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

Percentage Accurate: 77.1% → 91.1%

Time: 4.1s

Alternatives: 13

Speedup: 0.9×

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: 77.1% 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: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - \left(z - t\right) \cdot \frac{y}{a - t}\right)\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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-138)
     t_1
     (if (<= t_2 0.0) (+ (- (/ (- (* 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-138) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		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-138)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) 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-138) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		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-138:
		tmp = t_1
	elif t_2 <= 0.0:
		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-138)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		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-138)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		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-138], t$95$1, If[LessEqual[t$95$2, 0.0], 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))) < -2.00000000000000013e-138 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 77.1%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 87.7

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

   3. Applied rewrites 87.7%

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

   if -2.00000000000000013e-138 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 77.1%

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

   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 57.5

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

   4. Applied rewrites 57.5%

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

Alternative 2: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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-138)
     t_1
     (if (<= t_2 0.0) (+ (- (/ (- (* 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-138) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		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-138)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) 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-138) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		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-138:
		tmp = t_1
	elif t_2 <= 0.0:
		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-138)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		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-138)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		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-138], t$95$1, If[LessEqual[t$95$2, 0.0], 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))) < -2.00000000000000013e-138 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 77.1%

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

   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 82.4

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

   4. Applied rewrites 82.4%

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

   if -2.00000000000000013e-138 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 77.1%

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

   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 57.5

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

   4. Applied rewrites 57.5%

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

Alternative 3: 83.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+174}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+174) (* 1.0 x) (- (+ x y) (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+174) {
		tmp = 1.0 * x;
	} else {
		tmp = (x + y) - (y * (z / (a - t)));
	}
	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) :: tmp
    if (t <= (-2.7d+174)) then
        tmp = 1.0d0 * x
    else
        tmp = (x + y) - (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+174) {
		tmp = 1.0 * x;
	} else {
		tmp = (x + y) - (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+174:
		tmp = 1.0 * x
	else:
		tmp = (x + y) - (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+174)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+174)
		tmp = 1.0 * x;
	else
		tmp = (x + y) - (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+174], N[(1.0 * x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6999999999999999e174

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]

   if -2.6999999999999999e174 < t

   1. Initial program 77.1%

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

   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 82.4

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

   4. Applied rewrites 82.4%

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

Alternative 4: 72.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+26}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+130}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.35e+26)
   (* 1.0 x)
   (if (<= t 9.5e+130) (- (+ x y) (* y (/ z a))) (* 1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.35e+26) {
		tmp = 1.0 * x;
	} else if (t <= 9.5e+130) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = 1.0 * x;
	}
	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) :: tmp
    if (t <= (-2.35d+26)) then
        tmp = 1.0d0 * x
    else if (t <= 9.5d+130) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.35e+26) {
		tmp = 1.0 * x;
	} else if (t <= 9.5e+130) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.35e+26:
		tmp = 1.0 * x
	elif t <= 9.5e+130:
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.35e+26)
		tmp = Float64(1.0 * x);
	elseif (t <= 9.5e+130)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.35e+26)
		tmp = 1.0 * x;
	elseif (t <= 9.5e+130)
		tmp = (x + y) - (y * (z / a));
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.35e+26], N[(1.0 * x), $MachinePrecision], If[LessEqual[t, 9.5e+130], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3499999999999999e26 or 9.5000000000000009e130 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]

   if -2.3499999999999999e26 < t < 9.5000000000000009e130

   1. Initial program 77.1%

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

   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 82.4

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

   4. Applied rewrites 82.4%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 67.0

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

   7. Applied rewrites 67.0%

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

Alternative 5: 65.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{z}{a - t}\right) \cdot y\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-44}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ z (- a t))) y)))
   (if (<= y -2.15e+33) t_1 (if (<= y 5.8e-44) (* 1.0 x) 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 <= -2.15e+33) {
		tmp = t_1;
	} else if (y <= 5.8e-44) {
		tmp = 1.0 * 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) :: tmp
    t_1 = (1.0d0 - (z / (a - t))) * y
    if (y <= (-2.15d+33)) then
        tmp = t_1
    else if (y <= 5.8d-44) then
        tmp = 1.0d0 * 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 = (1.0 - (z / (a - t))) * y;
	double tmp;
	if (y <= -2.15e+33) {
		tmp = t_1;
	} else if (y <= 5.8e-44) {
		tmp = 1.0 * x;
	} 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 <= -2.15e+33:
		tmp = t_1
	elif y <= 5.8e-44:
		tmp = 1.0 * x
	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 <= -2.15e+33)
		tmp = t_1;
	elseif (y <= 5.8e-44)
		tmp = Float64(1.0 * x);
	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 <= -2.15e+33)
		tmp = t_1;
	elseif (y <= 5.8e-44)
		tmp = 1.0 * x;
	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, -2.15e+33], t$95$1, If[LessEqual[y, 5.8e-44], N[(1.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15000000000000014e33 or 5.8000000000000003e-44 < y

