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

Percentage Accurate: 99.0% → 98.7%

Time: 13.7s

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: 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: 98.7% accurate, 0.8× speedup

Math

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

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 (/ (/ 1.0 (- y t)) (/ (- z y) x))))

C

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

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 + ((1.0d0 / (y - t)) / ((z - y) / x))
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 + ((1.0 / (y - t)) / ((z - y) / x));
}

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 + ((1.0 / (y - t)) / ((z - y) / x));
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[(N[(1.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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 98.8%

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

   2. inv-pow 98.8%

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

   3. *-commutative 98.8%

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

   4. associate-/l* 98.2%

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

4. Applied egg-rr 98.2%

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

   1. unpow-1 98.2%

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

6. Simplified 98.2%

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

   1. frac-2neg 98.2%

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

   2. metadata-eval 98.2%

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

   3. div-inv 98.2%

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

   4. distribute-neg-frac2 98.2%

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

   5. associate-/r* 98.2%

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

   6. distribute-neg-frac 98.2%

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

   7. distribute-neg-frac 98.2%

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

   8. metadata-eval 98.2%

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

8. Applied egg-rr 98.2%

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

   1. neg-mul-1 98.2%

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

   2. distribute-neg-frac 98.2%

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

   3. distribute-neg-frac 98.2%

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

   4. metadata-eval 98.2%

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

10. Simplified 98.2%

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

11. Final simplification 98.2%

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

Alternative 2: 92.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-170}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -9e-170)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 1.4e-71)
     (+ 1.0 (/ (/ x y) (- z y)))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9e-170) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.4e-71) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	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 <= (-9d-170)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.4d-71) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    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 <= -9e-170) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.4e-71) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -9e-170:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.4e-71:
		tmp = 1.0 + ((x / y) / (z - y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9e-170)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.4e-71)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	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 <= -9e-170)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.4e-71)
		tmp = 1.0 + ((x / y) / (z - y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	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, -9e-170], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-71], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.00000000000000003e-170

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/r* 77.4%

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

   5. Simplified 77.4%

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

   if -9.00000000000000003e-170 < t < 1.4e-71

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0 86.6%

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

      1. associate-/r* 89.5%

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

   5. Simplified 89.5%

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

   if 1.4e-71 < 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 97.9%

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

      1. +-commutative 97.9%

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

      2. associate-/r* 97.9%

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

   5. Simplified 97.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-170}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-65}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-33}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 (<= y -5.2e-65) 1.0 (if (<= y 6.5e-33) (- 1.0 (/ x (* t z))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-65) {
		tmp = 1.0;
	} else if (y <= 6.5e-33) {
		tmp = 1.0 - (x / (t * 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 (y <= (-5.2d-65)) then
        tmp = 1.0d0
    else if (y <= 6.5d-33) then
        tmp = 1.0d0 - (x / (t * 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 (y <= -5.2e-65) {
		tmp = 1.0;
	} else if (y <= 6.5e-33) {
		tmp = 1.0 - (x / (t * 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 y <= -5.2e-65:
		tmp = 1.0
	elif y <= 6.5e-33:
		tmp = 1.0 - (x / (t * 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 (y <= -5.2e-65)
		tmp = 1.0;
	elseif (y <= 6.5e-33)
		tmp = Float64(1.0 - Float64(x / Float64(t * 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 (y <= -5.2e-65)
		tmp = 1.0;
	elseif (y <= 6.5e-33)
		tmp = 1.0 - (x / (t * 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[y, -5.2e-65], 1.0, If[LessEqual[y, 6.5e-33], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.20000000000000019e-65 or 6.4999999999999993e-33 < 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 x around 0 88.4%

