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

Percentage Accurate: 77.5% → 96.5%

Time: 13.3s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

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: 77.5% accurate, 1.0× speedup

Math

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

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: 96.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := x - \left(\frac{y}{a - t} \cdot \left(z - t\right) - y\right)\\ \mathbf{if}\;x \leq -140000000000000000959427848218759767512090254448657972060114688665452544:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3299999999999999986428798326532941143297361994102300032786005566284043072254603818945699398355660046336:\\ \;\;\;\;y \cdot \left(-1 \cdot \frac{a - z}{t - a} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (- (* (/ y (- a t)) (- z t)) y))))
  (if (<=
       x
       -140000000000000000959427848218759767512090254448657972060114688665452544)
    t_1
    (if (<=
         x
         3299999999999999986428798326532941143297361994102300032786005566284043072254603818945699398355660046336)
      (* y (+ (* -1 (/ (- a z) (- t a))) (/ x y)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y / (a - t)) * (z - t)) - y);
	double tmp;
	if (x <= -1.4e+71) {
		tmp = t_1;
	} else if (x <= 3.3e+102) {
		tmp = y * ((-1.0 * ((a - z) / (t - a))) + (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y / (a - t)) * (z - t)) - y)
    if (x <= (-1.4d+71)) then
        tmp = t_1
    else if (x <= 3.3d+102) then
        tmp = y * (((-1.0d0) * ((a - z) / (t - a))) + (x / y))
    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 / (a - t)) * (z - t)) - y);
	double tmp;
	if (x <= -1.4e+71) {
		tmp = t_1;
	} else if (x <= 3.3e+102) {
		tmp = y * ((-1.0 * ((a - z) / (t - a))) + (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y / (a - t)) * (z - t)) - y)
	tmp = 0
	if x <= -1.4e+71:
		tmp = t_1
	elif x <= 3.3e+102:
		tmp = y * ((-1.0 * ((a - z) / (t - a))) + (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y / Float64(a - t)) * Float64(z - t)) - y))
	tmp = 0.0
	if (x <= -1.4e+71)
		tmp = t_1;
	elseif (x <= 3.3e+102)
		tmp = Float64(y * Float64(Float64(-1.0 * Float64(Float64(a - z) / Float64(t - a))) + Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y / (a - t)) * (z - t)) - y);
	tmp = 0.0;
	if (x <= -1.4e+71)
		tmp = t_1;
	elseif (x <= 3.3e+102)
		tmp = y * ((-1.0 * ((a - z) / (t - a))) + (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -140000000000000000959427848218759767512090254448657972060114688665452544], t$95$1, If[LessEqual[x, 3299999999999999986428798326532941143297361994102300032786005566284043072254603818945699398355660046336], N[(y * N[(N[(-1 * N[(N[(a - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e71 or 3.3e102 < x

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   if -1.4e71 < x < 3.3e102

   1. Initial program 77.5%

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

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

      3. sub-to-fraction N/A

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

      4. mult-flip N/A

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

      5. *-commutative N/A

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

      6. sub-flip N/A

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

      7. +-commutative N/A

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

      8. add-flip-rev N/A

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

      9. distribute-rgt-neg-out N/A

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

      10. lift-*.f64 N/A

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

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

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. *-commutative N/A

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

      15. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(t - z\right), y, \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), \left(x + y\right)\right)} \]

   3. Applied rewrites 85.4%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(t - z\right), y, \left(t - a\right), \left(y + x\right)\right)} \]

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 86.6%

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

   6. Applied rewrites 86.6%

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

Alternative 2: 91.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x - \frac{a - z}{t} \cdot y\\ \mathbf{if}\;t \leq -3100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6499999999999999593644510990384774520498798802555127355660083857349028219105312768:\\ \;\;\;\;\left(x + y\right) - \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), z, y, t, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (* (/ (- a z) t) y))))
  (if (<= t -3100000)
    t_1
    (if (<=
         t
         6499999999999999593644510990384774520498798802555127355660083857349028219105312768)
      (- (+ x y) (134-z0z1z2z3z4 (/ -1 (- t a)) z y t y))
      t_1))))

