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

Percentage Accurate: 99.0% → 99.0%

Time: 7.2s

Alternatives: 8

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

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

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]

Derivation

1. Initial program 99.5%

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

Alternative 2: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \lor \neg \left(t\_1 \leq 2\right):\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- y z) (- y t))))))
   (if (or (<= t_1 -2.0) (not (<= t_1 2.0))) (/ x (* (- y t) z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if ((t_1 <= -2.0) || !(t_1 <= 2.0)) {
		tmp = x / ((y - t) * z);
	} else {
		tmp = 1.0;
	}
	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 / ((y - z) * (y - t)))
    if ((t_1 <= (-2.0d0)) .or. (.not. (t_1 <= 2.0d0))) then
        tmp = x / ((y - t) * z)
    else
        tmp = 1.0d0
    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 / ((y - z) * (y - t)));
	double tmp;
	if ((t_1 <= -2.0) || !(t_1 <= 2.0)) {
		tmp = x / ((y - t) * z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((y - z) * (y - t)))
	tmp = 0
	if (t_1 <= -2.0) or not (t_1 <= 2.0):
		tmp = x / ((y - t) * z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
	tmp = 0.0
	if ((t_1 <= -2.0) || !(t_1 <= 2.0))
		tmp = Float64(x / Float64(Float64(y - t) * z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / ((y - z) * (y - t)));
	tmp = 0.0;
	if ((t_1 <= -2.0) || ~((t_1 <= 2.0)))
		tmp = x / ((y - t) * z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2.0], N[Not[LessEqual[t$95$1, 2.0]], $MachinePrecision]], N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 89.8

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

   5. Applied rewrites 89.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 53.5%

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

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

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.2%

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

4. Final simplification 86.2%

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

Alternative 3: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \lor \neg \left(t\_1 \leq 2\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- y z) (- y t))))))
   (if (or (<= t_1 -2.0) (not (<= t_1 2.0))) (/ (- x) (* z t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if ((t_1 <= -2.0) || !(t_1 <= 2.0)) {
		tmp = -x / (z * t);
	} else {
		tmp = 1.0;
	}
	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 / ((y - z) * (y - t)))
    if ((t_1 <= (-2.0d0)) .or. (.not. (t_1 <= 2.0d0))) then
        tmp = -x / (z * t)
    else
        tmp = 1.0d0
    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 / ((y - z) * (y - t)));
	double tmp;
	if ((t_1 <= -2.0) || !(t_1 <= 2.0)) {
		tmp = -x / (z * t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((y - z) * (y - t)))
	tmp = 0
	if (t_1 <= -2.0) or not (t_1 <= 2.0):
		tmp = -x / (z * t)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
	tmp = 0.0
	if ((t_1 <= -2.0) || !(t_1 <= 2.0))
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / ((y - z) * (y - t)));
	tmp = 0.0;
	if ((t_1 <= -2.0) || ~((t_1 <= 2.0)))
		tmp = -x / (z * t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2.0], N[Not[LessEqual[t$95$1, 2.0]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 89.8

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

   5. Applied rewrites 89.8%

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

   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 40.7%

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

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

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.2%

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

4. Final simplification 82.5%

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

Alternative 4: 89.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -1e+18)
     (/ x (* (- y t) z))
     (if (<= t_1 5e-6) 1.0 (/ (- x) (* (- z y) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = x / ((y - t) * z);
	} else if (t_1 <= 5e-6) {
		tmp = 1.0;
	} else {
		tmp = -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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if (t_1 <= (-1d+18)) then
        tmp = x / ((y - t) * z)
    else if (t_1 <= 5d-6) then
        tmp = 1.0d0
    else
        tmp = -x / ((z - y) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = x / ((y - t) * z);
	} else if (t_1 <= 5e-6) {
		tmp = 1.0;
	} else {
		tmp = -x / ((z - y) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -1e+18:
		tmp = x / ((y - t) * z)
	elif t_1 <= 5e-6:
		tmp = 1.0
	else:
		tmp = -x / ((z - y) * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -1e+18)
		tmp = Float64(x / Float64(Float64(y - t) * z));
	elseif (t_1 <= 5e-6)
		tmp = 1.0;
	else
		tmp = Float64(Float64(-x) / Float64(Float64(z - y) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -1e+18)
		tmp = x / ((y - t) * z);
	elseif (t_1 <= 5e-6)
		tmp = 1.0;
	else
		tmp = -x / ((z - y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+18], N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-6], 1.0, N[((-x) / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e18

   1. Initial program 99.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.9

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 53.9%

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

   if -1e18 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.00000000000000041e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.2%

