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

Percentage Accurate: 98.9% → 98.6%

Time: 16.7s

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: 98.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 1.0× speedup

Math

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

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 z)) (- y t))))

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 98.1%

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

   1. associate-/r* 98.1%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 2: 90.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-168}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-244}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.8e+15)
   (- 1.0 (/ x (* z (- t y))))
   (if (<= z -1.8e-168)
     (- 1.0 (/ x (* y (- y z))))
     (if (<= z 1.2e-244)
       (- 1.0 (/ x (* y (- y t))))
       (- 1.0 (/ x (* t (- z y))))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.8e+15) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else if (z <= -1.8e-168) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (z <= 1.2e-244) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - (x / (t * (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 (z <= (-8.8d+15)) then
        tmp = 1.0d0 - (x / (z * (t - y)))
    else if (z <= (-1.8d-168)) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else if (z <= 1.2d-244) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 - (x / (t * (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 (z <= -8.8e+15) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else if (z <= -1.8e-168) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (z <= 1.2e-244) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -8.8e+15:
		tmp = 1.0 - (x / (z * (t - y)))
	elif z <= -1.8e-168:
		tmp = 1.0 - (x / (y * (y - z)))
	elif z <= 1.2e-244:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.8e+15)
		tmp = Float64(1.0 - Float64(x / Float64(z * Float64(t - y))));
	elseif (z <= -1.8e-168)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	elseif (z <= 1.2e-244)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(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 (z <= -8.8e+15)
		tmp = 1.0 - (x / (z * (t - y)));
	elseif (z <= -1.8e-168)
		tmp = 1.0 - (x / (y * (y - z)));
	elseif (z <= 1.2e-244)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 - (x / (t * (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[LessEqual[z, -8.8e+15], N[(1.0 - N[(x / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-168], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-244], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.8e15

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.4%

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

      1. associate-*r* 98.4%

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

      2. mul-1-neg 98.4%

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

   4. Simplified 98.4%

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

   if -8.8e15 < z < -1.7999999999999999e-168

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 81.0%

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

   if -1.7999999999999999e-168 < z < 1.20000000000000008e-244

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 86.0%

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

   if 1.20000000000000008e-244 < z

   1. Initial program 99.2%

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

   2. Taylor expanded in t around inf 86.6%

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

      1. associate-*r* 86.6%

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

      2. mul-1-neg 86.6%

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

   4. Simplified 86.6%

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

      1. clear-num 86.6%

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

      2. div-inv 86.6%

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

      3. clear-num 86.6%

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

      4. distribute-lft-neg-out 86.6%

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

      5. distribute-rgt-neg-in 86.6%

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

      6. associate-/r* 86.7%

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

      7. sub-neg 86.7%

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

      8. +-commutative 86.7%

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

      9. distribute-neg-in 86.7%

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

      10. remove-double-neg 86.7%

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

   6. Applied egg-rr 86.7%

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

      1. *-lft-identity 86.7%

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

      2. associate-/l/ 86.6%

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

      3. unsub-neg 86.6%

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

   8. Simplified 86.6%

      \[\leadsto 1 - \color{blue}{\frac{x}{\left(z - y\right) \cdot t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-168}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-244}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]

Alternative 3: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-129} \lor \neg \left(y \leq 4.5 \cdot 10^{-104}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

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 -3.2e-129) (not (<= y 4.5e-104)))
   (- 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 <= -3.2e-129) || !(y <= 4.5e-104)) {
		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 <= (-3.2d-129)) .or. (.not. (y <= 4.5d-104))) 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 <= -3.2e-129) || !(y <= 4.5e-104)) {
		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 <= -3.2e-129) or not (y <= 4.5e-104):
		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 <= -3.2e-129) || !(y <= 4.5e-104))
		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 <= -3.2e-129) || ~((y <= 4.5e-104)))
		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, -3.2e-129], N[Not[LessEqual[y, 4.5e-104]], $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 < -3.2000000000000003e-129 or 4.4999999999999997e-104 < 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 94.2%

