Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 76.8% → 90.4%

Time: 3.5s

Alternatives: 12

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- (+ x y) (/ (* (- z t) y) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return (x + y) - (((z - t) * y) / (a - t));
}

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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x + y) - (((z - t) * y) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (x + y) - (((z - t) * y) / (a - t));
}

Python

def code(x, y, z, t, a):
	return (x + y) - (((z - t) * y) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (x + y) - (((z - t) * y) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- (+ x y) (/ (* (- z t) y) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return (x + y) - (((z - t) * y) / (a - t));
}

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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x + y) - (((z - t) * y) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (x + y) - (((z - t) * y) / (a - t));
}

Python

def code(x, y, z, t, a):
	return (x + y) - (((z - t) * y) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (x + y) - (((z - t) * y) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - \left(z - t\right) \cdot \frac{y}{a - t}\right)\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-277}:\\ \;\;\;\;\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y (* (- z t) (/ y (- a t))))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -2e-116)
     t_1
     (if (<= t_2 2e-277) (+ (- (/ (- (* a y) (* z y)) t)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - ((z - t) * (y / (a - t))));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -2e-116) {
		tmp = t_1;
	} else if (t_2 <= 2e-277) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else {
		tmp = t_1;
	}
	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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y - ((z - t) * (y / (a - t))))
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-2d-116)) then
        tmp = t_1
    else if (t_2 <= 2d-277) then
        tmp = -(((a * y) - (z * y)) / t) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - ((z - t) * (y / (a - t))));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -2e-116) {
		tmp = t_1;
	} else if (t_2 <= 2e-277) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - ((z - t) * (y / (a - t))))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -2e-116:
		tmp = t_1
	elif t_2 <= 2e-277:
		tmp = -(((a * y) - (z * y)) / t) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - Float64(Float64(z - t) * Float64(y / Float64(a - t)))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-116)
		tmp = t_1;
	elseif (t_2 <= 2e-277)
		tmp = Float64(Float64(-Float64(Float64(Float64(a * y) - Float64(z * y)) / t)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - ((z - t) * (y / (a - t))));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e-116)
		tmp = t_1;
	elseif (t_2 <= 2e-277)
		tmp = -(((a * y) - (z * y)) / t) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-116], t$95$1, If[LessEqual[t$95$2, 2e-277], N[((-N[(N[(N[(a * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-116 or 1.99999999999999994e-277 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + y\right)} - \frac{\left(z - t\right) \cdot y}{a - t} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}} \]

      3. lift--.f64 N/A

         \[\leadsto \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{\color{blue}{a - t}} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

      6. lift--.f64 N/A

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{\left(z - t\right)} \cdot y}{a - t} \]

      7. *-commutative N/A

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y \cdot \left(z - t\right)}}{a - t} \]

      8. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(y - \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

      9. lower-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(y - \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

      10. *-commutative N/A

          \[\leadsto x + \left(y - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t}\right) \]

      11. lower--.f64 N/A

          \[\leadsto x + \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]

      12. associate-/l* N/A

          \[\leadsto x + \left(y - \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto x + \left(y - \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}}\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(y - \color{blue}{\left(z - t\right)} \cdot \frac{y}{a - t}\right) \]

      15. lower-/.f64 N/A

          \[\leadsto x + \left(y - \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right) \]

      16. lift--.f64 86.3

          \[\leadsto x + \left(y - \left(z - t\right) \cdot \frac{y}{\color{blue}{a - t}}\right) \]

   3. Applied rewrites 86.3%

      \[\leadsto \color{blue}{x + \left(y - \left(z - t\right) \cdot \frac{y}{a - t}\right)} \]

   if -2e-116 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.99999999999999994e-277

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{a \cdot y - y \cdot z}{t}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{a \cdot y - y \cdot z}{t}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{a \cdot y - y \cdot z}{t}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{a \cdot y - y \cdot z}{t}\right) + x \]

      7. lower-*.f64 N/A

         \[\leadsto \left(-\frac{a \cdot y - y \cdot z}{t}\right) + x \]

      8. *-commutative N/A

         \[\leadsto \left(-\frac{a \cdot y - z \cdot y}{t}\right) + x \]

      9. lower-*.f64 57.9

         \[\leadsto \left(-\frac{a \cdot y - z \cdot y}{t}\right) + x \]