Derivation

1. Split input into 2 regimes

2. if t < -3.1e6 or 6.4999999999999996e81 < t

   1. Initial program 77.5%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 57.6%

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

   4. Applied rewrites 57.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. distribute-frac-neg2 N/A

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

      9. frac-2neg N/A

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

      10. lift-/.f64 57.6%

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 57.9%

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

   6. Applied rewrites 57.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 60.3%

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

   8. Applied rewrites 60.3%

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

   if -3.1e6 < t < 6.4999999999999996e81

   1. Initial program 77.5%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. distribute-rgt-in N/A

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

      9. fp-cancel-sub-sign N/A

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

      10. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \left(x + y\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), z, y, t, y\right)} \]

      11. frac-2neg N/A

          \[\leadsto \left(x + y\right) - \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, z, y, t, y\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(x + y\right) - \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), z, y, t, y\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \left(x + y\right) - \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, z, y, t, y\right) \]

      14. lift--.f64 N/A

          \[\leadsto \left(x + y\right) - \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), z, y, t, y\right) \]

      15. sub-negate-rev N/A

          \[\leadsto \left(x + y\right) - \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), z, y, t, y\right) \]

      16. lower--.f64 85.6%

          \[\leadsto \left(x + y\right) - \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), z, y, t, y\right) \]

   3. Applied rewrites 85.6%

      \[\leadsto \left(x + y\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), z, y, t, y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x - \frac{a - z}{t} \cdot y\\ \mathbf{if}\;t \leq -1399999999999999900203233431268652273291712969981745991179757449936038368516204096864475053543900305296086173322588784333804428058190581690313277506617355347169378304:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 13799999999999999440971610140959812744900457990581986660825254493315091665584806574573350325060890000217524680209619688111305757435101184:\\ \;\;\;\;x - \left(\frac{y}{a - t} \cdot \left(z - t\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (* (/ (- a z) t) y))))
  (if (<=
       t
       -1399999999999999900203233431268652273291712969981745991179757449936038368516204096864475053543900305296086173322588784333804428058190581690313277506617355347169378304)
    t_1
    (if (<=
         t
         13799999999999999440971610140959812744900457990581986660825254493315091665584806574573350325060890000217524680209619688111305757435101184)
      (- x (- (* (/ y (- a t)) (- z t)) y))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((a - z) / t) * y);
	double tmp;
	if (t <= -1.4e+165) {
		tmp = t_1;
	} else if (t <= 1.38e+136) {
		tmp = x - (((y / (a - t)) * (z - t)) - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((a - z) / t) * y)
    if (t <= (-1.4d+165)) then
        tmp = t_1
    else if (t <= 1.38d+136) then
        tmp = x - (((y / (a - t)) * (z - t)) - y)
    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 - (((a - z) / t) * y);
	double tmp;
	if (t <= -1.4e+165) {
		tmp = t_1;
	} else if (t <= 1.38e+136) {
		tmp = x - (((y / (a - t)) * (z - t)) - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((a - z) / t) * y)
	tmp = 0
	if t <= -1.4e+165:
		tmp = t_1
	elif t <= 1.38e+136:
		tmp = x - (((y / (a - t)) * (z - t)) - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(a - z) / t) * y))
	tmp = 0.0
	if (t <= -1.4e+165)
		tmp = t_1;
	elseif (t <= 1.38e+136)
		tmp = Float64(x - Float64(Float64(Float64(y / Float64(a - t)) * Float64(z - t)) - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((a - z) / t) * y);
	tmp = 0.0;
	if (t <= -1.4e+165)
		tmp = t_1;
	elseif (t <= 1.38e+136)
		tmp = x - (((y / (a - t)) * (z - t)) - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1399999999999999900203233431268652273291712969981745991179757449936038368516204096864475053543900305296086173322588784333804428058190581690313277506617355347169378304], t$95$1, If[LessEqual[t, 13799999999999999440971610140959812744900457990581986660825254493315091665584806574573350325060890000217524680209619688111305757435101184], N[(x - N[(N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3999999999999999e165 or 1.3799999999999999e136 < t

