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

Percentage Accurate: 99.0% → 99.0%

Time: 9.4s

Alternatives: 9

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

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + (x / ((y - z) * (t - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Final simplification 99.6%

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

Alternative 2: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-221} \lor \neg \left(y \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e-221) (not (<= y 4e-50)))
   (+ 1.0 (/ x (* y (- z y))))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e-221) || !(y <= 4e-50)) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 - (x / (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 ((y <= (-9d-221)) .or. (.not. (y <= 4d-50))) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e-221) || !(y <= 4e-50)) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e-221) or not (y <= 4e-50):
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e-221) || !(y <= 4e-50))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e-221) || ~((y <= 4e-50)))
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e-221], N[Not[LessEqual[y, 4e-50]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000052e-221 or 4.00000000000000003e-50 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 84.0%

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

   if -9.00000000000000052e-221 < y < 4.00000000000000003e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 88.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-221} \lor \neg \left(y \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-119}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.2e-75)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 1.7e-119)
     (+ 1.0 (/ (/ x (- z y)) y))
     (+ 1.0 (/ x (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-75) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.7e-119) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} 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 (t <= (-1.2d-75)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.7d-119) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    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 (t <= -1.2e-75) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.7e-119) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.2e-75:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.7e-119:
		tmp = 1.0 + ((x / (z - y)) / y)
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.2e-75)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.7e-119)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	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 (t <= -1.2e-75)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.7e-119)
		tmp = 1.0 + ((x / (z - y)) / y);
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.2e-75], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-119], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $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 t < -1.2000000000000001e-75

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. associate-/r* 69.2%

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

      3. distribute-neg-frac 69.2%

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

   5. Simplified 69.2%

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

   if -1.2000000000000001e-75 < t < 1.70000000000000012e-119

   1. Initial program 98.8%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 98.8%

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

   4. Applied egg-rr 98.8%

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

   5. Taylor expanded in t around 0 90.8%

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

      1. *-lft-identity 90.8%

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

      2. times-frac 90.9%

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

      3. associate-*l/ 90.9%

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

      4. *-lft-identity 90.9%

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

   7. Simplified 90.9%

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

   if 1.70000000000000012e-119 < t

   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 95.6%

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

      1. associate-*r/ 95.6%

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

      2. neg-mul-1 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-119}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-221}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-221)
   (+ 1.0 (/ (/ x (- z y)) y))
   (if (<= y 3.4e-50) (- 1.0 (/ x (* z t))) (+ 1.0 (/ (/ x y) (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-221) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else if (y <= 3.4e-50) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + ((x / y) / (z - 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 (y <= (-9d-221)) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    else if (y <= 3.4d-50) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 + ((x / y) / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-221) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else if (y <= 3.4e-50) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + ((x / y) / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e-221:
		tmp = 1.0 + ((x / (z - y)) / y)
	elif y <= 3.4e-50:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 + ((x / y) / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e-221)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	elseif (y <= 3.4e-50)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e-221)
		tmp = 1.0 + ((x / (z - y)) / y);
	elseif (y <= 3.4e-50)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 + ((x / y) / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e-221], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-50], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000052e-221

   1. Initial program 99.1%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in t around 0 80.9%

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

      1. *-lft-identity 80.9%

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

      2. times-frac 80.9%

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

      3. associate-*l/ 80.9%

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

      4. *-lft-identity 80.9%

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

   7. Simplified 80.9%

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

   if -9.00000000000000052e-221 < y < 3.40000000000000014e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 88.7%

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

   if 3.40000000000000014e-50 < y

   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 0 87.8%

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

      1. associate-/r* 87.8%

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

   5. Simplified 87.8%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-221}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-221}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e-221)
   (+ 1.0 (/ x (* y (- z y))))
   (if (<= y 4e-50) (- 1.0 (/ x (* z t))) (+ 1.0 (/ (/ x y) (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-221) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else if (y <= 4e-50) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + ((x / y) / (z - 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 (y <= (-8.5d-221)) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else if (y <= 4d-50) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 + ((x / y) / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-221) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else if (y <= 4e-50) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + ((x / y) / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e-221:
		tmp = 1.0 + (x / (y * (z - y)))
	elif y <= 4e-50:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 + ((x / y) / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e-221)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	elseif (y <= 4e-50)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.5e-221)
		tmp = 1.0 + (x / (y * (z - y)));
	elseif (y <= 4e-50)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 + ((x / y) / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e-221], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-50], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999984e-221

   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 0 80.9%

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

   if -8.49999999999999984e-221 < y < 4.00000000000000003e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 88.7%

