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

Percentage Accurate: 99.5% → 99.5%

Time: 3.3s

Alternatives: 10

Speedup: 1.7×

• could not determine a ground truth

  1. z0 = 6.806449564800888e-276
  2. z1 = -2.1070999167350667e-247
  3. z3 = -1.6088198875503712e+76
  4. z2 = -6.731574464164068e-7

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{z3 \cdot z2}{z1}\\ \mathbf{if}\;z1 \leq -9.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{e^{-t\_0}}{2} \cdot z0\\ \mathbf{elif}\;z1 \leq 0.00135:\\ \;\;\;\;\frac{z0}{\left(\sinh \left(\frac{1}{z1}\right) \cdot \left(z1 + z1\right)\right) \cdot 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{2 \cdot e^{t\_0}}\\ \end{array} \]

FPCore

(FPCore (z0 z1 z3 z2)
  :precision binary64
  (let* ((t_0 (/ (* z3 z2) z1)))
  (if (<= z1 -9.2e+14)
    (* (/ (exp (- t_0)) 2.0) z0)
    (if (<= z1 0.00135)
      (/ z0 (* (* (sinh (/ 1.0 z1)) (+ z1 z1)) 1.0))
      (/ z0 (* 2.0 (exp t_0)))))))

C

double code(double z0, double z1, double z3, double z2) {
	double t_0 = (z3 * z2) / z1;
	double tmp;
	if (z1 <= -9.2e+14) {
		tmp = (exp(-t_0) / 2.0) * z0;
	} else if (z1 <= 0.00135) {
		tmp = z0 / ((sinh((1.0 / z1)) * (z1 + z1)) * 1.0);
	} else {
		tmp = z0 / (2.0 * exp(t_0));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1, z3, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z3 * z2) / z1
    if (z1 <= (-9.2d+14)) then
        tmp = (exp(-t_0) / 2.0d0) * z0
    else if (z1 <= 0.00135d0) then
        tmp = z0 / ((sinh((1.0d0 / z1)) * (z1 + z1)) * 1.0d0)
    else
        tmp = z0 / (2.0d0 * exp(t_0))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1, double z3, double z2) {
	double t_0 = (z3 * z2) / z1;
	double tmp;
	if (z1 <= -9.2e+14) {
		tmp = (Math.exp(-t_0) / 2.0) * z0;
	} else if (z1 <= 0.00135) {
		tmp = z0 / ((Math.sinh((1.0 / z1)) * (z1 + z1)) * 1.0);
	} else {
		tmp = z0 / (2.0 * Math.exp(t_0));
	}
	return tmp;
}

Python

def code(z0, z1, z3, z2):
	t_0 = (z3 * z2) / z1
	tmp = 0
	if z1 <= -9.2e+14:
		tmp = (math.exp(-t_0) / 2.0) * z0
	elif z1 <= 0.00135:
		tmp = z0 / ((math.sinh((1.0 / z1)) * (z1 + z1)) * 1.0)
	else:
		tmp = z0 / (2.0 * math.exp(t_0))
	return tmp

Julia

function code(z0, z1, z3, z2)
	t_0 = Float64(Float64(z3 * z2) / z1)
	tmp = 0.0
	if (z1 <= -9.2e+14)
		tmp = Float64(Float64(exp(Float64(-t_0)) / 2.0) * z0);
	elseif (z1 <= 0.00135)
		tmp = Float64(z0 / Float64(Float64(sinh(Float64(1.0 / z1)) * Float64(z1 + z1)) * 1.0));
	else
		tmp = Float64(z0 / Float64(2.0 * exp(t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1, z3, z2)
	t_0 = (z3 * z2) / z1;
	tmp = 0.0;
	if (z1 <= -9.2e+14)
		tmp = (exp(-t_0) / 2.0) * z0;
	elseif (z1 <= 0.00135)
		tmp = z0 / ((sinh((1.0 / z1)) * (z1 + z1)) * 1.0);
	else
		tmp = z0 / (2.0 * exp(t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_, z3_, z2_] := Block[{t$95$0 = N[(N[(z3 * z2), $MachinePrecision] / z1), $MachinePrecision]}, If[LessEqual[z1, -9.2e+14], N[(N[(N[Exp[(-t$95$0)], $MachinePrecision] / 2.0), $MachinePrecision] * z0), $MachinePrecision], If[LessEqual[z1, 0.00135], N[(z0 / N[(N[(N[Sinh[N[(1.0 / z1), $MachinePrecision]], $MachinePrecision] * N[(z1 + z1), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision], N[(z0 / N[(2.0 * N[Exp[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z1 < -9.2e14

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

   4. Applied rewrites 81.8%

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

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{2 \cdot e^{\frac{z3 \cdot z2}{z1}}}} \]

      2. mult-flip N/A

         \[\leadsto \color{blue}{z0 \cdot \frac{1}{2 \cdot e^{\frac{z3 \cdot z2}{z1}}}} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{2 \cdot e^{\frac{z3 \cdot z2}{z1}}} \cdot z0} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{2 \cdot e^{\frac{z3 \cdot z2}{z1}}} \cdot z0} \]