   4. Applied rewrites 57.9%

      \[\leadsto \color{blue}{\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-277}:\\ \;\;\;\;\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z (- a t)))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -2e-116)
     t_1
     (if (<= t_2 2e-277) (+ (- (/ (- (* a y) (* z y)) t)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -2e-116) {
		tmp = t_1;
	} else if (t_2 <= 2e-277) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else {
		tmp = t_1;
	}
	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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) - (y * (z / (a - t)))
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-2d-116)) then
        tmp = t_1
    else if (t_2 <= 2d-277) then
        tmp = -(((a * y) - (z * y)) / t) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -2e-116) {
		tmp = t_1;
	} else if (t_2 <= 2e-277) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (z / (a - t)))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -2e-116:
		tmp = t_1
	elif t_2 <= 2e-277:
		tmp = -(((a * y) - (z * y)) / t) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-116)
		tmp = t_1;
	elseif (t_2 <= 2e-277)
		tmp = Float64(Float64(-Float64(Float64(Float64(a * y) - Float64(z * y)) / t)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (z / (a - t)));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e-116)
		tmp = t_1;
	elseif (t_2 <= 2e-277)
		tmp = -(((a * y) - (z * y)) / t) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-116], t$95$1, If[LessEqual[t$95$2, 2e-277], N[((-N[(N[(N[(a * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-116 or 1.99999999999999994e-277 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{\color{blue}{a - t}} \]

      4. lift--.f64 81.5

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{a - \color{blue}{t}} \]

   4. Applied rewrites 81.5%

      \[\leadsto \left(x + y\right) - \color{blue}{y \cdot \frac{z}{a - t}} \]

   if -2e-116 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.99999999999999994e-277

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{a \cdot y - y \cdot z}{t}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{a \cdot y - y \cdot z}{t}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{a \cdot y - y \cdot z}{t}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{a \cdot y - y \cdot z}{t}\right) + x \]

      7. lower-*.f64 N/A

         \[\leadsto \left(-\frac{a \cdot y - y \cdot z}{t}\right) + x \]

      8. *-commutative N/A

         \[\leadsto \left(-\frac{a \cdot y - z \cdot y}{t}\right) + x \]

      9. lower-*.f64 57.9

         \[\leadsto \left(-\frac{a \cdot y - z \cdot y}{t}\right) + x \]

   4. Applied rewrites 57.9%

      \[\leadsto \color{blue}{\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;-1 \cdot \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z (- a t)))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -5e-277)
     t_1
     (if (<= t_2 0.0) (* -1.0 (/ (* y (- a z)) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -5e-277) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 * ((y * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) - (y * (z / (a - t)))
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-5d-277)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = (-1.0d0) * ((y * (a - z)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -5e-277) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 * ((y * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (z / (a - t)))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -5e-277:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = -1.0 * ((y * (a - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-277)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(-1.0 * Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (z / (a - t)));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -5e-277)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = -1.0 * ((y * (a - z)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-277], t$95$1, If[LessEqual[t$95$2, 0.0], N[(-1.0 * N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5e-277 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{\color{blue}{a - t}} \]

      4. lift--.f64 81.5

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{a - \color{blue}{t}} \]

   4. Applied rewrites 81.5%

      \[\leadsto \left(x + y\right) - \color{blue}{y \cdot \frac{z}{a - t}} \]

   if -5e-277 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in t around -inf

      \[\leadsto -1 \cdot \color{blue}{\frac{y \cdot \left(a - z\right)}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