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

   if -3.2000000000000003e-129 < y < 4.4999999999999997e-104

   1. Initial program 94.1%

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

   2. Taylor expanded in t around inf 83.2%

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

      1. associate-*r* 83.2%

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

      2. mul-1-neg 83.2%

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

   4. Simplified 83.2%

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

      1. clear-num 83.2%

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

      2. div-inv 83.2%

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

      3. clear-num 83.2%

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

      4. distribute-lft-neg-out 83.2%

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

      5. distribute-rgt-neg-in 83.2%

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

      6. associate-/r* 85.6%

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

      7. sub-neg 85.6%

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

      8. +-commutative 85.6%

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

      9. distribute-neg-in 85.6%

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

      10. remove-double-neg 85.6%

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

   6. Applied egg-rr 85.6%

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

      1. *-lft-identity 85.6%

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

      2. associate-/l/ 83.2%

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

      3. unsub-neg 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in z around inf 82.0%

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

       1. associate-/l/ 80.8%

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

   11. Simplified 80.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-129} \lor \neg \left(y \leq 4.5 \cdot 10^{-104}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 4: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-127} \lor \neg \left(t \leq 9 \cdot 10^{-27}\right):\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e-127) (not (<= t 9e-27)))
   (- 1.0 (/ x (* t (- z y))))
   (- 1.0 (/ x (* y (- y z))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-127) || !(t <= 9e-27)) {
		tmp = 1.0 - (x / (t * (z - y)));
	} 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 ((t <= (-5.2d-127)) .or. (.not. (t <= 9d-27))) then
        tmp = 1.0d0 - (x / (t * (z - y)))
    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 ((t <= -5.2e-127) || !(t <= 9e-27)) {
		tmp = 1.0 - (x / (t * (z - y)));
	} 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 (t <= -5.2e-127) or not (t <= 9e-27):
		tmp = 1.0 - (x / (t * (z - y)))
	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 ((t <= -5.2e-127) || !(t <= 9e-27))
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	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 ((t <= -5.2e-127) || ~((t <= 9e-27)))
		tmp = 1.0 - (x / (t * (z - y)));
	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[Or[LessEqual[t, -5.2e-127], N[Not[LessEqual[t, 9e-27]], $MachinePrecision]], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999982e-127 or 9.0000000000000003e-27 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 95.7%

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

      1. associate-*r* 95.7%

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

      2. mul-1-neg 95.7%

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

   4. Simplified 95.7%

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

      1. clear-num 95.6%

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

      2. div-inv 95.6%

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

      3. clear-num 95.7%

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

      4. distribute-lft-neg-out 95.7%

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

      5. distribute-rgt-neg-in 95.7%

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

      6. associate-/r* 95.0%

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

      7. sub-neg 95.0%

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

      8. +-commutative 95.0%

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

      9. distribute-neg-in 95.0%

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

      10. remove-double-neg 95.0%

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

   6. Applied egg-rr 95.0%

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

      1. *-lft-identity 95.0%

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

      2. associate-/l/ 95.7%

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

      3. unsub-neg 95.7%

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

   8. Simplified 95.7%

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

   if -5.19999999999999982e-127 < t < 9.0000000000000003e-27

   1. Initial program 95.2%

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

   2. Taylor expanded in t around 0 85.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-127} \lor \neg \left(t \leq 9 \cdot 10^{-27}\right):\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 5: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-43} \lor \neg \left(y \leq 10^{-98}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t - y}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e-43) (not (<= y 1e-98)))
   (- 1.0 (/ x (* y (- y t))))
   (- 1.0 (/ (/ x (- t y)) z))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e-43) || !(y <= 1e-98)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} 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 ((y <= (-3d-43)) .or. (.not. (y <= 1d-98))) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    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 ((y <= -3e-43) || !(y <= 1e-98)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} 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 (y <= -3e-43) or not (y <= 1e-98):
		tmp = 1.0 - (x / (y * (y - t)))
	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 ((y <= -3e-43) || !(y <= 1e-98))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(t - 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 <= -3e-43) || ~((y <= 1e-98)))
		tmp = 1.0 - (x / (y * (y - t)));
	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[Or[LessEqual[y, -3e-43], N[Not[LessEqual[y, 1e-98]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000003e-43 or 9.99999999999999939e-99 < 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 95.7%