   1. Initial program 77.5%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 57.6%

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

   4. Applied rewrites 57.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. distribute-frac-neg2 N/A

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

      9. frac-2neg N/A

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

      10. lift-/.f64 57.6%

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 57.9%

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

   6. Applied rewrites 57.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 60.3%

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

   8. Applied rewrites 60.3%

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

   if -1.3999999999999999e165 < t < 1.3799999999999999e136

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

Alternative 4: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x - \frac{a - z}{t} \cdot y\\ \mathbf{if}\;t \leq -3100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 105000000000000008560894109403544066905437438919810482176:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (* (/ (- a z) t) y))))
  (if (<= t -3100000)
    t_1
    (if (<=
         t
         105000000000000008560894109403544066905437438919810482176)
      (- (+ x y) (/ (* y z) (- a t)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((a - z) / t) * y);
	double tmp;
	if (t <= -3100000.0) {
		tmp = t_1;
	} else if (t <= 1.05e+56) {
		tmp = (x + y) - ((y * z) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((a - z) / t) * y)
    if (t <= (-3100000.0d0)) then
        tmp = t_1
    else if (t <= 1.05d+56) then
        tmp = (x + y) - ((y * z) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((a - z) / t) * y);
	double tmp;
	if (t <= -3100000.0) {
		tmp = t_1;
	} else if (t <= 1.05e+56) {
		tmp = (x + y) - ((y * z) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((a - z) / t) * y)
	tmp = 0
	if t <= -3100000.0:
		tmp = t_1
	elif t <= 1.05e+56:
		tmp = (x + y) - ((y * z) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(a - z) / t) * y))
	tmp = 0.0
	if (t <= -3100000.0)
		tmp = t_1;
	elseif (t <= 1.05e+56)
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((a - z) / t) * y);
	tmp = 0.0;
	if (t <= -3100000.0)
		tmp = t_1;
	elseif (t <= 1.05e+56)
		tmp = (x + y) - ((y * z) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3100000], t$95$1, If[LessEqual[t, 105000000000000008560894109403544066905437438919810482176], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1e6 or 1.0500000000000001e56 < t

   1. Initial program 77.5%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 57.6%

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

   4. Applied rewrites 57.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. distribute-frac-neg2 N/A

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

      9. frac-2neg N/A

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

      10. lift-/.f64 57.6%

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 57.9%

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

   6. Applied rewrites 57.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 60.3%

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

   8. Applied rewrites 60.3%

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

   if -3.1e6 < t < 1.0500000000000001e56

   1. Initial program 77.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 78.7%

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

   4. Applied rewrites 78.7%

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

Alternative 5: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \left(x + y\right) - \frac{z}{a} \cdot y\\ \mathbf{if}\;a \leq \frac{-1519771171239775}{3618502788666131106986593281521497120414687020801267626233049500247285301248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 64999999999999997811068662022740957101817856:\\ \;\;\;\;x - \frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- (+ x y) (* (/ z a) y))))
  (if (<=
       a
       -1519771171239775/3618502788666131106986593281521497120414687020801267626233049500247285301248)
    t_1
    (if (<= a 64999999999999997811068662022740957101817856)
      (- x (* (/ z (- a t)) y))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((z / a) * y);
	double tmp;
	if (a <= -4.2e-61) {
		tmp = t_1;
	} else if (a <= 6.5e+43) {
		tmp = x - ((z / (a - t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((z / a) * y)
    if (a <= (-4.2d-61)) then
        tmp = t_1
    else if (a <= 6.5d+43) then
        tmp = x - ((z / (a - t)) * y)
    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 / a) * y);
	double tmp;
	if (a <= -4.2e-61) {
		tmp = t_1;
	} else if (a <= 6.5e+43) {
		tmp = x - ((z / (a - t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((z / a) * y)
	tmp = 0
	if a <= -4.2e-61:
		tmp = t_1
	elif a <= 6.5e+43:
		tmp = x - ((z / (a - t)) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(z / a) * y))
	tmp = 0.0
	if (a <= -4.2e-61)
		tmp = t_1;
	elseif (a <= 6.5e+43)
		tmp = Float64(x - Float64(Float64(z / Float64(a - t)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((z / a) * y);
	tmp = 0.0;
	if (a <= -4.2e-61)
		tmp = t_1;
	elseif (a <= 6.5e+43)
		tmp = x - ((z / (a - t)) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1519771171239775/3618502788666131106986593281521497120414687020801267626233049500247285301248], t$95$1, If[LessEqual[a, 64999999999999997811068662022740957101817856], N[(x - N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1999999999999998e-61 or 6.4999999999999998e43 < a

