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

Percentage Accurate: 99.0% → 98.7%

Time: 8.9s

Alternatives: 14

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

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

FPCore

NOTE: 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)) (/ (- y z) x))))

C

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

Fortran

NOTE: 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)) / ((y - z) / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: 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[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.6%

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

   1. clear-num 98.6%

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

   2. inv-pow 98.6%

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

   3. *-commutative 98.6%

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

   4. associate-/l* 98.1%

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

3. Applied egg-rr 98.1%

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

   1. unpow-1 98.1%

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

   2. clear-num 98.1%

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

   3. clear-num 98.1%

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

   4. associate-/l/ 98.7%

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

   5. associate-/r* 98.7%

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

5. Applied egg-rr 98.7%

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

6. Final simplification 98.7%

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

Alternative 2: 80.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 1 - \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;y \leq -62000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-118}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-46}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ x y) y))))
   (if (<= y -62000000000.0)
     t_1
     (if (<= y -9e-118)
       (+ 1.0 (/ x (* y t)))
       (if (<= y 4e-46) (- 1.0 (/ (/ x z) t)) t_1)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((x / y) / y);
	double tmp;
	if (y <= -62000000000.0) {
		tmp = t_1;
	} else if (y <= -9e-118) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 4e-46) {
		tmp = 1.0 - ((x / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: 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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - ((x / y) / y)
    if (y <= (-62000000000.0d0)) then
        tmp = t_1
    else if (y <= (-9d-118)) then
        tmp = 1.0d0 + (x / (y * t))
    else if (y <= 4d-46) then
        tmp = 1.0d0 - ((x / z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((x / y) / y);
	double tmp;
	if (y <= -62000000000.0) {
		tmp = t_1;
	} else if (y <= -9e-118) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 4e-46) {
		tmp = 1.0 - ((x / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	t_1 = 1.0 - ((x / y) / y)
	tmp = 0
	if y <= -62000000000.0:
		tmp = t_1
	elif y <= -9e-118:
		tmp = 1.0 + (x / (y * t))
	elif y <= 4e-46:
		tmp = 1.0 - ((x / z) / t)
	else:
		tmp = t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(Float64(x / y) / y))
	tmp = 0.0
	if (y <= -62000000000.0)
		tmp = t_1;
	elseif (y <= -9e-118)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	elseif (y <= 4e-46)
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - ((x / y) / y);
	tmp = 0.0;
	if (y <= -62000000000.0)
		tmp = t_1;
	elseif (y <= -9e-118)
		tmp = 1.0 + (x / (y * t));
	elseif (y <= 4e-46)
		tmp = 1.0 - ((x / z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -62000000000.0], t$95$1, If[LessEqual[y, -9e-118], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-46], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2e10 or 4.00000000000000009e-46 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-/r* 98.0%

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

   4. Simplified 98.0%

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

   5. Taylor expanded in y around inf 93.2%

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

   if -6.2e10 < y < -9.0000000000000001e-118

   1. Initial program 99.8%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 92.9%

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

   3. Applied egg-rr 92.9%

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

   4. Taylor expanded in t around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. associate-/r* 78.4%

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

      3. distribute-neg-frac 78.4%

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

      4. distribute-neg-frac 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in y around inf 60.6%

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

      1. associate-*r/ 60.6%

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

      2. neg-mul-1 60.6%

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

   9. Simplified 60.6%

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

   if -9.0000000000000001e-118 < y < 4.00000000000000009e-46

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 73.9%

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

      1. *-un-lft-identity 73.9%

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

      2. times-frac 74.7%

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

   4. Applied egg-rr 74.7%

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

      1. associate-*l/ 74.7%

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

      2. *-lft-identity 74.7%

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

   6. Simplified 74.7%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62000000000:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-118}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-46}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]

