z4) + z0) / (z0 * z0)) * (z0 + z0)) * z0)) * t_0;
	} else if (z0 <= 90000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmax(Math.abs(z1), Math.abs(z2));
	double t_1 = fmin(Math.abs(z1), Math.abs(z2));
	double t_2 = t_1 * ((0.5 * t_0) / (Math.exp(((z4 * z3) / z0)) * z0));
	double t_3 = t_0 * (t_1 / ((1.0 * Math.sinh((1.0 / z0))) * ((z0 + z0) * z0)));
	double tmp;
	if (z0 <= -255.0) {
		tmp = t_2;
	} else if (z0 <= -2.1e-153) {
		tmp = t_3;
	} else if (z0 <= 1e-162) {
		tmp = (t_1 / (((((z3 * z4) + z0) / (z0 * z0)) * (z0 + z0)) * z0)) * t_0;
	} else if (z0 <= 90000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmax(math.fabs(z1), math.fabs(z2))
	t_1 = fmin(math.fabs(z1), math.fabs(z2))
	t_2 = t_1 * ((0.5 * t_0) / (math.exp(((z4 * z3) / z0)) * z0))
	t_3 = t_0 * (t_1 / ((1.0 * math.sinh((1.0 / z0))) * ((z0 + z0) * z0)))
	tmp = 0
	if z0 <= -255.0:
		tmp = t_2
	elif z0 <= -2.1e-153:
		tmp = t_3
	elif z0 <= 1e-162:
		tmp = (t_1 / (((((z3 * z4) + z0) / (z0 * z0)) * (z0 + z0)) * z0)) * t_0
	elif z0 <= 90000000.0:
		tmp = t_3
	else:
		tmp = t_2
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmax(abs(z1), abs(z2))
	t_1 = fmin(abs(z1), abs(z2))
	t_2 = Float64(t_1 * Float64(Float64(0.5 * t_0) / Float64(exp(Float64(Float64(z4 * z3) / z0)) * z0)))
	t_3 = Float64(t_0 * Float64(t_1 / Float64(Float64(1.0 * sinh(Float64(1.0 / z0))) * Float64(Float64(z0 + z0) * z0))))
	tmp = 0.0
	if (z0 <= -255.0)
		tmp = t_2;
	elseif (z0 <= -2.1e-153)
		tmp = t_3;
	elseif (z0 <= 1e-162)
		tmp = Float64(Float64(t_1 / Float64(Float64(Float64(Float64(Float64(z3 * z4) + z0) / Float64(z0 * z0)) * Float64(z0 + z0)) * z0)) * t_0);
	elseif (z0 <= 90000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = max(abs(z1), abs(z2));
	t_1 = min(abs(z1), abs(z2));
	t_2 = t_1 * ((0.5 * t_0) / (exp(((z4 * z3) / z0)) * z0));
	t_3 = t_0 * (t_1 / ((1.0 * sinh((1.0 / z0))) * ((z0 + z0) * z0)));
	tmp = 0.0;
	if (z0 <= -255.0)
		tmp = t_2;
	elseif (z0 <= -2.1e-153)
		tmp = t_3;
	elseif (z0 <= 1e-162)
		tmp = (t_1 / (((((z3 * z4) + z0) / (z0 * z0)) * (z0 + z0)) * z0)) * t_0;
	elseif (z0 <= 90000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(N[(0.5 * t$95$0), $MachinePrecision] / N[(N[Exp[N[(N[(z4 * z3), $MachinePrecision] / z0), $MachinePrecision]], $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * N[(t$95$1 / N[(N[(1.0 * N[Sinh[N[(1.0 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(z0 + z0), $MachinePrecision] * z0), $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z0, -255.0], t$95$2, If[LessEqual[z0, -2.1e-153], t$95$3, If[LessEqual[z0, 1e-162], N[(N[(t$95$1 / N[(N[(N[(N[(N[(z3 * z4), $MachinePrecision] + z0), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision] * N[(z0 + z0), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[z0, 90000000.0], t$95$3, t$95$2]]]]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -255 or 9e7 < z0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. distribute-rgt-in N/A

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

      12. count-2 N/A

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

      13. associate-/r* N/A

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

      14. lower-/.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 58.8%

          \[\leadsto z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \color{blue}{\frac{z2}{\sinh \left(\frac{1}{z0}\right) \cdot e^{\frac{z4 \cdot z3}{z0}}}}\right) \]

   3. Applied rewrites 58.8%

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \frac{z2}{e^{\frac{z3 \cdot z4}{z0}} \cdot \sinh \left(\frac{1}{z0}\right)}\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/r* N/A

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

      8. associate-*l/ N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/r* N/A

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

      12. frac-times N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 N/A

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

   5. Applied rewrites 85.3%

      \[\leadsto z1 \cdot \color{blue}{\frac{\left(\frac{0.5}{z0} \cdot z2\right) \cdot \frac{-1}{\sinh \left(\frac{-1}{z0}\right)}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0}} \]

   6. Taylor expanded in z0 around inf

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

      1. lower-*.f64 78.2%

         \[\leadsto z1 \cdot \frac{0.5 \cdot \color{blue}{z2}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0} \]

   8. Applied rewrites 78.2%

      \[\leadsto z1 \cdot \frac{\color{blue}{0.5 \cdot z2}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0} \]

   if -255 < z0 < -2.1e-153 or 9.9999999999999995e-163 < z0 < 9e7

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

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

   4. Applied rewrites 55.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 58.6%

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 58.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 58.6%

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 58.6%

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

   6. Applied rewrites 58.6%

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

   if -2.1e-153 < z0 < 9.9999999999999995e-163

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 50.5%

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

Alternative 2: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ t_2 := t\_0 \cdot \frac{0.5 \cdot t\_1}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0}\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;z0 \leq -255:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z0 \leq 90000000:\\ \;\;\;\;\frac{t\_1 \cdot \frac{t\_0}{\left(1 \cdot \sinh \left(\frac{1}{z0}\right)\right) \cdot \left(z0 + z0\right)}}{z0}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2)))
       (t_2 (* t_0 (/ (* 0.5 t_1) (* (exp (/ (* z4 z3) z0)) z0)))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= z0 -255.0)
      t_2
      (if (<= z0 90000000.0)
        (/ (* t_1 (/ t_0 (* (* 1.0 (sinh (/ 1.0 z0))) (+ z0 z0)))) z0)
        t_2))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double t_2 = t_0 * ((0.5 * t_1) / (exp(((z4 * z3) / z0)) * z0));
	double tmp;
	if (z0 <= -255.0) {
		tmp = t_2;
	} else if (z0 <= 90000000.0) {
		tmp = (t_1 * (t_0 / ((1.0 * sinh((1.0 / z0))) * (z0 + z0)))) / z0;
	} else {
		tmp = t_2;
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double t_2 = t_0 * ((0.5 * t_1) / (Math.exp(((z4 * z3) / z0)) * z0));
	double tmp;
	if (z0 <= -255.0) {
		tmp = t_2;
	} else if (z0 <= 90000000.0) {
		tmp = (t_1 * (t_0 / ((1.0 * Math.sinh((1.0 / z0))) * (z0 + z0)))) / z0;
	} else {
		tmp = t_2;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	t_2 = t_0 * ((0.5 * t_1) / (math.exp(((z4 * z3) / z0)) * z0))
	tmp = 0
	if z0 <= -255.0:
		tmp = t_2
	elif z0 <= 90000000.0:
		tmp = (t_1 * (t_0 / ((1.0 * math.sinh((1.0 / z0))) * (z0 + z0)))) / z0
	else:
		tmp = t_2
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	t_2 = Float64(t_0 * Float64(Float64(0.5 * t_1) / Float64(exp(Float64(Float64(z4 * z3) / z0)) * z0)))
	tmp = 0.0
	if (z0 <= -255.0)
		tmp = t_2;
	elseif (z0 <= 90000000.0)
		tmp = Float64(Float64(t_1 * Float64(t_0 / Float64(Float64(1.0 * sinh(Float64(1.0 / z0))) * Float64(z0 + z0)))) / z0);
	else
		tmp = t_2;
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	t_2 = t_0 * ((0.5 * t_1) / (exp(((z4 * z3) / z0)) * z0));
	tmp = 0.0;
	if (z0 <= -255.0)
		tmp = t_2;
	elseif (z0 <= 90000000.0)
		tmp = (t_1 * (t_0 / ((1.0 * sinh((1.0 / z0))) * (z0 + z0)))) / z0;
	else
		tmp = t_2;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * N[(N[(0.5 * t$95$1), $MachinePrecision] / N[(N[Exp[N[(N[(z4 * z3), $MachinePrecision] / z0), $MachinePrecision]], $MachinePrecision] * z0), $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z0, -255.0], t$95$2, If[LessEqual[z0, 90000000.0], N[(N[(t$95$1 * N[(t$95$0 / N[(N[(1.0 * N[Sinh[N[(1.0 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision], t$95$2]]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z0 < -255 or 9e7 < z0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. distribute-rgt-in N/A