   1. Initial program 77.5%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 64.3%

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

   4. Applied rewrites 64.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 66.1%

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

   6. Applied rewrites 66.1%

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

   if -4.1999999999999998e-61 < a < 6.4999999999999998e43

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.6%

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

   9. Applied rewrites 73.6%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 76.3%

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

   11. Applied rewrites 76.3%

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

Alternative 6: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq \frac{-7098843361278085}{633825300114114700748351602688}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 64999999999999997811068662022740957101817856:\\ \;\;\;\;x - \frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- (+ x y) (* z (/ y a)))))
  (if (<= a -7098843361278085/633825300114114700748351602688)
    t_1
    (if (<= a 64999999999999997811068662022740957101817856)
      (- x (* (/ z (- a t)) y))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (z * (y / a));
	double tmp;
	if (a <= -1.12e-14) {
		tmp = t_1;
	} else if (a <= 6.5e+43) {
		tmp = x - ((z / (a - t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (z * (y / a))
    if (a <= (-1.12d-14)) then
        tmp = t_1
    else if (a <= 6.5d+43) then
        tmp = x - ((z / (a - t)) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (z * (y / a));
	double tmp;
	if (a <= -1.12e-14) {
		tmp = t_1;
	} else if (a <= 6.5e+43) {
		tmp = x - ((z / (a - t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (z * (y / a))
	tmp = 0
	if a <= -1.12e-14:
		tmp = t_1
	elif a <= 6.5e+43:
		tmp = x - ((z / (a - t)) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.12e-14)
		tmp = t_1;
	elseif (a <= 6.5e+43)
		tmp = Float64(x - Float64(Float64(z / Float64(a - t)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (z * (y / a));
	tmp = 0.0;
	if (a <= -1.12e-14)
		tmp = t_1;
	elseif (a <= 6.5e+43)
		tmp = x - ((z / (a - t)) * y);
	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[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7098843361278085/633825300114114700748351602688], t$95$1, If[LessEqual[a, 64999999999999997811068662022740957101817856], N[(x - N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1200000000000001e-14 or 6.4999999999999998e43 < a

   1. Initial program 77.5%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 64.3%

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

   4. Applied rewrites 64.3%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. mult-flip-rev N/A

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

      8. lower-/.f64 66.3%

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

   6. Applied rewrites 66.3%

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

   if -1.1200000000000001e-14 < a < 6.4999999999999998e43

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.6%

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

   9. Applied rewrites 73.6%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 76.3%

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

   11. Applied rewrites 76.3%

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

Alternative 7: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq -18999999999999999372737526393527479213844812791808:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1600000000000000132252141346013980646946023622824710961127370204984986009601639603374216973286408832068967823086973685020378115268670332314107856711878259818402975154563453039165720875006574998605330053237867864265850880:\\ \;\;\;\;x - \frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (- y))))
  (if (<= a -18999999999999999372737526393527479213844812791808)
    t_1
    (if (<=
         a
         1600000000000000132252141346013980646946023622824710961127370204984986009601639603374216973286408832068967823086973685020378115268670332314107856711878259818402975154563453039165720875006574998605330053237867864265850880)
      (- x (* (/ z (- a t)) y))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -1.9e+49) {
		tmp = t_1;
	} else if (a <= 1.6e+219) {
		tmp = x - ((z / (a - t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - -y
    if (a <= (-1.9d+49)) then
        tmp = t_1
    else if (a <= 1.6d+219) then
        tmp = x - ((z / (a - t)) * y)
    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;
	double tmp;
	if (a <= -1.9e+49) {
		tmp = t_1;
	} else if (a <= 1.6e+219) {
		tmp = x - ((z / (a - t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -1.9e+49:
		tmp = t_1
	elif a <= 1.6e+219:
		tmp = x - ((z / (a - t)) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -1.9e+49)
		tmp = t_1;
	elseif (a <= 1.6e+219)
		tmp = Float64(x - Float64(Float64(z / Float64(a - t)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -1.9e+49)
		tmp = t_1;
	elseif (a <= 1.6e+219)
		tmp = x - ((z / (a - t)) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -18999999999999999372737526393527479213844812791808], t$95$1, If[LessEqual[a, 1600000000000000132252141346013980646946023622824710961127370204984986009601639603374216973286408832068967823086973685020378115268670332314107856711878259818402975154563453039165720875006574998605330053237867864265850880], N[(x - N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999e49 or 1.6000000000000001e219 < a

