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

Percentage Accurate: 99.0% → 98.4%

Time: 9.9s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 - pow(((y - t) / (x / (y - z))), -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 - (((y - t) / (x / (y - z))) ** (-1.0d0))
end function

Java

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

Python

def code(x, y, z, t):
	return 1.0 - math.pow(((y - t) / (x / (y - z))), -1.0)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

   1. clear-num 98.2%

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

   2. inv-pow 98.2%

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

   3. *-commutative 98.2%

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

   4. associate-/l* 98.8%

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

3. Applied egg-rr 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-197}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-137}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-39)
   1.0
   (if (<= y 9.8e-197)
     (- 1.0 (/ x (* t z)))
     (if (<= y 4.4e-137) (+ 1.0 (/ x (* y z))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-39) {
		tmp = 1.0;
	} else if (y <= 9.8e-197) {
		tmp = 1.0 - (x / (t * z));
	} else if (y <= 4.4e-137) {
		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 (y <= (-2.5d-39)) then
        tmp = 1.0d0
    else if (y <= 9.8d-197) then
        tmp = 1.0d0 - (x / (t * z))
    else if (y <= 4.4d-137) 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 (y <= -2.5e-39) {
		tmp = 1.0;
	} else if (y <= 9.8e-197) {
		tmp = 1.0 - (x / (t * z));
	} else if (y <= 4.4e-137) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-39:
		tmp = 1.0
	elif y <= 9.8e-197:
		tmp = 1.0 - (x / (t * z))
	elif y <= 4.4e-137:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-39)
		tmp = 1.0;
	elseif (y <= 9.8e-197)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	elseif (y <= 4.4e-137)
		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 (y <= -2.5e-39)
		tmp = 1.0;
	elseif (y <= 9.8e-197)
		tmp = 1.0 - (x / (t * z));
	elseif (y <= 4.4e-137)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-39], 1.0, If[LessEqual[y, 9.8e-197], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-137], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999999e-39 or 4.4000000000000002e-137 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 91.2%

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

   3. Taylor expanded in x around 0 88.4%

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

   if -2.4999999999999999e-39 < y < 9.8000000000000004e-197

   1. Initial program 94.2%

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

   2. Taylor expanded in y around 0 78.2%

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

   if 9.8000000000000004e-197 < y < 4.4000000000000002e-137

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 59.8%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-197}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-137}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-197}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-140}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-38)
   1.0
   (if (<= y 9.8e-197)
     (- 1.0 (/ (/ x t) z))
     (if (<= y 3.5e-140) (+ 1.0 (/ x (* y z))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-38) {
		tmp = 1.0;
	} else if (y <= 9.8e-197) {
		tmp = 1.0 - ((x / t) / z);
	} else if (y <= 3.5e-140) {
		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 (y <= (-1.05d-38)) then
        tmp = 1.0d0
    else if (y <= 9.8d-197) then
        tmp = 1.0d0 - ((x / t) / z)
    else if (y <= 3.5d-140) 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 (y <= -1.05e-38) {
		tmp = 1.0;
	} else if (y <= 9.8e-197) {
		tmp = 1.0 - ((x / t) / z);
	} else if (y <= 3.5e-140) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-38:
		tmp = 1.0
	elif y <= 9.8e-197:
		tmp = 1.0 - ((x / t) / z)
	elif y <= 3.5e-140:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-38)
		tmp = 1.0;
	elseif (y <= 9.8e-197)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	elseif (y <= 3.5e-140)
		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 (y <= -1.05e-38)
		tmp = 1.0;
	elseif (y <= 9.8e-197)
		tmp = 1.0 - ((x / t) / z);
	elseif (y <= 3.5e-140)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e-38], 1.0, If[LessEqual[y, 9.8e-197], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-140], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000006e-38 or 3.4999999999999998e-140 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 91.2%