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

      12. count-2 N/A

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

      13. associate-/r* N/A

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

      14. lower-/.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 58.8%

          \[\leadsto z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \color{blue}{\frac{z2}{\sinh \left(\frac{1}{z0}\right) \cdot e^{\frac{z4 \cdot z3}{z0}}}}\right) \]

   3. Applied rewrites 58.8%

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \frac{z2}{e^{\frac{z3 \cdot z4}{z0}} \cdot \sinh \left(\frac{1}{z0}\right)}\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/r* N/A

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

      8. associate-*l/ N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/r* N/A

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

      12. frac-times N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 N/A

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

   5. Applied rewrites 85.3%

      \[\leadsto z1 \cdot \color{blue}{\frac{\left(\frac{0.5}{z0} \cdot z2\right) \cdot \frac{-1}{\sinh \left(\frac{-1}{z0}\right)}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0}} \]

   6. Taylor expanded in z0 around inf

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

      1. lower-*.f64 78.2%

         \[\leadsto z1 \cdot \frac{0.5 \cdot \color{blue}{z2}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0} \]

   8. Applied rewrites 78.2%

      \[\leadsto z1 \cdot \frac{\color{blue}{0.5 \cdot z2}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0} \]

   if -255 < z0 < 9e7

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

   6. Applied rewrites 88.3%

      \[\leadsto \frac{z2 \cdot \frac{z1}{\left(\color{blue}{1} \cdot \sinh \left(\frac{1}{z0}\right)\right) \cdot \left(z0 + z0\right)}}{z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;z0 \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t\_0 \cdot \frac{0.5 \cdot t\_1}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 \cdot \frac{t\_0}{\left(e^{\frac{z3 \cdot z4}{z0}} \cdot \sinh \left(\frac{1}{z0}\right)\right) \cdot \left(z0 + z0\right)}}{z0}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= z0 -2e+45)
      (* t_0 (/ (* 0.5 t_1) (* (exp (/ (* z4 z3) z0)) z0)))
      (/
       (*
        t_1
        (/
         t_0
         (* (* (exp (/ (* z3 z4) z0)) (sinh (/ 1.0 z0))) (+ z0 z0))))
       z0))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double tmp;
	if (z0 <= -2e+45) {
		tmp = t_0 * ((0.5 * t_1) / (exp(((z4 * z3) / z0)) * z0));
	} else {
		tmp = (t_1 * (t_0 / ((exp(((z3 * z4) / z0)) * sinh((1.0 / z0))) * (z0 + z0)))) / z0;
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double tmp;
	if (z0 <= -2e+45) {
		tmp = t_0 * ((0.5 * t_1) / (Math.exp(((z4 * z3) / z0)) * z0));
	} else {
		tmp = (t_1 * (t_0 / ((Math.exp(((z3 * z4) / z0)) * Math.sinh((1.0 / z0))) * (z0 + z0)))) / z0;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	tmp = 0
	if z0 <= -2e+45:
		tmp = t_0 * ((0.5 * t_1) / (math.exp(((z4 * z3) / z0)) * z0))
	else:
		tmp = (t_1 * (t_0 / ((math.exp(((z3 * z4) / z0)) * math.sinh((1.0 / z0))) * (z0 + z0)))) / z0
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	tmp = 0.0
	if (z0 <= -2e+45)
		tmp = Float64(t_0 * Float64(Float64(0.5 * t_1) / Float64(exp(Float64(Float64(z4 * z3) / z0)) * z0)));
	else
		tmp = Float64(Float64(t_1 * Float64(t_0 / Float64(Float64(exp(Float64(Float64(z3 * z4) / z0)) * sinh(Float64(1.0 / z0))) * Float64(z0 + z0)))) / z0);
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	tmp = 0.0;
	if (z0 <= -2e+45)
		tmp = t_0 * ((0.5 * t_1) / (exp(((z4 * z3) / z0)) * z0));
	else
		tmp = (t_1 * (t_0 / ((exp(((z3 * z4) / z0)) * sinh((1.0 / z0))) * (z0 + z0)))) / z0;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z0, -2e+45], N[(t$95$0 * N[(N[(0.5 * t$95$1), $MachinePrecision] / N[(N[Exp[N[(N[(z4 * z3), $MachinePrecision] / z0), $MachinePrecision]], $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[(t$95$0 / N[(N[(N[Exp[N[(N[(z3 * z4), $MachinePrecision] / z0), $MachinePrecision]], $MachinePrecision] * N[Sinh[N[(1.0 / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z0 < -1.9999999999999999e45

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. distribute-rgt-in N/A

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

      12. count-2 N/A

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

      13. associate-/r* N/A

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

      14. lower-/.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 58.8%

          \[\leadsto z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \color{blue}{\frac{z2}{\sinh \left(\frac{1}{z0}\right) \cdot e^{\frac{z4 \cdot z3}{z0}}}}\right) \]

   3. Applied rewrites 58.8%

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \frac{z2}{e^{\frac{z3 \cdot z4}{z0}} \cdot \sinh \left(\frac{1}{z0}\right)}\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/r* N/A

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

      8. associate-*l/ N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/r* N/A

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

      12. frac-times N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 N/A

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

   5. Applied rewrites 85.3%

      \[\leadsto z1 \cdot \color{blue}{\frac{\left(\frac{0.5}{z0} \cdot z2\right) \cdot \frac{-1}{\sinh \left(\frac{-1}{z0}\right)}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0}} \]

   6. Taylor expanded in z0 around inf

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

      1. lower-*.f64 78.2%

         \[\leadsto z1 \cdot \frac{0.5 \cdot \color{blue}{z2}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0} \]

   8. Applied rewrites 78.2%

      \[\leadsto z1 \cdot \frac{\color{blue}{0.5 \cdot z2}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0} \]

   if -1.9999999999999999e45 < z0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

