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

Percentage Accurate: 99.0% → 99.0%

Time: 7.9s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Final simplification 99.2%

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

Alternative 2: 87.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;t\_1 \leq 100:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_1 -1e+233)
     (/ x (* (- z y) y))
     (if (<= t_1 -5e+47)
       (/ x (* t (- y z)))
       (if (<= t_1 100.0) 1.0 (/ x (* (- y t) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_1 <= -1e+233) {
		tmp = x / ((z - y) * y);
	} else if (t_1 <= -5e+47) {
		tmp = x / (t * (y - z));
	} else if (t_1 <= 100.0) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - t) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    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 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_1 <= (-1d+233)) then
        tmp = x / ((z - y) * y)
    else if (t_1 <= (-5d+47)) then
        tmp = x / (t * (y - z))
    else if (t_1 <= 100.0d0) then
        tmp = 1.0d0
    else
        tmp = x / ((y - t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_1 <= -1e+233) {
		tmp = x / ((z - y) * y);
	} else if (t_1 <= -5e+47) {
		tmp = x / (t * (y - z));
	} else if (t_1 <= 100.0) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_1 <= -1e+233:
		tmp = x / ((z - y) * y)
	elif t_1 <= -5e+47:
		tmp = x / (t * (y - z))
	elif t_1 <= 100.0:
		tmp = 1.0
	else:
		tmp = x / ((y - t) * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_1 <= -1e+233)
		tmp = Float64(x / Float64(Float64(z - y) * y));
	elseif (t_1 <= -5e+47)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (t_1 <= 100.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(y - t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_1 <= -1e+233)
		tmp = x / ((z - y) * y);
	elseif (t_1 <= -5e+47)
		tmp = x / (t * (y - z));
	elseif (t_1 <= 100.0)
		tmp = 1.0;
	else
		tmp = x / ((y - t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+233], N[(x / N[(N[(z - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+47], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100.0], 1.0, N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -9.99999999999999974e232

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.2

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

   5. Applied rewrites 93.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 68.3%

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

   if -9.99999999999999974e232 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5.00000000000000022e47

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 94.1

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 62.2%

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

   if -5.00000000000000022e47 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 100

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 96.5%

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

   if 100 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 95.0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 61.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -1 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 100:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -0.004:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+223}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- z y) (- t y)))))
   (if (<= t_1 -0.004)
     (- 1.0 (/ x (* (- t y) z)))
     (if (<= t_1 5e+33)
       1.0
       (if (<= t_1 5e+223) (/ x (* t (- y z))) (/ x (* (- z y) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((z - y) * (t - y));
	double tmp;
	if (t_1 <= -0.004) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t_1 <= 5e+33) {
		tmp = 1.0;
	} else if (t_1 <= 5e+223) {
		tmp = x / (t * (y - z));
	} else {
		tmp = x / ((z - y) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    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 - y) * (t - y))
    if (t_1 <= (-0.004d0)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (t_1 <= 5d+33) then
        tmp = 1.0d0
    else if (t_1 <= 5d+223) then
        tmp = x / (t * (y - z))
    else
        tmp = x / ((z - y) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((z - y) * (t - y));
	double tmp;
	if (t_1 <= -0.004) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t_1 <= 5e+33) {
		tmp = 1.0;
	} else if (t_1 <= 5e+223) {
		tmp = x / (t * (y - z));
	} else {
		tmp = x / ((z - y) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((z - y) * (t - y))
	tmp = 0
	if t_1 <= -0.004:
		tmp = 1.0 - (x / ((t - y) * z))
	elif t_1 <= 5e+33:
		tmp = 1.0
	elif t_1 <= 5e+223:
		tmp = x / (t * (y - z))
	else:
		tmp = x / ((z - y) * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(z - y) * Float64(t - y)))
	tmp = 0.0
	if (t_1 <= -0.004)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (t_1 <= 5e+33)
		tmp = 1.0;
	elseif (t_1 <= 5e+223)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(x / Float64(Float64(z - y) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((z - y) * (t - y));
	tmp = 0.0;
	if (t_1 <= -0.004)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (t_1 <= 5e+33)
		tmp = 1.0;
	elseif (t_1 <= 5e+223)
		tmp = x / (t * (y - z));
	else
		tmp = x / ((z - y) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.004], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+33], 1.0, If[LessEqual[t$95$1, 5e+223], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(z - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -0.0040000000000000001

