Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 92.9% → 98.5%

Time: 57.3s

Alternatives: 10

Speedup: 1.0×

• 75.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{z - x}{t} \cdot y\\ t_2 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1000000000000000007630473539575035660514778335511710750780086664439969510636494954611131549135839186513983455555395220895687860544809584999829725260594873271087399626486606146442550988840016917394626449536395208620267012778077787723395914064607119962069483324573977857832138825282954985472:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ x (* (/ (- z x) t) y)))
       (t_2 (+ x (/ (* y (- z x)) t))))
  (if (<= t_2 (- INFINITY))
    t_1
    (if (<=
         t_2
         1000000000000000007630473539575035660514778335511710750780086664439969510636494954611131549135839186513983455555395220895687860544809584999829725260594873271087399626486606146442550988840016917394626449536395208620267012778077787723395914064607119962069483324573977857832138825282954985472)
      t_2
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) / t) * y);
	double t_2 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) / t) * y);
	double t_2 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 1e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((z - x) / t) * y)
	t_2 = x + ((y * (z - x)) / t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 1e+288:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(z - x) / t) * y))
	t_2 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+288)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((z - x) / t) * y);
	t_2 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 1e+288)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1000000000000000007630473539575035660514778335511710750780086664439969510636494954611131549135839186513983455555395220895687860544809584999829725260594873271087399626486606146442550988840016917394626449536395208620267012778077787723395914064607119962069483324573977857832138825282954985472], t$95$2, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0 or 1e288 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 92.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 93.3%

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

   3. Applied rewrites 93.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 1e288

   1. Initial program 92.9%

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

Alternative 2: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. lift-+.f64 N/A

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

   2. add-flip N/A

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

   3. lower--.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. mult-flip N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

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

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

   10. lift--.f64 N/A

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

   11. sub-negate-rev N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 N/A

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

   14. mult-flip-rev N/A

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

   15. lower-/.f64 N/A

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

   16. lower--.f64 97.8%

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

3. Applied rewrites 97.8%

   \[\leadsto \color{blue}{x - \frac{y}{t} \cdot \left(x - z\right)} \]
4. Add Preprocessing

Alternative 3: 95.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{z - x}{t} \cdot y\\ \mathbf{if}\;y \leq \frac{-8048257981283417}{24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899385989241370687309994439728955392}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq \frac{2948408144391829}{29484081443918291814387145163970850710288447034503440846689111720668938768688662906922865040450459121417721679927842538279457692421287442441886205089317937841010900992}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ x (* (/ (- z x) t) y))))
  (if (<=
       y
       -8048257981283417/24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899385989241370687309994439728955392)
    t_1
    (if (<=
         y
         2948408144391829/29484081443918291814387145163970850710288447034503440846689111720668938768688662906922865040450459121417721679927842538279457692421287442441886205089317937841010900992)
      (+ x (/ (* y z) t))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) / t) * y);
	double tmp;
	if (y <= -3.3e-127) {
		tmp = t_1;
	} else if (y <= 1e-151) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (((z - x) / t) * y)
    if (y <= (-3.3d-127)) then
        tmp = t_1
    else if (y <= 1d-151) then
        tmp = x + ((y * z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) / t) * y);
	double tmp;
	if (y <= -3.3e-127) {
		tmp = t_1;
	} else if (y <= 1e-151) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((z - x) / t) * y)
	tmp = 0
	if y <= -3.3e-127:
		tmp = t_1
	elif y <= 1e-151:
		tmp = x + ((y * z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(z - x) / t) * y))
	tmp = 0.0
	if (y <= -3.3e-127)
		tmp = t_1;
	elseif (y <= 1e-151)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((z - x) / t) * y);
	tmp = 0.0;
	if (y <= -3.3e-127)
		tmp = t_1;
	elseif (y <= 1e-151)
		tmp = x + ((y * z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8048257981283417/24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899385989241370687309994439728955392], t$95$1, If[LessEqual[y, 2948408144391829/29484081443918291814387145163970850710288447034503440846689111720668938768688662906922865040450459121417721679927842538279457692421287442441886205089317937841010900992], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2999999999999998e-127 or 9.9999999999999994e-152 < y