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-neg.f64 60.2%

         \[\leadsto x - \left(-y\right) \]

   8. Applied rewrites 60.2%

      \[\leadsto x - \left(-y\right) \]

   if -1.8999999999999999e49 < a < 1.6000000000000001e219

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.6%

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

   9. Applied rewrites 73.6%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 76.3%

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

   11. Applied rewrites 76.3%

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

Alternative 8: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq -16000000000000000701533488721219157674144762429440:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 101999999999999997731603845368375289752342362849906699345834936350186795924394979613921904737278646871526473728:\\ \;\;\;\;x - \frac{y}{a - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (- y))))
  (if (<= a -16000000000000000701533488721219157674144762429440)
    t_1
    (if (<=
         a
         101999999999999997731603845368375289752342362849906699345834936350186795924394979613921904737278646871526473728)
      (- x (* (/ y (- a t)) z))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -1.6e+49) {
		tmp = t_1;
	} else if (a <= 1.02e+110) {
		tmp = x - ((y / (a - t)) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - -y
    if (a <= (-1.6d+49)) then
        tmp = t_1
    else if (a <= 1.02d+110) then
        tmp = x - ((y / (a - t)) * z)
    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;
	double tmp;
	if (a <= -1.6e+49) {
		tmp = t_1;
	} else if (a <= 1.02e+110) {
		tmp = x - ((y / (a - t)) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -1.6e+49:
		tmp = t_1
	elif a <= 1.02e+110:
		tmp = x - ((y / (a - t)) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -1.6e+49)
		tmp = t_1;
	elseif (a <= 1.02e+110)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -1.6e+49)
		tmp = t_1;
	elseif (a <= 1.02e+110)
		tmp = x - ((y / (a - t)) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -16000000000000000701533488721219157674144762429440], t$95$1, If[LessEqual[a, 101999999999999997731603845368375289752342362849906699345834936350186795924394979613921904737278646871526473728], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6000000000000001e49 or 1.02e110 < a

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-neg.f64 60.2%

         \[\leadsto x - \left(-y\right) \]

   8. Applied rewrites 60.2%

      \[\leadsto x - \left(-y\right) \]

   if -1.6000000000000001e49 < a < 1.02e110

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.6%

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

   9. Applied rewrites 73.6%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lift--.f64 N/A

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

       5. lower-*.f64 N/A

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

       6. lift--.f64 N/A

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

       7. lower-/.f64 76.2%

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

   11. Applied rewrites 76.2%

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

Alternative 9: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq \frac{-4553130216154053}{1897137590064188545819787018382342682267975428761855001222473056385648716020711424}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 480000000000000036083753719928740141186285950889155942471796369131727644116359298238979728526923857005567658418649212636805201920:\\ \;\;\;\;x - \frac{a - z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (- y))))
  (if (<=
       a
       -4553130216154053/1897137590064188545819787018382342682267975428761855001222473056385648716020711424)
    t_1
    (if (<=
         a
         480000000000000036083753719928740141186285950889155942471796369131727644116359298238979728526923857005567658418649212636805201920)
      (- x (* (/ (- a z) t) y))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -2.4e-66) {
		tmp = t_1;
	} else if (a <= 4.8e+128) {
		tmp = x - (((a - z) / t) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - -y
    if (a <= (-2.4d-66)) then
        tmp = t_1
    else if (a <= 4.8d+128) then
        tmp = x - (((a - z) / t) * y)
    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;
	double tmp;
	if (a <= -2.4e-66) {
		tmp = t_1;
	} else if (a <= 4.8e+128) {
		tmp = x - (((a - z) / t) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -2.4e-66:
		tmp = t_1
	elif a <= 4.8e+128:
		tmp = x - (((a - z) / t) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -2.4e-66)
		tmp = t_1;
	elseif (a <= 4.8e+128)
		tmp = Float64(x - Float64(Float64(Float64(a - z) / t) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -2.4e-66)
		tmp = t_1;
	elseif (a <= 4.8e+128)
		tmp = x - (((a - z) / t) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -4553130216154053/1897137590064188545819787018382342682267975428761855001222473056385648716020711424], t$95$1, If[LessEqual[a, 480000000000000036083753719928740141186285950889155942471796369131727644116359298238979728526923857005567658418649212636805201920], N[(x - N[(N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4000000000000003e-66 or 4.8000000000000004e128 < a

