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

Percentage Accurate: 99.2% → 99.2%

Time: 8.5s

Alternatives: 4

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 98.7%

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

3. Final simplification 98.7%

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

Alternative 2: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ t_2 := 1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_2 \leq -400:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- y z))))
        (t_2 (- 1.0 (/ x (* (- t y) (- z y))))))
   (if (<= t_2 -400.0) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (y - z));
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -400.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - y) * (y - z))
    t_2 = 1.0d0 - (x / ((t - y) * (z - y)))
    if (t_2 <= (-400.0d0)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (y - z));
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -400.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (y - z))
	t_2 = 1.0 - (x / ((t - y) * (z - y)))
	tmp = 0
	if t_2 <= -400.0:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(y - z)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * Float64(z - y))))
	tmp = 0.0
	if (t_2 <= -400.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (y - z));
	t_2 = 1.0 - (x / ((t - y) * (z - y)));
	tmp = 0.0;
	if (t_2 <= -400.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -400.0], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -400 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 94.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower--.f64 92.3

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

   5. Applied rewrites 92.3%

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

   if -400 < (-.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 t around inf

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

   5. Applied rewrites 99.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -400:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ \mathbf{elif}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{t \cdot z}\\ t_2 := 1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_2 \leq -400:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* t z)))) (t_2 (- 1.0 (/ x (* (- t y) (- z y))))))
   (if (<= t_2 -400.0) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (t * z));
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -400.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 - (x / (t * z))
    t_2 = 1.0d0 - (x / ((t - y) * (z - y)))
    if (t_2 <= (-400.0d0)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (t * z));
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -400.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / (t * z))
	t_2 = 1.0 - (x / ((t - y) * (z - y)))
	tmp = 0
	if t_2 <= -400.0:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(t * z)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * Float64(z - y))))
	tmp = 0.0
	if (t_2 <= -400.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / (t * z));
	t_2 = 1.0 - (x / ((t - y) * (z - y)));
	tmp = 0.0;
	if (t_2 <= -400.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -400.0], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -400 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 94.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 46.9

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

   5. Applied rewrites 46.9%

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

   if -400 < (-.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 t around inf

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

   5. Applied rewrites 99.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -400:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% 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 98.7%

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

3. Taylor expanded in t around inf

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

5. Applied rewrites 76.1%

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

Reproduce

herbie shell --seed 2024235 
(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)))))