   6. Applied rewrites 81.8%

      \[\leadsto \color{blue}{\frac{e^{-\frac{z3 \cdot z2}{z1}}}{2} \cdot z0} \]

   if -9.2e14 < z1 < 0.0013500000000000001

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

   4. Applied rewrites 89.4%

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

   if 0.0013500000000000001 < z1

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

   4. Applied rewrites 81.8%

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

Alternative 2: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/r* N/A

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

   4. frac-2neg N/A

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

   5. mult-flip N/A

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

   6. lower-*.f64 N/A

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

3. Applied rewrites 99.5%

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

Alternative 3: 81.8% accurate, 1.9× speedup

Math

\[\frac{z0}{2 \cdot e^{\frac{z3 \cdot z2}{z1}}} \]

FPCore

(FPCore (z0 z1 z3 z2)
  :precision binary64
  (/ z0 (* 2.0 (exp (/ (* z3 z2) z1)))))

C

double code(double z0, double z1, double z3, double z2) {
	return z0 / (2.0 * exp(((z3 * z2) / z1)));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1, z3, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    code = z0 / (2.0d0 * exp(((z3 * z2) / z1)))
end function

Java

public static double code(double z0, double z1, double z3, double z2) {
	return z0 / (2.0 * Math.exp(((z3 * z2) / z1)));
}

Python

def code(z0, z1, z3, z2):
	return z0 / (2.0 * math.exp(((z3 * z2) / z1)))

Julia

function code(z0, z1, z3, z2)
	return Float64(z0 / Float64(2.0 * exp(Float64(Float64(z3 * z2) / z1))))
end

MATLAB

function tmp = code(z0, z1, z3, z2)
	tmp = z0 / (2.0 * exp(((z3 * z2) / z1)));
end

Wolfram

code[z0_, z1_, z3_, z2_] := N[(z0 / N[(2.0 * N[Exp[N[(N[(z3 * z2), $MachinePrecision] / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z1 around inf

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

4. Applied rewrites 81.8%

   \[\leadsto \frac{z0}{\color{blue}{2} \cdot e^{\frac{z3 \cdot z2}{z1}}} \]
5. Add Preprocessing

Alternative 4: 68.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(z3, z2\right) + \mathsf{min}\left(z3, z2\right)\\ t_1 := \left(\mathsf{min}\left(z3, z2\right) \cdot \mathsf{max}\left(z3, z2\right)\right) \cdot z1\\ t_2 := \frac{\mathsf{max}\left(z3, z2\right)}{z1} \cdot t\_0\\ \mathbf{if}\;z1 \leq -1.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{z0}{2 + \frac{t\_0 \cdot \mathsf{max}\left(z3, z2\right)}{z1}}\\ \mathbf{elif}\;z1 \leq 2.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{z0}{2 + \frac{t\_1 + t\_1}{z1 \cdot z1}}\\ \mathbf{elif}\;z1 \leq 9.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z0 \cdot \left(z1 \cdot \left(\mathsf{max}\left(z3, z2\right) \cdot \mathsf{min}\left(z3, z2\right)\right)\right)\right)}{z1 \cdot z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{\frac{t\_2 \cdot t\_2 - 2 \cdot 2}{t\_2 - 2}}\\ \end{array} \]

FPCore

(FPCore (z0 z1 z3 z2)
  :precision binary64
  (let* ((t_0 (+ (fmin z3 z2) (fmin z3 z2)))
       (t_1 (* (* (fmin z3 z2) (fmax z3 z2)) z1))
       (t_2 (* (/ (fmax z3 z2) z1) t_0)))
  (if (<= z1 -1.2e+168)
    (/ z0 (+ 2.0 (/ (* t_0 (fmax z3 z2)) z1)))
    (if (<= z1 2.5e-135)
      (/ z0 (+ 2.0 (/ (+ t_1 t_1) (* z1 z1))))
      (if (<= z1 9.2e-67)
        (/
         (* -0.5 (* z0 (* z1 (* (fmax z3 z2) (fmin z3 z2)))))
         (* z1 z1))
        (/ z0 (/ (- (* t_2 t_2) (* 2.0 2.0)) (- t_2 2.0))))))))