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-neg.f64 60.2%

         \[\leadsto x - \left(-y\right) \]

   8. Applied rewrites 60.2%

      \[\leadsto x - \left(-y\right) \]

   if -2.4000000000000003e-66 < a < 4.8000000000000004e128

   1. Initial program 77.5%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 57.6%

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

   4. Applied rewrites 57.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. distribute-frac-neg2 N/A

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

      9. frac-2neg N/A

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

      10. lift-/.f64 57.6%

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 57.9%

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

   6. Applied rewrites 57.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 60.3%

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

   8. Applied rewrites 60.3%

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

Alternative 10: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq \frac{-8256342791959349}{121416805764108066932466369176469931665150427440758720078238275608681517825325531136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 480000000000000036083753719928740141186285950889155942471796369131727644116359298238979728526923857005567658418649212636805201920:\\ \;\;\;\;x - \left(a - z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (- y))))
  (if (<=
       a
       -8256342791959349/121416805764108066932466369176469931665150427440758720078238275608681517825325531136)
    t_1
    (if (<=
         a
         480000000000000036083753719928740141186285950889155942471796369131727644116359298238979728526923857005567658418649212636805201920)
      (- x (* (- a z) (/ y t)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -6.8e-68) {
		tmp = t_1;
	} else if (a <= 4.8e+128) {
		tmp = x - ((a - z) * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - -y
    if (a <= (-6.8d-68)) then
        tmp = t_1
    else if (a <= 4.8d+128) then
        tmp = x - ((a - z) * (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -6.8e-68) {
		tmp = t_1;
	} else if (a <= 4.8e+128) {
		tmp = x - ((a - z) * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -6.8e-68:
		tmp = t_1
	elif a <= 4.8e+128:
		tmp = x - ((a - z) * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -6.8e-68)
		tmp = t_1;
	elseif (a <= 4.8e+128)
		tmp = Float64(x - Float64(Float64(a - z) * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -6.8e-68)
		tmp = t_1;
	elseif (a <= 4.8e+128)
		tmp = x - ((a - z) * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -8256342791959349/121416805764108066932466369176469931665150427440758720078238275608681517825325531136], t$95$1, If[LessEqual[a, 480000000000000036083753719928740141186285950889155942471796369131727644116359298238979728526923857005567658418649212636805201920], N[(x - N[(N[(a - z), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.8000000000000004e-68 or 4.8000000000000004e128 < a

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-neg.f64 60.2%

         \[\leadsto x - \left(-y\right) \]

   8. Applied rewrites 60.2%

      \[\leadsto x - \left(-y\right) \]

   if -6.8000000000000004e-68 < a < 4.8000000000000004e128

   1. Initial program 77.5%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 57.6%

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

   4. Applied rewrites 57.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. distribute-frac-neg2 N/A

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

      9. frac-2neg N/A

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

      10. lift-/.f64 57.6%

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 57.9%

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

   6. Applied rewrites 57.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 60.5%

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

   8. Applied rewrites 60.5%

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

Alternative 11: 76.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq \frac{-4360718064785109}{2535301200456458802993406410752}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 600000000000000046473455524883116661202489643467779290086853867826709171176518251711725606799149906700271616:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (- y))))
  (if (<= a -4360718064785109/2535301200456458802993406410752)
    t_1
    (if (<=
         a
         600000000000000046473455524883116661202489643467779290086853867826709171176518251711725606799149906700271616)
      (+ x (* (/ z t) y))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -1.72e-15) {
		tmp = t_1;
	} else if (a <= 6e+107) {
		tmp = x + ((z / t) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - -y
    if (a <= (-1.72d-15)) then
        tmp = t_1
    else if (a <= 6d+107) then
        tmp = x + ((z / t) * y)
    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;
	double tmp;
	if (a <= -1.72e-15) {
		tmp = t_1;
	} else if (a <= 6e+107) {
		tmp = x + ((z / t) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -1.72e-15:
		tmp = t_1
	elif a <= 6e+107:
		tmp = x + ((z / t) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -1.72e-15)
		tmp = t_1;
	elseif (a <= 6e+107)
		tmp = Float64(x + Float64(Float64(z / t) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -1.72e-15)
		tmp = t_1;
	elseif (a <= 6e+107)
		tmp = x + ((z / t) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -4360718064785109/2535301200456458802993406410752], t$95$1, If[LessEqual[a, 600000000000000046473455524883116661202489643467779290086853867826709171176518251711725606799149906700271616], N[(x + N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7199999999999999e-15 or 6.0000000000000005e107 < a

