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

Percentage Accurate: 99.1% → 99.1%

Time: 5.6s

Alternatives: 7

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: 99.1% 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: 99.1% 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: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-5} \lor \neg \left(t\_1 \leq 10^{-23}\right):\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -1e-5) (not (<= t_1 1e-23)))
     (+ (/ x (* (- y t) z)) 1.0)
     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 <= -1e-5) || !(t_1 <= 1e-23)) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} 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 <= (-1d-5)) .or. (.not. (t_1 <= 1d-23))) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    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 <= -1e-5) || !(t_1 <= 1e-23)) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} 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 <= -1e-5) or not (t_1 <= 1e-23):
		tmp = (x / ((y - t) * z)) + 1.0
	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 <= -1e-5) || !(t_1 <= 1e-23))
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	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 <= -1e-5) || ~((t_1 <= 1e-23)))
		tmp = (x / ((y - t) * z)) + 1.0;
	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, -1e-5], N[Not[LessEqual[t$95$1, 1e-23]], $MachinePrecision]], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.00000000000000008e-5 or 9.9999999999999996e-24 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 64.9

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

   5. Applied rewrites 64.9%

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

   if -1.00000000000000008e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 9.9999999999999996e-24

   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 99.7%

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

4. Final simplification 91.4%

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

Alternative 3: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \mathbf{elif}\;t\_1 \leq 10^{-23}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -1e-5)
     (+ (/ x (* (- y z) t)) 1.0)
     (if (<= t_1 1e-23) 1.0 (+ (/ x (* (- y t) z)) 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 <= -1e-5) {
		tmp = (x / ((y - z) * t)) + 1.0;
	} else if (t_1 <= 1e-23) {
		tmp = 1.0;
	} else {
		tmp = (x / ((y - t) * z)) + 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 <= (-1d-5)) then
        tmp = (x / ((y - z) * t)) + 1.0d0
    else if (t_1 <= 1d-23) then
        tmp = 1.0d0
    else
        tmp = (x / ((y - t) * z)) + 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 <= -1e-5) {
		tmp = (x / ((y - z) * t)) + 1.0;
	} else if (t_1 <= 1e-23) {
		tmp = 1.0;
	} else {
		tmp = (x / ((y - t) * z)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -1e-5:
		tmp = (x / ((y - z) * t)) + 1.0
	elif t_1 <= 1e-23:
		tmp = 1.0
	else:
		tmp = (x / ((y - t) * z)) + 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 <= -1e-5)
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 1.0);
	elseif (t_1 <= 1e-23)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 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 <= -1e-5)
		tmp = (x / ((y - z) * t)) + 1.0;
	elseif (t_1 <= 1e-23)
		tmp = 1.0;
	else
		tmp = (x / ((y - t) * z)) + 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[LessEqual[t$95$1, -1e-5], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t$95$1, 1e-23], 1.0, N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.00000000000000008e-5

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 74.3

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

   5. Applied rewrites 74.3%

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

   if -1.00000000000000008e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 9.9999999999999996e-24

   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 99.7%

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

   if 9.9999999999999996e-24 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 68.8

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

   5. Applied rewrites 68.8%

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

Alternative 4: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-5} \lor \neg \left(t\_1 \leq 10^{-23}\right):\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -1e-5) (not (<= t_1 1e-23))) (- 1.0 (/ x (* t z))) 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 <= -1e-5) || !(t_1 <= 1e-23)) {
		tmp = 1.0 - (x / (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 = x / ((y - z) * (y - t))
    if ((t_1 <= (-1d-5)) .or. (.not. (t_1 <= 1d-23))) then
        tmp = 1.0d0 - (x / (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 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -1e-5) || !(t_1 <= 1e-23)) {
		tmp = 1.0 - (x / (t * z));
	} 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 <= -1e-5) or not (t_1 <= 1e-23):
		tmp = 1.0 - (x / (t * z))
	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 <= -1e-5) || !(t_1 <= 1e-23))
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	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 <= -1e-5) || ~((t_1 <= 1e-23)))
		tmp = 1.0 - (x / (t * z));
	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, -1e-5], N[Not[LessEqual[t$95$1, 1e-23]], $MachinePrecision]], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.00000000000000008e-5 or 9.9999999999999996e-24 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 47.7