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

   if 5.00000000000000041e-6 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 97.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 55.1%

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

Alternative 5: 81.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+21} \lor \neg \left(t\_1 \leq 10\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -5e+21) (not (<= t_1 10.0))) (/ x (* z y)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -5e+21) || !(t_1 <= 10.0)) {
		tmp = x / (z * y);
	} else {
		tmp = 1.0;
	}
	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 / ((y - z) * (y - t))
    if ((t_1 <= (-5d+21)) .or. (.not. (t_1 <= 10.0d0))) then
        tmp = x / (z * y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -5e+21) || !(t_1 <= 10.0)) {
		tmp = x / (z * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if (t_1 <= -5e+21) or not (t_1 <= 10.0):
		tmp = x / (z * y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if ((t_1 <= -5e+21) || !(t_1 <= 10.0))
		tmp = Float64(x / Float64(z * y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if ((t_1 <= -5e+21) || ~((t_1 <= 10.0)))
		tmp = x / (z * y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+21], N[Not[LessEqual[t$95$1, 10.0]], $MachinePrecision]], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5e21 or 10 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 98.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.6

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

   5. Applied rewrites 91.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 54.1%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 26.2%

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

   if -5e21 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -5 \cdot 10^{+21} \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 10\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+41}:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -5e+41)
     (/ (- x) (* y y))
     (if (<= t_1 10.0) 1.0 (/ x (* z y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -5e+41) {
		tmp = -x / (y * y);
	} else if (t_1 <= 10.0) {
		tmp = 1.0;
	} else {
		tmp = x / (z * 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 / ((y - z) * (y - t))
    if (t_1 <= (-5d+41)) then
        tmp = -x / (y * y)
    else if (t_1 <= 10.0d0) then
        tmp = 1.0d0
    else
        tmp = x / (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -5e+41) {
		tmp = -x / (y * y);
	} else if (t_1 <= 10.0) {
		tmp = 1.0;
	} else {
		tmp = x / (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -5e+41:
		tmp = -x / (y * y)
	elif t_1 <= 10.0:
		tmp = 1.0
	else:
		tmp = x / (z * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -5e+41)
		tmp = Float64(Float64(-x) / Float64(y * y));
	elseif (t_1 <= 10.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -5e+41)
		tmp = -x / (y * y);
	elseif (t_1 <= 10.0)
		tmp = 1.0;
	else
		tmp = x / (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+41], N[((-x) / N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10.0], 1.0, N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.00000000000000022e41

   1. Initial program 99.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.1

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

   5. Applied rewrites 91.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\frac{x}{{y}^{2}}} \]
   7. Step-by-step derivation

   8. Applied rewrites 50.1%

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

   if -5.00000000000000022e41 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.8%

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

   if 10 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 97.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.6

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

   5. Applied rewrites 91.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 27.0%

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

Alternative 7: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.1 \cdot 10^{-242}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-61}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.1e-242)
   (- 1.0 (/ x (* (- t y) z)))
   (if (<= t 2.4e-61) (- 1.0 (/ x (* y y))) (- 1.0 (/ x (* (- z y) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.1e-242) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t <= 2.4e-61) {
		tmp = 1.0 - (x / (y * 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 <= 2.1d-242) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (t <= 2.4d-61) then
        tmp = 1.0d0 - (x / (y * 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 <= 2.1e-242) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t <= 2.4e-61) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.1e-242:
		tmp = 1.0 - (x / ((t - y) * z))
	elif t <= 2.4e-61:
		tmp = 1.0 - (x / (y * y))
	else:
		tmp = 1.0 - (x / ((z - y) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.1e-242)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (t <= 2.4e-61)
		tmp = Float64(1.0 - Float64(x / Float64(y * 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 <= 2.1e-242)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (t <= 2.4e-61)
		tmp = 1.0 - (x / (y * y));
	else
		tmp = 1.0 - (x / ((z - y) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.1e-242], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-61], N[(1.0 - N[(x / N[(y * 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 < 2.10000000000000019e-242

   1. Initial program 99.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 78.9

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

   5. Applied rewrites 78.9%

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

   if 2.10000000000000019e-242 < t < 2.4000000000000001e-61

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto 1 - \frac{x}{\color{blue}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. lower-*.f64 72.2

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

   5. Applied rewrites 72.2%

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

   if 2.4000000000000001e-61 < 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 98.6

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

   5. Applied rewrites 98.6%

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

Alternative 8: 75.9% 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 99.5%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 71.8%

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

Reproduce

herbie shell --seed 2024318 
(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)))))