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-neg.f64 60.2%

         \[\leadsto x - \left(-y\right) \]

   8. Applied rewrites 60.2%

      \[\leadsto x - \left(-y\right) \]

   if -1.7199999999999999e-15 < a < 6.0000000000000005e107

   1. Initial program 77.5%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 57.6%

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

   4. Applied rewrites 57.6%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 60.2%

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

   7. Applied rewrites 60.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 61.4%

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

   9. Applied rewrites 61.4%

      \[\leadsto x + \frac{z}{t} \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq \frac{-4360718064785109}{2535301200456458802993406410752}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 600000000000000046473455524883116661202489643467779290086853867826709171176518251711725606799149906700271616:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (- y))))
  (if (<= a -4360718064785109/2535301200456458802993406410752)
    t_1
    (if (<=
         a
         600000000000000046473455524883116661202489643467779290086853867826709171176518251711725606799149906700271616)
      (+ x (* z (/ y t)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -1.72e-15) {
		tmp = t_1;
	} else if (a <= 6e+107) {
		tmp = x + (z * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - -y
    if (a <= (-1.72d-15)) then
        tmp = t_1
    else if (a <= 6d+107) then
        tmp = x + (z * (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -1.72e-15) {
		tmp = t_1;
	} else if (a <= 6e+107) {
		tmp = x + (z * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -1.72e-15:
		tmp = t_1
	elif a <= 6e+107:
		tmp = x + (z * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -1.72e-15)
		tmp = t_1;
	elseif (a <= 6e+107)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -1.72e-15)
		tmp = t_1;
	elseif (a <= 6e+107)
		tmp = x + (z * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -4360718064785109/2535301200456458802993406410752], t$95$1, If[LessEqual[a, 600000000000000046473455524883116661202489643467779290086853867826709171176518251711725606799149906700271616], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7199999999999999e-15 or 6.0000000000000005e107 < a

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-neg.f64 60.2%

         \[\leadsto x - \left(-y\right) \]

   8. Applied rewrites 60.2%

      \[\leadsto x - \left(-y\right) \]

   if -1.7199999999999999e-15 < a < 6.0000000000000005e107

   1. Initial program 77.5%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 57.6%

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

   4. Applied rewrites 57.6%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 60.2%

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

   7. Applied rewrites 60.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 61.1%

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

   9. Applied rewrites 61.1%

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

Alternative 13: 64.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{y \cdot z}{t - a}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1000000000000000017216064596736454828831087825013238982328892017892380671244575047987920451875459594568606138861698291060311049225532948520696938805711440650122628514669428460356992624968028329550689224175284346730060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208:\\ \;\;\;\;x - \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* y z) (- t a)))
       (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
  (if (<= t_2 (- INFINITY))
    t_1
    (if (<=
         t_2
         1000000000000000017216064596736454828831087825013238982328892017892380671244575047987920451875459594568606138861698291060311049225532948520696938805711440650122628514669428460356992624968028329550689224175284346730060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208)
      (- x (- y))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / (t - a);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+306) {
		tmp = x - -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / (t - a);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 1e+306) {
		tmp = x - -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / (t - a)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 1e+306:
		tmp = x - -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / Float64(t - a))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+306)
		tmp = Float64(x - Float64(-y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / (t - a);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 1e+306)
		tmp = x - -y;
	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] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1000000000000000017216064596736454828831087825013238982328892017892380671244575047987920451875459594568606138861698291060311049225532948520696938805711440650122628514669428460356992624968028329550689224175284346730060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208], N[(x - (-y)), $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))) < -inf.0 or 1e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 77.5%