      4. lower--.f64 22.7

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

   7. Applied rewrites 22.7%

      \[\leadsto -1 \cdot \color{blue}{\frac{y \cdot \left(a - z\right)}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 72.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ t_2 := \left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y - y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;-1 \cdot \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y - \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t))))
        (t_2 (- (+ x y) (/ (* z y) a))))
   (if (<= t_1 (- INFINITY))
     (- y (* y (/ z (- a t))))
     (if (<= t_1 -5e-198)
       t_2
       (if (<= t_1 0.0)
         (* -1.0 (/ (* y (- a z)) t))
         (if (<= t_1 4e+301) t_2 (- y (* (- z t) (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double t_2 = (x + y) - ((z * y) / a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y - (y * (z / (a - t)));
	} else if (t_1 <= -5e-198) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = -1.0 * ((y * (a - z)) / t);
	} else if (t_1 <= 4e+301) {
		tmp = t_2;
	} else {
		tmp = y - ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double t_2 = (x + y) - ((z * y) / a);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y - (y * (z / (a - t)));
	} else if (t_1 <= -5e-198) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = -1.0 * ((y * (a - z)) / t);
	} else if (t_1 <= 4e+301) {
		tmp = t_2;
	} else {
		tmp = y - ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	t_2 = (x + y) - ((z * y) / a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y - (y * (z / (a - t)))
	elif t_1 <= -5e-198:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = -1.0 * ((y * (a - z)) / t)
	elif t_1 <= 4e+301:
		tmp = t_2
	else:
		tmp = y - ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	t_2 = Float64(Float64(x + y) - Float64(Float64(z * y) / a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y - Float64(y * Float64(z / Float64(a - t))));
	elseif (t_1 <= -5e-198)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(-1.0 * Float64(Float64(y * Float64(a - z)) / t));
	elseif (t_1 <= 4e+301)
		tmp = t_2;
	else
		tmp = Float64(y - Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	t_2 = (x + y) - ((z * y) / a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y - (y * (z / (a - t)));
	elseif (t_1 <= -5e-198)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = -1.0 * ((y * (a - z)) / t);
	elseif (t_1 <= 4e+301)
		tmp = t_2;
	else
		tmp = y - ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-198], t$95$2, If[LessEqual[t$95$1, 0.0], N[(-1.0 * N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+301], t$95$2, N[(y - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{\color{blue}{a - t}} \]

      4. lift--.f64 81.5

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{a - \color{blue}{t}} \]

   4. Applied rewrites 81.5%

      \[\leadsto \left(x + y\right) - \color{blue}{y \cdot \frac{z}{a - t}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a - t} \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a - t} \]

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.9999999999999999e-198 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 4.00000000000000021e301

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \frac{y \cdot z}{\color{blue}{a}} \]

      2. *-commutative N/A

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

      3. lower-*.f64 64.3

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

   4. Applied rewrites 64.3%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z \cdot y}{a}} \]

   if -4.9999999999999999e-198 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in t around -inf

      \[\leadsto -1 \cdot \color{blue}{\frac{y \cdot \left(a - z\right)}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

      4. lower--.f64 22.7

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

   7. Applied rewrites 22.7%

      \[\leadsto -1 \cdot \color{blue}{\frac{y \cdot \left(a - z\right)}{t}} \]

   if 4.00000000000000021e301 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y - \frac{y \cdot \left(z - t\right)}{a - t}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y - \frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t} \]

      2. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

      3. associate-/l* N/A

         \[\leadsto y - \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

      4. lower-*.f64 N/A

         \[\leadsto y - \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

      5. lift--.f64 N/A

         \[\leadsto y - \left(z - t\right) \cdot \frac{\color{blue}{y}}{a - t} \]

      6. lower-/.f64 N/A

         \[\leadsto y - \left(z - t\right) \cdot \frac{y}{\color{blue}{a - t}} \]

      7. lift--.f64 39.9

         \[\leadsto y - \left(z - t\right) \cdot \frac{y}{a - \color{blue}{t}} \]