C

double code(double z0, double z1, double z3, double z2) {
	double t_0 = fmin(z3, z2) + fmin(z3, z2);
	double t_1 = (fmin(z3, z2) * fmax(z3, z2)) * z1;
	double t_2 = (fmax(z3, z2) / z1) * t_0;
	double tmp;
	if (z1 <= -1.2e+168) {
		tmp = z0 / (2.0 + ((t_0 * fmax(z3, z2)) / z1));
	} else if (z1 <= 2.5e-135) {
		tmp = z0 / (2.0 + ((t_1 + t_1) / (z1 * z1)));
	} else if (z1 <= 9.2e-67) {
		tmp = (-0.5 * (z0 * (z1 * (fmax(z3, z2) * fmin(z3, z2))))) / (z1 * z1);
	} else {
		tmp = z0 / (((t_2 * t_2) - (2.0 * 2.0)) / (t_2 - 2.0));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1, z3, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = fmin(z3, z2) + fmin(z3, z2)
    t_1 = (fmin(z3, z2) * fmax(z3, z2)) * z1
    t_2 = (fmax(z3, z2) / z1) * t_0
    if (z1 <= (-1.2d+168)) then
        tmp = z0 / (2.0d0 + ((t_0 * fmax(z3, z2)) / z1))
    else if (z1 <= 2.5d-135) then
        tmp = z0 / (2.0d0 + ((t_1 + t_1) / (z1 * z1)))
    else if (z1 <= 9.2d-67) then
        tmp = ((-0.5d0) * (z0 * (z1 * (fmax(z3, z2) * fmin(z3, z2))))) / (z1 * z1)
    else
        tmp = z0 / (((t_2 * t_2) - (2.0d0 * 2.0d0)) / (t_2 - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1, double z3, double z2) {
	double t_0 = fmin(z3, z2) + fmin(z3, z2);
	double t_1 = (fmin(z3, z2) * fmax(z3, z2)) * z1;
	double t_2 = (fmax(z3, z2) / z1) * t_0;
	double tmp;
	if (z1 <= -1.2e+168) {
		tmp = z0 / (2.0 + ((t_0 * fmax(z3, z2)) / z1));
	} else if (z1 <= 2.5e-135) {
		tmp = z0 / (2.0 + ((t_1 + t_1) / (z1 * z1)));
	} else if (z1 <= 9.2e-67) {
		tmp = (-0.5 * (z0 * (z1 * (fmax(z3, z2) * fmin(z3, z2))))) / (z1 * z1);
	} else {
		tmp = z0 / (((t_2 * t_2) - (2.0 * 2.0)) / (t_2 - 2.0));
	}
	return tmp;
}

Python

def code(z0, z1, z3, z2):
	t_0 = fmin(z3, z2) + fmin(z3, z2)
	t_1 = (fmin(z3, z2) * fmax(z3, z2)) * z1
	t_2 = (fmax(z3, z2) / z1) * t_0
	tmp = 0
	if z1 <= -1.2e+168:
		tmp = z0 / (2.0 + ((t_0 * fmax(z3, z2)) / z1))
	elif z1 <= 2.5e-135:
		tmp = z0 / (2.0 + ((t_1 + t_1) / (z1 * z1)))
	elif z1 <= 9.2e-67:
		tmp = (-0.5 * (z0 * (z1 * (fmax(z3, z2) * fmin(z3, z2))))) / (z1 * z1)
	else:
		tmp = z0 / (((t_2 * t_2) - (2.0 * 2.0)) / (t_2 - 2.0))
	return tmp

Julia

function code(z0, z1, z3, z2)
	t_0 = Float64(fmin(z3, z2) + fmin(z3, z2))
	t_1 = Float64(Float64(fmin(z3, z2) * fmax(z3, z2)) * z1)
	t_2 = Float64(Float64(fmax(z3, z2) / z1) * t_0)
	tmp = 0.0
	if (z1 <= -1.2e+168)
		tmp = Float64(z0 / Float64(2.0 + Float64(Float64(t_0 * fmax(z3, z2)) / z1)));
	elseif (z1 <= 2.5e-135)
		tmp = Float64(z0 / Float64(2.0 + Float64(Float64(t_1 + t_1) / Float64(z1 * z1))));
	elseif (z1 <= 9.2e-67)
		tmp = Float64(Float64(-0.5 * Float64(z0 * Float64(z1 * Float64(fmax(z3, z2) * fmin(z3, z2))))) / Float64(z1 * z1));
	else
		tmp = Float64(z0 / Float64(Float64(Float64(t_2 * t_2) - Float64(2.0 * 2.0)) / Float64(t_2 - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1, z3, z2)
	t_0 = min(z3, z2) + min(z3, z2);
	t_1 = (min(z3, z2) * max(z3, z2)) * z1;
	t_2 = (max(z3, z2) / z1) * t_0;
	tmp = 0.0;
	if (z1 <= -1.2e+168)
		tmp = z0 / (2.0 + ((t_0 * max(z3, z2)) / z1));
	elseif (z1 <= 2.5e-135)
		tmp = z0 / (2.0 + ((t_1 + t_1) / (z1 * z1)));
	elseif (z1 <= 9.2e-67)
		tmp = (-0.5 * (z0 * (z1 * (max(z3, z2) * min(z3, z2))))) / (z1 * z1);
	else
		tmp = z0 / (((t_2 * t_2) - (2.0 * 2.0)) / (t_2 - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_, z3_, z2_] := Block[{t$95$0 = N[(N[Min[z3, z2], $MachinePrecision] + N[Min[z3, z2], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Min[z3, z2], $MachinePrecision] * N[Max[z3, z2], $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Max[z3, z2], $MachinePrecision] / z1), $MachinePrecision] * t$95$0), $MachinePrecision]}, If[LessEqual[z1, -1.2e+168], N[(z0 / N[(2.0 + N[(N[(t$95$0 * N[Max[z3, z2], $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 2.5e-135], N[(z0 / N[(2.0 + N[(N[(t$95$1 + t$95$1), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 9.2e-67], N[(N[(-0.5 * N[(z0 * N[(z1 * N[(N[Max[z3, z2], $MachinePrecision] * N[Min[z3, z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision], N[(z0 / N[(N[(N[(t$95$2 * t$95$2), $MachinePrecision] - N[(2.0 * 2.0), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z1 < -1.2e168