      \[\leadsto \color{blue}{\frac{z2 \cdot \frac{z1}{\left(e^{\frac{z3 \cdot z4}{z0}} \cdot \sinh \left(\frac{1}{z0}\right)\right) \cdot \left(z0 + z0\right)}}{z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ t_2 := t\_0 \cdot \frac{0.5 \cdot t\_1}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0}\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;z0 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z0 \leq -2.1 \cdot 10^{-153}:\\ \;\;\;\;\frac{t\_1 \cdot \frac{t\_0}{\frac{\left(z3 \cdot z4\right) \cdot z0 + \left(z0 \cdot z0\right) \cdot 1}{\left(z0 \cdot z0\right) \cdot z0} \cdot \left(z0 + z0\right)}}{z0}\\ \mathbf{elif}\;z0 \leq 1.28 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{\frac{t\_0}{\frac{z3 \cdot z4 + z0}{z0 \cdot z0}} \cdot t\_1}{z0 + z0}}{z0}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2)))
       (t_2 (* t_0 (/ (* 0.5 t_1) (* (exp (/ (* z4 z3) z0)) z0)))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= z0 -1e-100)
      t_2
      (if (<= z0 -2.1e-153)
        (/
         (*
          t_1
          (/
           t_0
           (*
            (/
             (+ (* (* z3 z4) z0) (* (* z0 z0) 1.0))
             (* (* z0 z0) z0))
            (+ z0 z0))))
         z0)
        (if (<= z0 1.28e-110)
          (/
           (/
            (* (/ t_0 (/ (+ (* z3 z4) z0) (* z0 z0))) t_1)
            (+ z0 z0))
           z0)
          t_2)))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double t_2 = t_0 * ((0.5 * t_1) / (exp(((z4 * z3) / z0)) * z0));
	double tmp;
	if (z0 <= -1e-100) {
		tmp = t_2;
	} else if (z0 <= -2.1e-153) {
		tmp = (t_1 * (t_0 / (((((z3 * z4) * z0) + ((z0 * z0) * 1.0)) / ((z0 * z0) * z0)) * (z0 + z0)))) / z0;
	} else if (z0 <= 1.28e-110) {
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	} else {
		tmp = t_2;
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double t_2 = t_0 * ((0.5 * t_1) / (Math.exp(((z4 * z3) / z0)) * z0));
	double tmp;
	if (z0 <= -1e-100) {
		tmp = t_2;
	} else if (z0 <= -2.1e-153) {
		tmp = (t_1 * (t_0 / (((((z3 * z4) * z0) + ((z0 * z0) * 1.0)) / ((z0 * z0) * z0)) * (z0 + z0)))) / z0;
	} else if (z0 <= 1.28e-110) {
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	} else {
		tmp = t_2;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	t_2 = t_0 * ((0.5 * t_1) / (math.exp(((z4 * z3) / z0)) * z0))
	tmp = 0
	if z0 <= -1e-100:
		tmp = t_2
	elif z0 <= -2.1e-153:
		tmp = (t_1 * (t_0 / (((((z3 * z4) * z0) + ((z0 * z0) * 1.0)) / ((z0 * z0) * z0)) * (z0 + z0)))) / z0
	elif z0 <= 1.28e-110:
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0
	else:
		tmp = t_2
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	t_2 = Float64(t_0 * Float64(Float64(0.5 * t_1) / Float64(exp(Float64(Float64(z4 * z3) / z0)) * z0)))
	tmp = 0.0
	if (z0 <= -1e-100)
		tmp = t_2;
	elseif (z0 <= -2.1e-153)
		tmp = Float64(Float64(t_1 * Float64(t_0 / Float64(Float64(Float64(Float64(Float64(z3 * z4) * z0) + Float64(Float64(z0 * z0) * 1.0)) / Float64(Float64(z0 * z0) * z0)) * Float64(z0 + z0)))) / z0);
	elseif (z0 <= 1.28e-110)
		tmp = Float64(Float64(Float64(Float64(t_0 / Float64(Float64(Float64(z3 * z4) + z0) / Float64(z0 * z0))) * t_1) / Float64(z0 + z0)) / z0);
	else
		tmp = t_2;
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	t_2 = t_0 * ((0.5 * t_1) / (exp(((z4 * z3) / z0)) * z0));
	tmp = 0.0;
	if (z0 <= -1e-100)
		tmp = t_2;
	elseif (z0 <= -2.1e-153)
		tmp = (t_1 * (t_0 / (((((z3 * z4) * z0) + ((z0 * z0) * 1.0)) / ((z0 * z0) * z0)) * (z0 + z0)))) / z0;
	elseif (z0 <= 1.28e-110)
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	else
		tmp = t_2;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * N[(N[(0.5 * t$95$1), $MachinePrecision] / N[(N[Exp[N[(N[(z4 * z3), $MachinePrecision] / z0), $MachinePrecision]], $MachinePrecision] * z0), $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z0, -1e-100], t$95$2, If[LessEqual[z0, -2.1e-153], N[(N[(t$95$1 * N[(t$95$0 / N[(N[(N[(N[(N[(z3 * z4), $MachinePrecision] * z0), $MachinePrecision] + N[(N[(z0 * z0), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision] / N[(N[(z0 * z0), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision] * N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision], If[LessEqual[z0, 1.28e-110], N[(N[(N[(N[(t$95$0 / N[(N[(N[(z3 * z4), $MachinePrecision] + z0), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(z0 + z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision], t$95$2]]]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -1e-100 or 1.2799999999999999e-110 < z0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. distribute-rgt-in N/A

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

      12. count-2 N/A

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

      13. associate-/r* N/A

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

      14. lower-/.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 58.8%

          \[\leadsto z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \color{blue}{\frac{z2}{\sinh \left(\frac{1}{z0}\right) \cdot e^{\frac{z4 \cdot z3}{z0}}}}\right) \]

   3. Applied rewrites 58.8%

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \frac{z2}{e^{\frac{z3 \cdot z4}{z0}} \cdot \sinh \left(\frac{1}{z0}\right)}\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/r* N/A

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

      8. associate-*l/ N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/r* N/A

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

      12. frac-times N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 N/A

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

   5. Applied rewrites 85.3%

      \[\leadsto z1 \cdot \color{blue}{\frac{\left(\frac{0.5}{z0} \cdot z2\right) \cdot \frac{-1}{\sinh \left(\frac{-1}{z0}\right)}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0}} \]

   6. Taylor expanded in z0 around inf

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

      1. lower-*.f64 78.2%

         \[\leadsto z1 \cdot \frac{0.5 \cdot \color{blue}{z2}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0} \]

   8. Applied rewrites 78.2%

      \[\leadsto z1 \cdot \frac{\color{blue}{0.5 \cdot z2}}{e^{\frac{z4 \cdot z3}{z0}} \cdot z0} \]

   if -1e-100 < z0 < -2.1e-153

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. frac-add N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 38.1%

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

   8. Applied rewrites 38.1%

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

   if -2.1e-153 < z0 < 1.2799999999999999e-110

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}}}{z0 + z0}} \cdot z2}{z0} \]

      6. associate-*l/ N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}} \cdot z2}{z0 + z0}}}{z0} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}} \cdot z2}{z0 + z0}}}{z0} \]

   8. Applied rewrites 50.8%

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

Alternative 5: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;z0 \leq -2 \cdot 10^{+78}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z0 + z0}\\ \mathbf{elif}\;z0 \leq -2.1 \cdot 10^{-153}:\\ \;\;\;\;\frac{t\_1 \cdot \frac{t\_0}{\frac{\left(z3 \cdot z4\right) \cdot z0 + \left(z0 \cdot z0\right) \cdot 1}{\left(z0 \cdot z0\right) \cdot z0} \cdot \left(z0 + z0\right)}}{z0}\\ \mathbf{elif}\;z0 \leq 4.9 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{\frac{t\_0}{\frac{z3 \cdot z4 + z0}{z0 \cdot z0}} \cdot t\_1}{z0 + z0}}{z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 \cdot \frac{t\_0}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= z0 -2e+78)
      (* t_0 (/ t_1 (+ z0 z0)))
      (if (<= z0 -2.1e-153)
        (/
         (*
          t_1
          (/
           t_0
           (*
            (/
             (+ (* (* z3 z4) z0) (* (* z0 z0) 1.0))
             (* (* z0 z0) z0))
            (+ z0 z0))))
         z0)
        (if (<= z0 4.9e-86)
          (/
           (/
            (* (/ t_0 (/ (+ (* z3 z4) z0) (* z0 z0))) t_1)
            (+ z0 z0))
           z0)
          (/
           (* t_1 (/ t_0 (+ 2.0 (* 2.0 (/ (* z3 z4) z0)))))
           z0))))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double tmp;
	if (z0 <= -2e+78) {
		tmp = t_0 * (t_1 / (z0 + z0));
	} else if (z0 <= -2.1e-153) {
		tmp = (t_1 * (t_0 / (((((z3 * z4) * z0) + ((z0 * z0) * 1.0)) / ((z0 * z0) * z0)) * (z0 + z0)))) / z0;
	} else if (z0 <= 4.9e-86) {
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	} else {
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double tmp;
	if (z0 <= -2e+78) {
		tmp = t_0 * (t_1 / (z0 + z0));
	} else if (z0 <= -2.1e-153) {
		tmp = (t_1 * (t_0 / (((((z3 * z4) * z0) + ((z0 * z0) * 1.0)) / ((z0 * z0) * z0)) * (z0 + z0)))) / z0;
	} else if (z0 <= 4.9e-86) {
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	} else {
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	tmp = 0
	if z0 <= -2e+78:
		tmp = t_0 * (t_1 / (z0 + z0))
	elif z0 <= -2.1e-153:
		tmp = (t_1 * (t_0 / (((((z3 * z4) * z0) + ((z0 * z0) * 1.0)) / ((z0 * z0) * z0)) * (z0 + z0)))) / z0
	elif z0 <= 4.9e-86:
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0
	else:
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	tmp = 0.0
	if (z0 <= -2e+78)
		tmp = Float64(t_0 * Float64(t_1 / Float64(z0 + z0)));
	elseif (z0 <= -2.1e-153)
		tmp = Float64(Float64(t_1 * Float64(t_0 / Float64(Float64(Float64(Float64(Float64(z3 * z4) * z0) + Float64(Float64(z0 * z0) * 1.0)) / Float64(Float64(z0 * z0) * z0)) * Float64(z0 + z0)))) / z0);
	elseif (z0 <= 4.9e-86)
		tmp = Float64(Float64(Float64(Float64(t_0 / Float64(Float64(Float64(z3 * z4) + z0) / Float64(z0 * z0))) * t_1) / Float64(z0 + z0)) / z0);
	else
		tmp = Float64(Float64(t_1 * Float64(t_0 / Float64(2.0 + Float64(2.0 * Float64(Float64(z3 * z4) / z0))))) / z0);
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	tmp = 0.0;
	if (z0 <= -2e+78)
		tmp = t_0 * (t_1 / (z0 + z0));
	elseif (z0 <= -2.1e-153)
		tmp = (t_1 * (t_0 / (((((z3 * z4) * z0) + ((z0 * z0) * 1.0)) / ((z0 * z0) * z0)) * (z0 + z0)))) / z0;
	elseif (z0 <= 4.9e-86)
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	else
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z0, -2e+78], N[(t$95$0 * N[(t$95$1 / N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, -2.1e-153], N[(N[(t$95$1 * N[(t$95$0 / N[(N[(N[(N[(N[(z3 * z4), $MachinePrecision] * z0), $MachinePrecision] + N[(N[(z0 * z0), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision] / N[(N[(z0 * z0), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision] * N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision], If[LessEqual[z0, 4.9e-86], N[(N[(N[(N[(t$95$0 / N[(N[(N[(z3 * z4), $MachinePrecision] + z0), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(z0 + z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision], N[(N[(t$95$1 * N[(t$95$0 / N[(2.0 + N[(2.0 * N[(N[(z3 * z4), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if z0 < -2e78