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

   if 4.00000000000000003e-50 < y

   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 0 87.8%

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

      1. associate-/r* 87.8%

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

   5. Simplified 87.8%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-221}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+249}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+249)
   (- 1.0 (/ x (* z t)))
   (if (<= z -1.95e-28) (+ 1.0 (/ (/ x z) y)) (+ 1.0 (/ x (* y (- t y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+249) {
		tmp = 1.0 - (x / (z * t));
	} else if (z <= -1.95e-28) {
		tmp = 1.0 + ((x / z) / y);
	} 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 <= (-1.7d+249)) then
        tmp = 1.0d0 - (x / (z * t))
    else if (z <= (-1.95d-28)) then
        tmp = 1.0d0 + ((x / z) / y)
    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 <= -1.7e+249) {
		tmp = 1.0 - (x / (z * t));
	} else if (z <= -1.95e-28) {
		tmp = 1.0 + ((x / z) / y);
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+249:
		tmp = 1.0 - (x / (z * t))
	elif z <= -1.95e-28:
		tmp = 1.0 + ((x / z) / y)
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+249)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (z <= -1.95e-28)
		tmp = Float64(1.0 + Float64(Float64(x / z) / y));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.7e+249)
		tmp = 1.0 - (x / (z * t));
	elseif (z <= -1.95e-28)
		tmp = 1.0 + ((x / z) / y);
	else
		tmp = 1.0 + (x / (y * (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+249], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-28], N[(1.0 + N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000006e249

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -1.70000000000000006e249 < z < -1.94999999999999999e-28

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 85.3%

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

      1. *-lft-identity 85.3%

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

      2. times-frac 85.2%

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

      3. associate-*l/ 85.3%

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

      4. *-lft-identity 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in y around 0 82.9%

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

      1. associate-*r/ 82.9%

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

      2. mul-1-neg 82.9%

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

   10. Simplified 82.9%

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

   if -1.94999999999999999e-28 < 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 z around 0 79.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+249}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-111}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-63}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e-111) 1.0 (if (<= y 2.25e-63) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e-111) {
		tmp = 1.0;
	} else if (y <= 2.25e-63) {
		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 <= (-7.2d-111)) then
        tmp = 1.0d0
    else if (y <= 2.25d-63) 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 <= -7.2e-111) {
		tmp = 1.0;
	} else if (y <= 2.25e-63) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.2e-111:
		tmp = 1.0
	elif y <= 2.25e-63:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.2e-111)
		tmp = 1.0;
	elseif (y <= 2.25e-63)
		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 <= -7.2e-111)
		tmp = 1.0;
	elseif (y <= 2.25e-63)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.2e-111], 1.0, If[LessEqual[y, 2.25e-63], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000019e-111 or 2.25e-63 < y

   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 0 88.4%

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

   4. Taylor expanded in y around 0 62.3%

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

      1. associate-*r/ 62.3%

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

      2. neg-mul-1 62.3%

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

      3. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in x around 0 87.0%

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

   if -7.20000000000000019e-111 < y < 2.25e-63

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 79.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-111}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-63}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.5 \cdot 10^{-119}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.5e-119) (+ 1.0 (/ (/ x (- z y)) y)) (+ 1.0 (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.5e-119) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} 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 (t <= 3.5d-119) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    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 (t <= 3.5e-119) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3.5e-119:
		tmp = 1.0 + ((x / (z - y)) / y)
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.5e-119)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	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 (t <= 3.5e-119)
		tmp = 1.0 + ((x / (z - y)) / y);
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3.5e-119], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $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 < 3.5e-119

   1. Initial program 99.4%

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

      1. clear-num 99.4%

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

      2. associate-/r/ 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in t around 0 73.5%

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

      1. *-lft-identity 73.5%

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

      2. times-frac 73.6%

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

      3. associate-*l/ 73.6%

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

      4. *-lft-identity 73.6%

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

   7. Simplified 73.6%

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

   if 3.5e-119 < t

   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 95.6%

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

      1. associate-*r/ 95.6%

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

      2. neg-mul-1 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.5 \cdot 10^{-119}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% 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 99.6%

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

3. Taylor expanded in t around 0 72.7%

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

4. Taylor expanded in y around 0 53.8%

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

   1. associate-*r/ 53.8%

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

   2. neg-mul-1 53.8%

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

   3. *-commutative 53.8%

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

6. Simplified 53.8%

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

7. Taylor expanded in x around 0 74.9%

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

Reproduce

herbie shell --seed 2024085 
(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)))))