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

Percentage Accurate: 99.0% → 99.6%

Time: 12.4s

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: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{+50}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.3e+50)
   (+ 1.0 (/ (/ x (- z y)) (- y t)))
   (+ 1.0 (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.3e+50) {
		tmp = 1.0 + ((x / (z - y)) / (y - t));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= 2.3d+50) then
        tmp = 1.0d0 + ((x / (z - y)) / (y - t))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.3e+50) {
		tmp = 1.0 + ((x / (z - y)) / (y - t));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 2.3e+50:
		tmp = 1.0 + ((x / (z - y)) / (y - t))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.3e+50)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.3e+50)
		tmp = 1.0 + ((x / (z - y)) / (y - t));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 2.3e+50], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $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 2 regimes

2. if t < 2.29999999999999997e50

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. neg-mul-1 99.4%

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

      3. *-commutative 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-/r* 98.9%

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

      6. associate-*r/ 98.9%

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

      7. metadata-eval 98.9%

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

      8. times-frac 98.9%

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

      9. *-lft-identity 98.9%

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

      10. neg-mul-1 98.9%

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

      11. sub-neg 98.9%

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

      12. +-commutative 98.9%

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

      13. distribute-neg-out 98.9%

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

      14. remove-double-neg 98.9%

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

      15. sub-neg 98.9%

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

   3. Simplified 98.9%

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

   if 2.29999999999999997e50 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 99.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{+50}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-18}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.35e-6) 1.0 (if (<= y 1.35e-18) (+ 1.0 (/ x (* (- y z) t))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.35e-6) {
		tmp = 1.0;
	} else if (y <= 1.35e-18) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-3.35d-6)) then
        tmp = 1.0d0
    else if (y <= 1.35d-18) then
        tmp = 1.0d0 + (x / ((y - z) * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.35e-6) {
		tmp = 1.0;
	} else if (y <= 1.35e-18) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.35e-6:
		tmp = 1.0
	elif y <= 1.35e-18:
		tmp = 1.0 + (x / ((y - z) * t))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.35e-6)
		tmp = 1.0;
	elseif (y <= 1.35e-18)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.35e-6)
		tmp = 1.0;
	elseif (y <= 1.35e-18)
		tmp = 1.0 + (x / ((y - z) * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.35e-6], 1.0, If[LessEqual[y, 1.35e-18], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.35e-6 or 1.34999999999999994e-18 < y

   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. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 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. Add Preprocessing

   5. Taylor expanded in x around 0 97.0%

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

   if -3.35e-6 < y < 1.34999999999999994e-18

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf 80.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-18}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-132}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-142}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-132)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 1.42e-142)
     (- 1.0 (/ x (* y (- y t))))
     (+ 1.0 (/ x (* (- y z) t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-132) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 1.42e-142) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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-132)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 1.42d-142) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-132) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 1.42e-142) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-132:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 1.42e-142:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-132)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 1.42e-142)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e-132)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 1.42e-142)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-132], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e-142], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $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 < -4.80000000000000031e-132

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 98.8%

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

      6. associate-*r/ 98.8%

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

      7. metadata-eval 98.8%

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

      8. times-frac 98.8%

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

      9. *-lft-identity 98.8%

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

      10. neg-mul-1 98.8%

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

      11. sub-neg 98.8%

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

      12. +-commutative 98.8%

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

      13. distribute-neg-out 98.8%

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

      14. remove-double-neg 98.8%

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

      15. sub-neg 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around inf 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-/r* 94.5%

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

   7. Simplified 94.5%

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

   if -4.80000000000000031e-132 < z < 1.42000000000000007e-142

   1. Initial program 98.6%

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

      1. sub-neg 98.6%

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

      2. neg-mul-1 98.6%

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

      3. *-commutative 98.6%

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

      4. *-commutative 98.6%

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

      5. associate-/r* 94.7%

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

      6. associate-*r/ 94.7%

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

      7. metadata-eval 94.7%

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

      8. times-frac 94.7%

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

      9. *-lft-identity 94.7%

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

      10. neg-mul-1 94.7%

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

      11. sub-neg 94.7%

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

      12. +-commutative 94.7%

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

      13. distribute-neg-out 94.7%

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

      14. remove-double-neg 94.7%

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

      15. sub-neg 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 91.5%

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

      1. mul-1-neg 91.5%

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

      2. sub-neg 91.5%

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

   7. Simplified 91.5%

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

   if 1.42000000000000007e-142 < z

   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 76.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-132}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-142}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-100}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-274}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.2e-100) 1.0 (if (<= t 7e-274) (+ 1.0 (/ x (* y z))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-100) {
		tmp = 1.0;
	} else if (t <= 7e-274) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.2d-100)) then
        tmp = 1.0d0
    else if (t <= 7d-274) then
        tmp = 1.0d0 + (x / (y * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-100) {
		tmp = 1.0;
	} else if (t <= 7e-274) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.2e-100:
		tmp = 1.0
	elif t <= 7e-274:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.2e-100)
		tmp = 1.0;
	elseif (t <= 7e-274)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.2e-100)
		tmp = 1.0;
	elseif (t <= 7e-274)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.2e-100], 1.0, If[LessEqual[t, 7e-274], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2000000000000001e-100 or 6.99999999999999963e-274 < t