Alternative 3: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-118} \lor \neg \left(y \leq 6.4 \cdot 10^{-83}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.85e-118) (not (<= y 6.4e-83)))
   (- 1.0 (/ x (* y (- y t))))
   (- 1.0 (/ (/ x z) t))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e-118) || !(y <= 6.4e-83)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - ((x / z) / t);
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.85d-118)) .or. (.not. (y <= 6.4d-83))) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 - ((x / z) / t)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e-118) || !(y <= 6.4e-83)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - ((x / z) / t);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -1.85e-118) or not (y <= 6.4e-83):
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 - ((x / z) / t)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.85e-118) || !(y <= 6.4e-83))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.85e-118) || ~((y <= 6.4e-83)))
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 - ((x / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.85e-118], N[Not[LessEqual[y, 6.4e-83]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000007e-118 or 6.4000000000000002e-83 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.9%

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

   if -1.85000000000000007e-118 < y < 6.4000000000000002e-83

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 74.9%

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

      1. *-un-lft-identity 74.9%

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

      2. times-frac 75.7%

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

   4. Applied egg-rr 75.7%

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

      1. associate-*l/ 75.7%

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

      2. *-lft-identity 75.7%

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

   6. Simplified 75.7%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-118} \lor \neg \left(y \leq 6.4 \cdot 10^{-83}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 4: 90.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-124} \lor \neg \left(t \leq 1.8 \cdot 10^{-196}\right):\\ \;\;\;\;1 + \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65e-124) (not (<= t 1.8e-196)))
   (+ 1.0 (/ x (* t (- y z))))
   (- 1.0 (/ (/ x (- y z)) y))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e-124) || !(t <= 1.8e-196)) {
		tmp = 1.0 + (x / (t * (y - z)));
	} else {
		tmp = 1.0 - ((x / (y - z)) / y);
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.65d-124)) .or. (.not. (t <= 1.8d-196))) then
        tmp = 1.0d0 + (x / (t * (y - z)))
    else
        tmp = 1.0d0 - ((x / (y - z)) / y)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e-124) || !(t <= 1.8e-196)) {
		tmp = 1.0 + (x / (t * (y - z)));
	} else {
		tmp = 1.0 - ((x / (y - z)) / y);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65e-124) or not (t <= 1.8e-196):
		tmp = 1.0 + (x / (t * (y - z)))
	else:
		tmp = 1.0 - ((x / (y - z)) / y)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65e-124) || !(t <= 1.8e-196))
		tmp = Float64(1.0 + Float64(x / Float64(t * Float64(y - z))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - z)) / y));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.65e-124) || ~((t <= 1.8e-196)))
		tmp = 1.0 + (x / (t * (y - z)));
	else
		tmp = 1.0 - ((x / (y - z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65e-124], N[Not[LessEqual[t, 1.8e-196]], $MachinePrecision]], N[(1.0 + N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.64999999999999992e-124 or 1.8e-196 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 90.7%

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

      1. associate-*r/ 90.7%

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

      2. neg-mul-1 90.7%

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

   4. Simplified 90.7%

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

   if -1.64999999999999992e-124 < t < 1.8e-196

   1. Initial program 94.8%

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

   2. Taylor expanded in t around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/r* 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-124} \lor \neg \left(t \leq 1.8 \cdot 10^{-196}\right):\\ \;\;\;\;1 + \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \end{array} \]

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-118}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-48}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-118)
   (- 1.0 (/ x (* y (- y t))))
   (if (<= y 9.6e-48) (- 1.0 (/ (/ x z) t)) (- 1.0 (/ x (* y (- y z)))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-118) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else if (y <= 9.6e-48) {
		tmp = 1.0 - ((x / z) / t);
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.45d-118)) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else if (y <= 9.6d-48) then
        tmp = 1.0d0 - ((x / z) / t)
    else
        tmp = 1.0d0 - (x / (y * (y - z)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-118) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else if (y <= 9.6e-48) {
		tmp = 1.0 - ((x / z) / t);
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-118:
		tmp = 1.0 - (x / (y * (y - t)))
	elif y <= 9.6e-48:
		tmp = 1.0 - ((x / z) / t)
	else:
		tmp = 1.0 - (x / (y * (y - z)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-118)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	elseif (y <= 9.6e-48)
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e-118)
		tmp = 1.0 - (x / (y * (y - t)));
	elseif (y <= 9.6e-48)
		tmp = 1.0 - ((x / z) / t);
	else
		tmp = 1.0 - (x / (y * (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-118], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e-48], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e-118

