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

Percentage Accurate: 99.2% → 99.2%

Time: 8.8s

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 99.0%

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

3. Final simplification 99.0%

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

Alternative 2: 83.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-136}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-183}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-132}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-62}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-136)
   1.0
   (if (<= y 1.85e-183)
     (- 1.0 (/ x (* z t)))
     (if (<= y 5.6e-132)
       (+ 1.0 (/ x (* y t)))
       (if (<= y 6.4e-62) (- 1.0 (/ (/ x t) z)) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-136) {
		tmp = 1.0;
	} else if (y <= 1.85e-183) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 5.6e-132) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 6.4e-62) {
		tmp = 1.0 - ((x / t) / 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 (y <= (-1.7d-136)) then
        tmp = 1.0d0
    else if (y <= 1.85d-183) then
        tmp = 1.0d0 - (x / (z * t))
    else if (y <= 5.6d-132) then
        tmp = 1.0d0 + (x / (y * t))
    else if (y <= 6.4d-62) then
        tmp = 1.0d0 - ((x / t) / 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 (y <= -1.7e-136) {
		tmp = 1.0;
	} else if (y <= 1.85e-183) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 5.6e-132) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 6.4e-62) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e-136:
		tmp = 1.0
	elif y <= 1.85e-183:
		tmp = 1.0 - (x / (z * t))
	elif y <= 5.6e-132:
		tmp = 1.0 + (x / (y * t))
	elif y <= 6.4e-62:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e-136)
		tmp = 1.0;
	elseif (y <= 1.85e-183)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (y <= 5.6e-132)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	elseif (y <= 6.4e-62)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-136)
		tmp = 1.0;
	elseif (y <= 1.85e-183)
		tmp = 1.0 - (x / (z * t));
	elseif (y <= 5.6e-132)
		tmp = 1.0 + (x / (y * t));
	elseif (y <= 6.4e-62)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e-136], 1.0, If[LessEqual[y, 1.85e-183], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-132], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-62], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7e-136 or 6.40000000000000043e-62 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 88.9%

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

   4. Taylor expanded in y around 0 70.2%

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

      1. associate-*r/ 70.2%

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

      2. neg-mul-1 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in x around 0 85.2%

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

   if -1.7e-136 < y < 1.8499999999999999e-183

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 80.6%

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

   if 1.8499999999999999e-183 < y < 5.60000000000000005e-132

   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 64.0%

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

      1. associate-/r* 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in y around 0 64.0%

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

      1. associate-*r/ 64.0%

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

      2. mul-1-neg 64.0%

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

      3. *-commutative 64.0%

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

   8. Simplified 64.0%

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

   if 5.60000000000000005e-132 < y < 6.40000000000000043e-62

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0 71.2%

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

      1. associate-/r* 76.0%

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

      2. div-inv 76.0%

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

   5. Applied egg-rr 76.0%

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

      1. un-div-inv 76.0%

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

   7. Applied egg-rr 76.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-136}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-183}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-132}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-62}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-76} \lor \neg \left(y \leq 1.85 \cdot 10^{-183}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.32e-76) (not (<= y 1.85e-183)))
   (+ 1.0 (/ x (* y (- t y))))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.32e-76) || !(y <= 1.85e-183)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.32d-76)) .or. (.not. (y <= 1.85d-183))) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.32e-76) || !(y <= 1.85e-183)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.32e-76) or not (y <= 1.85e-183):
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.32e-76) || !(y <= 1.85e-183))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.32e-76) || ~((y <= 1.85e-183)))
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.32e-76], N[Not[LessEqual[y, 1.85e-183]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.31999999999999996e-76 or 1.8499999999999999e-183 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 89.9%

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

   if -1.31999999999999996e-76 < y < 1.8499999999999999e-183

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 79.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-76} \lor \neg \left(y \leq 1.85 \cdot 10^{-183}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-37}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e-37)
   (+ 1.0 (/ x (* y (- z y))))
   (if (<= z 3.5e-16) (+ 1.0 (/ x (* y (- t y)))) (- 1.0 (/ (/ x t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-37) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else if (z <= 3.5e-16) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - ((x / t) / 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 (z <= (-1.1d-37)) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else if (z <= 3.5d-16) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-37) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else if (z <= 3.5e-16) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e-37:
		tmp = 1.0 + (x / (y * (z - y)))
	elif z <= 3.5e-16:
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e-37)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	elseif (z <= 3.5e-16)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e-37)
		tmp = 1.0 + (x / (y * (z - y)));
	elseif (z <= 3.5e-16)
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e-37], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-16], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000001e-37

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0 83.5%

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

   if -1.10000000000000001e-37 < z < 3.50000000000000017e-16

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 85.4%

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

   if 3.50000000000000017e-16 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.5%

