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

Percentage Accurate: 97.3% → 97.3%

Time: 3.3s

Alternatives: 13

Speedup: 1.0×

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: 97.3% 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: 97.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z - y} + \frac{t \cdot x}{z - y}} \]
3. 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 97.3

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

4. Applied rewrites 97.3%

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

Alternative 2: 97.3% 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]

Derivation

1. Initial program 97.3%

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

Alternative 3: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;\frac{-y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -1000000.0)
     t_2
     (if (<= t_1 0.05)
       (* (/ (- x y) z) t)
       (if (<= t_1 4.0) (* (/ (- y) (- z y)) 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 / (z - y)) * t;
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 4.0) {
		tmp = (-y / (z - y)) * 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 / (z - y)) * t
    if (t_1 <= (-1000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.05d0) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 4.0d0) then
        tmp = (-y / (z - y)) * 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 / (z - y)) * t;
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 4.0) {
		tmp = (-y / (z - y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -1000000.0:
		tmp = t_2
	elif t_1 <= 0.05:
		tmp = ((x - y) / z) * t
	elif t_1 <= 4.0:
		tmp = (-y / (z - y)) * 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(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.05)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 4.0)
		tmp = Float64(Float64(Float64(-y) / Float64(z - y)) * 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 / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.05)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 4.0)
		tmp = (-y / (z - y)) * 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[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000.0], t$95$2, If[LessEqual[t$95$1, 0.05], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 4.0], N[(N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e6 or 4 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 53.3%

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

   if -1e6 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.050000000000000003

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 50.9%

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

   if 0.050000000000000003 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4

   1. Initial program 97.3%

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

   2. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 54.7

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

   4. Applied rewrites 54.7%

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

Alternative 4: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \mathsf{fma}\left(t, \frac{x}{z - y}, t\right)\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (fma t (/ x (- z y)) t)))
   (if (<= t_1 -1000000.0) t_2 (if (<= t_1 0.05) (* (/ (- x y) z) t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = fma(t, (x / (z - y)), t);
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) / z) * 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 = fma(t, Float64(x / Float64(z - y)), t)
	tmp = 0.0
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.05)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	else
		tmp = t_2;
	end
	return 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[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000.0], t$95$2, If[LessEqual[t$95$1, 0.05], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e6 or 0.050000000000000003 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z - y} + \frac{t \cdot x}{z - y}} \]
   3. 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 97.3

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

   4. Applied rewrites 97.3%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 65.9%

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

   if -1e6 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.050000000000000003

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 50.9%

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

Alternative 5: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -1000000.0)
     t_2
     (if (<= t_1 0.05) (* (/ (- x y) z) t) (if (<= t_1 4.0) 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 / (z - y)) * t;
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 4.0) {
		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 / (z - y)) * t
    if (t_1 <= (-1000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.05d0) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 4.0d0) 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 / (z - y)) * t;
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -1000000.0:
		tmp = t_2
	elif t_1 <= 0.05:
		tmp = ((x - y) / z) * t
	elif t_1 <= 4.0:
		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(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.05)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 4.0)
		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 / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.05)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 4.0)
		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[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000.0], t$95$2, If[LessEqual[t$95$1, 0.05], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 4.0], t, t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e6 or 4 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 53.3%

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

   if -1e6 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.050000000000000003

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 50.9%

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

   if 0.050000000000000003 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 6: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -0.001:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -0.001)
     t_2
     (if (<= t_1 0.05) (/ (* (- x y) t) z) (if (<= t_1 4.0) 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 / (z - y)) * t;
	double tmp;
	if (t_1 <= -0.001) {
		tmp = t_2;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 4.0) {
		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 / (z - y)) * t
    if (t_1 <= (-0.001d0)) then
        tmp = t_2
    else if (t_1 <= 0.05d0) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 4.0d0) 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 / (z - y)) * t;
	double tmp;
	if (t_1 <= -0.001) {
		tmp = t_2;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -0.001:
		tmp = t_2
	elif t_1 <= 0.05:
		tmp = ((x - y) * t) / z
	elif t_1 <= 4.0:
		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(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -0.001)
		tmp = t_2;
	elseif (t_1 <= 0.05)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 4.0)
		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 / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -0.001)
		tmp = t_2;
	elseif (t_1 <= 0.05)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 4.0)
		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[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -0.001], t$95$2, If[LessEqual[t$95$1, 0.05], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 4.0], t, t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e-3 or 4 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 53.3%