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

      3. lower-*.f64 51.5%

         \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. frac-times N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. count-2 N/A

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

      13. lift-+.f64 N/A

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

      14. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0} + z0} \]

      16. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      17. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      18. lower-/.f64 49.0%

          \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

   6. Applied rewrites 49.0%

      \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

   if -2e78 < z0 < -2.1e-153

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l/ N/A

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

      7. lift-*.f64 N/A

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

      8. frac-add N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 38.1%

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

   8. Applied rewrites 38.1%

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

   if -2.1e-153 < z0 < 4.8999999999999997e-86

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}}}{z0 + z0}} \cdot z2}{z0} \]

      6. associate-*l/ N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}} \cdot z2}{z0 + z0}}}{z0} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}} \cdot z2}{z0 + z0}}}{z0} \]

   8. Applied rewrites 50.8%

      \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{z3 \cdot z4 + z0}{z0 \cdot z0}} \cdot z2}{z0 + z0}}}{z0} \]

   if 4.8999999999999997e-86 < z0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + \color{blue}{2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \color{blue}{\frac{z3 \cdot z4}{z0}}}}{z0} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{\color{blue}{z0}}}}{z0} \]

      4. lower-*.f64 66.2%

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0} \]

   6. Applied rewrites 66.2%

      \[\leadsto \frac{z2 \cdot \frac{z1}{\color{blue}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 80.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ t_2 := \frac{z3 \cdot z4 + z0}{z0 \cdot z0}\\ t_3 := \frac{\frac{t\_0}{t\_2} \cdot t\_1}{\left(z0 + z0\right) \cdot z0}\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;z0 \leq -2 \cdot 10^{+78}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z0 + z0}\\ \mathbf{elif}\;z0 \leq -1.4 \cdot 10^{-148}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z0 \leq 10^{-162}:\\ \;\;\;\;\frac{t\_0}{\left(t\_2 \cdot \left(z0 + z0\right)\right) \cdot z0} \cdot t\_1\\ \mathbf{elif}\;z0 \leq 5 \cdot 10^{-48}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 \cdot \frac{t\_0}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2)))
       (t_2 (/ (+ (* z3 z4) z0) (* z0 z0)))
       (t_3 (/ (* (/ t_0 t_2) t_1) (* (+ z0 z0) z0))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= z0 -2e+78)
      (* t_0 (/ t_1 (+ z0 z0)))
      (if (<= z0 -1.4e-148)
        t_3
        (if (<= z0 1e-162)
          (* (/ t_0 (* (* t_2 (+ z0 z0)) z0)) t_1)
          (if (<= z0 5e-48)
            t_3
            (/
             (* t_1 (/ t_0 (+ 2.0 (* 2.0 (/ (* z3 z4) z0)))))
             z0)))))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double t_2 = ((z3 * z4) + z0) / (z0 * z0);
	double t_3 = ((t_0 / t_2) * t_1) / ((z0 + z0) * z0);
	double tmp;
	if (z0 <= -2e+78) {
		tmp = t_0 * (t_1 / (z0 + z0));
	} else if (z0 <= -1.4e-148) {
		tmp = t_3;
	} else if (z0 <= 1e-162) {
		tmp = (t_0 / ((t_2 * (z0 + z0)) * z0)) * t_1;
	} else if (z0 <= 5e-48) {
		tmp = t_3;
	} else {
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double t_2 = ((z3 * z4) + z0) / (z0 * z0);
	double t_3 = ((t_0 / t_2) * t_1) / ((z0 + z0) * z0);
	double tmp;
	if (z0 <= -2e+78) {
		tmp = t_0 * (t_1 / (z0 + z0));
	} else if (z0 <= -1.4e-148) {
		tmp = t_3;
	} else if (z0 <= 1e-162) {
		tmp = (t_0 / ((t_2 * (z0 + z0)) * z0)) * t_1;
	} else if (z0 <= 5e-48) {
		tmp = t_3;
	} else {
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	t_2 = ((z3 * z4) + z0) / (z0 * z0)
	t_3 = ((t_0 / t_2) * t_1) / ((z0 + z0) * z0)
	tmp = 0
	if z0 <= -2e+78:
		tmp = t_0 * (t_1 / (z0 + z0))
	elif z0 <= -1.4e-148:
		tmp = t_3
	elif z0 <= 1e-162:
		tmp = (t_0 / ((t_2 * (z0 + z0)) * z0)) * t_1
	elif z0 <= 5e-48:
		tmp = t_3
	else:
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	t_2 = Float64(Float64(Float64(z3 * z4) + z0) / Float64(z0 * z0))
	t_3 = Float64(Float64(Float64(t_0 / t_2) * t_1) / Float64(Float64(z0 + z0) * z0))
	tmp = 0.0
	if (z0 <= -2e+78)
		tmp = Float64(t_0 * Float64(t_1 / Float64(z0 + z0)));
	elseif (z0 <= -1.4e-148)
		tmp = t_3;
	elseif (z0 <= 1e-162)
		tmp = Float64(Float64(t_0 / Float64(Float64(t_2 * Float64(z0 + z0)) * z0)) * t_1);
	elseif (z0 <= 5e-48)
		tmp = t_3;
	else
		tmp = Float64(Float64(t_1 * Float64(t_0 / Float64(2.0 + Float64(2.0 * Float64(Float64(z3 * z4) / z0))))) / z0);
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	t_2 = ((z3 * z4) + z0) / (z0 * z0);
	t_3 = ((t_0 / t_2) * t_1) / ((z0 + z0) * z0);
	tmp = 0.0;
	if (z0 <= -2e+78)
		tmp = t_0 * (t_1 / (z0 + z0));
	elseif (z0 <= -1.4e-148)
		tmp = t_3;
	elseif (z0 <= 1e-162)
		tmp = (t_0 / ((t_2 * (z0 + z0)) * z0)) * t_1;
	elseif (z0 <= 5e-48)
		tmp = t_3;
	else
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z3 * z4), $MachinePrecision] + z0), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 / t$95$2), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(N[(z0 + z0), $MachinePrecision] * 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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z0, -2e+78], N[(t$95$0 * N[(t$95$1 / N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, -1.4e-148], t$95$3, If[LessEqual[z0, 1e-162], N[(N[(t$95$0 / N[(N[(t$95$2 * N[(z0 + z0), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[z0, 5e-48], t$95$3, N[(N[(t$95$1 * N[(t$95$0 / N[(2.0 + N[(2.0 * N[(N[(z3 * z4), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]]]]]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z0 < -2e78

