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

Percentage Accurate: 99.2% → 99.2%

Time: 7.1s

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: 99.2% 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: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* (- t y) (- y z)))))
   (if (<= t_1 -1e+23) t_2 (if (<= t_1 0.0002) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / ((t - y) * (y - z));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = t_2;
	} else if (t_1 <= 0.0002) {
		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 / ((t - y) * (z - y))
    t_2 = x / ((t - y) * (y - z))
    if (t_1 <= (-1d+23)) then
        tmp = t_2
    else if (t_1 <= 0.0002d0) 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 / ((t - y) * (z - y));
	double t_2 = x / ((t - y) * (y - z));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = t_2;
	} else if (t_1 <= 0.0002) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / ((t - y) * (y - z))
	tmp = 0
	if t_1 <= -1e+23:
		tmp = t_2
	elif t_1 <= 0.0002:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(x / Float64(Float64(t - y) * Float64(y - z)))
	tmp = 0.0
	if (t_1 <= -1e+23)
		tmp = t_2;
	elseif (t_1 <= 0.0002)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = x / ((t - y) * (y - z));
	tmp = 0.0;
	if (t_1 <= -1e+23)
		tmp = t_2;
	elseif (t_1 <= 0.0002)
		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[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+23], t$95$2, If[LessEqual[t$95$1, 0.0002], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.9999999999999992e22 or 2.0000000000000001e-4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   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

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. lft-mult-inverse N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 96.3

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

   8. Applied rewrites 96.3%

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

   if -9.9999999999999992e22 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.0000000000000001e-4

   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 99.1%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.0002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* t (- y z)))))
   (if (<= t_1 -5e+31) t_2 (if (<= t_1 0.0002) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / (t * (y - z));
	double tmp;
	if (t_1 <= -5e+31) {
		tmp = t_2;
	} else if (t_1 <= 0.0002) {
		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 / ((t - y) * (z - y))
    t_2 = x / (t * (y - z))
    if (t_1 <= (-5d+31)) then
        tmp = t_2
    else if (t_1 <= 0.0002d0) 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 / ((t - y) * (z - y));
	double t_2 = x / (t * (y - z));
	double tmp;
	if (t_1 <= -5e+31) {
		tmp = t_2;
	} else if (t_1 <= 0.0002) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / (t * (y - z))
	tmp = 0
	if t_1 <= -5e+31:
		tmp = t_2
	elif t_1 <= 0.0002:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(x / Float64(t * Float64(y - z)))
	tmp = 0.0
	if (t_1 <= -5e+31)
		tmp = t_2;
	elseif (t_1 <= 0.0002)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = x / (t * (y - z));
	tmp = 0.0;
	if (t_1 <= -5e+31)
		tmp = t_2;
	elseif (t_1 <= 0.0002)
		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[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+31], t$95$2, If[LessEqual[t$95$1, 0.0002], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.00000000000000027e31 or 2.0000000000000001e-4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   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

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. lft-mult-inverse N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 96.2

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

   8. Applied rewrites 96.2%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 74.2%

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

   if -5.00000000000000027e31 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.0000000000000001e-4

   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 98.7%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.0002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* (- y t) z))))
   (if (<= t_1 -5e+31) t_2 (if (<= t_1 0.0002) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / ((y - t) * z);
	double tmp;
	if (t_1 <= -5e+31) {
		tmp = t_2;
	} else if (t_1 <= 0.0002) {
		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 / ((t - y) * (z - y))
    t_2 = x / ((y - t) * z)
    if (t_1 <= (-5d+31)) then
        tmp = t_2
    else if (t_1 <= 0.0002d0) 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 / ((t - y) * (z - y));
	double t_2 = x / ((y - t) * z);
	double tmp;
	if (t_1 <= -5e+31) {
		tmp = t_2;
	} else if (t_1 <= 0.0002) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / ((y - t) * z)
	tmp = 0
	if t_1 <= -5e+31:
		tmp = t_2
	elif t_1 <= 0.0002:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(x / Float64(Float64(y - t) * z))
	tmp = 0.0
	if (t_1 <= -5e+31)
		tmp = t_2;
	elseif (t_1 <= 0.0002)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = x / ((y - t) * z);
	tmp = 0.0;
	if (t_1 <= -5e+31)
		tmp = t_2;
	elseif (t_1 <= 0.0002)
		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[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+31], t$95$2, If[LessEqual[t$95$1, 0.0002], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.00000000000000027e31 or 2.0000000000000001e-4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   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

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. lft-mult-inverse N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 96.2

