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

Percentage Accurate: 89.1% → 98.7%

Time: 9.3s

Alternatives: 12

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{\frac{x}{t - z}}{y - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+156}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))) (t_2 (/ (/ x (- t z)) (- y z))))
   (if (<= t_1 -1e+156) t_2 (if (<= t_1 5e+193) (/ x t_1) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = (x / (t - z)) / (y - z);
	double tmp;
	if (t_1 <= -1e+156) {
		tmp = t_2;
	} else if (t_1 <= 5e+193) {
		tmp = x / t_1;
	} 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 = (y - z) * (t - z)
    t_2 = (x / (t - z)) / (y - z)
    if (t_1 <= (-1d+156)) then
        tmp = t_2
    else if (t_1 <= 5d+193) then
        tmp = x / t_1
    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 - z) * (t - z);
	double t_2 = (x / (t - z)) / (y - z);
	double tmp;
	if (t_1 <= -1e+156) {
		tmp = t_2;
	} else if (t_1 <= 5e+193) {
		tmp = x / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	t_2 = (x / (t - z)) / (y - z)
	tmp = 0
	if t_1 <= -1e+156:
		tmp = t_2
	elif t_1 <= 5e+193:
		tmp = x / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	t_2 = Float64(Float64(x / Float64(t - z)) / Float64(y - z))
	tmp = 0.0
	if (t_1 <= -1e+156)
		tmp = t_2;
	elseif (t_1 <= 5e+193)
		tmp = Float64(x / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	t_2 = (x / (t - z)) / (y - z);
	tmp = 0.0;
	if (t_1 <= -1e+156)
		tmp = t_2;
	elseif (t_1 <= 5e+193)
		tmp = x / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+156], t$95$2, If[LessEqual[t$95$1, 5e+193], N[(x / t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -9.9999999999999998e155 or 4.99999999999999972e193 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 97.2

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

   3. Applied rewrites 97.2%

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

   if -9.9999999999999998e155 < (*.f64 (-.f64 y z) (-.f64 t z)) < 4.99999999999999972e193

   1. Initial program 89.1%

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

Alternative 2: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq -2 \cdot 10^{-256}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y - z, t, z \cdot \left(z - y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x (* (- y z) (- t z))) -2e-256)
   (/ x (fma (- y z) t (* z (- z y))))
   (/ (/ x (- z y)) (- z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / ((y - z) * (t - z))) <= -2e-256) {
		tmp = x / fma((y - z), t, (z * (z - y)));
	} else {
		tmp = (x / (z - y)) / (z - t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / Float64(Float64(y - z) * Float64(t - z))) <= -2e-256)
		tmp = Float64(x / fma(Float64(y - z), t, Float64(z * Float64(z - y))));
	else
		tmp = Float64(Float64(x / Float64(z - y)) / Float64(z - t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -2e-256], N[(x / N[(N[(y - z), $MachinePrecision] * t + N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -1.99999999999999995e-256

   1. Initial program 89.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. distribute-rgt-in N/A

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

      5. lift--.f64 N/A

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

      6. flip3-- N/A

         \[\leadsto \frac{x}{t \cdot \color{blue}{\frac{{y}^{3} - {z}^{3}}{y \cdot y + \left(z \cdot z + y \cdot z\right)}} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - z\right)} \]

      7. div-flip N/A

         \[\leadsto \frac{x}{t \cdot \color{blue}{\frac{1}{\frac{y \cdot y + \left(z \cdot z + y \cdot z\right)}{{y}^{3} - {z}^{3}}}} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - z\right)} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{t}{\frac{y \cdot y + \left(z \cdot z + y \cdot z\right)}{{y}^{3} - {z}^{3}}}} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - z\right)} \]

      9. *-lft-identity N/A

         \[\leadsto \frac{x}{\frac{\color{blue}{1 \cdot t}}{\frac{y \cdot y + \left(z \cdot z + y \cdot z\right)}{{y}^{3} - {z}^{3}}} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - z\right)} \]

      10. associate-*l/ N/A

          \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{y \cdot y + \left(z \cdot z + y \cdot z\right)}{{y}^{3} - {z}^{3}}} \cdot t} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - z\right)} \]

      11. div-flip N/A

          \[\leadsto \frac{x}{\color{blue}{\frac{{y}^{3} - {z}^{3}}{y \cdot y + \left(z \cdot z + y \cdot z\right)}} \cdot t + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - z\right)} \]