   1. Initial program 92.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 93.3%

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

   3. Applied rewrites 93.3%

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

   if -3.2999999999999998e-127 < y < 9.9999999999999994e-152

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 73.5%

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

Alternative 4: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -81999999999999999444117791297653494069860092239413248:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{elif}\;y \leq 2599999999999999954962905506906819895542902456088149751785670657918236645203684047229602691118266281430714048500701377979219968:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - x}{t} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= y -81999999999999999444117791297653494069860092239413248)
  (* (/ y t) (- z x))
  (if (<=
       y
       2599999999999999954962905506906819895542902456088149751785670657918236645203684047229602691118266281430714048500701377979219968)
    (+ x (/ (* y z) t))
    (* (/ (- z x) t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e+52) {
		tmp = (y / t) * (z - x);
	} else if (y <= 2.6e+126) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = ((z - x) / t) * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: tmp
    if (y <= (-8.2d+52)) then
        tmp = (y / t) * (z - x)
    else if (y <= 2.6d+126) then
        tmp = x + ((y * z) / t)
    else
        tmp = ((z - x) / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e+52) {
		tmp = (y / t) * (z - x);
	} else if (y <= 2.6e+126) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = ((z - x) / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e+52:
		tmp = (y / t) * (z - x)
	elif y <= 2.6e+126:
		tmp = x + ((y * z) / t)
	else:
		tmp = ((z - x) / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e+52)
		tmp = Float64(Float64(y / t) * Float64(z - x));
	elseif (y <= 2.6e+126)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(Float64(Float64(z - x) / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e+52)
		tmp = (y / t) * (z - x);
	elseif (y <= 2.6e+126)
		tmp = x + ((y * z) / t);
	else
		tmp = ((z - x) / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -81999999999999999444117791297653494069860092239413248], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2599999999999999954962905506906819895542902456088149751785670657918236645203684047229602691118266281430714048500701377979219968], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999999e52

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 56.3%

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

   4. Applied rewrites 56.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 57.8%

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

   6. Applied rewrites 57.8%

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

      1. frac-2neg 57.8%

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

      2. add-to-fraction 57.8%

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

      3. lift--.f64 N/A

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

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

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

      5. lift--.f64 57.8%

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

      6. sub-negate-rev 57.8%

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

      7. fp-cancel-sign-sub-inv 57.8%

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

      8. sub-to-fraction 57.8%

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

      9. associate-*l/ 57.8%

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

      10. frac-2neg 57.8%

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/l* N/A

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

      15. associate-*l/ N/A

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

      16. lift-/.f64 N/A

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

      17. lower-*.f64 60.2%

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

   8. Applied rewrites 60.2%

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

   if -8.1999999999999999e52 < y < 2.6e126

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 73.5%

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

   if 2.6e126 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 56.3%

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

   4. Applied rewrites 56.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 57.8%

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

   6. Applied rewrites 57.8%

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

Alternative 5: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -21499999999999998147276722000525200649264102916181455464280636586050489869271641210244186683797596901525258015604736:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8800000000000000:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* x (- 1 (/ y t)))))
  (if (<=
       x
       -21499999999999998147276722000525200649264102916181455464280636586050489869271641210244186683797596901525258015604736)
    t_1
    (if (<= x 8800000000000000) (+ x (* z (/ y t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -2.15e+115) {
		tmp = t_1;
	} else if (x <= 8.8e+15) {
		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)
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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    if (x <= (-2.15d+115)) then
        tmp = t_1
    else if (x <= 8.8d+15) 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 t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -2.15e+115) {
		tmp = t_1;
	} else if (x <= 8.8e+15) {
		tmp = x + (z * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -2.15e+115:
		tmp = t_1
	elif x <= 8.8e+15:
		tmp = x + (z * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -2.15e+115)
		tmp = t_1;
	elseif (x <= 8.8e+15)
		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)
	t_1 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -2.15e+115)
		tmp = t_1;
	elseif (x <= 8.8e+15)
		tmp = x + (z * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -21499999999999998147276722000525200649264102916181455464280636586050489869271641210244186683797596901525258015604736], t$95$1, If[LessEqual[x, 8800000000000000], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1499999999999998e115 or 8.8e15 < x

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 66.0%

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

   6. Applied rewrites 66.0%

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

   if -2.1499999999999998e115 < x < 8.8e15

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 73.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lift-/.f64 N/A