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

      3. lower-*.f64 51.5%

         \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. frac-times N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. count-2 N/A

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

      13. lift-+.f64 N/A

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

      14. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0} + z0} \]

      16. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      17. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      18. lower-/.f64 49.0%

          \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

   6. Applied rewrites 49.0%

      \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

   if -2e78 < z0 < -1.4e-148 or 9.9999999999999995e-163 < z0 < 4.9999999999999999e-48

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}}}{z0 + z0}} \cdot \frac{z2}{z0} \]

   8. Applied rewrites 31.1%

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

   if -1.4e-148 < z0 < 9.9999999999999995e-163

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 50.5%

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

   if 4.9999999999999999e-48 < z0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + \color{blue}{2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \color{blue}{\frac{z3 \cdot z4}{z0}}}}{z0} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{\color{blue}{z0}}}}{z0} \]

      4. lower-*.f64 66.2%

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0} \]

   6. Applied rewrites 66.2%

      \[\leadsto \frac{z2 \cdot \frac{z1}{\color{blue}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 80.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;z0 \leq -2 \cdot 10^{+78}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z0 + z0}\\ \mathbf{elif}\;z0 \leq 4.9 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{\frac{t\_0}{\frac{z3 \cdot z4 + z0}{z0 \cdot z0}} \cdot t\_1}{z0 + z0}}{z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 \cdot \frac{t\_0}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= z0 -2e+78)
      (* t_0 (/ t_1 (+ z0 z0)))
      (if (<= z0 4.9e-86)
        (/
         (/ (* (/ t_0 (/ (+ (* z3 z4) z0) (* z0 z0))) t_1) (+ z0 z0))
         z0)
        (/ (* t_1 (/ t_0 (+ 2.0 (* 2.0 (/ (* z3 z4) z0))))) z0)))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double tmp;
	if (z0 <= -2e+78) {
		tmp = t_0 * (t_1 / (z0 + z0));
	} else if (z0 <= 4.9e-86) {
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	} else {
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double tmp;
	if (z0 <= -2e+78) {
		tmp = t_0 * (t_1 / (z0 + z0));
	} else if (z0 <= 4.9e-86) {
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	} else {
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	tmp = 0
	if z0 <= -2e+78:
		tmp = t_0 * (t_1 / (z0 + z0))
	elif z0 <= 4.9e-86:
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0
	else:
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	tmp = 0.0
	if (z0 <= -2e+78)
		tmp = Float64(t_0 * Float64(t_1 / Float64(z0 + z0)));
	elseif (z0 <= 4.9e-86)
		tmp = Float64(Float64(Float64(Float64(t_0 / Float64(Float64(Float64(z3 * z4) + z0) / Float64(z0 * z0))) * t_1) / Float64(z0 + z0)) / z0);
	else
		tmp = Float64(Float64(t_1 * Float64(t_0 / Float64(2.0 + Float64(2.0 * Float64(Float64(z3 * z4) / z0))))) / z0);
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	tmp = 0.0;
	if (z0 <= -2e+78)
		tmp = t_0 * (t_1 / (z0 + z0));
	elseif (z0 <= 4.9e-86)
		tmp = (((t_0 / (((z3 * z4) + z0) / (z0 * z0))) * t_1) / (z0 + z0)) / z0;
	else
		tmp = (t_1 * (t_0 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z0, -2e+78], N[(t$95$0 * N[(t$95$1 / N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 4.9e-86], N[(N[(N[(N[(t$95$0 / N[(N[(N[(z3 * z4), $MachinePrecision] + z0), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(z0 + z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision], N[(N[(t$95$1 * N[(t$95$0 / N[(2.0 + N[(2.0 * N[(N[(z3 * z4), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -2e78

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

      3. lower-*.f64 51.5%

         \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. frac-times N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. count-2 N/A

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

      13. lift-+.f64 N/A

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

      14. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0} + z0} \]

      16. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      17. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      18. lower-/.f64 49.0%

          \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

   6. Applied rewrites 49.0%

      \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

   if -2e78 < z0 < 4.8999999999999997e-86

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}}}{z0 + z0}} \cdot z2}{z0} \]

      6. associate-*l/ N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}} \cdot z2}{z0 + z0}}}{z0} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{1 + \frac{z3 \cdot z4}{z0}}{z0}} \cdot z2}{z0 + z0}}}{z0} \]

   8. Applied rewrites 50.8%

      \[\leadsto \frac{\color{blue}{\frac{\frac{z1}{\frac{z3 \cdot z4 + z0}{z0 \cdot z0}} \cdot z2}{z0 + z0}}}{z0} \]

   if 4.8999999999999997e-86 < z0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + \color{blue}{2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \color{blue}{\frac{z3 \cdot z4}{z0}}}}{z0} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{\color{blue}{z0}}}}{z0} \]

      4. lower-*.f64 66.2%

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0} \]

   6. Applied rewrites 66.2%

      \[\leadsto \frac{z2 \cdot \frac{z1}{\color{blue}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 77.0% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z0 (+.f64 z0 z0)) (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z0)) (exp.f64 (/.f64 (*.f64 z4 z3) z0)))) < +inf.0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

   if +inf.0 < (*.f64 (*.f64 z0 (+.f64 z0 z0)) (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z0)) (exp.f64 (/.f64 (*.f64 z4 z3) z0))))

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 50.5%

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

Alternative 9: 76.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\left|z1\right|, z2\right)\\ t_1 := \mathsf{min}\left(\left|z1\right|, z2\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{t\_1 \cdot t\_0}{\left(z0 \cdot \left(z0 + z0\right)\right) \cdot \left(\sinh \left(\frac{1}{z0}\right) \cdot e^{\frac{z4 \cdot z3}{z0}}\right)} \leq 10^{+222}:\\ \;\;\;\;\frac{t\_0 \cdot \frac{t\_1}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(\frac{z3 \cdot z4 + z0}{z0 \cdot z0} \cdot \left(z0 + z0\right)\right) \cdot z0} \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmax (fabs z1) z2)) (t_1 (fmin (fabs z1) z2)))
  (*
   (copysign 1.0 z1)
   (if (<=
        (/
         (* t_1 t_0)
         (*
          (* z0 (+ z0 z0))
          (* (sinh (/ 1.0 z0)) (exp (/ (* z4 z3) z0)))))
        1e+222)
     (/ (* t_0 (/ t_1 (+ 2.0 (* 2.0 (/ (* z3 z4) z0))))) z0)
     (*
      (/ t_1 (* (* (/ (+ (* z3 z4) z0) (* z0 z0)) (+ z0 z0)) z0))
      t_0)))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmax(fabs(z1), z2);
	double t_1 = fmin(fabs(z1), z2);
	double tmp;
	if (((t_1 * t_0) / ((z0 * (z0 + z0)) * (sinh((1.0 / z0)) * exp(((z4 * z3) / z0))))) <= 1e+222) {
		tmp = (t_0 * (t_1 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	} else {
		tmp = (t_1 / (((((z3 * z4) + z0) / (z0 * z0)) * (z0 + z0)) * z0)) * t_0;
	}
	return copysign(1.0, z1) * tmp;
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmax(Math.abs(z1), z2);
	double t_1 = fmin(Math.abs(z1), z2);
	double tmp;
	if (((t_1 * t_0) / ((z0 * (z0 + z0)) * (Math.sinh((1.0 / z0)) * Math.exp(((z4 * z3) / z0))))) <= 1e+222) {
		tmp = (t_0 * (t_1 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	} else {
		tmp = (t_1 / (((((z3 * z4) + z0) / (z0 * z0)) * (z0 + z0)) * z0)) * t_0;
	}
	return Math.copySign(1.0, z1) * tmp;
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmax(math.fabs(z1), z2)
	t_1 = fmin(math.fabs(z1), z2)
	tmp = 0
	if ((t_1 * t_0) / ((z0 * (z0 + z0)) * (math.sinh((1.0 / z0)) * math.exp(((z4 * z3) / z0))))) <= 1e+222:
		tmp = (t_0 * (t_1 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0
	else:
		tmp = (t_1 / (((((z3 * z4) + z0) / (z0 * z0)) * (z0 + z0)) * z0)) * t_0
	return math.copysign(1.0, z1) * tmp