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

      1. associate-/r* 76.2%

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

      2. div-inv 76.1%

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

   5. Applied egg-rr 76.1%

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

      1. un-div-inv 76.2%

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

   7. Applied egg-rr 76.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-37}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-105}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-177}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.1e-105)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 3.5e-177)
     (+ 1.0 (/ x (* y (- t y))))
     (+ 1.0 (/ x (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.1e-105) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.5e-177) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.1d-105)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 3.5d-177) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.1e-105) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.5e-177) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.1e-105:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 3.5e-177:
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.1e-105)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 3.5e-177)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.1e-105)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 3.5e-177)
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.1e-105], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-177], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.09999999999999985e-105

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 92.4%

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

      1. mul-1-neg 92.4%

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

      2. associate-/r* 92.8%

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

      3. distribute-neg-frac 92.8%

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

   5. Simplified 92.8%

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

   if -6.09999999999999985e-105 < z < 3.5000000000000002e-177

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 91.6%

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

   if 3.5000000000000002e-177 < z

   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 82.4%

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

      1. associate-*r/ 82.4%

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

      2. neg-mul-1 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-105}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-177}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-106}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-177}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.4e-106)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 3.5e-177)
     (+ 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 (z <= -3.4e-106) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.5e-177) {
		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 (z <= (-3.4d-106)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 3.5d-177) 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 (z <= -3.4e-106) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.5e-177) {
		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 z <= -3.4e-106:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 3.5e-177:
		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 (z <= -3.4e-106)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 3.5e-177)
		tmp = Float64(1.0 + Float64(x / Float64(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 (z <= -3.4e-106)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 3.5e-177)
		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[z, -3.4e-106], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-177], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $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 z < -3.39999999999999982e-106

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 92.4%

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

      1. mul-1-neg 92.4%

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

      2. associate-/r* 92.8%

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

      3. distribute-neg-frac 92.8%

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

   5. Simplified 92.8%

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

   if -3.39999999999999982e-106 < z < 3.5000000000000002e-177

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 91.6%

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

   if 3.5000000000000002e-177 < z

   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. associate-/r* 96.2%

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

      2. div-inv 96.2%

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

   4. Applied egg-rr 96.2%

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

      1. associate-*l/ 98.1%

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

      2. un-div-inv 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in y around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. mul-1-neg 81.5%

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

   9. Simplified 81.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-106}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-177}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-158}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e-137) 1.0 (if (<= y 3.4e-158) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e-137) {
		tmp = 1.0;
	} else if (y <= 3.4e-158) {
		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 <= (-3.8d-137)) then
        tmp = 1.0d0
    else if (y <= 3.4d-158) 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 <= -3.8e-137) {
		tmp = 1.0;
	} else if (y <= 3.4e-158) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e-137:
		tmp = 1.0
	elif y <= 3.4e-158:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e-137)
		tmp = 1.0;
	elseif (y <= 3.4e-158)
		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 <= -3.8e-137)
		tmp = 1.0;
	elseif (y <= 3.4e-158)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.8e-137], 1.0, If[LessEqual[y, 3.4e-158], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999999e-137 or 3.3999999999999999e-158 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 85.5%

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

   4. Taylor expanded in y around 0 67.6%

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

      1. associate-*r/ 67.6%

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

      2. neg-mul-1 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in x around 0 83.0%

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

   if -3.79999999999999999e-137 < y < 3.3999999999999999e-158

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 77.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-158}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.65 \cdot 10^{-52}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.65e-52) (+ 1.0 (/ x (* y (- z y)))) (+ 1.0 (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.65e-52) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.65d-52) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.65e-52) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.65e-52:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.65e-52)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.65e-52)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.65e-52], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.64999999999999998e-52

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 78.3%

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

   if 1.64999999999999998e-52 < t

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 96.8%

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

      1. associate-*r/ 96.8%

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

      2. neg-mul-1 96.8%

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

   5. Simplified 96.8%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.65 \cdot 10^{-52}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.8 \cdot 10^{-163}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.8e-163) (+ 1.0 (/ x (* y z))) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.8e-163) {
		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 <= 2.8d-163) 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 <= 2.8e-163) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.8e-163:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.8e-163)
		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 <= 2.8e-163)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.8e-163], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < 2.8e-163

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 78.5%

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

   4. Taylor expanded in y around 0 65.6%

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

      1. associate-*r/ 65.6%

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

      2. neg-mul-1 65.6%

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

   6. Simplified 65.6%

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

   7. Taylor expanded in x around 0 65.6%

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

   if 2.8e-163 < t

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 63.1%

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

   4. Taylor expanded in y around 0 51.8%

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

      1. associate-*r/ 51.8%

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

      2. neg-mul-1 51.8%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in x around 0 76.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.8 \cdot 10^{-163}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.8% 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 99.0%

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

3. Taylor expanded in t around 0 72.4%

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

4. Taylor expanded in y around 0 60.2%

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

   1. associate-*r/ 60.2%

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

   2. neg-mul-1 60.2%

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

6. Simplified 60.2%

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

7. Taylor expanded in x around 0 72.0%

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

8. Final simplification 72.0%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(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)))))