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

   if -5.20000000000000019e-65 < y < 6.4999999999999993e-33

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 79.7%

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

Alternative 4: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-148}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-155}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 (<= z -1.4e-148) 1.0 (if (<= z 1.9e-155) (+ 1.0 (/ x (* y t))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e-148) {
		tmp = 1.0;
	} else if (z <= 1.9e-155) {
		tmp = 1.0 + (x / (y * 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 (z <= (-1.4d-148)) then
        tmp = 1.0d0
    else if (z <= 1.9d-155) then
        tmp = 1.0d0 + (x / (y * 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 (z <= -1.4e-148) {
		tmp = 1.0;
	} else if (z <= 1.9e-155) {
		tmp = 1.0 + (x / (y * 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 z <= -1.4e-148:
		tmp = 1.0
	elif z <= 1.9e-155:
		tmp = 1.0 + (x / (y * 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 (z <= -1.4e-148)
		tmp = 1.0;
	elseif (z <= 1.9e-155)
		tmp = Float64(1.0 + Float64(x / Float64(y * 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 (z <= -1.4e-148)
		tmp = 1.0;
	elseif (z <= 1.9e-155)
		tmp = 1.0 + (x / (y * 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[z, -1.4e-148], 1.0, If[LessEqual[z, 1.9e-155], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e-148 or 1.8999999999999999e-155 < z

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 79.3%

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

   if -1.4e-148 < z < 1.8999999999999999e-155

   1. Initial program 96.1%

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

   3. Taylor expanded in t around inf 84.8%

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

      1. +-commutative 84.8%

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

      2. associate-/r* 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in y around inf 77.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-148}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-155}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-82}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 3e-82) (+ 1.0 (/ (/ x z) (- y t))) (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3e-82) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	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 <= 3d-82) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    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 <= 3e-82) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 3e-82:
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3e-82)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	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 <= 3e-82)
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	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, 3e-82], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.9999999999999999e-82

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/r* 78.8%

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

   5. Simplified 78.8%

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

   if 2.9999999999999999e-82 < 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 97.9%

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

      1. +-commutative 97.9%

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

      2. associate-/r* 97.9%

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

   5. Simplified 97.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-82}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.5 \cdot 10^{-92}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 5.5e-92) (+ 1.0 (/ x (* y z))) (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.5e-92) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	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 <= 5.5d-92) then
        tmp = 1.0d0 + (x / (y * z))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    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 <= 5.5e-92) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 5.5e-92:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 5.5e-92)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	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 <= 5.5e-92)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	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, 5.5e-92], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.5000000000000002e-92

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0 80.4%

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

      1. associate-/r* 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 63.7%

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

   8. Simplified 63.7%

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

   if 5.5000000000000002e-92 < 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 98.0%

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

      1. +-commutative 98.0%

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

      2. associate-/r* 98.0%

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

   5. Simplified 98.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.5 \cdot 10^{-92}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.7% accurate, 0.8× speedup

Math

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

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 (/ -1.0 (* (/ (- z y) x) (- t y)))))

C

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

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 + ((-1.0d0) / (((z - y) / x) * (t - y)))
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 + (-1.0 / (((z - y) / x) * (t - y)));
}

Python

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

Julia

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

MATLAB

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

Derivation

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 98.8%

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

   2. inv-pow 98.8%

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

   3. *-commutative 98.8%

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

   4. associate-/l* 98.2%

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

4. Applied egg-rr 98.2%

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

   1. unpow-1 98.2%

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

6. Simplified 98.2%

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

7. Final simplification 98.2%

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

Alternative 8: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2.8 \cdot 10^{-45}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 2.8e-45) (+ 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 <= 2.8e-45) {
		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 <= 2.8d-45) 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 <= 2.8e-45) {
		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 <= 2.8e-45:
		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 <= 2.8e-45)
		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 <= 2.8e-45)
		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, 2.8e-45], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < 2.8000000000000001e-45

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 80.3%

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

      1. associate-/r* 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in z around inf 64.5%

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

      1. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if 2.8000000000000001e-45 < 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 x around 0 89.8%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.8 \cdot 10^{-45}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.0% accurate, 1.0× speedup

Math

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

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 t) (- z y)))))

C

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

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 - t) * (z - y)))
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 - t) * (z - y)));
}

Python

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

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 - t) * Float64(z - y))))
end

MATLAB

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

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

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

Alternative 10: 74.7% 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 98.8%

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

3. Taylor expanded in x around 0 78.0%

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

Reproduce

herbie shell --seed 2024111 
(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)))))