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmax(abs(z1), z2)
	t_1 = fmin(abs(z1), z2)
	tmp = 0.0
	if (Float64(Float64(t_1 * t_0) / Float64(Float64(z0 * Float64(z0 + z0)) * Float64(sinh(Float64(1.0 / z0)) * exp(Float64(Float64(z4 * z3) / z0))))) <= 1e+222)
		tmp = Float64(Float64(t_0 * Float64(t_1 / Float64(2.0 + Float64(2.0 * Float64(Float64(z3 * z4) / z0))))) / z0);
	else
		tmp = Float64(Float64(t_1 / Float64(Float64(Float64(Float64(Float64(z3 * z4) + z0) / Float64(z0 * z0)) * Float64(z0 + z0)) * z0)) * t_0);
	end
	return Float64(copysign(1.0, z1) * tmp)
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = max(abs(z1), z2);
	t_1 = min(abs(z1), z2);
	tmp = 0.0;
	if (((t_1 * t_0) / ((z0 * (z0 + z0)) * (sinh((1.0 / z0)) * exp(((z4 * z3) / z0))))) <= 1e+222)
		tmp = (t_0 * (t_1 / (2.0 + (2.0 * ((z3 * z4) / z0))))) / z0;
	else
		tmp = (t_1 / (((((z3 * z4) + z0) / (z0 * z0)) * (z0 + z0)) * z0)) * t_0;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * tmp;
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Max[N[Abs[z1], $MachinePrecision], z2], $MachinePrecision]}, Block[{t$95$1 = N[Min[N[Abs[z1], $MachinePrecision], z2], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[(t$95$1 * t$95$0), $MachinePrecision] / N[(N[(z0 * N[(z0 + z0), $MachinePrecision]), $MachinePrecision] * N[(N[Sinh[N[(1.0 / z0), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(N[(z4 * z3), $MachinePrecision] / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+222], N[(N[(t$95$0 * N[(t$95$1 / N[(2.0 + N[(2.0 * N[(N[(z3 * z4), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision], N[(N[(t$95$1 / N[(N[(N[(N[(N[(z3 * z4), $MachinePrecision] + z0), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision] * N[(z0 + z0), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z1 z2) (*.f64 (*.f64 z0 (+.f64 z0 z0)) (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z0)) (exp.f64 (/.f64 (*.f64 z4 z3) z0))))) < 1e222

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + \color{blue}{2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \color{blue}{\frac{z3 \cdot z4}{z0}}}}{z0} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{\color{blue}{z0}}}}{z0} \]

      4. lower-*.f64 66.2%

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0} \]

   6. Applied rewrites 66.2%

      \[\leadsto \frac{z2 \cdot \frac{z1}{\color{blue}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]

   if 1e222 < (/.f64 (*.f64 z1 z2) (*.f64 (*.f64 z0 (+.f64 z0 z0)) (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z0)) (exp.f64 (/.f64 (*.f64 z4 z3) z0)))))

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.9%

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

   6. Applied rewrites 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 50.5%

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

Alternative 10: 69.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z0 (+.f64 z0 z0)) (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z0)) (exp.f64 (/.f64 (*.f64 z4 z3) z0)))) < +inf.0

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z0 around inf

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

      1. lower-+.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + \color{blue}{2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \color{blue}{\frac{z3 \cdot z4}{z0}}}}{z0} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{\color{blue}{z0}}}}{z0} \]

      4. lower-*.f64 66.2%

         \[\leadsto \frac{z2 \cdot \frac{z1}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}{z0} \]

   6. Applied rewrites 66.2%

      \[\leadsto \frac{z2 \cdot \frac{z1}{\color{blue}{2 + 2 \cdot \frac{z3 \cdot z4}{z0}}}}{z0} \]

   if +inf.0 < (*.f64 (*.f64 z0 (+.f64 z0 z0)) (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z0)) (exp.f64 (/.f64 (*.f64 z4 z3) z0))))

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

   5. Applied rewrites 82.7%

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

   6. Taylor expanded in z0 around inf

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

      1. lower-*.f64 48.0%

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

   8. Applied rewrites 48.0%

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

Alternative 11: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;z0 \leq -5 \cdot 10^{+27}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z0 + z0}\\ \mathbf{elif}\;z0 \leq 50000000:\\ \;\;\;\;\frac{\frac{\left(z0 \cdot t\_0\right) \cdot t\_1}{z0 + z0}}{z0}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{1}{\frac{z0 + z0}{t\_1}}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= z0 -5e+27)
      (* t_0 (/ t_1 (+ z0 z0)))
      (if (<= z0 50000000.0)
        (/ (/ (* (* z0 t_0) t_1) (+ z0 z0)) z0)
        (* t_0 (/ 1.0 (/ (+ z0 z0) t_1)))))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double tmp;
	if (z0 <= -5e+27) {
		tmp = t_0 * (t_1 / (z0 + z0));
	} else if (z0 <= 50000000.0) {
		tmp = (((z0 * t_0) * t_1) / (z0 + z0)) / z0;
	} else {
		tmp = t_0 * (1.0 / ((z0 + z0) / t_1));
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double tmp;
	if (z0 <= -5e+27) {
		tmp = t_0 * (t_1 / (z0 + z0));
	} else if (z0 <= 50000000.0) {
		tmp = (((z0 * t_0) * t_1) / (z0 + z0)) / z0;
	} else {
		tmp = t_0 * (1.0 / ((z0 + z0) / t_1));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	tmp = 0
	if z0 <= -5e+27:
		tmp = t_0 * (t_1 / (z0 + z0))
	elif z0 <= 50000000.0:
		tmp = (((z0 * t_0) * t_1) / (z0 + z0)) / z0
	else:
		tmp = t_0 * (1.0 / ((z0 + z0) / t_1))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	tmp = 0.0
	if (z0 <= -5e+27)
		tmp = Float64(t_0 * Float64(t_1 / Float64(z0 + z0)));
	elseif (z0 <= 50000000.0)
		tmp = Float64(Float64(Float64(Float64(z0 * t_0) * t_1) / Float64(z0 + z0)) / z0);
	else
		tmp = Float64(t_0 * Float64(1.0 / Float64(Float64(z0 + z0) / t_1)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	tmp = 0.0;
	if (z0 <= -5e+27)
		tmp = t_0 * (t_1 / (z0 + z0));
	elseif (z0 <= 50000000.0)
		tmp = (((z0 * t_0) * t_1) / (z0 + z0)) / z0;
	else
		tmp = t_0 * (1.0 / ((z0 + z0) / t_1));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[z0, -5e+27], N[(t$95$0 * N[(t$95$1 / N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z0, 50000000.0], N[(N[(N[(N[(z0 * t$95$0), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(z0 + z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision], N[(t$95$0 * N[(1.0 / N[(N[(z0 + z0), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z0 < -4.9999999999999998e27

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

      3. lower-*.f64 51.5%

         \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. frac-times N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. count-2 N/A

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

      13. lift-+.f64 N/A

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

      14. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0} + z0} \]

      16. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      17. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      18. lower-/.f64 49.0%

          \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

   6. Applied rewrites 49.0%

      \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

   if -4.9999999999999998e27 < z0 < 5e7

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

   5. Applied rewrites 82.7%

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

   6. Taylor expanded in z0 around inf

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

      1. lower-*.f64 48.0%

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

   8. Applied rewrites 48.0%

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

   if 5e7 < z0

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

      3. lower-*.f64 51.5%

         \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. frac-times N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. count-2 N/A

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

      13. lift-+.f64 N/A

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

      14. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0} + z0} \]

      16. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      17. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      18. lower-/.f64 49.0%