      12. flip3-- N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-flip N/A

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

      16. +-commutative N/A

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

      17. distribute-rgt-in N/A

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

      18. sqr-neg-rev N/A

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

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

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

      20. sub-flip N/A

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

   3. Applied rewrites 88.7%

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

   if -1.99999999999999995e-256 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 97.2

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

   3. Applied rewrites 97.2%

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

Alternative 3: 97.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -2e-256) t_1 (/ (/ x (- z y)) (- z t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2e-256) {
		tmp = t_1;
	} else {
		tmp = (x / (z - y)) / (z - t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) * (t - z))
    if (t_1 <= (-2d-256)) then
        tmp = t_1
    else
        tmp = (x / (z - y)) / (z - 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) * (t - z));
	double tmp;
	if (t_1 <= -2e-256) {
		tmp = t_1;
	} else {
		tmp = (x / (z - y)) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -2e-256:
		tmp = t_1
	else:
		tmp = (x / (z - y)) / (z - t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -2e-256)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(z - y)) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -2e-256)
		tmp = t_1;
	else
		tmp = (x / (z - y)) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-256], t$95$1, N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -1.99999999999999995e-256

   1. Initial program 89.1%

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

   if -1.99999999999999995e-256 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 97.2

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

   3. Applied rewrites 97.2%

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

Alternative 4: 93.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.25e+101)
   (/ (/ x z) (- z y))
   (if (<= z 2.9e+127) (/ x (* (- y z) (- t z))) (/ (/ x z) (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e+101) {
		tmp = (x / z) / (z - y);
	} else if (z <= 2.9e+127) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.25d+101)) then
        tmp = (x / z) / (z - y)
    else if (z <= 2.9d+127) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / z) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e+101) {
		tmp = (x / z) / (z - y);
	} else if (z <= 2.9e+127) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.25e+101:
		tmp = (x / z) / (z - y)
	elif z <= 2.9e+127:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.25e+101)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 2.9e+127)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.25e+101)
		tmp = (x / z) / (z - y);
	elseif (z <= 2.9e+127)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.25e+101], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+127], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999997e101

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 97.2

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

   3. Applied rewrites 97.2%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. associate-*l/ N/A

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

      9. mult-flip-rev N/A

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

      10. div-flip-rev N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. frac-2neg N/A

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

      15. lift-/.f64 N/A

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

      16. metadata-eval N/A

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

      17. distribute-frac-neg N/A

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

      18. lift--.f64 N/A

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

      19. sub-negate-rev N/A

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

      20. lift--.f64 N/A

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

      21. frac-2neg-rev N/A

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

      22. lower-/.f64 N/A

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in z around inf

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

      1. lower-/.f64 58.7

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

   8. Applied rewrites 58.7%

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

   if -1.24999999999999997e101 < z < 2.9000000000000002e127

   1. Initial program 89.1%

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

   if 2.9000000000000002e127 < z

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 97.2

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

   3. Applied rewrites 97.2%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 58.8%

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

Alternative 5: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y - z}}{t}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+171}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (- y z)) t)))
   (if (<= t -3.3e-117)
     t_1
     (if (<= t 1.16e-30)
       (/ (/ x z) (- z y))
       (if (<= t 4.2e+171) (/ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / (y - z)) / t;
	double tmp;
	if (t <= -3.3e-117) {
		tmp = t_1;
	} else if (t <= 1.16e-30) {
		tmp = (x / z) / (z - y);
	} else if (t <= 4.2e+171) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (y - z)) / t
    if (t <= (-3.3d-117)) then
        tmp = t_1
    else if (t <= 1.16d-30) then
        tmp = (x / z) / (z - y)
    else if (t <= 4.2d+171) then
        tmp = x / ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / (y - z)) / t;
	double tmp;
	if (t <= -3.3e-117) {
		tmp = t_1;
	} else if (t <= 1.16e-30) {
		tmp = (x / z) / (z - y);
	} else if (t <= 4.2e+171) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / (y - z)) / t
	tmp = 0
	if t <= -3.3e-117:
		tmp = t_1
	elif t <= 1.16e-30:
		tmp = (x / z) / (z - y)
	elif t <= 4.2e+171:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(y - z)) / t)
	tmp = 0.0
	if (t <= -3.3e-117)
		tmp = t_1;
	elseif (t <= 1.16e-30)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (t <= 4.2e+171)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / (y - z)) / t;
	tmp = 0.0;
	if (t <= -3.3e-117)
		tmp = t_1;
	elseif (t <= 1.16e-30)
		tmp = (x / z) / (z - y);
	elseif (t <= 4.2e+171)
		tmp = x / ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -3.3e-117], t$95$1, If[LessEqual[t, 1.16e-30], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+171], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.30000000000000015e-117 or 4.2000000000000003e171 < t