   4. Applied rewrites 39.9%

      \[\leadsto \color{blue}{y - \left(z - t\right) \cdot \frac{y}{a - t}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 71.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ t_3 := \left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y - y \cdot t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-198}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;-1 \cdot \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\_1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- a t)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t))))
        (t_3 (- (+ x y) (/ (* z y) a))))
   (if (<= t_2 (- INFINITY))
     (- y (* y t_1))
     (if (<= t_2 -5e-198)
       t_3
       (if (<= t_2 0.0)
         (* -1.0 (/ (* y (- a z)) t))
         (if (<= t_2 4e+301) t_3 (* (- 1.0 t_1) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double t_3 = (x + y) - ((z * y) / a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y - (y * t_1);
	} else if (t_2 <= -5e-198) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 * ((y * (a - z)) / t);
	} else if (t_2 <= 4e+301) {
		tmp = t_3;
	} else {
		tmp = (1.0 - t_1) * y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double t_3 = (x + y) - ((z * y) / a);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y - (y * t_1);
	} else if (t_2 <= -5e-198) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 * ((y * (a - z)) / t);
	} else if (t_2 <= 4e+301) {
		tmp = t_3;
	} else {
		tmp = (1.0 - t_1) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a - t)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	t_3 = (x + y) - ((z * y) / a)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y - (y * t_1)
	elif t_2 <= -5e-198:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = -1.0 * ((y * (a - z)) / t)
	elif t_2 <= 4e+301:
		tmp = t_3
	else:
		tmp = (1.0 - t_1) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a - t))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	t_3 = Float64(Float64(x + y) - Float64(Float64(z * y) / a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y - Float64(y * t_1));
	elseif (t_2 <= -5e-198)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(-1.0 * Float64(Float64(y * Float64(a - z)) / t));
	elseif (t_2 <= 4e+301)
		tmp = t_3;
	else
		tmp = Float64(Float64(1.0 - t_1) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a - t);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	t_3 = (x + y) - ((z * y) / a);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y - (y * t_1);
	elseif (t_2 <= -5e-198)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = -1.0 * ((y * (a - z)) / t);
	elseif (t_2 <= 4e+301)
		tmp = t_3;
	else
		tmp = (1.0 - t_1) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-198], t$95$3, If[LessEqual[t$95$2, 0.0], N[(-1.0 * N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+301], t$95$3, N[(N[(1.0 - t$95$1), $MachinePrecision] * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{\color{blue}{a - t}} \]

      4. lift--.f64 81.5

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{a - \color{blue}{t}} \]

   4. Applied rewrites 81.5%

      \[\leadsto \left(x + y\right) - \color{blue}{y \cdot \frac{z}{a - t}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a - t} \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a - t} \]

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.9999999999999999e-198 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 4.00000000000000021e301

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \frac{y \cdot z}{\color{blue}{a}} \]

      2. *-commutative N/A

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

      3. lower-*.f64 64.3

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

   4. Applied rewrites 64.3%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z \cdot y}{a}} \]

   if -4.9999999999999999e-198 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in t around -inf

      \[\leadsto -1 \cdot \color{blue}{\frac{y \cdot \left(a - z\right)}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

      4. lower--.f64 22.7

         \[\leadsto -1 \cdot \frac{y \cdot \left(a - z\right)}{t} \]

   7. Applied rewrites 22.7%

      \[\leadsto -1 \cdot \color{blue}{\frac{y \cdot \left(a - z\right)}{t}} \]

   if 4.00000000000000021e301 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in t around 0

      \[\leadsto \left(1 - \frac{z}{a - t}\right) \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

      \[\leadsto \left(1 - \frac{z}{a - t}\right) \cdot y \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 71.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-84}:\\ \;\;\;\;\left(x + y\right) - y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* z y) a))))
   (if (<= a -1.9e-29)
     t_1
     (if (<= a 7.2e-84) (- (+ x y) (* y (- 1.0 (/ z t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((z * y) / a);
	double tmp;
	if (a <= -1.9e-29) {
		tmp = t_1;
	} else if (a <= 7.2e-84) {
		tmp = (x + y) - (y * (1.0 - (z / t)));
	} else {
		tmp = t_1;
	}
	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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((z * y) / a)
    if (a <= (-1.9d-29)) then
        tmp = t_1
    else if (a <= 7.2d-84) then
        tmp = (x + y) - (y * (1.0d0 - (z / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((z * y) / a);
	double tmp;
	if (a <= -1.9e-29) {
		tmp = t_1;
	} else if (a <= 7.2e-84) {
		tmp = (x + y) - (y * (1.0 - (z / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((z * y) / a)
	tmp = 0
	if a <= -1.9e-29:
		tmp = t_1
	elif a <= 7.2e-84:
		tmp = (x + y) - (y * (1.0 - (z / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(z * y) / a))
	tmp = 0.0
	if (a <= -1.9e-29)
		tmp = t_1;
	elseif (a <= 7.2e-84)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(1.0 - Float64(z / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((z * y) / a);
	tmp = 0.0;
	if (a <= -1.9e-29)
		tmp = t_1;
	elseif (a <= 7.2e-84)
		tmp = (x + y) - (y * (1.0 - (z / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e-29], t$95$1, If[LessEqual[a, 7.2e-84], N[(N[(x + y), $MachinePrecision] - N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.89999999999999988e-29 or 7.20000000000000007e-84 < a

