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

Percentage Accurate: 98.9% → 98.8%

Time: 11.0s

Alternatives: 10

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: 98.9% 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: 98.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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 + ((-1.0d0) / ((y - z) * ((y - t) / x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. associate-/l/ 99.9%

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

   2. clear-num 99.9%

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

   3. inv-pow 99.9%

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

   4. div-inv 99.8%

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

   5. clear-num 99.9%

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

3. Applied egg-rr 99.9%

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

   1. unpow-1 99.9%

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

5. Simplified 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-29}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-96}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-29) 1.0 (if (<= y 7.4e-96) (+ 1.0 (/ x (* z (- y t)))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-29) {
		tmp = 1.0;
	} else if (y <= 7.4e-96) {
		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 <= (-1.4d-29)) then
        tmp = 1.0d0
    else if (y <= 7.4d-96) 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 <= -1.4e-29) {
		tmp = 1.0;
	} else if (y <= 7.4e-96) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-29:
		tmp = 1.0
	elif y <= 7.4e-96:
		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 <= -1.4e-29)
		tmp = 1.0;
	elseif (y <= 7.4e-96)
		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 <= -1.4e-29)
		tmp = 1.0;
	elseif (y <= 7.4e-96)
		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, -1.4e-29], 1.0, If[LessEqual[y, 7.4e-96], 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 < -1.4000000000000001e-29 or 7.39999999999999972e-96 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 83.4%

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

      1. unpow2 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in x around 0 89.3%

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

   if -1.4000000000000001e-29 < y < 7.39999999999999972e-96

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. distribute-frac-neg 97.9%

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

      3. *-lft-identity 97.9%

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

      4. associate-/r* 95.9%

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

      5. associate-*r/ 95.9%

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

      6. metadata-eval 95.9%

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

      7. times-frac 95.9%

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

      8. neg-mul-1 95.9%

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

      9. remove-double-neg 95.9%

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

      10. neg-mul-1 95.9%

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

      11. sub-neg 95.9%

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

      12. +-commutative 95.9%

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

      13. distribute-neg-out 95.9%

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

      14. remove-double-neg 95.9%

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

      15. sub-neg 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around inf 82.8%

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

      1. *-commutative 82.8%

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

   6. Simplified 82.8%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-29}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-96}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-33}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-177}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e-33)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 6.6e-177)
     (- 1.0 (/ (/ x y) (- y t)))
     (+ 1.0 (/ x (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e-33) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 6.6e-177) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 + (x / ((y - z) * 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 <= (-3.7d-33)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 6.6d-177) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e-33) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 6.6e-177) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e-33:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 6.6e-177:
		tmp = 1.0 - ((x / y) / (y - t))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e-33)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 6.6e-177)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.7e-33)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 6.6e-177)
		tmp = 1.0 - ((x / y) / (y - t));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e-33], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-177], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.70000000000000014e-33

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. *-lft-identity 100.0%

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

      4. associate-/r* 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. times-frac 100.0%

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

      8. neg-mul-1 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 100.0%

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

   if -3.70000000000000014e-33 < z < 6.5999999999999999e-177

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 90.3%

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

      1. associate-/r* 90.3%

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

   4. Simplified 90.3%

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

   if 6.5999999999999999e-177 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 73.7%

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

      1. associate-*r/ 73.7%

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

      2. neg-mul-1 73.7%

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

   4. Simplified 73.7%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-33}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-177}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 4: 82.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-100}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-207) 1.0 (if (<= y 5e-100) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-207) {
		tmp = 1.0;
	} else if (y <= 5e-100) {
		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 <= (-1.15d-207)) then
        tmp = 1.0d0
    else if (y <= 5d-100) 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 <= -1.15e-207) {
		tmp = 1.0;
	} else if (y <= 5e-100) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-207:
		tmp = 1.0
	elif y <= 5e-100:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-207)
		tmp = 1.0;
	elseif (y <= 5e-100)
		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 <= -1.15e-207)
		tmp = 1.0;
	elseif (y <= 5e-100)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-207], 1.0, If[LessEqual[y, 5e-100], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-207 or 5.0000000000000001e-100 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. unpow2 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in x around 0 85.1%

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

   if -1.15e-207 < y < 5.0000000000000001e-100

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 85.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-100}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-100}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-207) 1.0 (if (<= y 2.05e-100) (- 1.0 (/ (/ x t) z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-207) {
		tmp = 1.0;
	} else if (y <= 2.05e-100) {
		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) :: tmp
    if (y <= (-1.15d-207)) then
        tmp = 1.0d0
    else if (y <= 2.05d-100) 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 tmp;
	if (y <= -1.15e-207) {
		tmp = 1.0;
	} else if (y <= 2.05e-100) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-207:
		tmp = 1.0
	elif y <= 2.05e-100:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-207)
		tmp = 1.0;
	elseif (y <= 2.05e-100)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e-207)
		tmp = 1.0;
	elseif (y <= 2.05e-100)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-207], 1.0, If[LessEqual[y, 2.05e-100], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-207 or 2.0499999999999999e-100 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. unpow2 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in x around 0 85.1%

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

   if -1.15e-207 < y < 2.0499999999999999e-100

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 85.6%

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

      1. associate-/r* 87.3%

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

   4. Simplified 87.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-100}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-33}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e-33) (+ 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 <= -1.05e-33) {
		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 <= (-1.05d-33)) 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 <= -1.05e-33) {
		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 <= -1.05e-33:
		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 <= -1.05e-33)
		tmp = Float64(1.0 + Float64(Float64(x / 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 <= -1.05e-33)
		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, -1.05e-33], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $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 < -1.05e-33

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. *-lft-identity 100.0%

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

      4. associate-/r* 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. times-frac 100.0%

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

      8. neg-mul-1 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 100.0%

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

   if -1.05e-33 < z

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 77.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-33}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 7: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{\frac{x}{z - y}}{y - t} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. sub-neg 99.2%

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

   2. distribute-frac-neg 99.2%

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

   3. *-lft-identity 99.2%

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

   4. associate-/r* 98.1%

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

   5. associate-*r/ 98.1%

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

   6. metadata-eval 98.1%

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

   7. times-frac 98.1%

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

   8. neg-mul-1 98.1%

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

   9. remove-double-neg 98.1%

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

   10. neg-mul-1 98.1%

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

   11. sub-neg 98.1%

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

   12. +-commutative 98.1%

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

   13. distribute-neg-out 98.1%

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

   14. remove-double-neg 98.1%

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

   15. sub-neg 98.1%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 8: 98.9% 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 99.2%

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

2. Final simplification 99.2%

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

Alternative 9: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{\frac{x}{y - t}}{y - z} \end{array} \]

FPCore

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

C

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

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 - t)) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. *-commutative 99.2%

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

   2. associate-/r* 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 10: 75.6% 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 99.2%

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

2. Taylor expanded in y around inf 58.9%

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

   1. unpow2 58.9%

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

4. Simplified 58.9%

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

5. Taylor expanded in x around 0 78.5%

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

6. Final simplification 78.5%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023277 
(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)))))