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 87.7%

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

   if -1.4499999999999999e-118 < y < 9.6e-48

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 73.9%

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

      1. *-un-lft-identity 73.9%

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

      2. times-frac 74.7%

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

   4. Applied egg-rr 74.7%

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

      1. associate-*l/ 74.7%

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

      2. *-lft-identity 74.7%

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

   6. Simplified 74.7%

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

   if 9.6e-48 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-118}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-48}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 6: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-118}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-48}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e-118)
   (- 1.0 (/ (/ x (- y t)) y))
   (if (<= y 6.5e-48) (- 1.0 (/ (/ x z) t)) (- 1.0 (/ x (* y (- y z)))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-118) {
		tmp = 1.0 - ((x / (y - t)) / y);
	} else if (y <= 6.5e-48) {
		tmp = 1.0 - ((x / z) / t);
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

Fortran

NOTE: 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-118)) then
        tmp = 1.0d0 - ((x / (y - t)) / y)
    else if (y <= 6.5d-48) then
        tmp = 1.0d0 - ((x / z) / t)
    else
        tmp = 1.0d0 - (x / (y * (y - z)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-118) {
		tmp = 1.0 - ((x / (y - t)) / y);
	} else if (y <= 6.5e-48) {
		tmp = 1.0 - ((x / z) / t);
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e-118:
		tmp = 1.0 - ((x / (y - t)) / y)
	elif y <= 6.5e-48:
		tmp = 1.0 - ((x / z) / t)
	else:
		tmp = 1.0 - (x / (y * (y - z)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e-118)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	elseif (y <= 6.5e-48)
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.3e-118)
		tmp = 1.0 - ((x / (y - t)) / y);
	elseif (y <= 6.5e-48)
		tmp = 1.0 - ((x / z) / t);
	else
		tmp = 1.0 - (x / (y * (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e-118], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-48], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000021e-118

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-/r* 87.7%

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

   4. Simplified 87.7%

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

   if -2.30000000000000021e-118 < y < 6.5e-48

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 73.9%

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

      1. *-un-lft-identity 73.9%

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

      2. times-frac 74.7%

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

   4. Applied egg-rr 74.7%

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

      1. associate-*l/ 74.7%

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

      2. *-lft-identity 74.7%

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

   6. Simplified 74.7%

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

   if 6.5e-48 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-118}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-48}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 7: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{-1}{y - z} \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e-121)
   (+ 1.0 (/ x (* (- y t) z)))
   (- 1.0 (* (/ -1.0 (- y z)) (/ x t)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-121) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else {
		tmp = 1.0 - ((-1.0 / (y - z)) * (x / t));
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.1d-121)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else
        tmp = 1.0d0 - (((-1.0d0) / (y - z)) * (x / t))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-121) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else {
		tmp = 1.0 - ((-1.0 / (y - z)) * (x / t));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e-121:
		tmp = 1.0 + (x / ((y - t) * z))
	else:
		tmp = 1.0 - ((-1.0 / (y - z)) * (x / t))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e-121)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	else
		tmp = Float64(1.0 - Float64(Float64(-1.0 / Float64(y - z)) * Float64(x / t)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e-121)
		tmp = 1.0 + (x / ((y - t) * z));
	else
		tmp = 1.0 - ((-1.0 / (y - z)) * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e-121], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(-1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000011e-121