   1. Initial program 77.1%

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

   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 44.8

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

   4. Applied rewrites 44.8%

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

   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 -2.15000000000000014e33 < y < 5.8000000000000003e-44

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 63.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-z}{a - t} \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+307}:\\ \;\;\;\;\left(1 + \frac{y}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- z) (- a t)) y))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -1e+308) t_1 (if (<= t_2 1e+307) (* (+ 1.0 (/ y x)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-z / (a - t)) * y;
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+308) {
		tmp = t_1;
	} else if (t_2 <= 1e+307) {
		tmp = (1.0 + (y / x)) * 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 = (-z / (a - t)) * y
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-1d+308)) then
        tmp = t_1
    else if (t_2 <= 1d+307) then
        tmp = (1.0d0 + (y / x)) * 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 = (-z / (a - t)) * y;
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+308) {
		tmp = t_1;
	} else if (t_2 <= 1e+307) {
		tmp = (1.0 + (y / x)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-z / (a - t)) * y
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -1e+308:
		tmp = t_1
	elif t_2 <= 1e+307:
		tmp = (1.0 + (y / x)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-z) / Float64(a - t)) * y)
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e+308)
		tmp = t_1;
	elseif (t_2 <= 1e+307)
		tmp = Float64(Float64(1.0 + Float64(y / x)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-z / (a - t)) * y;
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -1e+308)
		tmp = t_1;
	elseif (t_2 <= 1e+307)
		tmp = (1.0 + (y / x)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $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, -1e+308], t$95$1, If[LessEqual[t$95$2, 1e+307], N[(N[(1.0 + N[(y / x), $MachinePrecision]), $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))) < -1e308 or 9.99999999999999986e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 77.1%

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

   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 44.8

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

   4. Applied rewrites 44.8%

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

   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%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

         \[\leadsto \frac{-1 \cdot z}{a - t} \cdot y \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot z}{a - t} \cdot y \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 28.9

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

   10. Applied rewrites 28.9%

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

   if -1e308 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.99999999999999986e306

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in a around inf

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

      1. lower-+.f64 N/A

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

      2. lift-/.f64 58.0

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

   7. Applied rewrites 58.0%

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

Alternative 7: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{z}{a}\right) \cdot y\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+94}:\\ \;\;\;\;\left(1 + \frac{y}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ z a)) y)))
   (if (<= y -7.5e+167) t_1 (if (<= y 8.5e+94) (* (+ 1.0 (/ y x)) x) 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 <= -7.5e+167) {
		tmp = t_1;
	} else if (y <= 8.5e+94) {
		tmp = (1.0 + (y / x)) * 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) :: tmp
    t_1 = (1.0d0 - (z / a)) * y
    if (y <= (-7.5d+167)) then
        tmp = t_1
    else if (y <= 8.5d+94) then
        tmp = (1.0d0 + (y / x)) * 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 = (1.0 - (z / a)) * y;
	double tmp;
	if (y <= -7.5e+167) {
		tmp = t_1;
	} else if (y <= 8.5e+94) {
		tmp = (1.0 + (y / x)) * x;
	} 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 <= -7.5e+167:
		tmp = t_1
	elif y <= 8.5e+94:
		tmp = (1.0 + (y / x)) * x
	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 <= -7.5e+167)
		tmp = t_1;
	elseif (y <= 8.5e+94)
		tmp = Float64(Float64(1.0 + Float64(y / x)) * x);
	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 <= -7.5e+167)
		tmp = t_1;
	elseif (y <= 8.5e+94)
		tmp = (1.0 + (y / x)) * x;
	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, -7.5e+167], t$95$1, If[LessEqual[y, 8.5e+94], N[(N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999995e167 or 8.50000000000000054e94 < y