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 66.6%

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

   4. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. div-flip N/A

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

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

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

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

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

      7. lower-*.f64 66.6%

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 66.6%

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

   6. Applied rewrites 66.6%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip-rev N/A

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

      4. lower-/.f64 66.6%

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. count-2-rev N/A

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

      10. lower-+.f64 66.6%

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

   8. Applied rewrites 66.6%

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

   if -1.2e168 < z1 < 2.5000000000000001e-135

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 66.6%

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

   4. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. common-denominator N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 60.4%

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

   6. Applied rewrites 60.4%

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

   if 2.5000000000000001e-135 < z1 < 9.2000000000000002e-67

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 47.1%

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z3\right)}{z1} + 0.5 \cdot z0} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. lift-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-out-- N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 47.1%

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

      9. lift-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-/l* N/A

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

      12. lift-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 49.1%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 49.1%

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

   6. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. distribute-rgt-out-- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. associate-*l/ N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l/ N/A

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

      16. lift-*.f64 N/A

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

      17. add-to-fraction-rev N/A

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

      18. lift-*.f64 N/A

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

   8. Applied rewrites 20.7%

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

   9. Taylor expanded in z1 around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-*.f64 11.0%

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

   11. Applied rewrites 11.0%

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

   if 9.2000000000000002e-67 < z1

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 66.6%

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

   4. Applied rewrites 66.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. flip-+ N/A

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

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

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

   6. Applied rewrites 58.1%

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

Alternative 5: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(\mathsf{min}\left(z3, z2\right) \cdot \mathsf{max}\left(z3, z2\right)\right) \cdot z1\\ \mathbf{if}\;z1 \leq -1.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{z0}{2 + \frac{\left(\mathsf{min}\left(z3, z2\right) + \mathsf{min}\left(z3, z2\right)\right) \cdot \mathsf{max}\left(z3, z2\right)}{z1}}\\ \mathbf{elif}\;z1 \leq 2.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{z0}{2 + \frac{t\_0 + t\_0}{z1 \cdot z1}}\\ \mathbf{elif}\;z1 \leq 8.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z0 \cdot \left(z1 \cdot \left(\mathsf{max}\left(z3, z2\right) \cdot \mathsf{min}\left(z3, z2\right)\right)\right)\right)}{z1 \cdot z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{2 + \frac{\mathsf{min}\left(z3, z2\right)}{z1} \cdot \left(\mathsf{max}\left(z3, z2\right) + \mathsf{max}\left(z3, z2\right)\right)}\\ \end{array} \]

FPCore

(FPCore (z0 z1 z3 z2)
  :precision binary64
  (let* ((t_0 (* (* (fmin z3 z2) (fmax z3 z2)) z1)))
  (if (<= z1 -1.2e+168)
    (/
     z0
     (+ 2.0 (/ (* (+ (fmin z3 z2) (fmin z3 z2)) (fmax z3 z2)) z1)))
    (if (<= z1 2.5e-135)
      (/ z0 (+ 2.0 (/ (+ t_0 t_0) (* z1 z1))))
      (if (<= z1 8.2e-78)
        (/
         (* -0.5 (* z0 (* z1 (* (fmax z3 z2) (fmin z3 z2)))))
         (* z1 z1))
        (/
         z0
         (+
          2.0
          (* (/ (fmin z3 z2) z1) (+ (fmax z3 z2) (fmax z3 z2))))))))))