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

   if -1e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.050000000000000003

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t \cdot \left(x - y\right)}{z}} \]
   3. 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 47.9

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

   4. Applied rewrites 47.9%

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

   if 0.050000000000000003 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 7: 79.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;\frac{x}{-y} \cdot t\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -1000000.0)
     (* (/ x (- y)) t)
     (if (<= t_1 0.05)
       (/ (* (- x y) t) z)
       (if (<= t_1 4.0)
         t
         (if (<= t_1 4e+55) (* (/ x z) t) (/ (* t x) (- y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = (x / -y) * t;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else if (t_1 <= 4e+55) {
		tmp = (x / z) * t;
	} else {
		tmp = (t * x) / -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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-1000000.0d0)) then
        tmp = (x / -y) * t
    else if (t_1 <= 0.05d0) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 4.0d0) then
        tmp = t
    else if (t_1 <= 4d+55) then
        tmp = (x / z) * t
    else
        tmp = (t * x) / -y
    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 <= -1000000.0) {
		tmp = (x / -y) * t;
	} else if (t_1 <= 0.05) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else if (t_1 <= 4e+55) {
		tmp = (x / z) * t;
	} else {
		tmp = (t * x) / -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -1000000.0:
		tmp = (x / -y) * t
	elif t_1 <= 0.05:
		tmp = ((x - y) * t) / z
	elif t_1 <= 4.0:
		tmp = t
	elif t_1 <= 4e+55:
		tmp = (x / z) * t
	else:
		tmp = (t * x) / -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 <= -1000000.0)
		tmp = Float64(Float64(x / Float64(-y)) * t);
	elseif (t_1 <= 0.05)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 4.0)
		tmp = t;
	elseif (t_1 <= 4e+55)
		tmp = Float64(Float64(x / z) * t);
	else
		tmp = Float64(Float64(t * x) / 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 <= -1000000.0)
		tmp = (x / -y) * t;
	elseif (t_1 <= 0.05)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 4.0)
		tmp = t;
	elseif (t_1 <= 4e+55)
		tmp = (x / z) * t;
	else
		tmp = (t * x) / -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, -1000000.0], N[(N[(x / (-y)), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 0.05], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 4.0], t, If[LessEqual[t$95$1, 4e+55], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e6

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 53.3%

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

   5. Taylor expanded in y around inf

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

      1. flip-- N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 47.0

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

   7. Applied rewrites 47.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 40.1%

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

   11. Taylor expanded in y around inf

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

       1. mul-1-neg N/A

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

       2. lift-neg.f64 22.6

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

   13. Applied rewrites 22.6%

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

   if -1e6 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.050000000000000003

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t \cdot \left(x - y\right)}{z}} \]
   3. 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 47.9

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

   4. Applied rewrites 47.9%

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

   if 0.050000000000000003 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

   if 4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.00000000000000004e55

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 40.1

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

   4. Applied rewrites 40.1%

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

   if 4.00000000000000004e55 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 52.3