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 88.9

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 56.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. mul-1-neg N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/r* N/A

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

      7. distribute-neg-frac N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. distribute-neg-frac2 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lift--.f64 N/A

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

      15. lower-/.f64 63.1

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

   8. Applied rewrites 63.1%

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

   if -3.30000000000000015e-117 < t < 1.16e-30

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 97.2

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

   3. Applied rewrites 97.2%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. associate-*l/ N/A

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

      9. mult-flip-rev N/A

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

      10. div-flip-rev N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. frac-2neg N/A

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

      15. lift-/.f64 N/A

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

      16. metadata-eval N/A

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

      17. distribute-frac-neg N/A

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

      18. lift--.f64 N/A

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

      19. sub-negate-rev N/A

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

      20. lift--.f64 N/A

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

      21. frac-2neg-rev N/A

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

      22. lower-/.f64 N/A

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in z around inf

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

      1. lower-/.f64 58.7

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

   8. Applied rewrites 58.7%

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

   if 1.16e-30 < t < 4.2000000000000003e171

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 56.9%

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

Alternative 6: 80.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y - z}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+182}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) (- y z))))
   (if (<= t -1.25e-105)
     t_1
     (if (<= t 1.16e-30)
       (/ (/ x z) (- z y))
       (if (<= t 5.2e+182) (/ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (y - z);
	double tmp;
	if (t <= -1.25e-105) {
		tmp = t_1;
	} else if (t <= 1.16e-30) {
		tmp = (x / z) / (z - y);
	} else if (t <= 5.2e+182) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / (y - z)
    if (t <= (-1.25d-105)) then
        tmp = t_1
    else if (t <= 1.16d-30) then
        tmp = (x / z) / (z - y)
    else if (t <= 5.2d+182) then
        tmp = x / ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (y - z);
	double tmp;
	if (t <= -1.25e-105) {
		tmp = t_1;
	} else if (t <= 1.16e-30) {
		tmp = (x / z) / (z - y);
	} else if (t <= 5.2e+182) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) / (y - z)
	tmp = 0
	if t <= -1.25e-105:
		tmp = t_1
	elif t <= 1.16e-30:
		tmp = (x / z) / (z - y)
	elif t <= 5.2e+182:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / Float64(y - z))
	tmp = 0.0
	if (t <= -1.25e-105)
		tmp = t_1;
	elseif (t <= 1.16e-30)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (t <= 5.2e+182)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / (y - z);
	tmp = 0.0;
	if (t <= -1.25e-105)
		tmp = t_1;
	elseif (t <= 1.16e-30)
		tmp = (x / z) / (z - y);
	elseif (t <= 5.2e+182)
		tmp = x / ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-105], t$95$1, If[LessEqual[t, 1.16e-30], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+182], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.24999999999999991e-105 or 5.2e182 < t

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. associate-/r/ N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. lift--.f64 N/A

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

      8. flip3-- N/A

         \[\leadsto \frac{\frac{1}{\color{blue}{\frac{{t}^{3} - {z}^{3}}{t \cdot t + \left(z \cdot z + t \cdot z\right)}}}}{y - z} \cdot x \]

      9. div-flip-rev N/A

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

      10. associate-*l/ N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 97.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 58.7

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

   6. Applied rewrites 58.7%

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

   if -1.24999999999999991e-105 < t < 1.16e-30

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 97.2

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

   3. Applied rewrites 97.2%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. associate-*l/ N/A

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

      9. mult-flip-rev N/A

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

      10. div-flip-rev N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. frac-2neg N/A