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

   if -3.00000000000000003e-43 < y < 9.99999999999999939e-99

   1. Initial program 95.1%

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

      1. associate-/r* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around 0 89.2%

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

      1. mul-1-neg 89.2%

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

   6. Simplified 89.2%

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

      1. distribute-frac-neg 89.2%

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

      2. neg-sub0 89.2%

         \[\leadsto 1 - \color{blue}{\left(0 - \frac{\frac{x}{z}}{y - t}\right)} \]

      3. sub-neg 89.2%

         \[\leadsto 1 - \color{blue}{\left(0 + \left(-\frac{\frac{x}{z}}{y - t}\right)\right)} \]

      4. frac-2neg 89.2%

         \[\leadsto 1 - \left(0 + \left(-\frac{\color{blue}{\frac{-x}{-z}}}{y - t}\right)\right) \]

      5. associate-/l/ 89.2%

         \[\leadsto 1 - \left(0 + \left(-\color{blue}{\frac{-x}{\left(y - t\right) \cdot \left(-z\right)}}\right)\right) \]

      6. distribute-neg-frac 89.2%

         \[\leadsto 1 - \left(0 + \color{blue}{\frac{-\left(-x\right)}{\left(y - t\right) \cdot \left(-z\right)}}\right) \]

      7. remove-double-neg 89.2%

         \[\leadsto 1 - \left(0 + \frac{\color{blue}{x}}{\left(y - t\right) \cdot \left(-z\right)}\right) \]

      8. neg-mul-1 89.2%

         \[\leadsto 1 - \left(0 + \frac{x}{\left(y - t\right) \cdot \color{blue}{\left(-1 \cdot z\right)}}\right) \]

      9. metadata-eval 89.2%

         \[\leadsto 1 - \left(0 + \frac{x}{\left(y - t\right) \cdot \left(\color{blue}{\left(-1\right)} \cdot z\right)}\right) \]

      10. associate-*r* 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\color{blue}{\left(\left(y - t\right) \cdot \left(-1\right)\right) \cdot z}}\right) \]

      11. *-commutative 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\color{blue}{\left(\left(-1\right) \cdot \left(y - t\right)\right)} \cdot z}\right) \]

      12. metadata-eval 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\left(\color{blue}{-1} \cdot \left(y - t\right)\right) \cdot z}\right) \]

      13. neg-mul-1 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\color{blue}{\left(-\left(y - t\right)\right)} \cdot z}\right) \]

      14. neg-sub0 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\color{blue}{\left(0 - \left(y - t\right)\right)} \cdot z}\right) \]

      15. sub-neg 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\left(0 - \color{blue}{\left(y + \left(-t\right)\right)}\right) \cdot z}\right) \]

      16. +-commutative 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\left(0 - \color{blue}{\left(\left(-t\right) + y\right)}\right) \cdot z}\right) \]

      17. associate--r+ 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\color{blue}{\left(\left(0 - \left(-t\right)\right) - y\right)} \cdot z}\right) \]

      18. neg-sub0 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\left(\color{blue}{\left(-\left(-t\right)\right)} - y\right) \cdot z}\right) \]

      19. remove-double-neg 89.2%

          \[\leadsto 1 - \left(0 + \frac{x}{\left(\color{blue}{t} - y\right) \cdot z}\right) \]

   8. Applied egg-rr 89.2%

      \[\leadsto 1 - \color{blue}{\left(0 + \frac{x}{\left(t - y\right) \cdot z}\right)} \]
   9. Step-by-step derivation

      1. +-lft-identity 89.2%

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

      2. associate-/r* 87.4%

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

   10. Simplified 87.4%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-43} \lor \neg \left(y \leq 10^{-98}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t - y}}{z}\\ \end{array} \]

Alternative 6: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-44} \lor \neg \left(y \leq 7.8 \cdot 10^{-97}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