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

   4. Applied rewrites 52.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 44.4

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

      8. flip-- 44.4

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

   6. Applied rewrites 44.4%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 23.7

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

   9. Applied rewrites 23.7%

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

Alternative 8: 71.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\left(-\frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x z) t)))
   (if (<= t_1 -2e-139)
     t_2
     (if (<= t_1 0.002)
       (* (- (/ y z)) t)
       (if (<= t_1 4.0) t (if (<= t_1 4e+55) t_2 (/ (* t x) (- y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= -2e-139) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = -(y / z) * t;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else if (t_1 <= 4e+55) {
		tmp = t_2;
	} else {
		tmp = (t * x) / -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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / z) * t
    if (t_1 <= (-2d-139)) then
        tmp = t_2
    else if (t_1 <= 0.002d0) then
        tmp = -(y / z) * t
    else if (t_1 <= 4.0d0) then
        tmp = t
    else if (t_1 <= 4d+55) then
        tmp = t_2
    else
        tmp = (t * x) / -y
    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 / z) * t;
	double tmp;
	if (t_1 <= -2e-139) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = -(y / z) * t;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else if (t_1 <= 4e+55) {
		tmp = t_2;
	} else {
		tmp = (t * x) / -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= -2e-139:
		tmp = t_2
	elif t_1 <= 0.002:
		tmp = -(y / z) * t
	elif t_1 <= 4.0:
		tmp = t
	elif t_1 <= 4e+55:
		tmp = t_2
	else:
		tmp = (t * x) / -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= -2e-139)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(-Float64(y / z)) * t);
	elseif (t_1 <= 4.0)
		tmp = t;
	elseif (t_1 <= 4e+55)
		tmp = t_2;
	else
		tmp = Float64(Float64(t * x) / Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / z) * t;
	tmp = 0.0;
	if (t_1 <= -2e-139)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = -(y / z) * t;
	elseif (t_1 <= 4.0)
		tmp = t;
	elseif (t_1 <= 4e+55)
		tmp = t_2;
	else
		tmp = (t * x) / -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]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-139], t$95$2, If[LessEqual[t$95$1, 0.002], N[((-N[(y / z), $MachinePrecision]) * t), $MachinePrecision], If[LessEqual[t$95$1, 4.0], t, If[LessEqual[t$95$1, 4e+55], t$95$2, N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2.00000000000000006e-139 or 4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.00000000000000004e55

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 40.1

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

   4. Applied rewrites 40.1%

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

   if -2.00000000000000006e-139 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 97.3%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. lower-/.f64 N/A

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

      4. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{{z}^{2}} - y \cdot y}{z + y}} \cdot t \]

      5. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{{z}^{2} - \color{blue}{{y}^{2}}}{z + y}} \cdot t \]

      6. lower--.f64 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{{z}^{2} - {y}^{2}}}{z + y}} \cdot t \]

      7. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{z \cdot z} - {y}^{2}}{z + y}} \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{z \cdot z} - {y}^{2}}{z + y}} \cdot t \]

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 57.2

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

   3. Applied rewrites 57.2%

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

   4. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(y \cdot \left(\frac{x}{{z}^{2}} - \frac{1}{z}\right) + \frac{x}{z}\right)} \cdot t \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{x}{{z}^{2}} - \frac{1}{z}}, \frac{x}{z}\right) \cdot t \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{x}{{z}^{2}} - \color{blue}{\frac{1}{z}}, \frac{x}{z}\right) \cdot t \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{x}{{z}^{2}} - \frac{\color{blue}{1}}{z}, \frac{x}{z}\right) \cdot t \]

      4. pow2 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 45.3

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

   6. Applied rewrites 45.3%

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

   7. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lift-/.f64 23.4

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

   9. Applied rewrites 23.4%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

   if 4.00000000000000004e55 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 52.3