C

double code(double z0, double z1, double z3, double z2) {
	double t_0 = (fmin(z3, z2) * fmax(z3, z2)) * z1;
	double tmp;
	if (z1 <= -1.2e+168) {
		tmp = z0 / (2.0 + (((fmin(z3, z2) + fmin(z3, z2)) * fmax(z3, z2)) / z1));
	} else if (z1 <= 2.5e-135) {
		tmp = z0 / (2.0 + ((t_0 + t_0) / (z1 * z1)));
	} else if (z1 <= 8.2e-78) {
		tmp = (-0.5 * (z0 * (z1 * (fmax(z3, z2) * fmin(z3, z2))))) / (z1 * z1);
	} else {
		tmp = z0 / (2.0 + ((fmin(z3, z2) / z1) * (fmax(z3, z2) + fmax(z3, z2))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1, z3, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (fmin(z3, z2) * fmax(z3, z2)) * z1
    if (z1 <= (-1.2d+168)) then
        tmp = z0 / (2.0d0 + (((fmin(z3, z2) + fmin(z3, z2)) * fmax(z3, z2)) / z1))
    else if (z1 <= 2.5d-135) then
        tmp = z0 / (2.0d0 + ((t_0 + t_0) / (z1 * z1)))
    else if (z1 <= 8.2d-78) then
        tmp = ((-0.5d0) * (z0 * (z1 * (fmax(z3, z2) * fmin(z3, z2))))) / (z1 * z1)
    else
        tmp = z0 / (2.0d0 + ((fmin(z3, z2) / z1) * (fmax(z3, z2) + fmax(z3, z2))))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1, double z3, double z2) {
	double t_0 = (fmin(z3, z2) * fmax(z3, z2)) * z1;
	double tmp;
	if (z1 <= -1.2e+168) {
		tmp = z0 / (2.0 + (((fmin(z3, z2) + fmin(z3, z2)) * fmax(z3, z2)) / z1));
	} else if (z1 <= 2.5e-135) {
		tmp = z0 / (2.0 + ((t_0 + t_0) / (z1 * z1)));
	} else if (z1 <= 8.2e-78) {
		tmp = (-0.5 * (z0 * (z1 * (fmax(z3, z2) * fmin(z3, z2))))) / (z1 * z1);
	} else {
		tmp = z0 / (2.0 + ((fmin(z3, z2) / z1) * (fmax(z3, z2) + fmax(z3, z2))));
	}
	return tmp;
}

Python

def code(z0, z1, z3, z2):
	t_0 = (fmin(z3, z2) * fmax(z3, z2)) * z1
	tmp = 0
	if z1 <= -1.2e+168:
		tmp = z0 / (2.0 + (((fmin(z3, z2) + fmin(z3, z2)) * fmax(z3, z2)) / z1))
	elif z1 <= 2.5e-135:
		tmp = z0 / (2.0 + ((t_0 + t_0) / (z1 * z1)))
	elif z1 <= 8.2e-78:
		tmp = (-0.5 * (z0 * (z1 * (fmax(z3, z2) * fmin(z3, z2))))) / (z1 * z1)
	else:
		tmp = z0 / (2.0 + ((fmin(z3, z2) / z1) * (fmax(z3, z2) + fmax(z3, z2))))
	return tmp

Julia

function code(z0, z1, z3, z2)
	t_0 = Float64(Float64(fmin(z3, z2) * fmax(z3, z2)) * z1)
	tmp = 0.0
	if (z1 <= -1.2e+168)
		tmp = Float64(z0 / Float64(2.0 + Float64(Float64(Float64(fmin(z3, z2) + fmin(z3, z2)) * fmax(z3, z2)) / z1)));
	elseif (z1 <= 2.5e-135)
		tmp = Float64(z0 / Float64(2.0 + Float64(Float64(t_0 + t_0) / Float64(z1 * z1))));
	elseif (z1 <= 8.2e-78)
		tmp = Float64(Float64(-0.5 * Float64(z0 * Float64(z1 * Float64(fmax(z3, z2) * fmin(z3, z2))))) / Float64(z1 * z1));
	else
		tmp = Float64(z0 / Float64(2.0 + Float64(Float64(fmin(z3, z2) / z1) * Float64(fmax(z3, z2) + fmax(z3, z2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1, z3, z2)
	t_0 = (min(z3, z2) * max(z3, z2)) * z1;
	tmp = 0.0;
	if (z1 <= -1.2e+168)
		tmp = z0 / (2.0 + (((min(z3, z2) + min(z3, z2)) * max(z3, z2)) / z1));
	elseif (z1 <= 2.5e-135)
		tmp = z0 / (2.0 + ((t_0 + t_0) / (z1 * z1)));
	elseif (z1 <= 8.2e-78)
		tmp = (-0.5 * (z0 * (z1 * (max(z3, z2) * min(z3, z2))))) / (z1 * z1);
	else
		tmp = z0 / (2.0 + ((min(z3, z2) / z1) * (max(z3, z2) + max(z3, z2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_, z3_, z2_] := Block[{t$95$0 = N[(N[(N[Min[z3, z2], $MachinePrecision] * N[Max[z3, z2], $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]}, If[LessEqual[z1, -1.2e+168], N[(z0 / N[(2.0 + N[(N[(N[(N[Min[z3, z2], $MachinePrecision] + N[Min[z3, z2], $MachinePrecision]), $MachinePrecision] * N[Max[z3, z2], $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 2.5e-135], N[(z0 / N[(2.0 + N[(N[(t$95$0 + t$95$0), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 8.2e-78], N[(N[(-0.5 * N[(z0 * N[(z1 * N[(N[Max[z3, z2], $MachinePrecision] * N[Min[z3, z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision], N[(z0 / N[(2.0 + N[(N[(N[Min[z3, z2], $MachinePrecision] / z1), $MachinePrecision] * N[(N[Max[z3, z2], $MachinePrecision] + N[Max[z3, z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z1 < -1.2e168