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 91.6%

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

      1. associate-*r/ 91.6%

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

      2. neg-mul-1 91.6%

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

      3. *-commutative 91.6%

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

   4. Simplified 91.6%

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

   if -1.10000000000000011e-121 < z

   1. Initial program 97.9%

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

      1. clear-num 97.9%

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

      2. inv-pow 97.9%

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

      3. *-commutative 97.9%

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

      4. associate-/l* 97.1%

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

   3. Applied egg-rr 97.1%

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

   4. Taylor expanded in t around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. associate-/r* 81.1%

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

      3. distribute-neg-frac 81.1%

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

      4. distribute-neg-frac 81.1%

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

   6. Simplified 81.1%

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

      1. associate-/l/ 80.1%

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

      2. neg-mul-1 80.1%

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

      3. times-frac 81.1%

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

   8. Applied egg-rr 81.1%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{-1}{y - z} \cdot \frac{x}{t}\\ \end{array} \]

Alternative 8: 81.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -62000000000 \lor \neg \left(y \leq 7.5 \cdot 10^{-45}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -62000000000.0) (not (<= y 7.5e-45)))
   (- 1.0 (/ (/ x y) y))
   (- 1.0 (/ x (* t z)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -62000000000.0) || !(y <= 7.5e-45)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-62000000000.0d0)) .or. (.not. (y <= 7.5d-45))) then
        tmp = 1.0d0 - ((x / y) / y)
    else
        tmp = 1.0d0 - (x / (t * z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -62000000000.0) || !(y <= 7.5e-45)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -62000000000.0) or not (y <= 7.5e-45):
		tmp = 1.0 - ((x / y) / y)
	else:
		tmp = 1.0 - (x / (t * z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -62000000000.0) || !(y <= 7.5e-45))
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -62000000000.0) || ~((y <= 7.5e-45)))
		tmp = 1.0 - ((x / y) / y);
	else
		tmp = 1.0 - (x / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -62000000000.0], N[Not[LessEqual[y, 7.5e-45]], $MachinePrecision]], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2e10 or 7.5000000000000006e-45 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-/r* 98.0%

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

   4. Simplified 98.0%

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

   5. Taylor expanded in y around inf 93.2%

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

   if -6.2e10 < y < 7.5000000000000006e-45

   1. Initial program 97.1%

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

   2. Taylor expanded in y around 0 69.5%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62000000000 \lor \neg \left(y \leq 7.5 \cdot 10^{-45}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]

Alternative 9: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -65000000000 \lor \neg \left(y \leq 5.1 \cdot 10^{-46}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -65000000000.0) (not (<= y 5.1e-46)))
   (- 1.0 (/ (/ x y) y))
   (- 1.0 (/ (/ x z) t))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -65000000000.0) || !(y <= 5.1e-46)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 - ((x / z) / t);
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-65000000000.0d0)) .or. (.not. (y <= 5.1d-46))) then
        tmp = 1.0d0 - ((x / y) / y)
    else
        tmp = 1.0d0 - ((x / z) / t)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -65000000000.0) || !(y <= 5.1e-46)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 - ((x / z) / t);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -65000000000.0) or not (y <= 5.1e-46):
		tmp = 1.0 - ((x / y) / y)
	else:
		tmp = 1.0 - ((x / z) / t)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -65000000000.0) || !(y <= 5.1e-46))
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	else
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -65000000000.0) || ~((y <= 5.1e-46)))
		tmp = 1.0 - ((x / y) / y);
	else
		tmp = 1.0 - ((x / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -65000000000.0], N[Not[LessEqual[y, 5.1e-46]], $MachinePrecision]], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e10 or 5.0999999999999997e-46 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-/r* 98.0%