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 97.5%

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

      6. associate-*r/ 97.5%

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

      7. metadata-eval 97.5%

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

      8. times-frac 97.5%

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

      9. *-lft-identity 97.5%

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

      10. neg-mul-1 97.5%

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

      11. sub-neg 97.5%

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

      12. +-commutative 97.5%

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

      13. distribute-neg-out 97.5%

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

      14. remove-double-neg 97.5%

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

      15. sub-neg 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around 0 82.1%

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

   if -1.2000000000000001e-100 < t < 6.99999999999999963e-274

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. neg-mul-1 98.3%

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

      3. *-commutative 98.3%

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

      4. *-commutative 98.3%

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

      5. associate-/r* 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. times-frac 99.9%

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

      9. *-lft-identity 99.9%

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

      10. neg-mul-1 99.9%

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

      11. sub-neg 99.9%

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

      12. +-commutative 99.9%

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

      13. distribute-neg-out 99.9%

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

      14. remove-double-neg 99.9%

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

      15. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-/r* 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in y around inf 71.5%

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

      1. *-commutative 71.5%

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

   10. Simplified 71.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-100}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-274}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-86}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e-6) 1.0 (if (<= y 1.4e-86) (- 1.0 (/ x (* z t))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-6) {
		tmp = 1.0;
	} else if (y <= 1.4e-86) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.3d-6)) then
        tmp = 1.0d0
    else if (y <= 1.4d-86) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-6) {
		tmp = 1.0;
	} else if (y <= 1.4e-86) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e-6:
		tmp = 1.0
	elif y <= 1.4e-86:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e-6)
		tmp = 1.0;
	elseif (y <= 1.4e-86)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.3e-6)
		tmp = 1.0;
	elseif (y <= 1.4e-86)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e-6], 1.0, If[LessEqual[y, 1.4e-86], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e-6 or 1.40000000000000005e-86 < y

   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. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. times-frac 99.9%

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

      9. *-lft-identity 99.9%

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

      10. neg-mul-1 99.9%

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

      11. sub-neg 99.9%

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

      12. +-commutative 99.9%

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

      13. distribute-neg-out 99.9%

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

      14. remove-double-neg 99.9%

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

      15. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 93.3%

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

   if -2.3e-6 < y < 1.40000000000000005e-86

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. neg-mul-1 99.0%

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

      3. *-commutative 99.0%

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

      4. *-commutative 99.0%

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

      5. associate-/r* 95.5%

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

      6. associate-*r/ 95.5%

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

      7. metadata-eval 95.5%

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

      8. times-frac 95.5%

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

      9. *-lft-identity 95.5%

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

      10. neg-mul-1 95.5%

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

      11. sub-neg 95.5%

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

      12. +-commutative 95.5%

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

      13. distribute-neg-out 95.5%

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

      14. remove-double-neg 95.5%

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

      15. sub-neg 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. sub-neg 75.2%

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

   7. Simplified 75.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-86}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-50) (+ 1.0 (/ (/ x z) (- y t))) (+ 1.0 (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-50) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.6d-50)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-50) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-50:
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-50)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-50)
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-50], N[(1.0 + N[(N[(x / z), $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 2 regimes

2. if z < -1.6e-50

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. times-frac 99.9%

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

      9. *-lft-identity 99.9%

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

      10. neg-mul-1 99.9%

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

      11. sub-neg 99.9%

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

      12. +-commutative 99.9%

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

      13. distribute-neg-out 99.9%

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

      14. remove-double-neg 99.9%

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

      15. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-/r* 97.4%

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

   7. Simplified 97.4%

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

   if -1.6e-50 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 77.9%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / ((y - z) * (y - t)));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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. Final simplification 99.5%

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

Alternative 8: 75.7% accurate, 11.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 1.0)

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return 1.0
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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. Step-by-step derivation

   1. sub-neg 99.5%

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

   2. neg-mul-1 99.5%

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

   3. *-commutative 99.5%

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

   4. *-commutative 99.5%

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

   5. associate-/r* 98.1%

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

   6. associate-*r/ 98.1%

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

   7. metadata-eval 98.1%

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

   8. times-frac 98.1%

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

   9. *-lft-identity 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. Add Preprocessing

5. Taylor expanded in x around 0 76.9%

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

6. Final simplification 76.9%

   \[\leadsto 1 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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)))))