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 66.6%

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

   4. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. div-flip N/A

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

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

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

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

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

      7. lower-*.f64 66.6%

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 66.6%

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

   6. Applied rewrites 66.6%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip-rev N/A

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

      4. lower-/.f64 66.6%

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. count-2-rev N/A

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

      10. lower-+.f64 66.6%

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

   8. Applied rewrites 66.6%

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

   if -1.2e168 < z1 < 2.5000000000000001e-135

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 66.6%

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

   4. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. common-denominator N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 60.4%

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

   6. Applied rewrites 60.4%

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

   if 2.5000000000000001e-135 < z1 < 8.1999999999999996e-78

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 47.1%

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z3\right)}{z1} + 0.5 \cdot z0} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. lift-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-out-- N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 47.1%

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

      9. lift-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-/l* N/A

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

      12. lift-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 49.1%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 49.1%

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

   6. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. distribute-rgt-out-- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. associate-*l/ N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l/ N/A

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

      16. lift-*.f64 N/A

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

      17. add-to-fraction-rev N/A

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

      18. lift-*.f64 N/A

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

   8. Applied rewrites 20.7%

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

   9. Taylor expanded in z1 around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-*.f64 11.0%

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

   11. Applied rewrites 11.0%

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

   if 8.1999999999999996e-78 < z1

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 66.6%

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

   4. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-+.f64 66.7%

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

   6. Applied rewrites 66.7%

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

Alternative 6: 66.9% accurate, 0.7× speedup

Math

\[\frac{z0}{2 + \frac{\mathsf{min}\left(z3, z2\right)}{z1} \cdot \left(\mathsf{max}\left(z3, z2\right) + \mathsf{max}\left(z3, z2\right)\right)} \]

FPCore

(FPCore (z0 z1 z3 z2)
  :precision binary64
  (/ z0 (+ 2.0 (* (/ (fmin z3 z2) z1) (+ (fmax z3 z2) (fmax z3 z2))))))

C

double code(double z0, double z1, double z3, double z2) {
	return z0 / (2.0 + ((fmin(z3, z2) / z1) * (fmax(z3, z2) + fmax(z3, z2))));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1, z3, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    code = z0 / (2.0d0 + ((fmin(z3, z2) / z1) * (fmax(z3, z2) + fmax(z3, z2))))
end function

Java

public static double code(double z0, double z1, double z3, double z2) {
	return z0 / (2.0 + ((fmin(z3, z2) / z1) * (fmax(z3, z2) + fmax(z3, z2))));
}

Python

def code(z0, z1, z3, z2):
	return z0 / (2.0 + ((fmin(z3, z2) / z1) * (fmax(z3, z2) + fmax(z3, z2))))

Julia

function code(z0, z1, z3, z2)
	return Float64(z0 / Float64(2.0 + Float64(Float64(fmin(z3, z2) / z1) * Float64(fmax(z3, z2) + fmax(z3, z2)))))
end

MATLAB

function tmp = code(z0, z1, z3, z2)
	tmp = z0 / (2.0 + ((min(z3, z2) / z1) * (max(z3, z2) + max(z3, z2))));
end

Wolfram

code[z0_, z1_, z3_, z2_] := N[(z0 / N[(2.0 + N[(N[(N[Min[z3, z2], $MachinePrecision] / z1), $MachinePrecision] * N[(N[Max[z3, z2], $MachinePrecision] + N[Max[z3, z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z1 around inf

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lower-*.f64 66.6%

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

4. Applied rewrites 66.6%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. lift-/.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. associate-/l* N/A

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

   9. distribute-rgt-out N/A

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

   10. lower-*.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. lower-+.f64 66.7%

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

6. Applied rewrites 66.7%

   \[\leadsto \frac{z0}{2 + \frac{z3}{z1} \cdot \color{blue}{\left(z2 + z2\right)}} \]
7. Add Preprocessing

Alternative 7: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\sinh \left(\frac{1}{z1}\right) \cdot \left(z1 + z1\right)\right) \cdot e^{\frac{z3 \cdot z2}{z1}} \leq 4:\\ \;\;\;\;-0.5 \cdot \left(\left(\frac{z2}{z1} \cdot z3\right) \cdot z0 - z0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z0 \cdot \left(z2 \cdot z3\right)\right)}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1 z3 z2)
  :precision binary64
  (if (<=
     (* (* (sinh (/ 1.0 z1)) (+ z1 z1)) (exp (/ (* z3 z2) z1)))
     4.0)
  (* -0.5 (- (* (* (/ z2 z1) z3) z0) z0))
  (/ (* -0.5 (* z0 (* z2 z3))) z1)))