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \frac{y \cdot z}{\color{blue}{a}} \]

      2. *-commutative N/A

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

      3. lower-*.f64 64.3

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

   4. Applied rewrites 64.3%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z \cdot y}{a}} \]

   if -1.89999999999999988e-29 < a < 7.20000000000000007e-84

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in a around 0

      \[\leadsto \left(x + y\right) - \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(x + y\right) - \left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{t}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      5. lift--.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      6. lift-*.f64 49.9

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

   4. Applied rewrites 49.9%

      \[\leadsto \left(x + y\right) - \color{blue}{\left(-\frac{\left(z - t\right) \cdot y}{t}\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \color{blue}{\frac{z}{t}}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{\color{blue}{t}}\right) \]

      3. lower-/.f64 52.0

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{t}\right) \]

   7. Applied rewrites 52.0%

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y - y \cdot t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\_1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- a t))) (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 (- INFINITY))
     (- y (* y t_1))
     (if (<= t_2 4e+301) (- (+ x y) (/ (* z y) a)) (* (- 1.0 t_1) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y - (y * t_1);
	} else if (t_2 <= 4e+301) {
		tmp = (x + y) - ((z * y) / a);
	} else {
		tmp = (1.0 - t_1) * y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y - (y * t_1);
	} else if (t_2 <= 4e+301) {
		tmp = (x + y) - ((z * y) / a);
	} else {
		tmp = (1.0 - t_1) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a - t)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y - (y * t_1)
	elif t_2 <= 4e+301:
		tmp = (x + y) - ((z * y) / a)
	else:
		tmp = (1.0 - t_1) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a - t))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y - Float64(y * t_1));
	elseif (t_2 <= 4e+301)
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / a));
	else
		tmp = Float64(Float64(1.0 - t_1) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a - t);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y - (y * t_1);
	elseif (t_2 <= 4e+301)
		tmp = (x + y) - ((z * y) / a);
	else
		tmp = (1.0 - t_1) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+301], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t$95$1), $MachinePrecision] * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{\color{blue}{a - t}} \]

      4. lift--.f64 81.5

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{a - \color{blue}{t}} \]

   4. Applied rewrites 81.5%

      \[\leadsto \left(x + y\right) - \color{blue}{y \cdot \frac{z}{a - t}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a - t} \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a - t} \]

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 4.00000000000000021e301

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \frac{y \cdot z}{\color{blue}{a}} \]

      2. *-commutative N/A

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

      3. lower-*.f64 64.3

         \[\leadsto \left(x + y\right) - \frac{z \cdot y}{a} \]

   4. Applied rewrites 64.3%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z \cdot y}{a}} \]

   if 4.00000000000000021e301 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in t around 0

      \[\leadsto \left(1 - \frac{z}{a - t}\right) \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

      \[\leadsto \left(1 - \frac{z}{a - t}\right) \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 61.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - t}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;y - y \cdot t\_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-11}:\\ \;\;\;\;\left(x + y\right) - y \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\_1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- a t))))
   (if (<= y -2.4e+36)
     (- y (* y t_1))
     (if (<= y 2.45e-11) (- (+ x y) (* y 1.0)) (* (- 1.0 t_1) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double tmp;
	if (y <= -2.4e+36) {
		tmp = y - (y * t_1);
	} else if (y <= 2.45e-11) {
		tmp = (x + y) - (y * 1.0);
	} else {
		tmp = (1.0 - t_1) * y;
	}
	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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (a - t)
    if (y <= (-2.4d+36)) then
        tmp = y - (y * t_1)
    else if (y <= 2.45d-11) then
        tmp = (x + y) - (y * 1.0d0)
    else
        tmp = (1.0d0 - t_1) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double tmp;
	if (y <= -2.4e+36) {
		tmp = y - (y * t_1);
	} else if (y <= 2.45e-11) {
		tmp = (x + y) - (y * 1.0);
	} else {
		tmp = (1.0 - t_1) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a - t)
	tmp = 0
	if y <= -2.4e+36:
		tmp = y - (y * t_1)
	elif y <= 2.45e-11:
		tmp = (x + y) - (y * 1.0)
	else:
		tmp = (1.0 - t_1) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a - t))
	tmp = 0.0
	if (y <= -2.4e+36)
		tmp = Float64(y - Float64(y * t_1));
	elseif (y <= 2.45e-11)
		tmp = Float64(Float64(x + y) - Float64(y * 1.0));
	else
		tmp = Float64(Float64(1.0 - t_1) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a - t);
	tmp = 0.0;
	if (y <= -2.4e+36)
		tmp = y - (y * t_1);
	elseif (y <= 2.45e-11)
		tmp = (x + y) - (y * 1.0);
	else
		tmp = (1.0 - t_1) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+36], N[(y - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e-11], N[(N[(x + y), $MachinePrecision] - N[(y * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t$95$1), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999992e36