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

   5. Applied rewrites 47.7%

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

   if -1.00000000000000008e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 9.9999999999999996e-24

   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 99.7%

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

4. Final simplification 87.3%

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

Alternative 5: 80.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+189} \lor \neg \left(t\_1 \leq 10^{-23}\right):\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -2e+189) (not (<= t_1 1e-23))) (+ (/ x (* z y)) 1.0) 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 <= -2e+189) || !(t_1 <= 1e-23)) {
		tmp = (x / (z * y)) + 1.0;
	} 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 <= (-2d+189)) .or. (.not. (t_1 <= 1d-23))) then
        tmp = (x / (z * y)) + 1.0d0
    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 <= -2e+189) || !(t_1 <= 1e-23)) {
		tmp = (x / (z * y)) + 1.0;
	} 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 <= -2e+189) or not (t_1 <= 1e-23):
		tmp = (x / (z * y)) + 1.0
	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 <= -2e+189) || !(t_1 <= 1e-23))
		tmp = Float64(Float64(x / Float64(z * y)) + 1.0);
	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 <= -2e+189) || ~((t_1 <= 1e-23)))
		tmp = (x / (z * y)) + 1.0;
	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, -2e+189], N[Not[LessEqual[t$95$1, 1e-23]], $MachinePrecision]], N[(N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2e189 or 9.9999999999999996e-24 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 65.1

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

   5. Applied rewrites 65.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto \frac{x}{y \cdot z} + 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 29.2%

      \[\leadsto \frac{x}{z \cdot y} + 1 \]

   if -2e189 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 9.9999999999999996e-24

   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 94.9%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -2 \cdot 10^{+189} \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 10^{-23}\right):\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \mathbf{elif}\;t\_1 \leq 10^{-23}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -2e+39)
     (+ (/ x (* t y)) 1.0)
     (if (<= t_1 1e-23) 1.0 (+ (/ 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 <= -2e+39) {
		tmp = (x / (t * y)) + 1.0;
	} else if (t_1 <= 1e-23) {
		tmp = 1.0;
	} else {
		tmp = (x / (z * y)) + 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 <= (-2d+39)) then
        tmp = (x / (t * y)) + 1.0d0
    else if (t_1 <= 1d-23) then
        tmp = 1.0d0
    else
        tmp = (x / (z * y)) + 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 <= -2e+39) {
		tmp = (x / (t * y)) + 1.0;
	} else if (t_1 <= 1e-23) {
		tmp = 1.0;
	} else {
		tmp = (x / (z * y)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -2e+39:
		tmp = (x / (t * y)) + 1.0
	elif t_1 <= 1e-23:
		tmp = 1.0
	else:
		tmp = (x / (z * y)) + 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 <= -2e+39)
		tmp = Float64(Float64(x / Float64(t * y)) + 1.0);
	elseif (t_1 <= 1e-23)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x / Float64(z * y)) + 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 <= -2e+39)
		tmp = (x / (t * y)) + 1.0;
	elseif (t_1 <= 1e-23)
		tmp = 1.0;
	else
		tmp = (x / (z * y)) + 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[LessEqual[t$95$1, -2e+39], N[(N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t$95$1, 1e-23], 1.0, N[(N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.99999999999999988e39

   1. Initial program 96.5%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 74.2

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto \frac{x}{t \cdot y} + 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 42.3%

      \[\leadsto \frac{x}{t \cdot y} + 1 \]

   if -1.99999999999999988e39 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 9.9999999999999996e-24

   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 98.5%

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

   if 9.9999999999999996e-24 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 68.8

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

   5. Applied rewrites 68.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto \frac{x}{y \cdot z} + 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 40.0%

      \[\leadsto \frac{x}{z \cdot y} + 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 75.2% 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 76.8%

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

Reproduce

herbie shell --seed 2024326 
(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)))))