C

double code(double z0, double z1, double z3, double z2) {
	double tmp;
	if (((sinh((1.0 / z1)) * (z1 + z1)) * exp(((z3 * z2) / z1))) <= 4.0) {
		tmp = -0.5 * ((((z2 / z1) * z3) * z0) - z0);
	} else {
		tmp = (-0.5 * (z0 * (z2 * z3))) / z1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1, z3, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    real(8) :: tmp
    if (((sinh((1.0d0 / z1)) * (z1 + z1)) * exp(((z3 * z2) / z1))) <= 4.0d0) then
        tmp = (-0.5d0) * ((((z2 / z1) * z3) * z0) - z0)
    else
        tmp = ((-0.5d0) * (z0 * (z2 * z3))) / z1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1, double z3, double z2) {
	double tmp;
	if (((Math.sinh((1.0 / z1)) * (z1 + z1)) * Math.exp(((z3 * z2) / z1))) <= 4.0) {
		tmp = -0.5 * ((((z2 / z1) * z3) * z0) - z0);
	} else {
		tmp = (-0.5 * (z0 * (z2 * z3))) / z1;
	}
	return tmp;
}

Python

def code(z0, z1, z3, z2):
	tmp = 0
	if ((math.sinh((1.0 / z1)) * (z1 + z1)) * math.exp(((z3 * z2) / z1))) <= 4.0:
		tmp = -0.5 * ((((z2 / z1) * z3) * z0) - z0)
	else:
		tmp = (-0.5 * (z0 * (z2 * z3))) / z1
	return tmp

Julia

function code(z0, z1, z3, z2)
	tmp = 0.0
	if (Float64(Float64(sinh(Float64(1.0 / z1)) * Float64(z1 + z1)) * exp(Float64(Float64(z3 * z2) / z1))) <= 4.0)
		tmp = Float64(-0.5 * Float64(Float64(Float64(Float64(z2 / z1) * z3) * z0) - z0));
	else
		tmp = Float64(Float64(-0.5 * Float64(z0 * Float64(z2 * z3))) / z1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1, z3, z2)
	tmp = 0.0;
	if (((sinh((1.0 / z1)) * (z1 + z1)) * exp(((z3 * z2) / z1))) <= 4.0)
		tmp = -0.5 * ((((z2 / z1) * z3) * z0) - z0);
	else
		tmp = (-0.5 * (z0 * (z2 * z3))) / z1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_, z3_, z2_] := If[LessEqual[N[(N[(N[Sinh[N[(1.0 / z1), $MachinePrecision]], $MachinePrecision] * N[(z1 + z1), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(z3 * z2), $MachinePrecision] / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 4.0], N[(-0.5 * N[(N[(N[(N[(z2 / z1), $MachinePrecision] * z3), $MachinePrecision] * z0), $MachinePrecision] - z0), $MachinePrecision]), $MachinePrecision], N[(N[(-0.5 * N[(z0 * N[(z2 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z1)) (+.f64 z1 z1)) (exp.f64 (/.f64 (*.f64 z3 z2) z1))) < 4

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 47.1%

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z3\right)}{z1} + 0.5 \cdot z0} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. lift-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-out-- N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 47.1%

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

      9. lift-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-/l* N/A

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

      12. lift-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 49.1%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 49.1%

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

   6. Applied rewrites 49.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 49.1%

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

   8. Applied rewrites 49.1%

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

   if 4 < (*.f64 (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z1)) (+.f64 z1 z1)) (exp.f64 (/.f64 (*.f64 z3 z2) z1)))

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 47.1%

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z3\right)}{z1} + 0.5 \cdot z0} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. add-to-fraction N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 40.4%

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 40.4%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 40.4%

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

   6. Applied rewrites 40.4%

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

   7. Taylor expanded in z0 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 40.5%

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

   9. Applied rewrites 40.5%

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

   10. Taylor expanded in z1 around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 14.1%

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

   12. Applied rewrites 14.1%

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

Alternative 8: 59.2% accurate, 0.6× speedup

Math

\[\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{\left|z0\right|}{\left(\sinh \left(\frac{1}{z1}\right) \cdot \left(z1 + z1\right)\right) \cdot e^{\frac{z3 \cdot z2}{z1}}} \leq 0:\\ \;\;\;\;\frac{-0.5 \cdot \left(\left|z0\right| \cdot \left(z2 \cdot z3\right)\right)}{z1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left|z0\right|\\ \end{array} \]

FPCore

(FPCore (z0 z1 z3 z2)
  :precision binary64
  (*
 (copysign 1.0 z0)
 (if (<=
      (/
       (fabs z0)
       (* (* (sinh (/ 1.0 z1)) (+ z1 z1)) (exp (/ (* z3 z2) z1))))
      0.0)
   (/ (* -0.5 (* (fabs z0) (* z2 z3))) z1)
   (* 0.5 (fabs z0)))))

C

double code(double z0, double z1, double z3, double z2) {
	double tmp;
	if ((fabs(z0) / ((sinh((1.0 / z1)) * (z1 + z1)) * exp(((z3 * z2) / z1)))) <= 0.0) {
		tmp = (-0.5 * (fabs(z0) * (z2 * z3))) / z1;
	} else {
		tmp = 0.5 * fabs(z0);
	}
	return copysign(1.0, z0) * tmp;
}