          \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

   6. Applied rewrites 49.0%

      \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

      2. div-flip N/A

         \[\leadsto z1 \cdot \frac{1}{\color{blue}{\frac{z0 + z0}{z2}}} \]

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

         \[\leadsto z1 \cdot \frac{1}{\color{blue}{\frac{z0 + z0}{z2}}} \]

      4. lower-unsound-/.f64 48.6%

         \[\leadsto z1 \cdot \frac{1}{\frac{z0 + z0}{\color{blue}{z2}}} \]

   8. Applied rewrites 48.6%

      \[\leadsto z1 \cdot \frac{1}{\color{blue}{\frac{z0 + z0}{z2}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ t_2 := t\_0 \cdot t\_1\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{t\_2}{\left(z0 \cdot \left(z0 + z0\right)\right) \cdot \left(\sinh \left(\frac{1}{z0}\right) \cdot e^{\frac{z4 \cdot z3}{z0}}\right)} \leq 2 \cdot 10^{+237}:\\ \;\;\;\;\frac{t\_2}{z0 \cdot \left(2 + 2 \cdot \frac{z3 \cdot z4}{z0}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(z0 \cdot t\_0\right) \cdot t\_1}{z0 + z0}}{z0}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2)))
       (t_2 (* t_0 t_1)))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<=
         (/
          t_2
          (*
           (* z0 (+ z0 z0))
           (* (sinh (/ 1.0 z0)) (exp (/ (* z4 z3) z0)))))
         2e+237)
      (/ t_2 (* z0 (+ 2.0 (* 2.0 (/ (* z3 z4) z0)))))
      (/ (/ (* (* z0 t_0) t_1) (+ z0 z0)) z0))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double t_2 = t_0 * t_1;
	double tmp;
	if ((t_2 / ((z0 * (z0 + z0)) * (sinh((1.0 / z0)) * exp(((z4 * z3) / z0))))) <= 2e+237) {
		tmp = t_2 / (z0 * (2.0 + (2.0 * ((z3 * z4) / z0))));
	} else {
		tmp = (((z0 * t_0) * t_1) / (z0 + z0)) / z0;
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double t_2 = t_0 * t_1;
	double tmp;
	if ((t_2 / ((z0 * (z0 + z0)) * (Math.sinh((1.0 / z0)) * Math.exp(((z4 * z3) / z0))))) <= 2e+237) {
		tmp = t_2 / (z0 * (2.0 + (2.0 * ((z3 * z4) / z0))));
	} else {
		tmp = (((z0 * t_0) * t_1) / (z0 + z0)) / z0;
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	t_2 = t_0 * t_1
	tmp = 0
	if (t_2 / ((z0 * (z0 + z0)) * (math.sinh((1.0 / z0)) * math.exp(((z4 * z3) / z0))))) <= 2e+237:
		tmp = t_2 / (z0 * (2.0 + (2.0 * ((z3 * z4) / z0))))
	else:
		tmp = (((z0 * t_0) * t_1) / (z0 + z0)) / z0
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	t_2 = Float64(t_0 * t_1)
	tmp = 0.0
	if (Float64(t_2 / Float64(Float64(z0 * Float64(z0 + z0)) * Float64(sinh(Float64(1.0 / z0)) * exp(Float64(Float64(z4 * z3) / z0))))) <= 2e+237)
		tmp = Float64(t_2 / Float64(z0 * Float64(2.0 + Float64(2.0 * Float64(Float64(z3 * z4) / z0)))));
	else
		tmp = Float64(Float64(Float64(Float64(z0 * t_0) * t_1) / Float64(z0 + z0)) / z0);
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	t_2 = t_0 * t_1;
	tmp = 0.0;
	if ((t_2 / ((z0 * (z0 + z0)) * (sinh((1.0 / z0)) * exp(((z4 * z3) / z0))))) <= 2e+237)
		tmp = t_2 / (z0 * (2.0 + (2.0 * ((z3 * z4) / z0))));
	else
		tmp = (((z0 * t_0) * t_1) / (z0 + z0)) / z0;
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * t$95$1), $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(t$95$2 / N[(N[(z0 * N[(z0 + z0), $MachinePrecision]), $MachinePrecision] * N[(N[Sinh[N[(1.0 / z0), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(N[(z4 * z3), $MachinePrecision] / z0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+237], N[(t$95$2 / N[(z0 * N[(2.0 + N[(2.0 * N[(N[(z3 * z4), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z0 * t$95$0), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(z0 + z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z1 z2) (*.f64 (*.f64 z0 (+.f64 z0 z0)) (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z0)) (exp.f64 (/.f64 (*.f64 z4 z3) z0))))) < 1.9999999999999999e237

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 62.4%

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

   4. Applied rewrites 62.4%

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

   if 1.9999999999999999e237 < (/.f64 (*.f64 z1 z2) (*.f64 (*.f64 z0 (+.f64 z0 z0)) (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z0)) (exp.f64 (/.f64 (*.f64 z4 z3) z0)))))

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. times-frac N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 95.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

   5. Applied rewrites 82.7%

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

   6. Taylor expanded in z0 around inf

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

      1. lower-*.f64 48.0%

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

   8. Applied rewrites 48.0%

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

Alternative 13: 54.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 7.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{0.5}{z0 \cdot z0} \cdot \left(\left(t\_1 \cdot z0\right) \cdot t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z0 + z0}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z2)))
       (t_1 (fmax (fabs z1) (fabs z2))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= t_1 7.5e-77)
      (* (/ 0.5 (* z0 z0)) (* (* t_1 z0) t_0))
      (* t_0 (/ t_1 (+ z0 z0))))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(fabs(z1), fabs(z2));
	double t_1 = fmax(fabs(z1), fabs(z2));
	double tmp;
	if (t_1 <= 7.5e-77) {
		tmp = (0.5 / (z0 * z0)) * ((t_1 * z0) * t_0);
	} else {
		tmp = t_0 * (t_1 / (z0 + z0));
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z2));
	double t_1 = fmax(Math.abs(z1), Math.abs(z2));
	double tmp;
	if (t_1 <= 7.5e-77) {
		tmp = (0.5 / (z0 * z0)) * ((t_1 * z0) * t_0);
	} else {
		tmp = t_0 * (t_1 / (z0 + z0));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmin(math.fabs(z1), math.fabs(z2))
	t_1 = fmax(math.fabs(z1), math.fabs(z2))
	tmp = 0
	if t_1 <= 7.5e-77:
		tmp = (0.5 / (z0 * z0)) * ((t_1 * z0) * t_0)
	else:
		tmp = t_0 * (t_1 / (z0 + z0))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmin(abs(z1), abs(z2))
	t_1 = fmax(abs(z1), abs(z2))
	tmp = 0.0
	if (t_1 <= 7.5e-77)
		tmp = Float64(Float64(0.5 / Float64(z0 * z0)) * Float64(Float64(t_1 * z0) * t_0));
	else
		tmp = Float64(t_0 * Float64(t_1 / Float64(z0 + z0)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = min(abs(z1), abs(z2));
	t_1 = max(abs(z1), abs(z2));
	tmp = 0.0;
	if (t_1 <= 7.5e-77)
		tmp = (0.5 / (z0 * z0)) * ((t_1 * z0) * t_0);
	else
		tmp = t_0 * (t_1 / (z0 + z0));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, 7.5e-77], N[(N[(0.5 / N[(z0 * z0), $MachinePrecision]), $MachinePrecision] * N[(N[(t$95$1 * z0), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$1 / N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z2 < 7.5000000000000006e-77

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. distribute-rgt-in N/A

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

      12. count-2 N/A

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

      13. associate-/r* N/A

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

      14. lower-/.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 58.8%

          \[\leadsto z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \color{blue}{\frac{z2}{\sinh \left(\frac{1}{z0}\right) \cdot e^{\frac{z4 \cdot z3}{z0}}}}\right) \]

   3. Applied rewrites 58.8%

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \frac{z2}{e^{\frac{z3 \cdot z4}{z0}} \cdot \sinh \left(\frac{1}{z0}\right)}\right)} \]

   4. Taylor expanded in z0 around inf

      \[\leadsto z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \color{blue}{\left(z0 \cdot z2\right)}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 33.8%

         \[\leadsto z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \left(z0 \cdot \color{blue}{z2}\right)\right) \]