   1. Initial program 77.1%

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

   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 44.8

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

   4. Applied rewrites 44.8%

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

   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 30.6

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

   7. Applied rewrites 30.6%

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

   if -7.4999999999999995e167 < y < 8.50000000000000054e94

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in a around inf

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

      1. lower-+.f64 N/A

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

      2. lift-/.f64 58.0

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

   7. Applied rewrites 58.0%

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

Alternative 8: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{z}{a}\right) \cdot y\\ \mathbf{if}\;y \leq -9 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+73}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ z a)) y)))
   (if (<= y -9e+154) t_1 (if (<= y 4.2e+73) (* 1.0 x) 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 <= -9e+154) {
		tmp = t_1;
	} else if (y <= 4.2e+73) {
		tmp = 1.0 * 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) :: tmp
    t_1 = (1.0d0 - (z / a)) * y
    if (y <= (-9d+154)) then
        tmp = t_1
    else if (y <= 4.2d+73) then
        tmp = 1.0d0 * 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 = (1.0 - (z / a)) * y;
	double tmp;
	if (y <= -9e+154) {
		tmp = t_1;
	} else if (y <= 4.2e+73) {
		tmp = 1.0 * x;
	} 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 <= -9e+154:
		tmp = t_1
	elif y <= 4.2e+73:
		tmp = 1.0 * x
	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 <= -9e+154)
		tmp = t_1;
	elseif (y <= 4.2e+73)
		tmp = Float64(1.0 * x);
	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 <= -9e+154)
		tmp = t_1;
	elseif (y <= 4.2e+73)
		tmp = 1.0 * x;
	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, -9e+154], t$95$1, If[LessEqual[y, 4.2e+73], N[(1.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000018e154 or 4.2000000000000003e73 < y

   1. Initial program 77.1%

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

   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 44.8

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

   4. Applied rewrites 44.8%

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

   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 30.6

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

   7. Applied rewrites 30.6%

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

   if -9.00000000000000018e154 < y < 4.2000000000000003e73

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 57.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - a}{t}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+88}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z a) t))))
   (if (<= y -1.9e+163) t_1 (if (<= y 2.5e+88) (* 1.0 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - a) / t);
	double tmp;
	if (y <= -1.9e+163) {
		tmp = t_1;
	} else if (y <= 2.5e+88) {
		tmp = 1.0 * 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) :: tmp
    t_1 = y * ((z - a) / t)
    if (y <= (-1.9d+163)) then
        tmp = t_1
    else if (y <= 2.5d+88) then
        tmp = 1.0d0 * 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 = y * ((z - a) / t);
	double tmp;
	if (y <= -1.9e+163) {
		tmp = t_1;
	} else if (y <= 2.5e+88) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - a) / t)
	tmp = 0
	if y <= -1.9e+163:
		tmp = t_1
	elif y <= 2.5e+88:
		tmp = 1.0 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (y <= -1.9e+163)
		tmp = t_1;
	elseif (y <= 2.5e+88)
		tmp = Float64(1.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - a) / t);
	tmp = 0.0;
	if (y <= -1.9e+163)
		tmp = t_1;
	elseif (y <= 2.5e+88)
		tmp = 1.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+163], t$95$1, If[LessEqual[y, 2.5e+88], N[(1.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000004e163 or 2.49999999999999999e88 < y

   1. Initial program 77.1%

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

   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 44.8

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

   4. Applied rewrites 44.8%

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

   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%

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

   8. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 21.5

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

   10. Applied rewrites 21.5%

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

   11. Taylor expanded in y around 0

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

       1. lower-*.f64 N/A

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

       2. sub-div N/A

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

       3. lower-/.f64 N/A

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

       4. lower--.f64 24.4

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

   13. Applied rewrites 24.4%

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

   if -1.90000000000000004e163 < y < 2.49999999999999999e88

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 54.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(-y\right) \cdot z}{a}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+179}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y) z) a)))
   (if (<= z -3.4e+227) t_1 (if (<= z 2.25e+179) (* 1.0 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-y * z) / a;
	double tmp;
	if (z <= -3.4e+227) {
		tmp = t_1;
	} else if (z <= 2.25e+179) {
		tmp = 1.0 * 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) :: tmp
    t_1 = (-y * z) / a
    if (z <= (-3.4d+227)) then
        tmp = t_1
    else if (z <= 2.25d+179) then
        tmp = 1.0d0 * 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 = (-y * z) / a;
	double tmp;
	if (z <= -3.4e+227) {
		tmp = t_1;
	} else if (z <= 2.25e+179) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-y * z) / a
	tmp = 0
	if z <= -3.4e+227:
		tmp = t_1
	elif z <= 2.25e+179:
		tmp = 1.0 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-y) * z) / a)
	tmp = 0.0
	if (z <= -3.4e+227)
		tmp = t_1;
	elseif (z <= 2.25e+179)
		tmp = Float64(1.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-y * z) / a;
	tmp = 0.0;
	if (z <= -3.4e+227)
		tmp = t_1;
	elseif (z <= 2.25e+179)
		tmp = 1.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-y) * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -3.4e+227], t$95$1, If[LessEqual[z, 2.25e+179], N[(1.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.39999999999999989e227 or 2.2500000000000001e179 < z

