Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.7% → 96.5%

Time: 3.4s

Alternatives: 13

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y} \cdot t\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-29}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) (- z y)) t)))
   (if (<= y -8.8e-147) t_1 (if (<= y 4e-29) (* (- x y) (/ t (- z y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x - y) / (z - y)) * t;
	double tmp;
	if (y <= -8.8e-147) {
		tmp = t_1;
	} else if (y <= 4e-29) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 - y) / (z - y)) * t
    if (y <= (-8.8d-147)) then
        tmp = t_1
    else if (y <= 4d-29) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x - y) / (z - y)) * t;
	double tmp;
	if (y <= -8.8e-147) {
		tmp = t_1;
	} else if (y <= 4e-29) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x - y) / (z - y)) * t
	tmp = 0
	if y <= -8.8e-147:
		tmp = t_1
	elif y <= 4e-29:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x - y) / Float64(z - y)) * t)
	tmp = 0.0
	if (y <= -8.8e-147)
		tmp = t_1;
	elseif (y <= 4e-29)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x - y) / (z - y)) * t;
	tmp = 0.0;
	if (y <= -8.8e-147)
		tmp = t_1;
	elseif (y <= 4e-29)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -8.8e-147], t$95$1, If[LessEqual[y, 4e-29], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8000000000000004e-147 or 3.99999999999999977e-29 < y

   1. Initial program 99.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   if -8.8000000000000004e-147 < y < 3.99999999999999977e-29

   1. Initial program 92.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. div-sub N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 92.6

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

   4. Applied rewrites 92.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 92.0

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

   6. Applied rewrites 92.0%

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

Alternative 2: 78.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;t\_1 \leq 10^{-7}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 10^{+95}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 (- INFINITY))
     (/ (* x t) (- y))
     (if (<= t_1 1e-7)
       (/ (* (- x y) t) z)
       (if (<= t_1 2.0)
         t
         (if (<= t_1 1e+95) (* (/ x z) t) (* x (/ t (- y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * t) / -y;
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else if (t_1 <= 1e+95) {
		tmp = (x / z) * t;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * t) / -y;
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else if (t_1 <= 1e+95) {
		tmp = (x / z) * t;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * t) / -y
	elif t_1 <= 1e-7:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = t
	elif t_1 <= 1e+95:
		tmp = (x / z) * t
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (t_1 <= 1e-7)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = t;
	elseif (t_1 <= 1e+95)
		tmp = Float64(Float64(x / z) * t);
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * t) / -y;
	elseif (t_1 <= 1e-7)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = t;
	elseif (t_1 <= 1e+95)
		tmp = (x / z) * t;
	else
		tmp = x * (t / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[t$95$1, 1e-7], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t, If[LessEqual[t$95$1, 1e+95], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -inf.0

   1. Initial program 65.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 65.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 64.2

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

   10. Applied rewrites 64.2%

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

   if -inf.0 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-8

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 75.7

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

   5. Applied rewrites 75.7%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.2%

      \[\leadsto \color{blue}{t} \]

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000002e95

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 52.5

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

   5. Applied rewrites 52.5%

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

   if 1.00000000000000002e95 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 91.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 94.3