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

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

      3. sub-to-fraction N/A

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

      4. mult-flip N/A

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

      5. *-commutative N/A

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

      6. sub-flip N/A

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

      7. +-commutative N/A

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

      8. add-flip-rev N/A

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

      9. distribute-rgt-neg-out N/A

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

      10. lift-*.f64 N/A

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

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

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. *-commutative N/A

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

      15. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(t - z\right), y, \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), \left(x + y\right)\right)} \]

   3. Applied rewrites 85.4%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(t - z\right), y, \left(t - a\right), \left(y + x\right)\right)} \]

   4. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.8%

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

   6. Applied rewrites 26.8%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1e306

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-neg.f64 60.2%

         \[\leadsto x - \left(-y\right) \]

   8. Applied rewrites 60.2%

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

Alternative 14: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 1000000000000000017216064596736454828831087825013238982328892017892380671244575047987920451875459594568606138861698291060311049225532948520696938805711440650122628514669428460356992624968028329550689224175284346730060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208:\\ \;\;\;\;x - \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     (- (+ x y) (/ (* (- z t) y) (- a t)))
     1000000000000000017216064596736454828831087825013238982328892017892380671244575047987920451875459594568606138861698291060311049225532948520696938805711440650122628514669428460356992624968028329550689224175284346730060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208)
  (- x (- y))
  (/ (* y z) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x + y) - (((z - t) * y) / (a - t))) <= 1e+306) {
		tmp = x - -y;
	} else {
		tmp = (y * z) / 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 (((x + y) - (((z - t) * y) / (a - t))) <= 1d+306) then
        tmp = x - -y
    else
        tmp = (y * z) / 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 (((x + y) - (((z - t) * y) / (a - t))) <= 1e+306) {
		tmp = x - -y;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x + y) - (((z - t) * y) / (a - t))) <= 1e+306:
		tmp = x - -y
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t))) <= 1e+306)
		tmp = Float64(x - Float64(-y));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x + y) - (((z - t) * y) / (a - t))) <= 1e+306)
		tmp = x - -y;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1000000000000000017216064596736454828831087825013238982328892017892380671244575047987920451875459594568606138861698291060311049225532948520696938805711440650122628514669428460356992624968028329550689224175284346730060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208], N[(x - (-y)), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 77.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 80.5%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.5%

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

   3. Applied rewrites 87.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   5. Step-by-step derivation

      1. lower-*.f64 60.2%

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

   6. Applied rewrites 60.2%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - -1 \cdot \color{blue}{y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-neg.f64 60.2%

         \[\leadsto x - \left(-y\right) \]

   8. Applied rewrites 60.2%

      \[\leadsto x - \left(-y\right) \]

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

   1. Initial program 77.5%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 57.6%

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

   4. Applied rewrites 57.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. distribute-frac-neg2 N/A

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

      9. frac-2neg N/A

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

      10. lift-/.f64 57.6%

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 57.9%

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

   6. Applied rewrites 57.9%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 18.8%

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

   9. Applied rewrites 18.8%

      \[\leadsto \frac{y \cdot z}{\color{blue}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 60.2% accurate, 4.8× speedup

Math

\[x - \left(-y\right) \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.5%

   \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
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. associate--l+ N/A

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

   4. add-flip N/A

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

   5. sub-negate-rev N/A

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

   6. lower--.f64 N/A

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

   7. lower--.f64 80.5%

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

   8. lift-/.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. associate-/l* N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 N/A

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

   13. lower-/.f64 87.5%

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

3. Applied rewrites 87.5%

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

4. Taylor expanded in a around inf

   \[\leadsto x - \color{blue}{-1 \cdot y} \]
5. Step-by-step derivation

   1. lower-*.f64 60.2%

      \[\leadsto x - -1 \cdot \color{blue}{y} \]

6. Applied rewrites 60.2%

   \[\leadsto x - \color{blue}{-1 \cdot y} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto x - -1 \cdot \color{blue}{y} \]

   2. mul-1-neg N/A

      \[\leadsto x - \left(\mathsf{neg}\left(y\right)\right) \]

   3. lower-neg.f64 60.2%

      \[\leadsto x - \left(-y\right) \]

8. Applied rewrites 60.2%

   \[\leadsto x - \left(-y\right) \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(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))))