   1. Initial program 77.1%

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

   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. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 26.1

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

   4. Applied rewrites 26.1%

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

   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 18.3

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

   7. Applied rewrites 18.3%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-lft-neg-out N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 14.5

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

   10. Applied rewrites 14.5%

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

   if -3.39999999999999989e227 < z < 2.2500000000000001e179

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 53.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)))
   (if (<= y -1.15e+197) t_1 (if (<= y 4.2e+88) (* 1.0 x) 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 <= -1.15e+197) {
		tmp = t_1;
	} else if (y <= 4.2e+88) {
		tmp = 1.0 * 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) :: tmp
    t_1 = (z / t) * y
    if (y <= (-1.15d+197)) then
        tmp = t_1
    else if (y <= 4.2d+88) then
        tmp = 1.0d0 * 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 = (z / t) * y;
	double tmp;
	if (y <= -1.15e+197) {
		tmp = t_1;
	} else if (y <= 4.2e+88) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / t) * y
	tmp = 0
	if y <= -1.15e+197:
		tmp = t_1
	elif y <= 4.2e+88:
		tmp = 1.0 * x
	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 <= -1.15e+197)
		tmp = t_1;
	elseif (y <= 4.2e+88)
		tmp = Float64(1.0 * x);
	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 <= -1.15e+197)
		tmp = t_1;
	elseif (y <= 4.2e+88)
		tmp = 1.0 * x;
	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, -1.15e+197], t$95$1, If[LessEqual[y, 4.2e+88], N[(1.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e197 or 4.2e88 < y

   1. Initial program 77.1%

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

   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 44.8

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

   4. Applied rewrites 44.8%

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

   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 -1.15e197 < y < 4.2e88

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{t}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+116}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) t)))
   (if (<= y -2.2e+227) t_1 (if (<= y 1.6e+116) (* 1.0 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / t;
	double tmp;
	if (y <= -2.2e+227) {
		tmp = t_1;
	} else if (y <= 1.6e+116) {
		tmp = 1.0 * 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) :: tmp
    t_1 = (y * z) / t
    if (y <= (-2.2d+227)) then
        tmp = t_1
    else if (y <= 1.6d+116) then
        tmp = 1.0d0 * 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 = (y * z) / t;
	double tmp;
	if (y <= -2.2e+227) {
		tmp = t_1;
	} else if (y <= 1.6e+116) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / t
	tmp = 0
	if y <= -2.2e+227:
		tmp = t_1
	elif y <= 1.6e+116:
		tmp = 1.0 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / t)
	tmp = 0.0
	if (y <= -2.2e+227)
		tmp = t_1;
	elseif (y <= 1.6e+116)
		tmp = Float64(1.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / t;
	tmp = 0.0;
	if (y <= -2.2e+227)
		tmp = t_1;
	elseif (y <= 1.6e+116)
		tmp = 1.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[y, -2.2e+227], t$95$1, If[LessEqual[y, 1.6e+116], N[(1.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000002e227 or 1.6e116 < y

   1. Initial program 77.1%

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

   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. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 26.1

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

   4. Applied rewrites 26.1%

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

   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 18.3

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

   7. Applied rewrites 18.3%

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

   if -2.2000000000000002e227 < y < 1.6e116

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 51.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z, double t, double a) {
	return 1.0 * x;
}

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 = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 1.0 * x;
}

Python

def code(x, y, z, t, a):
	return 1.0 * x

Julia

function code(x, y, z, t, a)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 77.1%

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

2. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. associate--l+ N/A

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

   4. lower-+.f64 N/A

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

   5. lower--.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. *-commutative N/A

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

   9. lift--.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 N/A

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

   13. lift--.f64 70.3

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

4. Applied rewrites 70.3%

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

5. Taylor expanded in x around inf

   \[\leadsto 1 \cdot x \]
6. Step-by-step derivation

7. Applied rewrites 51.4%

   \[\leadsto 1 \cdot x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025127 
(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))))