Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A

Percentage Accurate: 99.1% → 99.1%

Time: 3.3s

Alternatives: 8

Speedup: 0.1×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 - (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 = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 - (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 = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 0.1× speedup

Math

\[1 - \frac{\frac{x}{\mathsf{min}\left(z, t\right) - y}}{\mathsf{max}\left(z, t\right) - y} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 - ((x / (fmin(z, t) - y)) / (fmax(z, t) - 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 = 1.0d0 - ((x / (fmin(z, t) - y)) / (fmax(z, t) - y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 - ((x / (fmin(z, t) - y)) / (fmax(z, t) - y));
}

Python

def code(x, y, z, t):
	return 1.0 - ((x / (fmin(z, t) - y)) / (fmax(z, t) - y))

Julia

function code(x, y, z, t)
	return Float64(1.0 - Float64(Float64(x / Float64(fmin(z, t) - y)) / Float64(fmax(z, t) - y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 - ((x / (min(z, t) - y)) / (max(z, t) - y));
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 - N[(N[(x / N[(N[Min[z, t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] / N[(N[Max[z, t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/r* N/A

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

   4. frac-2neg N/A

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

   5. lift--.f64 N/A

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

   6. sub-negate-rev N/A

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

   7. lower-/.f64 N/A

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

   8. distribute-neg-frac2 N/A

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

   9. lift--.f64 N/A

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

   10. sub-negate-rev N/A

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

   11. lower-/.f64 N/A

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

   12. lower--.f64 N/A

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

   13. lower--.f64 98.3%

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

3. Applied rewrites 98.3%

   \[\leadsto 1 - \color{blue}{\frac{\frac{x}{z - y}}{t - y}} \]
4. Add Preprocessing

Alternative 2: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ t_2 := 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ x (* (- t y) (- y z))))
       (t_2 (- 1.0 (/ x (* (- y z) (- y t))))))
  (if (<= t_2 -5e+19) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (y - z));
	double t_2 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if (t_2 <= -5e+19) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - y) * (y - z))
    t_2 = 1.0d0 - (x / ((y - z) * (y - t)))
    if (t_2 <= (-5d+19)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (y - z));
	double t_2 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if (t_2 <= -5e+19) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (y - z))
	t_2 = 1.0 - (x / ((y - z) * (y - t)))
	tmp = 0
	if t_2 <= -5e+19:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(y - z)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
	tmp = 0.0
	if (t_2 <= -5e+19)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (y - z));
	t_2 = 1.0 - (x / ((y - z) * (y - t)));
	tmp = 0.0;
	if (t_2 <= -5e+19)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+19], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e19 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 99.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 99.0%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 26.1%

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

   6. Applied rewrites 26.1%

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

   if -5e19 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 75.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := y - \mathsf{max}\left(z, t\right)\\ t_2 := y - \mathsf{min}\left(z, t\right)\\ t_3 := 1 - \frac{x}{t\_2 \cdot t\_1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{\mathsf{min}\left(z, t\right) \cdot t\_1}\\ \mathbf{elif}\;t\_3 \leq 20:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{max}\left(z, t\right) \cdot t\_2}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (- y (fmax z t)))
       (t_2 (- y (fmin z t)))
       (t_3 (- 1.0 (/ x (* t_2 t_1)))))
  (if (<= t_3 -5e+19)
    (/ x (* (fmin z t) t_1))
    (if (<= t_3 20.0) 1.0 (/ x (* (fmax z t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - fmax(z, t);
	double t_2 = y - fmin(z, t);
	double t_3 = 1.0 - (x / (t_2 * t_1));
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = x / (fmin(z, t) * t_1);
	} else if (t_3 <= 20.0) {
		tmp = 1.0;
	} else {
		tmp = x / (fmax(z, t) * 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) :: t_3
    real(8) :: tmp
    t_1 = y - fmax(z, t)
    t_2 = y - fmin(z, t)
    t_3 = 1.0d0 - (x / (t_2 * t_1))
    if (t_3 <= (-5d+19)) then
        tmp = x / (fmin(z, t) * t_1)
    else if (t_3 <= 20.0d0) then
        tmp = 1.0d0
    else
        tmp = x / (fmax(z, t) * t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y - fmax(z, t);
	double t_2 = y - fmin(z, t);
	double t_3 = 1.0 - (x / (t_2 * t_1));
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = x / (fmin(z, t) * t_1);
	} else if (t_3 <= 20.0) {
		tmp = 1.0;
	} else {
		tmp = x / (fmax(z, t) * t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - fmax(z, t)
	t_2 = y - fmin(z, t)
	t_3 = 1.0 - (x / (t_2 * t_1))
	tmp = 0
	if t_3 <= -5e+19:
		tmp = x / (fmin(z, t) * t_1)
	elif t_3 <= 20.0:
		tmp = 1.0
	else:
		tmp = x / (fmax(z, t) * t_2)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - fmax(z, t))
	t_2 = Float64(y - fmin(z, t))
	t_3 = Float64(1.0 - Float64(x / Float64(t_2 * t_1)))
	tmp = 0.0
	if (t_3 <= -5e+19)
		tmp = Float64(x / Float64(fmin(z, t) * t_1));
	elseif (t_3 <= 20.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(fmax(z, t) * t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - max(z, t);
	t_2 = y - min(z, t);
	t_3 = 1.0 - (x / (t_2 * t_1));
	tmp = 0.0;
	if (t_3 <= -5e+19)
		tmp = x / (min(z, t) * t_1);
	elseif (t_3 <= 20.0)
		tmp = 1.0;
	else
		tmp = x / (max(z, t) * t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[Max[z, t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[Min[z, t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 - N[(x / N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+19], N[(x / N[(N[Min[z, t], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 20.0], 1.0, N[(x / N[(N[Max[z, t], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e19