   6. Applied rewrites 33.8%

      \[\leadsto z1 \cdot \left(\frac{0.5}{z0 \cdot z0} \cdot \color{blue}{\left(z0 \cdot z2\right)}\right) \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. metadata-eval N/A

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

      5. associate-/r* N/A

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

      6. count-2 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. count-2 N/A

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

      11. associate-/r* N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 34.1%

          \[\leadsto z1 \cdot \left(\frac{\color{blue}{\frac{0.5}{z0}}}{z0} \cdot \left(z0 \cdot z2\right)\right) \]

   8. Applied rewrites 34.1%

      \[\leadsto z1 \cdot \left(\color{blue}{\frac{\frac{0.5}{z0}}{z0}} \cdot \left(z0 \cdot z2\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. associate-/l/ N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 33.9%

          \[\leadsto \frac{0.5}{z0 \cdot z0} \cdot \color{blue}{\left(\left(z0 \cdot z2\right) \cdot z1\right)} \]

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 33.9%

          \[\leadsto \frac{0.5}{z0 \cdot z0} \cdot \left(\left(z2 \cdot \color{blue}{z0}\right) \cdot z1\right) \]

   10. Applied rewrites 33.9%

       \[\leadsto \color{blue}{\frac{0.5}{z0 \cdot z0} \cdot \left(\left(z2 \cdot z0\right) \cdot z1\right)} \]

   if 7.5000000000000006e-77 < z2

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

      3. lower-*.f64 51.5%

         \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. frac-times N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. count-2 N/A

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

      13. lift-+.f64 N/A

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

      14. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0} + z0} \]

      16. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      17. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      18. lower-/.f64 49.0%

          \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

   6. Applied rewrites 49.0%

      \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 53.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)\\ t_1 := \mathsf{min}\left(\left|z1\right|, \left|z2\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 3.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{t\_1 \cdot t\_0}{z0 + z0}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{z0 + z0}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z1 z2 z0 z4 z3)
  :precision binary64
  (let* ((t_0 (fmax (fabs z1) (fabs z2)))
       (t_1 (fmin (fabs z1) (fabs z2))))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z2)
    (if (<= t_1 3.2e-97)
      (/ (* t_1 t_0) (+ z0 z0))
      (* t_0 (/ t_1 (+ z0 z0))))))))

C

double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmax(fabs(z1), fabs(z2));
	double t_1 = fmin(fabs(z1), fabs(z2));
	double tmp;
	if (t_1 <= 3.2e-97) {
		tmp = (t_1 * t_0) / (z0 + z0);
	} else {
		tmp = t_0 * (t_1 / (z0 + z0));
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z1, double z2, double z0, double z4, double z3) {
	double t_0 = fmax(Math.abs(z1), Math.abs(z2));
	double t_1 = fmin(Math.abs(z1), Math.abs(z2));
	double tmp;
	if (t_1 <= 3.2e-97) {
		tmp = (t_1 * t_0) / (z0 + z0);
	} else {
		tmp = t_0 * (t_1 / (z0 + z0));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z1, z2, z0, z4, z3):
	t_0 = fmax(math.fabs(z1), math.fabs(z2))
	t_1 = fmin(math.fabs(z1), math.fabs(z2))
	tmp = 0
	if t_1 <= 3.2e-97:
		tmp = (t_1 * t_0) / (z0 + z0)
	else:
		tmp = t_0 * (t_1 / (z0 + z0))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z1, z2, z0, z4, z3)
	t_0 = fmax(abs(z1), abs(z2))
	t_1 = fmin(abs(z1), abs(z2))
	tmp = 0.0
	if (t_1 <= 3.2e-97)
		tmp = Float64(Float64(t_1 * t_0) / Float64(z0 + z0));
	else
		tmp = Float64(t_0 * Float64(t_1 / Float64(z0 + z0)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z1, z2, z0, z4, z3)
	t_0 = max(abs(z1), abs(z2));
	t_1 = min(abs(z1), abs(z2));
	tmp = 0.0;
	if (t_1 <= 3.2e-97)
		tmp = (t_1 * t_0) / (z0 + z0);
	else
		tmp = t_0 * (t_1 / (z0 + z0));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z2_, z0_, z4_, z3_] := Block[{t$95$0 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, 3.2e-97], N[(N[(t$95$1 * t$95$0), $MachinePrecision] / N[(z0 + z0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$1 / N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z1 < 3.1999999999999998e-97

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

      3. lower-*.f64 51.5%

         \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. frac-times N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. count-2 N/A

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

      13. lift-+.f64 N/A

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

      14. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      15. lower-/.f64 51.5%

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

   6. Applied rewrites 51.5%

      \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

   if 3.1999999999999998e-97 < z1

   1. Initial program 59.6%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

      3. lower-*.f64 51.5%

         \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. frac-times N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. count-2 N/A

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

      13. lift-+.f64 N/A

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

      14. mult-flip N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0} + z0} \]

      16. associate-/l* N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      17. lower-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      18. lower-/.f64 49.0%

          \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

   6. Applied rewrites 49.0%

      \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

      2. lift-/.f64 N/A

         \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

      4. *-commutative N/A

         \[\leadsto \frac{z2 \cdot z1}{\color{blue}{z0} + z0} \]

      5. associate-/l* N/A

         \[\leadsto z2 \cdot \color{blue}{\frac{z1}{z0 + z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto z2 \cdot \color{blue}{\frac{z1}{z0 + z0}} \]

      7. lower-/.f64 49.1%

         \[\leadsto z2 \cdot \frac{z1}{\color{blue}{z0 + z0}} \]

   8. Applied rewrites 49.1%

      \[\leadsto z2 \cdot \color{blue}{\frac{z1}{z0 + z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 52.4% accurate, 0.6× speedup

Math

\[\mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \left(\mathsf{min}\left(\left|z1\right|, \left|z2\right|\right) \cdot \frac{\mathsf{max}\left(\left|z1\right|, \left|z2\right|\right)}{z0 + z0}\right)\right) \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[z1_, z2_, z0_, z4_, 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[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision] * N[(N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z2], $MachinePrecision]], $MachinePrecision] / N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 59.6%

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

2. Taylor expanded in z0 around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{z1 \cdot z2}{z0}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{z1 \cdot z2}{\color{blue}{z0}} \]

   3. lower-*.f64 51.5%

      \[\leadsto 0.5 \cdot \frac{z1 \cdot z2}{z0} \]

4. Applied rewrites 51.5%

   \[\leadsto \color{blue}{0.5 \cdot \frac{z1 \cdot z2}{z0}} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{z1 \cdot z2}{z0}} \]

   2. *-commutative N/A

      \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \color{blue}{\frac{1}{2}} \]

   3. lift-/.f64 N/A

      \[\leadsto \frac{z1 \cdot z2}{z0} \cdot \frac{1}{2} \]

   4. mult-flip N/A

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

   5. lift-/.f64 N/A

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

   6. associate-*l* N/A

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

   7. lift-/.f64 N/A

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

   8. metadata-eval N/A

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

   9. frac-times N/A

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

   10. metadata-eval N/A

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

   11. *-commutative N/A

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

   12. count-2 N/A

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

   13. lift-+.f64 N/A

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

   14. mult-flip N/A

       \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0 + z0}} \]

   15. lift-*.f64 N/A

       \[\leadsto \frac{z1 \cdot z2}{\color{blue}{z0} + z0} \]

   16. associate-/l* N/A

       \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

   17. lower-*.f64 N/A

       \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]

   18. lower-/.f64 49.0%

       \[\leadsto z1 \cdot \frac{z2}{\color{blue}{z0 + z0}} \]

6. Applied rewrites 49.0%

   \[\leadsto z1 \cdot \color{blue}{\frac{z2}{z0 + z0}} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z1 z2 z0 z4 z3)
  :name "(/ (* z1 z2) (* (* z0 (+ z0 z0)) (* (sinh (/ 1 z0)) (exp (/ (* z4 z3) z0)))))"
  :precision binary64
  (/ (* z1 z2) (* (* z0 (+ z0 z0)) (* (sinh (/ 1.0 z0)) (exp (/ (* z4 z3) z0))))))