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

   4. Applied rewrites 52.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 44.4

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

      8. flip-- 44.4

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

   6. Applied rewrites 44.4%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 23.7

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

   9. Applied rewrites 23.7%

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

Alternative 9: 71.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\left(-\frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x z) t)))
   (if (<= t_1 -2e-139)
     t_2
     (if (<= t_1 0.002)
       (* (- (/ y z)) t)
       (if (<= t_1 4.0) t (if (<= t_1 4e+55) t_2 (* (/ x (- y)) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= -2e-139) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = -(y / z) * t;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else if (t_1 <= 4e+55) {
		tmp = t_2;
	} else {
		tmp = (x / -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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / z) * t
    if (t_1 <= (-2d-139)) then
        tmp = t_2
    else if (t_1 <= 0.002d0) then
        tmp = -(y / z) * t
    else if (t_1 <= 4.0d0) then
        tmp = t
    else if (t_1 <= 4d+55) then
        tmp = t_2
    else
        tmp = (x / -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 t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= -2e-139) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = -(y / z) * t;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else if (t_1 <= 4e+55) {
		tmp = t_2;
	} else {
		tmp = (x / -y) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= -2e-139:
		tmp = t_2
	elif t_1 <= 0.002:
		tmp = -(y / z) * t
	elif t_1 <= 4.0:
		tmp = t
	elif t_1 <= 4e+55:
		tmp = t_2
	else:
		tmp = (x / -y) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= -2e-139)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(-Float64(y / z)) * t);
	elseif (t_1 <= 4.0)
		tmp = t;
	elseif (t_1 <= 4e+55)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(-y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / z) * t;
	tmp = 0.0;
	if (t_1 <= -2e-139)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = -(y / z) * t;
	elseif (t_1 <= 4.0)
		tmp = t;
	elseif (t_1 <= 4e+55)
		tmp = t_2;
	else
		tmp = (x / -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]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-139], t$95$2, If[LessEqual[t$95$1, 0.002], N[((-N[(y / z), $MachinePrecision]) * t), $MachinePrecision], If[LessEqual[t$95$1, 4.0], t, If[LessEqual[t$95$1, 4e+55], t$95$2, N[(N[(x / (-y)), $MachinePrecision] * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2.00000000000000006e-139 or 4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.00000000000000004e55

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 40.1

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

   4. Applied rewrites 40.1%

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

   if -2.00000000000000006e-139 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 97.3%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. lower-/.f64 N/A

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

      4. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{{z}^{2}} - y \cdot y}{z + y}} \cdot t \]

      5. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{{z}^{2} - \color{blue}{{y}^{2}}}{z + y}} \cdot t \]

      6. lower--.f64 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{{z}^{2} - {y}^{2}}}{z + y}} \cdot t \]

      7. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{z \cdot z} - {y}^{2}}{z + y}} \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{z \cdot z} - {y}^{2}}{z + y}} \cdot t \]

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 57.2

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

   3. Applied rewrites 57.2%

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

   4. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(y \cdot \left(\frac{x}{{z}^{2}} - \frac{1}{z}\right) + \frac{x}{z}\right)} \cdot t \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{x}{{z}^{2}} - \frac{1}{z}}, \frac{x}{z}\right) \cdot t \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{x}{{z}^{2}} - \color{blue}{\frac{1}{z}}, \frac{x}{z}\right) \cdot t \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{x}{{z}^{2}} - \frac{\color{blue}{1}}{z}, \frac{x}{z}\right) \cdot t \]

      4. pow2 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 45.3

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

   6. Applied rewrites 45.3%

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

   7. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lift-/.f64 23.4

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

   9. Applied rewrites 23.4%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

   if 4.00000000000000004e55 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 53.3%

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

   5. Taylor expanded in y around inf

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

      1. flip-- N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 47.0

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

   7. Applied rewrites 47.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 40.1%

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

   11. Taylor expanded in y around inf

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

       1. mul-1-neg N/A

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

       2. lift-neg.f64 22.6

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

   13. Applied rewrites 22.6%

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

Alternative 10: 70.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\left(-\frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x z) t)))
   (if (<= t_1 -2e-139)
     t_2
     (if (<= t_1 0.002) (* (- (/ y z)) t) (if (<= t_1 4.0) 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 / z) * t;
	double tmp;
	if (t_1 <= -2e-139) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = -(y / z) * t;
	} else if (t_1 <= 4.0) {
		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 / z) * t
    if (t_1 <= (-2d-139)) then
        tmp = t_2
    else if (t_1 <= 0.002d0) then
        tmp = -(y / z) * t
    else if (t_1 <= 4.0d0) 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 / z) * t;
	double tmp;
	if (t_1 <= -2e-139) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = -(y / z) * t;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= -2e-139:
		tmp = t_2
	elif t_1 <= 0.002:
		tmp = -(y / z) * t
	elif t_1 <= 4.0:
		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(x / z) * t)
	tmp = 0.0
	if (t_1 <= -2e-139)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(-Float64(y / z)) * t);
	elseif (t_1 <= 4.0)
		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 / z) * t;
	tmp = 0.0;
	if (t_1 <= -2e-139)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = -(y / z) * t;
	elseif (t_1 <= 4.0)
		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[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-139], t$95$2, If[LessEqual[t$95$1, 0.002], N[((-N[(y / z), $MachinePrecision]) * t), $MachinePrecision], If[LessEqual[t$95$1, 4.0], t, t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2.00000000000000006e-139 or 4 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 40.1