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 59.2

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

   5. Applied rewrites 59.2%

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

   if -0.0040000000000000001 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.99999999999999973e33

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 97.6%

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

   if 4.99999999999999973e33 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.99999999999999985e223

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 94.1

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 62.2%

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

   if 4.99999999999999985e223 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.2

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

   5. Applied rewrites 93.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 68.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -0.004:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 5 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 5 \cdot 10^{+223}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z}\\ t_2 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 100:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y t) z))) (t_2 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_2 -2e+33) t_1 (if (<= t_2 100.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - t) * z);
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 100.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - t) * z)
    t_2 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_2 <= (-2d+33)) then
        tmp = t_1
    else if (t_2 <= 100.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - t) * z);
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 100.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - t) * z)
	t_2 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_2 <= -2e+33:
		tmp = t_1
	elif t_2 <= 100.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - t) * z))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 100.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - t) * z);
	t_2 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 100.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+33], t$95$1, If[LessEqual[t$95$2, 100.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -1.9999999999999999e33 or 100 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 94.4

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

   5. Applied rewrites 94.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 65.6%

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

   if -1.9999999999999999e33 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 100

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 96.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 100:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot \left(y - z\right)}\\ t_2 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 100:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t (- y z)))) (t_2 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_2 -5e+47) t_1 (if (<= t_2 100.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t * (y - z));
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -5e+47) {
		tmp = t_1;
	} else if (t_2 <= 100.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (t * (y - z))
    t_2 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_2 <= (-5d+47)) then
        tmp = t_1
    else if (t_2 <= 100.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t * (y - z));
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -5e+47) {
		tmp = t_1;
	} else if (t_2 <= 100.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t * (y - z))
	t_2 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_2 <= -5e+47:
		tmp = t_1
	elif t_2 <= 100.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * Float64(y - z)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -5e+47)
		tmp = t_1;
	elseif (t_2 <= 100.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * (y - z));
	t_2 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -5e+47)
		tmp = t_1;
	elseif (t_2 <= 100.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+47], t$95$1, If[LessEqual[t$95$2, 100.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5.00000000000000022e47 or 100 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 94.3

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 57.5%

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

   if -5.00000000000000022e47 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 100

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 96.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 100:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{t \cdot z}\\ t_2 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -50000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 100:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* t z))) (t_2 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_2 -50000000.0) t_1 (if (<= t_2 100.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (t * z);
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -50000000.0) {
		tmp = t_1;
	} else if (t_2 <= 100.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -x / (t * z)
    t_2 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_2 <= (-50000000.0d0)) then
        tmp = t_1
    else if (t_2 <= 100.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (t * z);
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -50000000.0) {
		tmp = t_1;
	} else if (t_2 <= 100.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (t * z)
	t_2 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_2 <= -50000000.0:
		tmp = t_1
	elif t_2 <= 100.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(t * z))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -50000000.0)
		tmp = t_1;
	elseif (t_2 <= 100.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (t * z);
	t_2 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -50000000.0)
		tmp = t_1;
	elseif (t_2 <= 100.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -50000000.0], t$95$1, If[LessEqual[t$95$2, 100.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e7 or 100 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 40.6%