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 -2.95e-44) (not (<= y 7.8e-97)))
   (- 1.0 (/ x (* y (- y t))))
   (+ 1.0 (/ (/ x z) (- y t)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.95e-44) || !(y <= 7.8e-97)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / z) / (y - 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 <= (-2.95d-44)) .or. (.not. (y <= 7.8d-97))) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 + ((x / z) / (y - 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 <= -2.95e-44) || !(y <= 7.8e-97)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / z) / (y - t));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -2.95e-44) or not (y <= 7.8e-97):
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 + ((x / z) / (y - t))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.95e-44) || !(y <= 7.8e-97))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - 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 <= -2.95e-44) || ~((y <= 7.8e-97)))
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 + ((x / z) / (y - 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, -2.95e-44], N[Not[LessEqual[y, 7.8e-97]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.95000000000000018e-44 or 7.7999999999999997e-97 < 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 95.7%

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

   if -2.95000000000000018e-44 < y < 7.7999999999999997e-97

   1. Initial program 95.1%

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

      1. associate-/r* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around 0 89.2%

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

      1. mul-1-neg 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-44} \lor \neg \left(y \leq 7.8 \cdot 10^{-97}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 7: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-9} \lor \neg \left(y \leq 90\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

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 -1.9e-9) (not (<= y 90.0)))
   (- 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 <= -1.9e-9) || !(y <= 90.0)) {
		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 <= (-1.9d-9)) .or. (.not. (y <= 90.0d0))) 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 <= -1.9e-9) || !(y <= 90.0)) {
		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 <= -1.9e-9) or not (y <= 90.0):
		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 <= -1.9e-9) || !(y <= 90.0))
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(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 <= -1.9e-9) || ~((y <= 90.0)))
		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, -1.9e-9], N[Not[LessEqual[y, 90.0]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000006e-9 or 90 < y

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. metadata-eval 100.0%

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

      4. sqr-pow 87.6%

         \[\leadsto 1 - \color{blue}{{\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)}} \]

      5. div-inv 87.6%

         \[\leadsto 1 - {\color{blue}{\left(\left(\left(y - z\right) \cdot \left(y - t\right)\right) \cdot \frac{1}{x}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      6. associate-*l* 79.8%

         \[\leadsto 1 - {\color{blue}{\left(\left(y - z\right) \cdot \left(\left(y - t\right) \cdot \frac{1}{x}\right)\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      7. div-inv 79.8%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \color{blue}{\frac{y - t}{x}}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      8. metadata-eval 79.8%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 79.8%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. div-inv 79.8%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\left(\left(y - z\right) \cdot \left(y - t\right)\right) \cdot \frac{1}{x}\right)}}^{\left(\frac{-1}{2}\right)} \]

      11. associate-*l* 79.8%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\left(y - z\right) \cdot \left(\left(y - t\right) \cdot \frac{1}{x}\right)\right)}}^{\left(\frac{-1}{2}\right)} \]

      12. div-inv 79.8%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \color{blue}{\frac{y - t}{x}}\right)}^{\left(\frac{-1}{2}\right)} \]

      13. metadata-eval 79.8%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \]

      14. metadata-eval 79.8%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 79.8%

      \[\leadsto 1 - \color{blue}{{\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. pow-sqr 100.0%

         \[\leadsto 1 - \color{blue}{{\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 100.0%

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

      3. unpow-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 94.4%

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

      1. unpow2 94.4%

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

   8. Simplified 94.4%

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

   if -1.90000000000000006e-9 < y < 90

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 76.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-9} \lor \neg \left(y \leq 90\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 8: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-9}:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot y}{x}}\\ \mathbf{elif}\;y \leq 23500:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-9)
   (+ 1.0 (/ -1.0 (/ (* y y) x)))
   (if (<= y 23500.0) (- 1.0 (/ x (* z t))) (- 1.0 (/ x (* y y))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-9) {
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	} else if (y <= 23500.0) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - (x / (y * 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 (y <= (-3.4d-9)) then
        tmp = 1.0d0 + ((-1.0d0) / ((y * y) / x))
    else if (y <= 23500.0d0) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 - (x / (y * 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 (y <= -3.4e-9) {
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	} else if (y <= 23500.0) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-9:
		tmp = 1.0 + (-1.0 / ((y * y) / x))
	elif y <= 23500.0:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 - (x / (y * y))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-9)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(Float64(y * y) / x)));
	elseif (y <= 23500.0)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-9)
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	elseif (y <= 23500.0)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 - (x / (y * 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[y, -3.4e-9], N[(1.0 + N[(-1.0 / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 23500.0], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3999999999999998e-9