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\frac{z}{a - t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{\color{blue}{a - t}} \]

      4. lift--.f64 81.5

         \[\leadsto \left(x + y\right) - y \cdot \frac{z}{a - \color{blue}{t}} \]

   4. Applied rewrites 81.5%

      \[\leadsto \left(x + y\right) - \color{blue}{y \cdot \frac{z}{a - t}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a - t} \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a - t} \]

   if -2.39999999999999992e36 < y < 2.4499999999999999e-11

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in a around 0

      \[\leadsto \left(x + y\right) - \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(x + y\right) - \left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{t}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      5. lift--.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      6. lift-*.f64 49.9

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

   4. Applied rewrites 49.9%

      \[\leadsto \left(x + y\right) - \color{blue}{\left(-\frac{\left(z - t\right) \cdot y}{t}\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \color{blue}{\frac{z}{t}}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{\color{blue}{t}}\right) \]

      3. lower-/.f64 52.0

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{t}\right) \]

   7. Applied rewrites 52.0%

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(x + y\right) - y \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 44.9%

       \[\leadsto \left(x + y\right) - y \cdot 1 \]

   if 2.4499999999999999e-11 < y

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in t around 0

      \[\leadsto \left(1 - \frac{z}{a - t}\right) \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

      \[\leadsto \left(1 - \frac{z}{a - t}\right) \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 61.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{z}{a - t}\right) \cdot y\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-11}:\\ \;\;\;\;\left(x + y\right) - y \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ z (- a t))) y)))
   (if (<= y -2.4e+36) t_1 (if (<= y 2.45e-11) (- (+ x y) (* y 1.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 - (z / (a - t))) * y;
	double tmp;
	if (y <= -2.4e+36) {
		tmp = t_1;
	} else if (y <= 2.45e-11) {
		tmp = (x + y) - (y * 1.0);
	} else {
		tmp = t_1;
	}
	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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - (z / (a - t))) * y
    if (y <= (-2.4d+36)) then
        tmp = t_1
    else if (y <= 2.45d-11) then
        tmp = (x + y) - (y * 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 - (z / (a - t))) * y;
	double tmp;
	if (y <= -2.4e+36) {
		tmp = t_1;
	} else if (y <= 2.45e-11) {
		tmp = (x + y) - (y * 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (1.0 - (z / (a - t))) * y
	tmp = 0
	if y <= -2.4e+36:
		tmp = t_1
	elif y <= 2.45e-11:
		tmp = (x + y) - (y * 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(1.0 - Float64(z / Float64(a - t))) * y)
	tmp = 0.0
	if (y <= -2.4e+36)
		tmp = t_1;
	elseif (y <= 2.45e-11)
		tmp = Float64(Float64(x + y) - Float64(y * 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (1.0 - (z / (a - t))) * y;
	tmp = 0.0;
	if (y <= -2.4e+36)
		tmp = t_1;
	elseif (y <= 2.45e-11)
		tmp = (x + y) - (y * 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.4e+36], t$95$1, If[LessEqual[y, 2.45e-11], N[(N[(x + y), $MachinePrecision] - N[(y * 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999992e36 or 2.4499999999999999e-11 < y

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in t around 0

      \[\leadsto \left(1 - \frac{z}{a - t}\right) \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

      \[\leadsto \left(1 - \frac{z}{a - t}\right) \cdot y \]

   if -2.39999999999999992e36 < y < 2.4499999999999999e-11

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in a around 0

      \[\leadsto \left(x + y\right) - \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(x + y\right) - \left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{t}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      5. lift--.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      6. lift-*.f64 49.9