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

   7. Applied rewrites 94.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 94.9

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

   9. Applied rewrites 94.9%

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

   10. Taylor expanded in y around inf

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

       1. mul-1-neg N/A

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

       2. lift-neg.f64 56.7

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

   12. Applied rewrites 56.7%

       \[\leadsto x \cdot \frac{t}{\color{blue}{-y}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 69.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot t\\ t_2 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;t\_2 \leq 7 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_2 \leq 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) t)) (t_2 (/ (- x y) (- z y))))
   (if (<= t_2 (- INFINITY))
     (/ (* x t) (- y))
     (if (<= t_2 7e-36)
       t_1
       (if (<= t_2 2.0) t (if (<= t_2 1e+95) t_1 (* x (/ t (- y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * t;
	double t_2 = (x - y) / (z - y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x * t) / -y;
	} else if (t_2 <= 7e-36) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = t;
	} else if (t_2 <= 1e+95) {
		tmp = t_1;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * t;
	double t_2 = (x - y) / (z - y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * t) / -y;
	} else if (t_2 <= 7e-36) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = t;
	} else if (t_2 <= 1e+95) {
		tmp = t_1;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * t
	t_2 = (x - y) / (z - y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (x * t) / -y
	elif t_2 <= 7e-36:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = t
	elif t_2 <= 1e+95:
		tmp = t_1
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * t)
	t_2 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (t_2 <= 7e-36)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = t;
	elseif (t_2 <= 1e+95)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * t;
	t_2 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (x * t) / -y;
	elseif (t_2 <= 7e-36)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = t;
	elseif (t_2 <= 1e+95)
		tmp = t_1;
	else
		tmp = x * (t / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[t$95$2, 7e-36], t$95$1, If[LessEqual[t$95$2, 2.0], t, If[LessEqual[t$95$2, 1e+95], t$95$1, N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -inf.0

   1. Initial program 65.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 65.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 64.2

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

   10. Applied rewrites 64.2%

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

   if -inf.0 < (/.f64 (-.f64 x y) (-.f64 z y)) < 6.9999999999999999e-36 or 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000002e95

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 57.2

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

   5. Applied rewrites 57.2%

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

   if 6.9999999999999999e-36 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 90.2%

      \[\leadsto \color{blue}{t} \]

   if 1.00000000000000002e95 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 91.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 94.3

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

   7. Applied rewrites 94.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 94.9

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

   9. Applied rewrites 94.9%

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

   10. Taylor expanded in y around inf

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

       1. mul-1-neg N/A

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

       2. lift-neg.f64 56.7

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

   12. Applied rewrites 56.7%

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

Alternative 4: 69.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot t\\ t_2 := \frac{x - y}{z - y}\\ t_3 := x \cdot \frac{t}{-y}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 7 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_2 \leq 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) t)) (t_2 (/ (- x y) (- z y))) (t_3 (* x (/ t (- y)))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 7e-36) t_1 (if (<= t_2 2.0) t (if (<= t_2 1e+95) t_1 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * t;
	double t_2 = (x - y) / (z - y);
	double t_3 = x * (t / -y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 7e-36) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = t;
	} else if (t_2 <= 1e+95) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * t;
	double t_2 = (x - y) / (z - y);
	double t_3 = x * (t / -y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= 7e-36) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = t;
	} else if (t_2 <= 1e+95) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * t
	t_2 = (x - y) / (z - y)
	t_3 = x * (t / -y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= 7e-36:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = t
	elif t_2 <= 1e+95:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * t)
	t_2 = Float64(Float64(x - y) / Float64(z - y))
	t_3 = Float64(x * Float64(t / Float64(-y)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 7e-36)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = t;
	elseif (t_2 <= 1e+95)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * t;
	t_2 = (x - y) / (z - y);
	t_3 = x * (t / -y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= 7e-36)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = t;
	elseif (t_2 <= 1e+95)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 7e-36], t$95$1, If[LessEqual[t$95$2, 2.0], t, If[LessEqual[t$95$2, 1e+95], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -inf.0 or 1.00000000000000002e95 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 87.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 87.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 95.2

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

   7. Applied rewrites 95.2%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 95.7

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

   9. Applied rewrites 95.7%

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

   10. Taylor expanded in y around inf

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

       1. mul-1-neg N/A

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

       2. lift-neg.f64 57.9

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

   12. Applied rewrites 57.9%

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

   if -inf.0 < (/.f64 (-.f64 x y) (-.f64 z y)) < 6.9999999999999999e-36 or 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000002e95