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

   3. Taylor expanded in x around 0 88.4%

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

   if -1.05000000000000006e-38 < y < 9.8000000000000004e-197

   1. Initial program 94.2%

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

      1. clear-num 94.2%

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

      2. inv-pow 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-/l* 96.3%

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

   3. Applied egg-rr 96.3%

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

   4. Taylor expanded in y around 0 78.2%

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

      1. associate-/r* 78.5%

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

   6. Simplified 78.5%

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

   if 9.8000000000000004e-197 < y < 3.4999999999999998e-140

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 59.8%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-197}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-140}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-13}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-197}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-139}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-13)
   (- 1.0 (/ (/ x y) y))
   (if (<= y 9.8e-197)
     (- 1.0 (/ (/ x t) z))
     (if (<= y 2e-139) (+ 1.0 (/ x (* y z))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-13) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 9.8e-197) {
		tmp = 1.0 - ((x / t) / z);
	} else if (y <= 2e-139) {
		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 (y <= (-9d-13)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (y <= 9.8d-197) then
        tmp = 1.0d0 - ((x / t) / z)
    else if (y <= 2d-139) 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 (y <= -9e-13) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 9.8e-197) {
		tmp = 1.0 - ((x / t) / z);
	} else if (y <= 2e-139) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e-13:
		tmp = 1.0 - ((x / y) / y)
	elif y <= 9.8e-197:
		tmp = 1.0 - ((x / t) / z)
	elif y <= 2e-139:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e-13)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (y <= 9.8e-197)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	elseif (y <= 2e-139)
		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 (y <= -9e-13)
		tmp = 1.0 - ((x / y) / y);
	elseif (y <= 9.8e-197)
		tmp = 1.0 - ((x / t) / z);
	elseif (y <= 2e-139)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e-13], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-197], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-139], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 4 regimes

2. if y < -9e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/r* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 96.9%

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

   if -9e-13 < y < 9.8000000000000004e-197

   1. Initial program 94.8%

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

      1. clear-num 94.8%

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

      2. inv-pow 94.8%

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

      3. *-commutative 94.8%

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

      4. associate-/l* 96.7%

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

   3. Applied egg-rr 96.7%

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

   4. Taylor expanded in y around 0 78.1%

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

      1. associate-/r* 78.5%

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

   6. Simplified 78.5%

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

   if 9.8000000000000004e-197 < y < 2.00000000000000006e-139

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 59.8%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   if 2.00000000000000006e-139 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 85.6%

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

   3. Taylor expanded in x around 0 85.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-13}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-197}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-139}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-12} \lor \neg \left(y \leq 0.225\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.8e-12) (not (<= y 0.225)))
   (- 1.0 (/ (/ x y) y))
   (+ 1.0 (/ x (* (- y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.8e-12) || !(y <= 0.225)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 + (x / ((y - 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 ((y <= (-9.8d-12)) .or. (.not. (y <= 0.225d0))) then
        tmp = 1.0d0 - ((x / y) / y)
    else
        tmp = 1.0d0 + (x / ((y - t) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.8e-12) || !(y <= 0.225)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 + (x / ((y - t) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.8e-12) or not (y <= 0.225):
		tmp = 1.0 - ((x / y) / y)
	else:
		tmp = 1.0 + (x / ((y - t) * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.8e-12) || !(y <= 0.225))
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.8e-12) || ~((y <= 0.225)))
		tmp = 1.0 - ((x / y) / y);
	else
		tmp = 1.0 + (x / ((y - t) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.8e-12], N[Not[LessEqual[y, 0.225]], $MachinePrecision]], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.79999999999999944e-12 or 0.225000000000000006 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 97.7%

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

      1. *-commutative 97.7%

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

      2. associate-/r* 97.7%

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

   4. Simplified 97.7%

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

   5. Taylor expanded in y around inf 95.8%

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

   if -9.79999999999999944e-12 < y < 0.225000000000000006

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

      3. *-commutative 78.2%

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

   4. Simplified 78.2%

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

      1. div-inv 78.2%

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

      2. cancel-sign-sub 78.2%

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

      3. div-inv 78.2%

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

      4. +-commutative 78.2%

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

   6. Applied egg-rr 78.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-12} \lor \neg \left(y \leq 0.225\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]

