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

Percentage Accurate: 99.2% → 99.2%

Time: 11.3s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Final simplification 99.6%

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

Alternative 2: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-173}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;1 + \frac{1}{\frac{y \cdot \left(z - y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.8e-173)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 1.55e-68)
     (+ 1.0 (/ 1.0 (/ (* y (- z y)) x)))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e-173) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.55e-68) {
		tmp = 1.0 + (1.0 / ((y * (z - y)) / x));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.8d-173)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.55d-68) then
        tmp = 1.0d0 + (1.0d0 / ((y * (z - y)) / x))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e-173) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.55e-68) {
		tmp = 1.0 + (1.0 / ((y * (z - y)) / x));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.8e-173:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.55e-68:
		tmp = 1.0 + (1.0 / ((y * (z - y)) / x))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.8e-173)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.55e-68)
		tmp = Float64(1.0 + Float64(1.0 / Float64(Float64(y * Float64(z - y)) / x)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.8e-173)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.55e-68)
		tmp = 1.0 + (1.0 / ((y * (z - y)) / x));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.8e-173], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-68], N[(1.0 + N[(1.0 / N[(N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7999999999999997e-173

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. associate-/r* 79.8%

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

   5. Simplified 79.8%

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

   if -5.7999999999999997e-173 < t < 1.55e-68

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. associate-/l* 99.0%

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

   4. Applied egg-rr 99.0%

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

      1. unpow-1 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in t around 0 88.6%

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

   if 1.55e-68 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 96.9%

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

      1. associate-/r* 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-173}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;1 + \frac{1}{\frac{y \cdot \left(z - y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.2 \cdot 10^{-176}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-72}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.2e-176)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 6.8e-72)
     (+ 1.0 (/ (/ x y) (- t y)))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.2e-176) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 6.8e-72) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 2.2d-176) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 6.8d-72) then
        tmp = 1.0d0 + ((x / y) / (t - y))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.2e-176) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 6.8e-72) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.2e-176:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 6.8e-72:
		tmp = 1.0 + ((x / y) / (t - y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.2e-176)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 6.8e-72)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.2e-176)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 6.8e-72)
		tmp = 1.0 + ((x / y) / (t - y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.2e-176], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-72], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.1999999999999999e-176

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. associate-/r* 82.4%

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

   5. Simplified 82.4%

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

   if 2.1999999999999999e-176 < t < 6.7999999999999997e-72

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.4%

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

      1. sub-neg 84.4%

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

      2. associate-/r* 84.5%

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

      3. distribute-neg-frac2 84.5%

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

      4. neg-sub0 84.5%

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

      5. sub-neg 84.5%

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

      6. +-commutative 84.5%

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

      7. associate--r+ 84.5%

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

      8. neg-sub0 84.5%

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

      9. remove-double-neg 84.5%

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

   5. Simplified 84.5%

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

   if 6.7999999999999997e-72 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 96.9%

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

      1. associate-/r* 97.0%

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

   5. Simplified 97.0%

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

Alternative 4: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.5 \cdot 10^{-174}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.5e-174)
   (+ 1.0 (/ x (* z (- y t))))
   (if (<= t 1.05e-67)
     (+ 1.0 (/ (/ x y) (- t y)))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.5e-174) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 1.05e-67) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.5d-174) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else if (t <= 1.05d-67) then
        tmp = 1.0d0 + ((x / y) / (t - y))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.5e-174) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 1.05e-67) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.5e-174:
		tmp = 1.0 + (x / (z * (y - t)))
	elif t <= 1.05e-67:
		tmp = 1.0 + ((x / y) / (t - y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.5e-174)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	elseif (t <= 1.05e-67)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.5e-174)
		tmp = 1.0 + (x / (z * (y - t)));
	elseif (t <= 1.05e-67)
		tmp = 1.0 + ((x / y) / (t - y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.5e-174], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-67], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.50000000000000011e-174

   1. Initial program 99.3%

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

      1. clear-num 99.3%

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

      2. inv-pow 99.3%

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

      3. associate-/l* 99.1%

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

   4. Applied egg-rr 99.1%

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

      1. unpow-1 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in z around inf 82.3%

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

   if 1.50000000000000011e-174 < t < 1.0500000000000001e-67

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.4%

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

      1. sub-neg 84.4%

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

      2. associate-/r* 84.5%

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

      3. distribute-neg-frac2 84.5%

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

      4. neg-sub0 84.5%

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

      5. sub-neg 84.5%

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

      6. +-commutative 84.5%

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

      7. associate--r+ 84.5%

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

      8. neg-sub0 84.5%

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

      9. remove-double-neg 84.5%

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

   5. Simplified 84.5%

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

   if 1.0500000000000001e-67 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 96.9%

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

      1. associate-/r* 97.0%

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

   5. Simplified 97.0%

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

Alternative 5: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{-175}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-74}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 6e-175)
   (+ 1.0 (/ x (* z (- y t))))
   (if (<= t 9.2e-74) (- 1.0 (/ (/ x y) y)) (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6e-175) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 9.2e-74) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 6d-175) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else if (t <= 9.2d-74) then
        tmp = 1.0d0 - ((x / y) / y)
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6e-175) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 9.2e-74) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 6e-175:
		tmp = 1.0 + (x / (z * (y - t)))
	elif t <= 9.2e-74:
		tmp = 1.0 - ((x / y) / y)
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6e-175)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	elseif (t <= 9.2e-74)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6e-175)
		tmp = 1.0 + (x / (z * (y - t)));
	elseif (t <= 9.2e-74)
		tmp = 1.0 - ((x / y) / y);
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 6e-175], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-74], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 6e-175