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. metadata-eval 100.0%

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

      4. sqr-pow 85.3%

         \[\leadsto 1 - \color{blue}{{\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)}} \]

      5. div-inv 85.3%

         \[\leadsto 1 - {\color{blue}{\left(\left(\left(y - z\right) \cdot \left(y - t\right)\right) \cdot \frac{1}{x}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      6. associate-*l* 76.5%

         \[\leadsto 1 - {\color{blue}{\left(\left(y - z\right) \cdot \left(\left(y - t\right) \cdot \frac{1}{x}\right)\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      7. div-inv 76.5%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \color{blue}{\frac{y - t}{x}}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      8. metadata-eval 76.5%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 76.5%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. div-inv 76.5%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\left(\left(y - z\right) \cdot \left(y - t\right)\right) \cdot \frac{1}{x}\right)}}^{\left(\frac{-1}{2}\right)} \]

      11. associate-*l* 76.5%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\left(y - z\right) \cdot \left(\left(y - t\right) \cdot \frac{1}{x}\right)\right)}}^{\left(\frac{-1}{2}\right)} \]

      12. div-inv 76.5%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \color{blue}{\frac{y - t}{x}}\right)}^{\left(\frac{-1}{2}\right)} \]

      13. metadata-eval 76.5%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \]

      14. metadata-eval 76.5%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 76.5%

      \[\leadsto 1 - \color{blue}{{\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. pow-sqr 100.0%

         \[\leadsto 1 - \color{blue}{{\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 100.0%

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

      3. unpow-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 93.8%

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

      1. unpow2 93.8%

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

   8. Simplified 93.8%

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

   if -3.3999999999999998e-9 < y < 23500

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 76.4%

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

   if 23500 < y

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. metadata-eval 100.0%

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

      4. sqr-pow 90.1%

         \[\leadsto 1 - \color{blue}{{\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)}} \]

      5. div-inv 90.1%

         \[\leadsto 1 - {\color{blue}{\left(\left(\left(y - z\right) \cdot \left(y - t\right)\right) \cdot \frac{1}{x}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      6. associate-*l* 83.6%

         \[\leadsto 1 - {\color{blue}{\left(\left(y - z\right) \cdot \left(\left(y - t\right) \cdot \frac{1}{x}\right)\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      7. div-inv 83.6%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \color{blue}{\frac{y - t}{x}}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      8. metadata-eval 83.6%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 83.6%

         \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. div-inv 83.6%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\left(\left(y - z\right) \cdot \left(y - t\right)\right) \cdot \frac{1}{x}\right)}}^{\left(\frac{-1}{2}\right)} \]

      11. associate-*l* 83.6%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\left(y - z\right) \cdot \left(\left(y - t\right) \cdot \frac{1}{x}\right)\right)}}^{\left(\frac{-1}{2}\right)} \]

      12. div-inv 83.6%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \color{blue}{\frac{y - t}{x}}\right)}^{\left(\frac{-1}{2}\right)} \]

      13. metadata-eval 83.6%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \]

      14. metadata-eval 83.6%

          \[\leadsto 1 - {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 83.6%

      \[\leadsto 1 - \color{blue}{{\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5} \cdot {\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. pow-sqr 100.0%

         \[\leadsto 1 - \color{blue}{{\left(\left(y - z\right) \cdot \frac{y - t}{x}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 100.0%

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

      3. unpow-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 95.2%

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

      1. unpow2 95.2%

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

   8. Simplified 95.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-9}:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot y}{x}}\\ \mathbf{elif}\;y \leq 23500:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \]

Alternative 9: 98.9% 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 98.1%

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

2. Final simplification 98.1%

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

Alternative 10: 60.8% accurate, 1.6× speedup

Math

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

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 (* z t))))

C

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

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 / (z * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 98.1%

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

2. Taylor expanded in y around 0 65.3%

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

3. Final simplification 65.3%

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

Reproduce

herbie shell --seed 2023297 
(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)))))