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

      6. lower-*.f64 77.4%

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

   6. Applied rewrites 77.4%

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

Alternative 6: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{if}\;z \leq -110000000000000000836380884533692889214012072090085205846122981705594305889423590684622848:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1350000000000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (/ y t) (- z x))))
  (if (<=
       z
       -110000000000000000836380884533692889214012072090085205846122981705594305889423590684622848)
    t_1
    (if (<= z 1350000000000000000000) (* x (- 1 (/ y t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * (z - x);
	double tmp;
	if (z <= -1.1e+89) {
		tmp = t_1;
	} else if (z <= 1.35e+21) {
		tmp = x * (1.0 - (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)
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) :: t_1
    real(8) :: tmp
    t_1 = (y / t) * (z - x)
    if (z <= (-1.1d+89)) then
        tmp = t_1
    else if (z <= 1.35d+21) then
        tmp = x * (1.0d0 - (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 t_1 = (y / t) * (z - x);
	double tmp;
	if (z <= -1.1e+89) {
		tmp = t_1;
	} else if (z <= 1.35e+21) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / t) * (z - x)
	tmp = 0
	if z <= -1.1e+89:
		tmp = t_1
	elif z <= 1.35e+21:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) * Float64(z - x))
	tmp = 0.0
	if (z <= -1.1e+89)
		tmp = t_1;
	elseif (z <= 1.35e+21)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / t) * (z - x);
	tmp = 0.0;
	if (z <= -1.1e+89)
		tmp = t_1;
	elseif (z <= 1.35e+21)
		tmp = x * (1.0 - (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -110000000000000000836380884533692889214012072090085205846122981705594305889423590684622848], t$95$1, If[LessEqual[z, 1350000000000000000000], N[(x * N[(1 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e89 or 1.35e21 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 56.3%

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

   4. Applied rewrites 56.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 57.8%

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

   6. Applied rewrites 57.8%

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

      1. frac-2neg 57.8%

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

      2. add-to-fraction 57.8%

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

      3. lift--.f64 N/A

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

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

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

      5. lift--.f64 57.8%

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

      6. sub-negate-rev 57.8%

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

      7. fp-cancel-sign-sub-inv 57.8%

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

      8. sub-to-fraction 57.8%

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

      9. associate-*l/ 57.8%

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

      10. frac-2neg 57.8%

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/l* N/A

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

      15. associate-*l/ N/A

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

      16. lift-/.f64 N/A

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

      17. lower-*.f64 60.2%

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

   8. Applied rewrites 60.2%

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

   if -1.1e89 < z < 1.35e21

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 66.0%

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

   6. Applied rewrites 66.0%

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

Alternative 7: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -274999999999999998126975107413708384815629263519276795901247533628514870651670854573542161701642402491262753141904895633260544:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 1400000000000000029874101805689864192:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - x}{t} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     z
     -274999999999999998126975107413708384815629263519276795901247533628514870651670854573542161701642402491262753141904895633260544)
  (* (/ y t) z)
  (if (<= z 1400000000000000029874101805689864192)
    (* x (- 1 (/ y t)))
    (* (/ (- z x) t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+125) {
		tmp = (y / t) * z;
	} else if (z <= 1.4e+36) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = ((z - x) / t) * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: tmp
    if (z <= (-2.75d+125)) then
        tmp = (y / t) * z
    else if (z <= 1.4d+36) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = ((z - x) / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+125) {
		tmp = (y / t) * z;
	} else if (z <= 1.4e+36) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = ((z - x) / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.75e+125:
		tmp = (y / t) * z
	elif z <= 1.4e+36:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = ((z - x) / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.75e+125)
		tmp = Float64(Float64(y / t) * z);
	elseif (z <= 1.4e+36)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(Float64(z - x) / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.75e+125)
		tmp = (y / t) * z;
	elseif (z <= 1.4e+36)
		tmp = x * (1.0 - (y / t));
	else
		tmp = ((z - x) / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -274999999999999998126975107413708384815629263519276795901247533628514870651670854573542161701642402491262753141904895633260544], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1400000000000000029874101805689864192], N[(x * N[(1 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.75e125

