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

Percentage Accurate: 99.0% → 99.0%

Time: 7.3s

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 98.9%

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

2. Final simplification 98.9%

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

Alternative 2: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.1 \cdot 10^{-213}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+59}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.1e-213)
   (+ 1.0 (/ x (* y z)))
   (if (<= t 6e-34) 1.0 (if (<= t 1.9e+59) (+ 1.0 (/ x (* y t))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.1e-213) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 6e-34) {
		tmp = 1.0;
	} else if (t <= 1.9e+59) {
		tmp = 1.0 + (x / (y * 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) :: tmp
    if (t <= 1.1d-213) then
        tmp = 1.0d0 + (x / (y * z))
    else if (t <= 6d-34) then
        tmp = 1.0d0
    else if (t <= 1.9d+59) then
        tmp = 1.0d0 + (x / (y * 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 tmp;
	if (t <= 1.1e-213) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 6e-34) {
		tmp = 1.0;
	} else if (t <= 1.9e+59) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.1e-213:
		tmp = 1.0 + (x / (y * z))
	elif t <= 6e-34:
		tmp = 1.0
	elif t <= 1.9e+59:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.1e-213)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif (t <= 6e-34)
		tmp = 1.0;
	elseif (t <= 1.9e+59)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.1e-213)
		tmp = 1.0 + (x / (y * z));
	elseif (t <= 6e-34)
		tmp = 1.0;
	elseif (t <= 1.9e+59)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.1e-213], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-34], 1.0, If[LessEqual[t, 1.9e+59], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.10000000000000005e-213

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 76.7%

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

      1. +-commutative 76.7%

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

      2. *-commutative 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in y around inf 60.7%

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

   if 1.10000000000000005e-213 < t < 6e-34 or 1.9e59 < t

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0 78.0%

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

   if 6e-34 < t < 1.9e59

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 64.7%

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

   3. Taylor expanded in y around 0 57.0%

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

      1. associate-*r/ 57.0%

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

      2. neg-mul-1 57.0%

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

      3. *-commutative 57.0%

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

   5. Simplified 57.0%

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

      1. expm1-log1p-u 49.9%

         \[\leadsto 1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-x}{y \cdot t}\right)\right)} \]

      2. expm1-udef 49.9%

         \[\leadsto 1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{-x}{y \cdot t}\right)} - 1\right)} \]

      3. add-sqr-sqrt 26.9%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{y \cdot t}\right)} - 1\right) \]

      4. sqrt-unprod 50.2%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{y \cdot t}\right)} - 1\right) \]

      5. sqr-neg 50.2%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{y \cdot t}\right)} - 1\right) \]

      6. sqrt-unprod 23.3%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{y \cdot t}\right)} - 1\right) \]

      7. add-sqr-sqrt 41.9%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{y \cdot t}\right)} - 1\right) \]

   7. Applied egg-rr 41.9%

      \[\leadsto 1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x}{y \cdot t}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 41.9%

         \[\leadsto 1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y \cdot t}\right)\right)} \]

      2. expm1-log1p 42.3%

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

      3. associate-/l/ 42.3%

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

   9. Simplified 42.3%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{t}}{y}} \]
   10. Step-by-step derivation

       1. sub-neg 42.3%

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

       2. distribute-frac-neg 42.3%

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

       3. +-commutative 42.3%

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

       4. add-sqr-sqrt 18.8%

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

       5. sqrt-unprod 42.1%

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

       6. sqr-neg 42.1%

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

       7. sqrt-unprod 23.3%

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

       8. add-sqr-sqrt 57.0%

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

       9. associate-/l/ 57.0%

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

   11. Applied egg-rr 57.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot t} + 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.1 \cdot 10^{-213}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+59}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-79}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e-77) 1.0 (if (<= y 1.7e-79) (+ 1.0 (/ x (* z (- y t)))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e-77) {
		tmp = 1.0;
	} else if (y <= 1.7e-79) {
		tmp = 1.0 + (x / (z * (y - 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) :: tmp
    if (y <= (-2.2d-77)) then
        tmp = 1.0d0
    else if (y <= 1.7d-79) then
        tmp = 1.0d0 + (x / (z * (y - 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 tmp;
	if (y <= -2.2e-77) {
		tmp = 1.0;
	} else if (y <= 1.7e-79) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e-77:
		tmp = 1.0
	elif y <= 1.7e-79:
		tmp = 1.0 + (x / (z * (y - t)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e-77)
		tmp = 1.0;
	elseif (y <= 1.7e-79)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.2e-77)
		tmp = 1.0;
	elseif (y <= 1.7e-79)
		tmp = 1.0 + (x / (z * (y - t)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e-77], 1.0, If[LessEqual[y, 1.7e-79], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.20000000000000007e-77 or 1.69999999999999988e-79 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.0%