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

   if -5e7 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 100

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 97.9%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -50000000:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 100:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ t_2 := \frac{x}{t \cdot y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- z y) (- t y)))) (t_2 (/ x (* t y))))
   (if (<= t_1 -2e+45) t_2 (if (<= t_1 5e+33) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((z - y) * (t - y));
	double t_2 = x / (t * y);
	double tmp;
	if (t_1 <= -2e+45) {
		tmp = t_2;
	} else if (t_1 <= 5e+33) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((z - y) * (t - y))
    t_2 = x / (t * y)
    if (t_1 <= (-2d+45)) then
        tmp = t_2
    else if (t_1 <= 5d+33) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((z - y) * (t - y));
	double t_2 = x / (t * y);
	double tmp;
	if (t_1 <= -2e+45) {
		tmp = t_2;
	} else if (t_1 <= 5e+33) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((z - y) * (t - y))
	t_2 = x / (t * y)
	tmp = 0
	if t_1 <= -2e+45:
		tmp = t_2
	elif t_1 <= 5e+33:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(z - y) * Float64(t - y)))
	t_2 = Float64(x / Float64(t * y))
	tmp = 0.0
	if (t_1 <= -2e+45)
		tmp = t_2;
	elseif (t_1 <= 5e+33)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((z - y) * (t - y));
	t_2 = x / (t * y);
	tmp = 0.0;
	if (t_1 <= -2e+45)
		tmp = t_2;
	elseif (t_1 <= 5e+33)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+45], t$95$2, If[LessEqual[t$95$1, 5e+33], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.9999999999999999e45 or 4.99999999999999973e33 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 43.4%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 30.1%

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

   if -1.9999999999999999e45 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.99999999999999973e33

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 95.2%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -2 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 5 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-212}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-82}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.2e-212)
   (- 1.0 (/ x (* (- t y) z)))
   (if (<= t 9.6e-82)
     (- 1.0 (/ x (* (- y z) y)))
     (- 1.0 (/ x (* (- z y) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.2e-212) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t <= 9.6e-82) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    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 <= (-6.2d-212)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (t <= 9.6d-82) then
        tmp = 1.0d0 - (x / ((y - z) * y))
    else
        tmp = 1.0d0 - (x / ((z - y) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.2e-212) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t <= 9.6e-82) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.2e-212:
		tmp = 1.0 - (x / ((t - y) * z))
	elif t <= 9.6e-82:
		tmp = 1.0 - (x / ((y - z) * y))
	else:
		tmp = 1.0 - (x / ((z - y) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.2e-212)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (t <= 9.6e-82)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(z - y) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.2e-212)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (t <= 9.6e-82)
		tmp = 1.0 - (x / ((y - z) * y));
	else
		tmp = 1.0 - (x / ((z - y) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.2e-212], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e-82], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000011e-212

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 79.0

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

   5. Applied rewrites 79.0%

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

   if -6.20000000000000011e-212 < t < 9.60000000000000033e-82

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 91.9

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

   5. Applied rewrites 91.9%

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

   if 9.60000000000000033e-82 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 93.1

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

   5. Applied rewrites 93.1%

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

Alternative 9: 82.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -820:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -820.0) (- 1.0 (/ x (* (- t y) z))) (- 1.0 (/ x (* (- y t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -820.0) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else {
		tmp = 1.0 - (x / ((y - t) * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    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 <= (-820.0d0)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else
        tmp = 1.0d0 - (x / ((y - t) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -820.0) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else {
		tmp = 1.0 - (x / ((y - t) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -820.0:
		tmp = 1.0 - (x / ((t - y) * z))
	else:
		tmp = 1.0 - (x / ((y - t) * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -820.0)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -820.0)
		tmp = 1.0 - (x / ((t - y) * z));
	else
		tmp = 1.0 - (x / ((y - t) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -820.0], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -820

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 99.2

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

   5. Applied rewrites 99.2%

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

   if -820 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

Alternative 10: 75.4% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in t around inf

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

5. Applied rewrites 74.9%

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

Reproduce

herbie shell --seed 2024249 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))