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

   4. Applied rewrites 40.1%

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

   if -2.00000000000000006e-139 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 97.3%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. lower-/.f64 N/A

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

      4. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{{z}^{2}} - y \cdot y}{z + y}} \cdot t \]

      5. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{{z}^{2} - \color{blue}{{y}^{2}}}{z + y}} \cdot t \]

      6. lower--.f64 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{{z}^{2} - {y}^{2}}}{z + y}} \cdot t \]

      7. unpow2 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{z \cdot z} - {y}^{2}}{z + y}} \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{x - y}{\frac{\color{blue}{z \cdot z} - {y}^{2}}{z + y}} \cdot t \]

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 57.2

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

   3. Applied rewrites 57.2%

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

   4. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(y \cdot \left(\frac{x}{{z}^{2}} - \frac{1}{z}\right) + \frac{x}{z}\right)} \cdot t \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{x}{{z}^{2}} - \frac{1}{z}}, \frac{x}{z}\right) \cdot t \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{x}{{z}^{2}} - \color{blue}{\frac{1}{z}}, \frac{x}{z}\right) \cdot t \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{x}{{z}^{2}} - \frac{\color{blue}{1}}{z}, \frac{x}{z}\right) \cdot t \]

      4. pow2 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 45.3

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

   6. Applied rewrites 45.3%

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

   7. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lift-/.f64 23.4

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

   9. Applied rewrites 23.4%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 11: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq 0.05:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x z) t)))
   (if (<= t_1 0.05) t_2 (if (<= t_1 4.0) 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 / z) * t;
	double tmp;
	if (t_1 <= 0.05) {
		tmp = t_2;
	} else if (t_1 <= 4.0) {
		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 / z) * t
    if (t_1 <= 0.05d0) then
        tmp = t_2
    else if (t_1 <= 4.0d0) 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 / z) * t;
	double tmp;
	if (t_1 <= 0.05) {
		tmp = t_2;
	} else if (t_1 <= 4.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= 0.05:
		tmp = t_2
	elif t_1 <= 4.0:
		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(x / z) * t)
	tmp = 0.0
	if (t_1 <= 0.05)
		tmp = t_2;
	elseif (t_1 <= 4.0)
		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 / z) * t;
	tmp = 0.0;
	if (t_1 <= 0.05)
		tmp = t_2;
	elseif (t_1 <= 4.0)
		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[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, 0.05], t$95$2, If[LessEqual[t$95$1, 4.0], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.050000000000000003 or 4 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 40.1

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

   4. Applied rewrites 40.1%

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

   if 0.050000000000000003 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 12: 68.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t \cdot x}{z}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ (* t x) z)))
   (if (<= t_1 5e-5) t_2 (if (<= t_1 5e+26) 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 <= 5e-5) {
		tmp = t_2;
	} else if (t_1 <= 5e+26) {
		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 <= 5d-5) then
        tmp = t_2
    else if (t_1 <= 5d+26) 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 <= 5e-5) {
		tmp = t_2;
	} else if (t_1 <= 5e+26) {
		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 <= 5e-5:
		tmp = t_2
	elif t_1 <= 5e+26:
		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 <= 5e-5)
		tmp = t_2;
	elseif (t_1 <= 5e+26)
		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 <= 5e-5)
		tmp = t_2;
	elseif (t_1 <= 5e+26)
		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, 5e-5], t$95$2, If[LessEqual[t$95$1, 5e+26], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000024e-5 or 5.0000000000000001e26 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 38.1

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

   4. Applied rewrites 38.1%

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

   if 5.00000000000000024e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000001e26

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 13: 35.1% accurate, 12.6× 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 97.3%

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

2. Taylor expanded in y around inf

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

4. Applied rewrites 35.1%

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

Reproduce

herbie shell --seed 2025123 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64
  (* (/ (- x y) (- z y)) t))