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

   8. Applied rewrites 96.2%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 74.2%

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

   12. Taylor expanded in z around inf

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

   14. Applied rewrites 67.4%

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

   if -5.00000000000000027e31 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.0000000000000001e-4

   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 98.7%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.0002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{\left(-z\right) \cdot t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* (- z) t))))
   (if (<= t_1 -5e+31) t_2 (if (<= t_1 0.0002) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / (-z * t);
	double tmp;
	if (t_1 <= -5e+31) {
		tmp = t_2;
	} else if (t_1 <= 0.0002) {
		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 / ((t - y) * (z - y))
    t_2 = x / (-z * t)
    if (t_1 <= (-5d+31)) then
        tmp = t_2
    else if (t_1 <= 0.0002d0) 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 / ((t - y) * (z - y));
	double t_2 = x / (-z * t);
	double tmp;
	if (t_1 <= -5e+31) {
		tmp = t_2;
	} else if (t_1 <= 0.0002) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / (-z * t)
	tmp = 0
	if t_1 <= -5e+31:
		tmp = t_2
	elif t_1 <= 0.0002:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(x / Float64(Float64(-z) * t))
	tmp = 0.0
	if (t_1 <= -5e+31)
		tmp = t_2;
	elseif (t_1 <= 0.0002)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = x / (-z * t);
	tmp = 0.0;
	if (t_1 <= -5e+31)
		tmp = t_2;
	elseif (t_1 <= 0.0002)
		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[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[((-z) * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+31], t$95$2, If[LessEqual[t$95$1, 0.0002], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.00000000000000027e31 or 2.0000000000000001e-4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   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

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. lft-mult-inverse N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 96.2

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

   8. Applied rewrites 96.2%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 74.2%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 58.1%

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

   if -5.00000000000000027e31 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.0000000000000001e-4

   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 98.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot t}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.0002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((1.0 - (x / ((t - y) * (z - y)))) <= -100.0) {
		tmp = x / (t * 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) :: tmp
    if ((1.0d0 - (x / ((t - y) * (z - y)))) <= (-100.0d0)) then
        tmp = x / (t * 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 tmp;
	if ((1.0 - (x / ((t - y) * (z - y)))) <= -100.0) {
		tmp = x / (t * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -100.0], N[(x / N[(t * y), $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)))) < -100

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. lft-mult-inverse N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 97.1

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

   8. Applied rewrites 97.1%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 73.0%

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

   12. Taylor expanded in y around inf

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

   14. Applied rewrites 31.5%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.0%

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

4. Final simplification 85.2%

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

Alternative 7: 88.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-11}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.75e-73)
   1.0
   (if (<= y 9.5e-11)
     (- 1.0 (/ x (* (- z y) t)))
     (- 1.0 (/ x (* (- y z) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.75e-73) {
		tmp = 1.0;
	} else if (y <= 9.5e-11) {
		tmp = 1.0 - (x / ((z - y) * t));
	} else {
		tmp = 1.0 - (x / ((y - 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) :: tmp
    if (y <= (-2.75d-73)) then
        tmp = 1.0d0
    else if (y <= 9.5d-11) then
        tmp = 1.0d0 - (x / ((z - y) * t))
    else
        tmp = 1.0d0 - (x / ((y - z) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.75e-73) {
		tmp = 1.0;
	} else if (y <= 9.5e-11) {
		tmp = 1.0 - (x / ((z - y) * t));
	} else {
		tmp = 1.0 - (x / ((y - z) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.75e-73:
		tmp = 1.0
	elif y <= 9.5e-11:
		tmp = 1.0 - (x / ((z - y) * t))
	else:
		tmp = 1.0 - (x / ((y - z) * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.75e-73)
		tmp = 1.0;
	elseif (y <= 9.5e-11)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(z - y) * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.75e-73)
		tmp = 1.0;
	elseif (y <= 9.5e-11)
		tmp = 1.0 - (x / ((z - y) * t));
	else
		tmp = 1.0 - (x / ((y - z) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.75e-73], 1.0, If[LessEqual[y, 9.5e-11], N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.75000000000000003e-73

   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 96.9%

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

   if -2.75000000000000003e-73 < y < 9.49999999999999951e-11

   1. Initial program 99.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 92.2

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

   5. Applied rewrites 92.2%

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

   if 9.49999999999999951e-11 < y

   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 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 96.1

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

   5. Applied rewrites 96.1%

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

Alternative 8: 75.5% 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 99.9%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 81.7%

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

Reproduce

herbie shell --seed 2024296 
(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)))))