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

   if -2.20000000000000007e-77 < y < 1.69999999999999988e-79

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 84.3%

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

      1. +-commutative 84.3%

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

      2. *-commutative 84.3%

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

   4. Simplified 84.3%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-79}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 83.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-81}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e-76) 1.0 (if (<= y 3.7e-81) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-76) {
		tmp = 1.0;
	} else if (y <= 3.7e-81) {
		tmp = 1.0 - (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) :: tmp
    if (y <= (-1.35d-76)) then
        tmp = 1.0d0
    else if (y <= 3.7d-81) then
        tmp = 1.0d0 - (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 tmp;
	if (y <= -1.35e-76) {
		tmp = 1.0;
	} else if (y <= 3.7e-81) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e-76:
		tmp = 1.0
	elif y <= 3.7e-81:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e-76)
		tmp = 1.0;
	elseif (y <= 3.7e-81)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e-76)
		tmp = 1.0;
	elseif (y <= 3.7e-81)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e-76], 1.0, If[LessEqual[y, 3.7e-81], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-76 or 3.69999999999999986e-81 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.0%

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

   if -1.35e-76 < y < 3.69999999999999986e-81

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 71.8%

      \[\leadsto 1 - \color{blue}{\frac{x}{t \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-81}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3300:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3300.0) (+ 1.0 (/ x (* z (- y t)))) (- 1.0 (/ x (* y (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3300.0) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0 - (x / (y * (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 (z <= (-3300.0d0)) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else
        tmp = 1.0d0 - (x / (y * (y - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3300.0) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0 - (x / (y * (y - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3300.0:
		tmp = 1.0 + (x / (z * (y - t)))
	else:
		tmp = 1.0 - (x / (y * (y - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3300.0)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3300.0)
		tmp = 1.0 + (x / (z * (y - t)));
	else
		tmp = 1.0 - (x / (y * (y - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3300.0], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3300

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 96.6%

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

      1. +-commutative 96.6%

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

      2. *-commutative 96.6%

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

   4. Simplified 96.6%

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

   if -3300 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 80.5%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3300:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 6: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3300:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3300.0) (+ 1.0 (/ x (* z (- y t)))) (- 1.0 (/ (/ x (- y t)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3300.0) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3300.0d0)) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else
        tmp = 1.0d0 - ((x / (y - t)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3300.0) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3300.0:
		tmp = 1.0 + (x / (z * (y - t)))
	else:
		tmp = 1.0 - ((x / (y - t)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3300.0)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3300.0)
		tmp = 1.0 + (x / (z * (y - t)));
	else
		tmp = 1.0 - ((x / (y - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3300.0], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3300

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 96.6%

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

      1. +-commutative 96.6%

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

      2. *-commutative 96.6%

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

   4. Simplified 96.6%

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

   if -3300 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 80.5%

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

      1. associate-/r* 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in x around 0 80.5%

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

      1. *-commutative 80.5%

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

      2. associate-/r* 81.0%

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

   7. Simplified 81.0%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - t}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3300:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 7: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-143}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-143) 1.0 (+ 1.0 (/ x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-143) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (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 (z <= (-4.8d-143)) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + (x / (y * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-143) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-143:
		tmp = 1.0
	else:
		tmp = 1.0 + (x / (y * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-143)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e-143)
		tmp = 1.0;
	else
		tmp = 1.0 + (x / (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-143], 1.0, N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7999999999999998e-143

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.0%

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

   if -4.7999999999999998e-143 < z

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 77.4%

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

   3. Taylor expanded in y around 0 60.9%

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

      1. associate-*r/ 60.9%

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

      2. neg-mul-1 60.9%

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

      3. *-commutative 60.9%

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

   5. Simplified 60.9%

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

      1. expm1-log1p-u 53.3%

         \[\leadsto 1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-x}{y \cdot t}\right)\right)} \]

      2. expm1-udef 53.3%

         \[\leadsto 1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{-x}{y \cdot t}\right)} - 1\right)} \]

      3. add-sqr-sqrt 26.3%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{y \cdot t}\right)} - 1\right) \]

      4. sqrt-unprod 46.8%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{y \cdot t}\right)} - 1\right) \]

      5. sqr-neg 46.8%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{y \cdot t}\right)} - 1\right) \]

      6. sqrt-unprod 26.1%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{y \cdot t}\right)} - 1\right) \]

      7. add-sqr-sqrt 49.1%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{y \cdot t}\right)} - 1\right) \]

   7. Applied egg-rr 49.1%

      \[\leadsto 1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x}{y \cdot t}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 49.1%

         \[\leadsto 1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y \cdot t}\right)\right)} \]

      2. expm1-log1p 51.9%

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

      3. associate-/l/ 51.9%

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

   9. Simplified 51.9%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{t}}{y}} \]
   10. Step-by-step derivation

       1. sub-neg 51.9%

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

       2. distribute-frac-neg 51.9%

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

       3. +-commutative 51.9%

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

       4. add-sqr-sqrt 30.0%

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

       5. sqrt-unprod 55.1%

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

       6. sqr-neg 55.1%

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

       7. sqrt-unprod 33.6%

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

       8. add-sqr-sqrt 61.3%

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

       9. associate-/l/ 60.9%

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

   11. Applied egg-rr 60.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot t} + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-143}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]

Alternative 8: 75.4% accurate, 11.0× 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 98.9%

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

2. Taylor expanded in x around 0 73.7%

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

3. Final simplification 73.7%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023336 
(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)))))