   1. Initial program 99.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 99.0%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 26.1%

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

   6. Applied rewrites 26.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

      11. distribute-frac-neg2 N/A

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

      12. frac-2neg-rev N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. frac-2neg-rev N/A

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

      20. lower-/.f64 25.3%

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

   8. Applied rewrites 25.3%

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

   9. Taylor expanded in z around inf

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 18.2%

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

   11. Applied rewrites 18.2%

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

   if -5e19 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 20

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 75.0%

      \[\leadsto \color{blue}{1} \]

   if 20 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 99.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 99.0%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 26.1%

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

   6. Applied rewrites 26.1%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 17.7%

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

Alternative 4: 89.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := y - \mathsf{max}\left(z, t\right)\\ t_2 := \frac{x}{\mathsf{min}\left(z, t\right) \cdot t\_1}\\ t_3 := 1 - \frac{x}{\left(y - \mathsf{min}\left(z, t\right)\right) \cdot t\_1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (- y (fmax z t)))
       (t_2 (/ x (* (fmin z t) t_1)))
       (t_3 (- 1.0 (/ x (* (- y (fmin z t)) t_1)))))
  (if (<= t_3 -5e+19) t_2 (if (<= t_3 2.0) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - fmax(z, t);
	double t_2 = x / (fmin(z, t) * t_1);
	double t_3 = 1.0 - (x / ((y - fmin(z, t)) * t_1));
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y - fmax(z, t)
    t_2 = x / (fmin(z, t) * t_1)
    t_3 = 1.0d0 - (x / ((y - fmin(z, t)) * t_1))
    if (t_3 <= (-5d+19)) then
        tmp = t_2
    else if (t_3 <= 2.0d0) then
        tmp = 1.0d0
    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 = y - fmax(z, t);
	double t_2 = x / (fmin(z, t) * t_1);
	double t_3 = 1.0 - (x / ((y - fmin(z, t)) * t_1));
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - fmax(z, t)
	t_2 = x / (fmin(z, t) * t_1)
	t_3 = 1.0 - (x / ((y - fmin(z, t)) * t_1))
	tmp = 0
	if t_3 <= -5e+19:
		tmp = t_2
	elif t_3 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - fmax(z, t))
	t_2 = Float64(x / Float64(fmin(z, t) * t_1))
	t_3 = Float64(1.0 - Float64(x / Float64(Float64(y - fmin(z, t)) * t_1)))
	tmp = 0.0
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - max(z, t);
	t_2 = x / (min(z, t) * t_1);
	t_3 = 1.0 - (x / ((y - min(z, t)) * t_1));
	tmp = 0.0;
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[Max[z, t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[Min[z, t], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 - N[(x / N[(N[(y - N[Min[z, t], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+19], t$95$2, If[LessEqual[t$95$3, 2.0], 1.0, t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e19 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 99.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 99.0%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 26.1%

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

   6. Applied rewrites 26.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

      11. distribute-frac-neg2 N/A

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

      12. frac-2neg-rev N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. frac-2neg-rev N/A