Alternative 6: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-37}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e-71)
   (+ 1.0 (/ x (* (- y t) z)))
   (if (<= z 7e-37) (- 1.0 (/ x (* y (- y t)))) (- 1.0 (/ x (* t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e-71) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 7e-37) {
		tmp = 1.0 - (x / (y * (y - t)));
	} 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 <= (-5.2d-71)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else if (z <= 7d-37) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    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 <= -5.2e-71) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 7e-37) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e-71:
		tmp = 1.0 + (x / ((y - t) * z))
	elif z <= 7e-37:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 - (x / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e-71)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	elseif (z <= 7e-37)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e-71)
		tmp = 1.0 + (x / ((y - t) * z));
	elseif (z <= 7e-37)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 - (x / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e-71], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-37], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e-71

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 96.5%

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

      1. associate-*r/ 96.5%

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

      2. neg-mul-1 96.5%

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

      3. *-commutative 96.5%

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

   4. Simplified 96.5%

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

      1. div-inv 96.5%

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

      2. cancel-sign-sub 96.5%

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

      3. div-inv 96.5%

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

      4. +-commutative 96.5%

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

   6. Applied egg-rr 96.5%

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

   if -5.1999999999999997e-71 < z < 7.0000000000000003e-37

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 86.1%

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

   if 7.0000000000000003e-37 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-37}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]

Alternative 7: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-36}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.2e-72)
   (+ 1.0 (/ x (* (- y t) z)))
   (if (<= z 2.3e-36) (- 1.0 (/ (/ x y) (- y t))) (- 1.0 (/ x (* t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.2e-72) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 2.3e-36) {
		tmp = 1.0 - ((x / y) / (y - t));
	} 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 <= (-3.2d-72)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else if (z <= 2.3d-36) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    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 <= -3.2e-72) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 2.3e-36) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.2e-72:
		tmp = 1.0 + (x / ((y - t) * z))
	elif z <= 2.3e-36:
		tmp = 1.0 - ((x / y) / (y - t))
	else:
		tmp = 1.0 - (x / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.2e-72)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	elseif (z <= 2.3e-36)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.2e-72)
		tmp = 1.0 + (x / ((y - t) * z));
	elseif (z <= 2.3e-36)
		tmp = 1.0 - ((x / y) / (y - t));
	else
		tmp = 1.0 - (x / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.2e-72], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-36], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999999e-72

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 96.5%

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

      1. associate-*r/ 96.5%

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

      2. neg-mul-1 96.5%

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

      3. *-commutative 96.5%

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

   4. Simplified 96.5%

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

      1. div-inv 96.5%

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

      2. cancel-sign-sub 96.5%

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

      3. div-inv 96.5%

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

      4. +-commutative 96.5%

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

   6. Applied egg-rr 96.5%

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

   if -3.19999999999999999e-72 < z < 2.29999999999999996e-36

   1. Initial program 95.4%

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

      1. clear-num 95.3%

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

      2. inv-pow 95.3%

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

      3. *-commutative 95.3%

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

      4. associate-/l* 97.0%

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

   3. Applied egg-rr 97.0%

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

   4. Taylor expanded in z around 0 86.1%

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

      1. associate-/r* 86.8%

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

   6. Simplified 86.8%

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

   if 2.29999999999999996e-36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-36}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]

Alternative 8: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.2e-71)
   (+ 1.0 (/ x (* (- y t) z)))
   (if (<= z 4.8e-36) (- 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 <= -3.2e-71) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 4.8e-36) {
		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 <= (-3.2d-71)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else if (z <= 4.8d-36) 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 <= -3.2e-71) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 4.8e-36) {
		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 <= -3.2e-71:
		tmp = 1.0 + (x / ((y - t) * z))
	elif z <= 4.8e-36:
		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 <= -3.2e-71)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	elseif (z <= 4.8e-36)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.2e-71)
		tmp = 1.0 + (x / ((y - t) * z));
	elseif (z <= 4.8e-36)
		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, -3.2e-71], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-36], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1999999999999999e-71