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

      15. lift-/.f64 N/A

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

      16. metadata-eval N/A

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

      17. distribute-frac-neg N/A

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

      18. lift--.f64 N/A

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

      19. sub-negate-rev N/A

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

      20. lift--.f64 N/A

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

      21. frac-2neg-rev N/A

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

      22. lower-/.f64 N/A

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in z around inf

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

      1. lower-/.f64 58.7

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

   8. Applied rewrites 58.7%

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

   if 1.16e-30 < t < 5.2e182

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 56.9%

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

Alternative 7: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y - z}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+182}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) (- y z))))
   (if (<= t -1.25e-105)
     t_1
     (if (<= t 3.4e-61)
       (/ x (* (- z y) z))
       (if (<= t 5.2e+182) (/ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (y - z);
	double tmp;
	if (t <= -1.25e-105) {
		tmp = t_1;
	} else if (t <= 3.4e-61) {
		tmp = x / ((z - y) * z);
	} else if (t <= 5.2e+182) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / (y - z)
    if (t <= (-1.25d-105)) then
        tmp = t_1
    else if (t <= 3.4d-61) then
        tmp = x / ((z - y) * z)
    else if (t <= 5.2d+182) then
        tmp = x / ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (y - z);
	double tmp;
	if (t <= -1.25e-105) {
		tmp = t_1;
	} else if (t <= 3.4e-61) {
		tmp = x / ((z - y) * z);
	} else if (t <= 5.2e+182) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) / (y - z)
	tmp = 0
	if t <= -1.25e-105:
		tmp = t_1
	elif t <= 3.4e-61:
		tmp = x / ((z - y) * z)
	elif t <= 5.2e+182:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / Float64(y - z))
	tmp = 0.0
	if (t <= -1.25e-105)
		tmp = t_1;
	elseif (t <= 3.4e-61)
		tmp = Float64(x / Float64(Float64(z - y) * z));
	elseif (t <= 5.2e+182)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / (y - z);
	tmp = 0.0;
	if (t <= -1.25e-105)
		tmp = t_1;
	elseif (t <= 3.4e-61)
		tmp = x / ((z - y) * z);
	elseif (t <= 5.2e+182)
		tmp = x / ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-105], t$95$1, If[LessEqual[t, 3.4e-61], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+182], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.24999999999999991e-105 or 5.2e182 < t

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. associate-/r/ N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. lift--.f64 N/A

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

      8. flip3-- N/A

         \[\leadsto \frac{\frac{1}{\color{blue}{\frac{{t}^{3} - {z}^{3}}{t \cdot t + \left(z \cdot z + t \cdot z\right)}}}}{y - z} \cdot x \]

      9. div-flip-rev N/A

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

      10. associate-*l/ N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 97.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 58.7

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

   6. Applied rewrites 58.7%

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

   if -1.24999999999999991e-105 < t < 3.3999999999999998e-61

   1. Initial program 89.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.0

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

   4. Applied rewrites 54.0%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 54.0

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

   6. Applied rewrites 54.0%

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

   if 3.3999999999999998e-61 < t < 5.2e182

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 56.9%

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

Alternative 8: 69.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.65e-122)
   (/ x (* y (- t z)))
   (if (<= t 3.4e-61) (/ x (* (- z y) z)) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e-122) {
		tmp = x / (y * (t - z));
	} else if (t <= 3.4e-61) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.65d-122)) then
        tmp = x / (y * (t - z))
    else if (t <= 3.4d-61) then
        tmp = x / ((z - y) * z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e-122) {
		tmp = x / (y * (t - z));
	} else if (t <= 3.4e-61) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.65e-122:
		tmp = x / (y * (t - z))
	elif t <= 3.4e-61:
		tmp = x / ((z - y) * z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.65e-122)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 3.4e-61)
		tmp = Float64(x / Float64(Float64(z - y) * z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.65e-122)
		tmp = x / (y * (t - z));
	elseif (t <= 3.4e-61)
		tmp = x / ((z - y) * z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.65e-122], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-61], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.65e-122