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

      20. lower-/.f64 25.3%

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

   8. Applied rewrites 25.3%

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

   9. Taylor expanded in z around inf

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 18.2%

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

   11. Applied rewrites 18.2%

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

   if -5e19 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 75.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y \cdot \left(\mathsf{min}\left(z, t\right) - y\right)}\\ t_2 := 1 - \frac{x}{\left(y - \mathsf{min}\left(z, t\right)\right) \cdot \left(y - \mathsf{max}\left(z, t\right)\right)}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+67}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ x (* y (- (fmin z t) y))))
       (t_2 (- 1.0 (/ x (* (- y (fmin z t)) (- y (fmax z t)))))))
  (if (<= t_2 -5e+19) t_1 (if (<= t_2 2e+67) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (fmin(z, t) - y));
	double t_2 = 1.0 - (x / ((y - fmin(z, t)) * (y - fmax(z, t))));
	double tmp;
	if (t_2 <= -5e+19) {
		tmp = t_1;
	} else if (t_2 <= 2e+67) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * (fmin(z, t) - y))
    t_2 = 1.0d0 - (x / ((y - fmin(z, t)) * (y - fmax(z, t))))
    if (t_2 <= (-5d+19)) then
        tmp = t_1
    else if (t_2 <= 2d+67) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (fmin(z, t) - y));
	double t_2 = 1.0 - (x / ((y - fmin(z, t)) * (y - fmax(z, t))));
	double tmp;
	if (t_2 <= -5e+19) {
		tmp = t_1;
	} else if (t_2 <= 2e+67) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y * (fmin(z, t) - y))
	t_2 = 1.0 - (x / ((y - fmin(z, t)) * (y - fmax(z, t))))
	tmp = 0
	if t_2 <= -5e+19:
		tmp = t_1
	elif t_2 <= 2e+67:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * Float64(fmin(z, t) - y)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(y - fmin(z, t)) * Float64(y - fmax(z, t)))))
	tmp = 0.0
	if (t_2 <= -5e+19)
		tmp = t_1;
	elseif (t_2 <= 2e+67)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * (min(z, t) - y));
	t_2 = 1.0 - (x / ((y - min(z, t)) * (y - max(z, t))));
	tmp = 0.0;
	if (t_2 <= -5e+19)
		tmp = t_1;
	elseif (t_2 <= 2e+67)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * N[(N[Min[z, t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(y - N[Min[z, t], $MachinePrecision]), $MachinePrecision] * N[(y - N[Max[z, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+19], t$95$1, If[LessEqual[t$95$2, 2e+67], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e19 or 2e67 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 99.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 99.0%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 26.1%

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

   6. Applied rewrites 26.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

      11. distribute-frac-neg2 N/A

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

      12. frac-2neg-rev N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. frac-2neg-rev N/A

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

      20. lower-/.f64 25.3%

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

   8. Applied rewrites 25.3%

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

   9. Taylor expanded in t around 0

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 13.7%

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

   11. Applied rewrites 13.7%

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

   if -5e19 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2e67

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 75.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 80.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{y \cdot t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ x (* (- y z) (- y t)))) (t_2 (/ x (* y t))))
  (if (<= t_1 -4e+25) t_2 (if (<= t_1 1e+20) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / (y * t);
	double tmp;
	if (t_1 <= -4e+25) {
		tmp = t_2;
	} else if (t_1 <= 1e+20) {
		tmp = 1.0;
	} 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))
    t_2 = x / (y * t)
    if (t_1 <= (-4d+25)) then
        tmp = t_2
    else if (t_1 <= 1d+20) then
        tmp = 1.0d0
    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 - t));
	double t_2 = x / (y * t);
	double tmp;
	if (t_1 <= -4e+25) {
		tmp = t_2;
	} else if (t_1 <= 1e+20) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	t_2 = x / (y * t)
	tmp = 0
	if t_1 <= -4e+25:
		tmp = t_2
	elif t_1 <= 1e+20:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	t_2 = Float64(x / Float64(y * t))
	tmp = 0.0
	if (t_1 <= -4e+25)
		tmp = t_2;
	elseif (t_1 <= 1e+20)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	t_2 = x / (y * t);
	tmp = 0.0;
	if (t_1 <= -4e+25)
		tmp = t_2;
	elseif (t_1 <= 1e+20)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+25], t$95$2, If[LessEqual[t$95$1, 1e+20], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4.0000000000000004e25 or 1e20 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 99.0%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 26.1%

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

   6. Applied rewrites 26.1%

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

   7. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 13.3%

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

   9. Applied rewrites 13.3%

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

   10. Taylor expanded in y around 0

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

   12. Applied rewrites 9.5%

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

   if -4.0000000000000004e25 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e20

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 75.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 75.0% accurate, 26.0× speedup

Math

\[1 \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 99.1%

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

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
3. Step-by-step derivation

4. Applied rewrites 75.0%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))