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 96.5%

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

      1. associate-*r/ 96.5%

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

      2. neg-mul-1 96.5%

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

      3. *-commutative 96.5%

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

   4. Simplified 96.5%

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

      1. div-inv 96.5%

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

      2. cancel-sign-sub 96.5%

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

      3. div-inv 96.5%

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

      4. +-commutative 96.5%

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

   6. Applied egg-rr 96.5%

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

   if -3.1999999999999999e-71 < z < 4.8e-36

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-/r* 87.9%

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

   4. Simplified 87.9%

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

   if 4.8e-36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.2%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]

Alternative 9: 87.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-160}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e-71)
   (+ 1.0 (/ x (* (- y t) z)))
   (if (<= z 6.5e-160)
     (- 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 <= -5e-71) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 6.5e-160) {
		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 <= (-5d-71)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else if (z <= 6.5d-160) 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 <= -5e-71) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 6.5e-160) {
		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 <= -5e-71:
		tmp = 1.0 + (x / ((y - t) * z))
	elif z <= 6.5e-160:
		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 <= -5e-71)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	elseif (z <= 6.5e-160)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	else
		tmp = Float64(1.0 + Float64(x / Float64(t * Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e-71)
		tmp = 1.0 + (x / ((y - t) * z));
	elseif (z <= 6.5e-160)
		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, -5e-71], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-160], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999998e-71

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 96.5%

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

      1. associate-*r/ 96.5%

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

      2. neg-mul-1 96.5%

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

      3. *-commutative 96.5%

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

   4. Simplified 96.5%

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

      1. div-inv 96.5%

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

      2. cancel-sign-sub 96.5%

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

      3. div-inv 96.5%

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

      4. +-commutative 96.5%

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

   6. Applied egg-rr 96.5%

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

   if -4.99999999999999998e-71 < z < 6.4999999999999996e-160

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-/r* 86.4%

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

   4. Simplified 86.4%

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

   if 6.4999999999999996e-160 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   4. Simplified 87.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-160}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 10: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 + ((x / (y - z)) * (-1.0 / (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)) * ((-1.0d0) / (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

   1. associate-/r* 98.8%

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

   2. div-inv 98.8%

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

3. Applied egg-rr 98.8%

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

4. Final simplification 98.8%

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

Alternative 11: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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 98.2%

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

2. Final simplification 98.2%

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

Alternative 12: 75.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+256}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.46e+256) (+ 1.0 (/ x (* y z))) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.46e+256) {
		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 (x <= (-1.46d+256)) 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 (x <= -1.46e+256) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.46e+256:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.46e+256)
		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 (x <= -1.46e+256)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.46e+256], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.46000000000000004e256

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 45.0%

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

   3. Taylor expanded in z around inf 45.0%

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

      1. +-commutative 45.0%

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

      2. *-commutative 45.0%

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

   5. Simplified 45.0%

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

   if -1.46000000000000004e256 < x

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 75.0%

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

   3. Taylor expanded in x around 0 77.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+256}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 73.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+165}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.1e+165) (/ (- x) (* t z)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.1e+165) {
		tmp = -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 (x <= (-1.1d+165)) then
        tmp = -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 (x <= -1.1e+165) {
		tmp = -x / (t * z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.1e+165:
		tmp = -x / (t * z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.1e+165)
		tmp = Float64(Float64(-x) / Float64(t * z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.1e+165)
		tmp = -x / (t * z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.1e+165], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e165

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

      3. *-commutative 64.9%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in x around inf 51.9%

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

      1. associate-/r* 43.4%

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

   7. Simplified 43.4%

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

   8. Taylor expanded in y around 0 47.1%

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

      1. mul-1-neg 47.1%

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

   10. Simplified 47.1%

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

   if -1.1e165 < x

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 75.7%

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

   3. Taylor expanded in x around 0 79.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+165}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14: 75.4% 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 98.2%

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

2. Taylor expanded in t around 0 74.0%

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

3. Taylor expanded in x around 0 75.1%

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

4. Final simplification 75.1%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023318 
(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)))))