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

   4. Simplified 98.0%

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

   5. Taylor expanded in y around inf 93.2%

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

   if -6.5e10 < y < 5.0999999999999997e-46

   1. Initial program 97.1%

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

   2. Taylor expanded in y around 0 69.5%

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

      1. *-un-lft-identity 69.5%

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

      2. times-frac 70.1%

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

   4. Applied egg-rr 70.1%

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

      1. associate-*l/ 70.1%

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

      2. *-lft-identity 70.1%

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

   6. Simplified 70.1%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -65000000000 \lor \neg \left(y \leq 5.1 \cdot 10^{-46}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 10: 83.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-90}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.1e-90) 1.0 (if (<= y 3.8e-75) (- 1.0 (/ x (* t z))) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.1e-90) {
		tmp = 1.0;
	} else if (y <= 3.8e-75) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-6.1d-90)) then
        tmp = 1.0d0
    else if (y <= 3.8d-75) then
        tmp = 1.0d0 - (x / (t * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.1e-90) {
		tmp = 1.0;
	} else if (y <= 3.8e-75) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -6.1e-90:
		tmp = 1.0
	elif y <= 3.8e-75:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.1e-90)
		tmp = 1.0;
	elseif (y <= 3.8e-75)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.1e-90)
		tmp = 1.0;
	elseif (y <= 3.8e-75)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -6.1e-90], 1.0, If[LessEqual[y, 3.8e-75], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.0999999999999999e-90 or 3.79999999999999994e-75 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 80.7%

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

      1. associate-*r/ 80.7%

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

      2. neg-mul-1 80.7%

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

      3. *-commutative 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in x around 0 88.7%

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

   if -6.0999999999999999e-90 < y < 3.79999999999999994e-75

   1. Initial program 96.5%

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

   2. Taylor expanded in y around 0 69.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-90}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-108}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e-108) (+ 1.0 (/ x (* (- y t) z))) (- 1.0 (/ (/ x (- y t)) y))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e-108) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-3.7d-108)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else
        tmp = 1.0d0 - ((x / (y - t)) / y)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e-108) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e-108:
		tmp = 1.0 + (x / ((y - t) * z))
	else:
		tmp = 1.0 - ((x / (y - t)) / y)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e-108)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.7e-108)
		tmp = 1.0 + (x / ((y - t) * z));
	else
		tmp = 1.0 - ((x / (y - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e-108], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e-108

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. neg-mul-1 93.5%

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

      3. *-commutative 93.5%

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

   4. Simplified 93.5%

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

   if -3.7e-108 < z

   1. Initial program 98.0%

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

   2. Taylor expanded in z around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-/r* 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-108}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 12: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-122}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.8e-122) (+ 1.0 (/ x (* (- y t) z))) (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e-122) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-7.8d-122)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e-122) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -7.8e-122:
		tmp = 1.0 + (x / ((y - t) * z))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.8e-122)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.8e-122)
		tmp = 1.0 + (x / ((y - t) * z));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -7.8e-122], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * 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 z < -7.79999999999999979e-122

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 91.7%

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

      1. associate-*r/ 91.7%

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

      2. neg-mul-1 91.7%

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

      3. *-commutative 91.7%

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

   4. Simplified 91.7%

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

   if -7.79999999999999979e-122 < z

   1. Initial program 97.9%

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

      1. clear-num 97.9%

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

      2. inv-pow 97.9%

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

      3. *-commutative 97.9%

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

      4. associate-/l* 97.0%

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

   3. Applied egg-rr 97.0%

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

   4. Taylor expanded in t around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. associate-/r* 81.0%

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

      3. distribute-neg-frac 81.0%

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

      4. distribute-neg-frac 81.0%

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

   6. Simplified 81.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-122}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 13: 99.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: 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) (- y z)))))

C

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

Fortran

NOTE: 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) * (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: 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[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.6%

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

2. Final simplification 98.6%

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

Alternative 14: 75.5% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 98.6%

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

2. Taylor expanded in z around inf 81.2%

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

   1. associate-*r/ 81.2%

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

   2. neg-mul-1 81.2%

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

   3. *-commutative 81.2%

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

4. Simplified 81.2%

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

5. Taylor expanded in x around 0 73.6%

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

6. Final simplification 73.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023308 
(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)))))