   1. Initial program 99.3%

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

      1. clear-num 99.3%

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

      2. inv-pow 99.3%

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

      3. associate-/l* 99.1%

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

   4. Applied egg-rr 99.1%

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

      1. unpow-1 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in z around inf 82.3%

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

   if 6e-175 < t < 9.19999999999999922e-74

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.4%

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

      1. sub-neg 84.4%

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

      2. associate-/r* 84.5%

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

      3. distribute-neg-frac2 84.5%

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

      4. neg-sub0 84.5%

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

      5. sub-neg 84.5%

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

      6. +-commutative 84.5%

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

      7. associate--r+ 84.5%

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

      8. neg-sub0 84.5%

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

      9. remove-double-neg 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in t around 0 84.6%

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

      1. neg-mul-1 84.6%

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

   8. Simplified 84.6%

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

   if 9.19999999999999922e-74 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 96.9%

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

      1. associate-/r* 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{-175}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-74}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-10}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+14}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e-10)
   (- 1.0 (/ (/ x y) y))
   (if (<= y 1.85e+14) (+ 1.0 (/ x (* z (- y t)))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-10) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 1.85e+14) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.3d-10)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (y <= 1.85d+14) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-10) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 1.85e+14) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e-10:
		tmp = 1.0 - ((x / y) / y)
	elif y <= 1.85e+14:
		tmp = 1.0 + (x / (z * (y - t)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e-10)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (y <= 1.85e+14)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e-10)
		tmp = 1.0 - ((x / y) / y);
	elseif (y <= 1.85e+14)
		tmp = 1.0 + (x / (z * (y - t)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e-10], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+14], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 95.0%

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

      1. sub-neg 95.0%

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

      2. associate-/r* 95.0%

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

      3. distribute-neg-frac2 95.0%

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

      4. neg-sub0 95.0%

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

      5. sub-neg 95.0%

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

      6. +-commutative 95.0%

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

      7. associate--r+ 95.0%

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

      8. neg-sub0 95.0%

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

      9. remove-double-neg 95.0%

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

   5. Simplified 95.0%

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

   6. Taylor expanded in t around 0 91.8%

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

      1. neg-mul-1 91.8%

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

   8. Simplified 91.8%

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

   if -3.3e-10 < y < 1.85e14

   1. Initial program 99.1%

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

      1. clear-num 99.1%

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

      2. inv-pow 99.1%

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

      3. associate-/l* 98.9%

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

   4. Applied egg-rr 98.9%

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

      1. unpow-1 98.9%

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

   6. Simplified 98.9%

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

   7. Taylor expanded in z around inf 82.1%

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

   if 1.85e14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-10}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+14}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-59}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-120}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-59)
   (- 1.0 (/ (/ x y) y))
   (if (<= y 6e-120) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-59) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 6e-120) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d-59)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (y <= 6d-120) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-59) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 6e-120) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-59:
		tmp = 1.0 - ((x / y) / y)
	elif y <= 6e-120:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-59)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (y <= 6e-120)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-59)
		tmp = 1.0 - ((x / y) / y);
	elseif (y <= 6e-120)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-59], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-120], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000018e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.1%

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

      1. sub-neg 94.1%

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

      2. associate-/r* 94.2%

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

      3. distribute-neg-frac2 94.2%

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

      4. neg-sub0 94.2%

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

      5. sub-neg 94.2%

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

      6. +-commutative 94.2%

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

      7. associate--r+ 94.2%

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

      8. neg-sub0 94.2%

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

      9. remove-double-neg 94.2%

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

   5. Simplified 94.2%

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

   6. Taylor expanded in t around 0 89.8%

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

      1. neg-mul-1 89.8%

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

   8. Simplified 89.8%

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

   if -3.40000000000000018e-59 < y < 6.00000000000000022e-120

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 82.5%

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

   if 6.00000000000000022e-120 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-59}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-120}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-118}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e-52) 1.0 (if (<= y 1e-118) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-52) {
		tmp = 1.0;
	} else if (y <= 1e-118) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3d-52)) then
        tmp = 1.0d0
    else if (y <= 1d-118) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-52) {
		tmp = 1.0;
	} else if (y <= 1e-118) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e-52:
		tmp = 1.0
	elif y <= 1e-118:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e-52)
		tmp = 1.0;
	elseif (y <= 1e-118)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3e-52)
		tmp = 1.0;
	elseif (y <= 1e-118)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e-52], 1.0, If[LessEqual[y, 1e-118], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3e-52 or 9.99999999999999985e-119 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.3%

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

   if -3e-52 < y < 9.99999999999999985e-119

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 82.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-118}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{-219}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.45e-219) (+ 1.0 (/ x (* y z))) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.45e-219) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.45d-219) then
        tmp = 1.0d0 + (x / (y * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.45e-219) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.45e-219:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.45e-219)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.45e-219)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.45e-219], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < 1.44999999999999992e-219

   1. Initial program 99.3%

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

      1. clear-num 99.3%

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

      2. inv-pow 99.3%

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

      3. associate-/l* 99.1%

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

   4. Applied egg-rr 99.1%

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

      1. unpow-1 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in z around inf 82.8%

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

   8. Taylor expanded in y around inf 63.3%

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

      1. *-commutative 63.3%

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

   10. Simplified 63.3%

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

   if 1.44999999999999992e-219 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.3%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{-219}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.1% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in x around 0 76.5%

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

Reproduce

herbie shell --seed 2024157 
(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)))))