Java

public static double code(double z0, double z1, double z3, double z2) {
	double tmp;
	if ((Math.abs(z0) / ((Math.sinh((1.0 / z1)) * (z1 + z1)) * Math.exp(((z3 * z2) / z1)))) <= 0.0) {
		tmp = (-0.5 * (Math.abs(z0) * (z2 * z3))) / z1;
	} else {
		tmp = 0.5 * Math.abs(z0);
	}
	return Math.copySign(1.0, z0) * tmp;
}

Python

def code(z0, z1, z3, z2):
	tmp = 0
	if (math.fabs(z0) / ((math.sinh((1.0 / z1)) * (z1 + z1)) * math.exp(((z3 * z2) / z1)))) <= 0.0:
		tmp = (-0.5 * (math.fabs(z0) * (z2 * z3))) / z1
	else:
		tmp = 0.5 * math.fabs(z0)
	return math.copysign(1.0, z0) * tmp

Julia

function code(z0, z1, z3, z2)
	tmp = 0.0
	if (Float64(abs(z0) / Float64(Float64(sinh(Float64(1.0 / z1)) * Float64(z1 + z1)) * exp(Float64(Float64(z3 * z2) / z1)))) <= 0.0)
		tmp = Float64(Float64(-0.5 * Float64(abs(z0) * Float64(z2 * z3))) / z1);
	else
		tmp = Float64(0.5 * abs(z0));
	end
	return Float64(copysign(1.0, z0) * tmp)
end

MATLAB

function tmp_2 = code(z0, z1, z3, z2)
	tmp = 0.0;
	if ((abs(z0) / ((sinh((1.0 / z1)) * (z1 + z1)) * exp(((z3 * z2) / z1)))) <= 0.0)
		tmp = (-0.5 * (abs(z0) * (z2 * z3))) / z1;
	else
		tmp = 0.5 * abs(z0);
	end
	tmp_2 = (sign(z0) * abs(1.0)) * tmp;
end

Wolfram

code[z0_, z1_, z3_, z2_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[Abs[z0], $MachinePrecision] / N[(N[(N[Sinh[N[(1.0 / z1), $MachinePrecision]], $MachinePrecision] * N[(z1 + z1), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(z3 * z2), $MachinePrecision] / z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0], N[(N[(-0.5 * N[(N[Abs[z0], $MachinePrecision] * N[(z2 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision], N[(0.5 * N[Abs[z0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z0 (*.f64 (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z1)) (+.f64 z1 z1)) (exp.f64 (/.f64 (*.f64 z3 z2) z1)))) < 0.0

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 47.1%

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z0 \cdot \left(z2 \cdot z3\right)}{z1} + 0.5 \cdot z0} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. add-to-fraction N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 40.4%

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 40.4%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 40.4%

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

   6. Applied rewrites 40.4%

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

   7. Taylor expanded in z0 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 40.5%

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

   9. Applied rewrites 40.5%

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

   10. Taylor expanded in z1 around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 14.1%

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

   12. Applied rewrites 14.1%

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

   if 0.0 < (/.f64 z0 (*.f64 (*.f64 (sinh.f64 (/.f64 #s(literal 1 binary64) z1)) (+.f64 z1 z1)) (exp.f64 (/.f64 (*.f64 z3 z2) z1))))

   1. Initial program 99.5%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-*.f64 49.3%

         \[\leadsto 0.5 \cdot \color{blue}{z0} \]

   4. Applied rewrites 49.3%

      \[\leadsto \color{blue}{0.5 \cdot z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 49.3% accurate, 42.0× speedup

Math

\[0.5 \cdot z0 \]

FPCore

(FPCore (z0 z1 z3 z2)
  :precision binary64
  (* 0.5 z0))

C

double code(double z0, double z1, double z3, double z2) {
	return 0.5 * 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(z0, z1, z3, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    code = 0.5d0 * z0
end function

Java

public static double code(double z0, double z1, double z3, double z2) {
	return 0.5 * z0;
}

Python

def code(z0, z1, z3, z2):
	return 0.5 * z0

Julia

function code(z0, z1, z3, z2)
	return Float64(0.5 * z0)
end

MATLAB

function tmp = code(z0, z1, z3, z2)
	tmp = 0.5 * z0;
end

Wolfram

code[z0_, z1_, z3_, z2_] := N[(0.5 * z0), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z1 around inf

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

   1. lower-*.f64 49.3%

      \[\leadsto 0.5 \cdot \color{blue}{z0} \]

4. Applied rewrites 49.3%

   \[\leadsto \color{blue}{0.5 \cdot z0} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0 z1 z3 z2)
  :name "(/ z0 (* (* (sinh (/ 1 z1)) (+ z1 z1)) (exp (/ (* z3 z2) z1))))"
  :precision binary64
  (/ z0 (* (* (sinh (/ 1.0 z1)) (+ z1 z1)) (exp (/ (* z3 z2) z1)))))