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

   4. Applied rewrites 49.9%

      \[\leadsto \left(x + y\right) - \color{blue}{\left(-\frac{\left(z - t\right) \cdot y}{t}\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \color{blue}{\frac{z}{t}}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{\color{blue}{t}}\right) \]

      3. lower-/.f64 52.0

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{t}\right) \]

   7. Applied rewrites 52.0%

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(x + y\right) - y \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 44.9%

       \[\leadsto \left(x + y\right) - y \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 56.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{z}{a}\right) \cdot y\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+78}:\\ \;\;\;\;\left(x + y\right) - y \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ z a)) y)))
   (if (<= y -4.2e+39) t_1 (if (<= y 5.6e+78) (- (+ x y) (* y 1.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 - (z / a)) * y;
	double tmp;
	if (y <= -4.2e+39) {
		tmp = t_1;
	} else if (y <= 5.6e+78) {
		tmp = (x + y) - (y * 1.0);
	} else {
		tmp = t_1;
	}
	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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - (z / a)) * y
    if (y <= (-4.2d+39)) then
        tmp = t_1
    else if (y <= 5.6d+78) then
        tmp = (x + y) - (y * 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 - (z / a)) * y;
	double tmp;
	if (y <= -4.2e+39) {
		tmp = t_1;
	} else if (y <= 5.6e+78) {
		tmp = (x + y) - (y * 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (1.0 - (z / a)) * y
	tmp = 0
	if y <= -4.2e+39:
		tmp = t_1
	elif y <= 5.6e+78:
		tmp = (x + y) - (y * 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(1.0 - Float64(z / a)) * y)
	tmp = 0.0
	if (y <= -4.2e+39)
		tmp = t_1;
	elseif (y <= 5.6e+78)
		tmp = Float64(Float64(x + y) - Float64(y * 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (1.0 - (z / a)) * y;
	tmp = 0.0;
	if (y <= -4.2e+39)
		tmp = t_1;
	elseif (y <= 5.6e+78)
		tmp = (x + y) - (y * 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.2e+39], t$95$1, If[LessEqual[y, 5.6e+78], N[(N[(x + y), $MachinePrecision] - N[(y * 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999997e39 or 5.6000000000000002e78 < y

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in t around 0

      \[\leadsto \left(1 - \frac{z}{a}\right) \cdot y \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(1 - \frac{z}{a}\right) \cdot y \]

      2. lower-/.f64 31.0

         \[\leadsto \left(1 - \frac{z}{a}\right) \cdot y \]

   7. Applied rewrites 31.0%

      \[\leadsto \left(1 - \frac{z}{a}\right) \cdot y \]

   if -4.1999999999999997e39 < y < 5.6000000000000002e78

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in a around 0

      \[\leadsto \left(x + y\right) - \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(x + y\right) - \left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{t}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      5. lift--.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      6. lift-*.f64 49.9

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

   4. Applied rewrites 49.9%

      \[\leadsto \left(x + y\right) - \color{blue}{\left(-\frac{\left(z - t\right) \cdot y}{t}\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \color{blue}{\frac{z}{t}}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{\color{blue}{t}}\right) \]

      3. lower-/.f64 52.0

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{t}\right) \]

   7. Applied rewrites 52.0%

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(x + y\right) - y \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 44.9%

       \[\leadsto \left(x + y\right) - y \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 49.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+86}:\\ \;\;\;\;\left(x + y\right) - y \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)))
   (if (<= y -3.6e+30) t_1 (if (<= y 1.8e+86) (- (+ x y) (* y 1.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / t) * y;
	double tmp;
	if (y <= -3.6e+30) {
		tmp = t_1;
	} else if (y <= 1.8e+86) {
		tmp = (x + y) - (y * 1.0);
	} else {
		tmp = t_1;
	}
	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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / t) * y
    if (y <= (-3.6d+30)) then
        tmp = t_1
    else if (y <= 1.8d+86) then
        tmp = (x + y) - (y * 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / t) * y;
	double tmp;
	if (y <= -3.6e+30) {
		tmp = t_1;
	} else if (y <= 1.8e+86) {
		tmp = (x + y) - (y * 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / t) * y
	tmp = 0
	if y <= -3.6e+30:
		tmp = t_1
	elif y <= 1.8e+86:
		tmp = (x + y) - (y * 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / t) * y)
	tmp = 0.0
	if (y <= -3.6e+30)
		tmp = t_1;
	elseif (y <= 1.8e+86)
		tmp = Float64(Float64(x + y) - Float64(y * 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / t) * y;
	tmp = 0.0;
	if (y <= -3.6e+30)
		tmp = t_1;
	elseif (y <= 1.8e+86)
		tmp = (x + y) - (y * 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.6e+30], t$95$1, If[LessEqual[y, 1.8e+86], N[(N[(x + y), $MachinePrecision] - N[(y * 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6000000000000002e30 or 1.80000000000000003e86 < y