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 37.1%

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

   6. Applied rewrites 37.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-/r/ N/A

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

      7. div-flip-rev N/A

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

      8. lift-/.f64 N/A

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

      9. lower-*.f64 40.6%

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

   8. Applied rewrites 40.6%

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

   if -2.75e125 < z < 1.4e36

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 66.0%

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

   6. Applied rewrites 66.0%

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

   if 1.4e36 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 56.3%

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

   4. Applied rewrites 56.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 57.8%

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

   6. Applied rewrites 57.8%

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

Alternative 8: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - x}{t} \cdot y\\ \mathbf{if}\;y \leq \frac{-4979986173918495}{118571099379011784113736688648896417641748464297615937576404566024103044751294464}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq \frac{2698025344585293}{93035356709837681990313447409664580397266094167976711716030745495121828878514934185752454491361736391777602765602070775492429008462675968}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (/ (- z x) t) y)))
  (if (<=
       y
       -4979986173918495/118571099379011784113736688648896417641748464297615937576404566024103044751294464)
    t_1
    (if (<=
         y
         2698025344585293/93035356709837681990313447409664580397266094167976711716030745495121828878514934185752454491361736391777602765602070775492429008462675968)
      (* x 1)
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - x) / t) * y;
	double tmp;
	if (y <= -4.2e-65) {
		tmp = t_1;
	} else if (y <= 2.9e-122) {
		tmp = x * 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = ((z - x) / t) * y
    if (y <= (-4.2d-65)) then
        tmp = t_1
    else if (y <= 2.9d-122) then
        tmp = x * 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((z - x) / t) * y;
	double tmp;
	if (y <= -4.2e-65) {
		tmp = t_1;
	} else if (y <= 2.9e-122) {
		tmp = x * 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - x) / t) * y
	tmp = 0
	if y <= -4.2e-65:
		tmp = t_1
	elif y <= 2.9e-122:
		tmp = x * 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - x) / t) * y)
	tmp = 0.0
	if (y <= -4.2e-65)
		tmp = t_1;
	elseif (y <= 2.9e-122)
		tmp = Float64(x * 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - x) / t) * y;
	tmp = 0.0;
	if (y <= -4.2e-65)
		tmp = t_1;
	elseif (y <= 2.9e-122)
		tmp = x * 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4979986173918495/118571099379011784113736688648896417641748464297615937576404566024103044751294464], t$95$1, If[LessEqual[y, 2698025344585293/93035356709837681990313447409664580397266094167976711716030745495121828878514934185752454491361736391777602765602070775492429008462675968], N[(x * 1), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2000000000000001e-65 or 2.9000000000000002e-122 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 56.3%

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

   4. Applied rewrites 56.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 57.8%

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

   6. Applied rewrites 57.8%

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

   if -4.2000000000000001e-65 < y < 2.9000000000000002e-122

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 66.0%

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

   6. Applied rewrites 66.0%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 39.4%

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

Alternative 9: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -104999999999999997626664616076826096398720561053696:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;t \leq \frac{3412647653636267}{4611686018427387904}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= t -104999999999999997626664616076826096398720561053696)
  (* x 1)
  (if (<= t 3412647653636267/4611686018427387904)
    (* (/ y t) z)
    (* x 1))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e+50) {
		tmp = x * 1.0;
	} else if (t <= 0.00074) {
		tmp = (y / t) * z;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: tmp
    if (t <= (-1.05d+50)) then
        tmp = x * 1.0d0
    else if (t <= 0.00074d0) then
        tmp = (y / t) * z
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e+50) {
		tmp = x * 1.0;
	} else if (t <= 0.00074) {
		tmp = (y / t) * z;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.05e+50:
		tmp = x * 1.0
	elif t <= 0.00074:
		tmp = (y / t) * z
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.05e+50)
		tmp = Float64(x * 1.0);
	elseif (t <= 0.00074)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.05e+50)
		tmp = x * 1.0;
	elseif (t <= 0.00074)
		tmp = (y / t) * z;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -104999999999999997626664616076826096398720561053696], N[(x * 1), $MachinePrecision], If[LessEqual[t, 3412647653636267/4611686018427387904], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], N[(x * 1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e50 or 7.3999999999999999e-4 < t

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 66.0%

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

   6. Applied rewrites 66.0%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 39.4%

      \[\leadsto x \cdot 1 \]

   if -1.05e50 < t < 7.3999999999999999e-4

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 37.1%

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

   6. Applied rewrites 37.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-/r/ N/A

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

      7. div-flip-rev N/A

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

      8. lift-/.f64 N/A

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

      9. lower-*.f64 40.6%

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

   8. Applied rewrites 40.6%

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

Alternative 10: 39.4% accurate, 3.8× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (* x 1))

C

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

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * 1), $MachinePrecision]

Derivation

1. Initial program 92.9%

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

   1. lift-+.f64 N/A

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

   2. add-flip N/A

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

   3. lower--.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. mult-flip N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

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

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

   10. lift--.f64 N/A

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

   11. sub-negate-rev N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 N/A

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

   14. mult-flip-rev N/A

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

   15. lower-/.f64 N/A

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

   16. lower--.f64 97.8%

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

3. Applied rewrites 97.8%

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

4. Taylor expanded in x around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-/.f64 66.0%

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

6. Applied rewrites 66.0%

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

7. Taylor expanded in y around 0

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

9. Applied rewrites 39.4%

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

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64
  (+ x (/ (* y (- z x)) t)))