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 57.2

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

   5. Applied rewrites 57.2%

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

   if 6.9999999999999999e-36 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 90.2%

      \[\leadsto \color{blue}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -10000000:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 10^{-7}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -10000000.0)
     (/ (* x t) (- z y))
     (if (<= t_1 1e-7)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) t (* (/ x (- z y)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -10000000.0) {
		tmp = (x * t) / (z - y);
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 - y) / (z - y)
    if (t_1 <= (-10000000.0d0)) then
        tmp = (x * t) / (z - y)
    else if (t_1 <= 1d-7) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = (x / (z - y)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -10000000.0) {
		tmp = (x * t) / (z - y);
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -10000000.0:
		tmp = (x * t) / (z - y)
	elif t_1 <= 1e-7:
		tmp = ((x - y) / z) * t
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = (x / (z - y)) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -10000000.0)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (t_1 <= 1e-7)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -10000000.0)
		tmp = (x * t) / (z - y);
	elseif (t_1 <= 1e-7)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = (x / (z - y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -10000000.0], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-7], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t, N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e7

   1. Initial program 95.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 94.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 87.4

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

   7. Applied rewrites 87.4%

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

   if -1e7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-8

   1. Initial program 95.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 93.2%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.2%

      \[\leadsto \color{blue}{t} \]

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 92.7%

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

Alternative 6: 92.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 10^{-7}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -1e+30)
     (* x (/ t (- z y)))
     (if (<= t_1 1e-7)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) t (* (/ x (- z y)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e+30) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 - y) / (z - y)
    if (t_1 <= (-1d+30)) then
        tmp = x * (t / (z - y))
    else if (t_1 <= 1d-7) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = (x / (z - y)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e+30) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -1e+30:
		tmp = x * (t / (z - y))
	elif t_1 <= 1e-7:
		tmp = ((x - y) / z) * t
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = (x / (z - y)) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -1e+30)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 1e-7)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -1e+30)
		tmp = x * (t / (z - y));
	elseif (t_1 <= 1e-7)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = (x / (z - y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+30], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-7], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t, N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e30

   1. Initial program 94.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 94.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 89.6

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

   7. Applied rewrites 89.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 92.0

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

   9. Applied rewrites 92.0%

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

   if -1e30 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-8

   1. Initial program 95.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 90.9%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.2%

      \[\leadsto \color{blue}{t} \]

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 92.7%

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

Alternative 7: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 10^{-7}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -1e+30)
     (* x (/ t (- z y)))
     (if (<= t_1 1e-7)
       (/ (* (- x y) t) z)
       (if (<= t_1 2.0) t (* (/ x (- z y)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e+30) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 - y) / (z - y)
    if (t_1 <= (-1d+30)) then
        tmp = x * (t / (z - y))
    else if (t_1 <= 1d-7) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = (x / (z - y)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e+30) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -1e+30:
		tmp = x * (t / (z - y))
	elif t_1 <= 1e-7:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = (x / (z - y)) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -1e+30)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 1e-7)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -1e+30)
		tmp = x * (t / (z - y));
	elseif (t_1 <= 1e-7)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = (x / (z - y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+30], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-7], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t, N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e30

   1. Initial program 94.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 94.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 89.6

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

   7. Applied rewrites 89.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 92.0

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

   9. Applied rewrites 92.0%

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

   if -1e30 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-8

   1. Initial program 95.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 85.4

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

   5. Applied rewrites 85.4%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.2%

      \[\leadsto \color{blue}{t} \]

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 92.7%

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

Alternative 8: 90.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-7}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t (- z y)))))
   (if (<= t_1 -1e+30)
     t_2
     (if (<= t_1 1e-7) (/ (* (- x y) t) z) (if (<= t_1 2.0) t t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= -1e+30) {
		tmp = t_2;
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = x * (t / (z - y))
    if (t_1 <= (-1d+30)) then
        tmp = t_2
    else if (t_1 <= 1d-7) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= -1e+30) {
		tmp = t_2;
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = x * (t / (z - y))
	tmp = 0
	if t_1 <= -1e+30:
		tmp = t_2
	elif t_1 <= 1e-7:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -1e+30)
		tmp = t_2;
	elseif (t_1 <= 1e-7)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (t_1 <= -1e+30)
		tmp = t_2;
	elseif (t_1 <= 1e-7)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+30], t$95$2, If[LessEqual[t$95$1, 1e-7], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t, t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e30 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 93.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 88.9