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

      9. lift--.f64 45.0

         \[\leadsto \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y \]

   4. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \cdot y} \]

   5. Taylor expanded in a around 0

      \[\leadsto \frac{z}{t} \cdot y \]
   6. Step-by-step derivation

      1. lower-/.f64 20.3

         \[\leadsto \frac{z}{t} \cdot y \]

   7. Applied rewrites 20.3%

      \[\leadsto \frac{z}{t} \cdot y \]

   if -3.6000000000000002e30 < y < 1.80000000000000003e86

   1. Initial program 76.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

   2. Taylor expanded in a around 0

      \[\leadsto \left(x + y\right) - \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(x + y\right) - \left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{t}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{y \cdot \left(z - t\right)}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      5. lift--.f64 N/A

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

      6. lift-*.f64 49.9

         \[\leadsto \left(x + y\right) - \left(-\frac{\left(z - t\right) \cdot y}{t}\right) \]

   4. Applied rewrites 49.9%

      \[\leadsto \left(x + y\right) - \color{blue}{\left(-\frac{\left(z - t\right) \cdot y}{t}\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \color{blue}{\frac{z}{t}}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{\color{blue}{t}}\right) \]

      3. lower-/.f64 52.0

         \[\leadsto \left(x + y\right) - y \cdot \left(1 - \frac{z}{t}\right) \]

   7. Applied rewrites 52.0%

      \[\leadsto \left(x + y\right) - y \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(x + y\right) - y \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 44.9%

       \[\leadsto \left(x + y\right) - y \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 18.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \frac{y \cdot z}{t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (* y z) t))

C

double code(double x, double y, double z, double t, double a) {
	return (y * z) / t;
}

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(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (y * z) / t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (y * z) / t;
}

Python

def code(x, y, z, t, a):
	return (y * z) / t

Julia

function code(x, y, z, t, a)
	return Float64(Float64(y * z) / t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (y * z) / t;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]

Derivation

1. Initial program 76.8%

   \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a - t}} \]
3. Step-by-step derivation

   1. associate-*r/ N/A

      \[\leadsto \frac{-1 \cdot \left(y \cdot z\right)}{\color{blue}{a - t}} \]

   2. mul-1-neg N/A

      \[\leadsto \frac{\mathsf{neg}\left(y \cdot z\right)}{\color{blue}{a} - t} \]

   3. sub-negate-rev N/A

      \[\leadsto \frac{\mathsf{neg}\left(y \cdot z\right)}{\mathsf{neg}\left(\left(t - a\right)\right)} \]

   4. frac-2neg-rev N/A

      \[\leadsto \frac{y \cdot z}{\color{blue}{t - a}} \]

   5. lower-/.f64 N/A

      \[\leadsto \frac{y \cdot z}{\color{blue}{t - a}} \]

   6. *-commutative N/A

      \[\leadsto \frac{z \cdot y}{\color{blue}{t} - a} \]

   7. lower-*.f64 N/A

      \[\leadsto \frac{z \cdot y}{\color{blue}{t} - a} \]

   8. lower--.f64 26.4

      \[\leadsto \frac{z \cdot y}{t - \color{blue}{a}} \]

4. Applied rewrites 26.4%

   \[\leadsto \color{blue}{\frac{z \cdot y}{t - a}} \]

5. Taylor expanded in t around inf

   \[\leadsto \frac{y \cdot z}{\color{blue}{t}} \]
6. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{y \cdot z}{t} \]

   2. lower-*.f64 18.8

      \[\leadsto \frac{y \cdot z}{t} \]

7. Applied rewrites 18.8%

   \[\leadsto \frac{y \cdot z}{\color{blue}{t}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025140 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64
  (- (+ x y) (/ (* (- z t) y) (- a t))))