   1. Initial program 89.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.2

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

   4. Applied rewrites 57.2%

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

   if -1.65e-122 < t < 3.3999999999999998e-61

   1. Initial program 89.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.0

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

   4. Applied rewrites 54.0%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 54.0

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

   6. Applied rewrites 54.0%

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

   if 3.3999999999999998e-61 < t

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 56.9%

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

Alternative 9: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-148)
   (/ x (* y (- t z)))
   (if (<= y 9.8e-32) (/ x (* z (- z t))) (/ x (* t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-148) {
		tmp = x / (y * (t - z));
	} else if (y <= 9.8e-32) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.6d-148)) then
        tmp = x / (y * (t - z))
    else if (y <= 9.8d-32) then
        tmp = x / (z * (z - t))
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-148) {
		tmp = x / (y * (t - z));
	} else if (y <= 9.8e-32) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-148:
		tmp = x / (y * (t - z))
	elif y <= 9.8e-32:
		tmp = x / (z * (z - t))
	else:
		tmp = x / (t * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-148)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 9.8e-32)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e-148)
		tmp = x / (y * (t - z));
	elseif (y <= 9.8e-32)
		tmp = x / (z * (z - t));
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-148], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-32], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999997e-148

   1. Initial program 89.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.2

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

   4. Applied rewrites 57.2%

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

   if -1.59999999999999997e-148 < y < 9.7999999999999996e-32

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 97.2

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

   3. Applied rewrites 97.2%

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

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.0

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

   6. Applied rewrites 54.0%

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

   if 9.7999999999999996e-32 < y

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.5

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

   4. Applied rewrites 39.5%

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

Alternative 10: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -4000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z t)))))
   (if (<= z -4000000.0) t_1 (if (<= z 1.7e-141) (/ x (* t y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -4000000.0) {
		tmp = t_1;
	} else if (z <= 1.7e-141) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z * (z - t))
    if (z <= (-4000000.0d0)) then
        tmp = t_1
    else if (z <= 1.7d-141) then
        tmp = x / (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -4000000.0) {
		tmp = t_1;
	} else if (z <= 1.7e-141) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (z - t))
	tmp = 0
	if z <= -4000000.0:
		tmp = t_1
	elif z <= 1.7e-141:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - t)))
	tmp = 0.0
	if (z <= -4000000.0)
		tmp = t_1;
	elseif (z <= 1.7e-141)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - t));
	tmp = 0.0;
	if (z <= -4000000.0)
		tmp = t_1;
	elseif (z <= 1.7e-141)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4000000.0], t$95$1, If[LessEqual[z, 1.7e-141], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4e6 or 1.6999999999999999e-141 < z

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 97.2

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

   3. Applied rewrites 97.2%

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

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.0

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

   6. Applied rewrites 54.0%

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

   if -4e6 < z < 1.6999999999999999e-141

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.5

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

   4. Applied rewrites 39.5%

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

Alternative 11: 46.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot y}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-48}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t y))))
   (if (<= y -1.35e-207) t_1 (if (<= y 1.55e-48) (/ (- x) (* t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t * y);
	double tmp;
	if (y <= -1.35e-207) {
		tmp = t_1;
	} else if (y <= 1.55e-48) {
		tmp = -x / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 / (t * y)
    if (y <= (-1.35d-207)) then
        tmp = t_1
    else if (y <= 1.55d-48) then
        tmp = -x / (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t * y);
	double tmp;
	if (y <= -1.35e-207) {
		tmp = t_1;
	} else if (y <= 1.55e-48) {
		tmp = -x / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t * y)
	tmp = 0
	if y <= -1.35e-207:
		tmp = t_1
	elif y <= 1.55e-48:
		tmp = -x / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * y))
	tmp = 0.0
	if (y <= -1.35e-207)
		tmp = t_1;
	elseif (y <= 1.55e-48)
		tmp = Float64(Float64(-x) / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * y);
	tmp = 0.0;
	if (y <= -1.35e-207)
		tmp = t_1;
	elseif (y <= 1.55e-48)
		tmp = -x / (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e-207], t$95$1, If[LessEqual[y, 1.55e-48], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-207 or 1.55000000000000008e-48 < y

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.5

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

   4. Applied rewrites 39.5%

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

   if -1.35e-207 < y < 1.55000000000000008e-48

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 88.9

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

   3. Applied rewrites 88.9%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 56.8%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 31.4%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*l/ N/A

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

       4. mul-1-neg N/A

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

       5. lower-/.f64 N/A

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

       6. lower-neg.f64 31.5

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 31.5

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

   11. Applied rewrites 31.5%

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

Alternative 12: 39.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.1%

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

2. Taylor expanded in z around 0

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

   1. lower-*.f64 39.5

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

4. Applied rewrites 39.5%

   \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025142 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64
  (/ x (* (- y z) (- t z))))