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

   7. Applied rewrites 88.9%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 90.2

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

   9. Applied rewrites 90.2%

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

   if -1e30 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-8

   1. Initial program 95.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 85.4

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

   5. Applied rewrites 85.4%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.2%

      \[\leadsto \color{blue}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -10000000:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 10^{-7}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{z - y}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -10000000.0)
     (/ (* x t) (- z y))
     (if (<= t_1 1e-7) (* (/ (- x y) z) t) (fma t (/ x (- z y)) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -10000000.0) {
		tmp = (x * t) / (z - y);
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) / z) * t;
	} else {
		tmp = fma(t, (x / (z - y)), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -10000000.0)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (t_1 <= 1e-7)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	else
		tmp = fma(t, Float64(x / Float64(z - y)), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -10000000.0], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-7], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e7

   1. Initial program 95.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 94.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 87.4

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

   7. Applied rewrites 87.4%

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

   if -1e7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-8

   1. Initial program 95.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 93.2%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 98.2

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

   5. Applied rewrites 98.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(t, \frac{x}{z - y}, t\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 95.4%

      \[\leadsto \mathsf{fma}\left(t, \frac{x}{z - y}, t\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t \cdot x}{z}\\ \mathbf{if}\;t\_1 \leq 7 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ (* t x) z)))
   (if (<= t_1 7e-36) t_2 (if (<= t_1 2.0) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t * x) / z;
	double tmp;
	if (t_1 <= 7e-36) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t * x) / z
    if (t_1 <= 7d-36) then
        tmp = t_2
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t * x) / z;
	double tmp;
	if (t_1 <= 7e-36) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t * x) / z
	tmp = 0
	if t_1 <= 7e-36:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t * x) / z)
	tmp = 0.0
	if (t_1 <= 7e-36)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t * x) / z;
	tmp = 0.0;
	if (t_1 <= 7e-36)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, 7e-36], t$95$2, If[LessEqual[t$95$1, 2.0], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 6.9999999999999999e-36 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 54.1

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

   5. Applied rewrites 54.1%

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

   if 6.9999999999999999e-36 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 90.2%

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

Alternative 11: 93.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.9999999:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{z - y}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- x y) (- z y)) 0.9999999)
   (* (- x y) (/ t (- z y)))
   (fma t (/ x (- z y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - y) / (z - y)) <= 0.9999999) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = fma(t, (x / (z - y)), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(z - y)) <= 0.9999999)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = fma(t, Float64(x / Float64(z - y)), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], 0.9999999], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.999999900000000053

   1. Initial program 95.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. div-sub N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 95.3

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

   4. Applied rewrites 95.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 89.3

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

   6. Applied rewrites 89.3%

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

   if 0.999999900000000053 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 98.1

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(t, \frac{x}{z - y}, t\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 96.9%

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

Alternative 12: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 7.6e-30) (/ (* (- x y) t) (- z y)) (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.6e-30) {
		tmp = ((x - y) * t) / (z - y);
	} else {
		tmp = (x - y) * (t / (z - 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 (t <= 7.6d-30) then
        tmp = ((x - y) * t) / (z - y)
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.6e-30) {
		tmp = ((x - y) * t) / (z - y);
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 7.6e-30:
		tmp = ((x - y) * t) / (z - y)
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 7.6e-30)
		tmp = Float64(Float64(Float64(x - y) * t) / Float64(z - y));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 7.6e-30)
		tmp = ((x - y) * t) / (z - y);
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 7.6e-30], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.6000000000000006e-30

   1. Initial program 96.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 88.0

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

   4. Applied rewrites 88.0%

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

   if 7.6000000000000006e-30 < t

   1. Initial program 96.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. div-sub N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 96.7

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

   4. Applied rewrites 96.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 96.3

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

   6. Applied rewrites 96.3%

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

Alternative 13: 34.8% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = t
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 96.7%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Applied rewrites 34.8%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 96.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 = t / ((z - y) / (x - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025089 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

  (* (/ (- x y) (- z y)) t))