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

Percentage Accurate: 99.1% → 99.1%

Time: 8.9s

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: 99.1% 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: 99.1% 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 99.7%

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

3. Final simplification 99.7%

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

Alternative 2: 77.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+168}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+32}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e+168)
   1.0
   (if (<= z -1.45e+32) (+ 1.0 (/ (/ x z) y)) (+ 1.0 (/ x (* y (- t y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+168) {
		tmp = 1.0;
	} else if (z <= -1.45e+32) {
		tmp = 1.0 + ((x / z) / y);
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	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 <= (-1.8d+168)) then
        tmp = 1.0d0
    else if (z <= (-1.45d+32)) then
        tmp = 1.0d0 + ((x / z) / y)
    else
        tmp = 1.0d0 + (x / (y * (t - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+168) {
		tmp = 1.0;
	} else if (z <= -1.45e+32) {
		tmp = 1.0 + ((x / z) / y);
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e+168:
		tmp = 1.0
	elif z <= -1.45e+32:
		tmp = 1.0 + ((x / z) / y)
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e+168)
		tmp = 1.0;
	elseif (z <= -1.45e+32)
		tmp = Float64(1.0 + Float64(Float64(x / z) / y));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e+168)
		tmp = 1.0;
	elseif (z <= -1.45e+32)
		tmp = 1.0 + ((x / z) / y);
	else
		tmp = 1.0 + (x / (y * (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e+168], 1.0, If[LessEqual[z, -1.45e+32], N[(1.0 + N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e168

   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 80.0%

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

      1. associate-*r/ 80.0%

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

      2. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in y around inf 52.8%

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

      1. associate-*r/ 52.8%

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

      2. mul-1-neg 52.8%

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

   8. Simplified 52.8%

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

      1. add-sqr-sqrt 22.5%

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

      2. sqrt-unprod 54.2%

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

      3. sqr-neg 54.2%

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

      4. sqrt-unprod 30.1%

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

      5. add-sqr-sqrt 52.5%

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

      6. *-un-lft-identity 52.5%

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

      7. *-commutative 52.5%

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

      8. associate-/r* 52.4%

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

   10. Applied egg-rr 52.4%

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

       1. *-lft-identity 52.4%

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

       2. associate-/l/ 52.5%

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

   12. Simplified 52.5%

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

   13. Taylor expanded in x around 0 87.4%

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

   if -1.8e168 < z < -1.45000000000000001e32

   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 81.8%

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

   4. Taylor expanded in y around 0 79.5%

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

      1. associate-*r/ 79.5%

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

      2. mul-1-neg 79.5%

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

      3. *-commutative 79.5%

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

   6. Simplified 79.5%

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

      1. div-inv 79.5%

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

      2. cancel-sign-sub 79.5%

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

      3. div-inv 79.5%

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

      4. +-commutative 79.5%

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

      5. associate-/r* 79.6%

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

   8. Applied egg-rr 79.6%

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

   if -1.45000000000000001e32 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 80.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+168}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+32}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-29}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.1e-14)
   1.0
   (if (<= t 4.8e-29)
     (+ 1.0 (/ x (* y (- z y))))
     (+ 1.0 (/ x (* y (- t y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-14) {
		tmp = 1.0;
	} else if (t <= 4.8e-29) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	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 <= (-2.1d-14)) then
        tmp = 1.0d0
    else if (t <= 4.8d-29) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + (x / (y * (t - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-14) {
		tmp = 1.0;
	} else if (t <= 4.8e-29) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e-14:
		tmp = 1.0
	elif t <= 4.8e-29:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.1e-14)
		tmp = 1.0;
	elseif (t <= 4.8e-29)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.1e-14)
		tmp = 1.0;
	elseif (t <= 4.8e-29)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + (x / (y * (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.1e-14], 1.0, If[LessEqual[t, 4.8e-29], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 94.4%

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

      1. associate-*r/ 94.4%

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

      2. neg-mul-1 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in y around inf 72.9%

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

      1. associate-*r/ 72.9%

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

      2. mul-1-neg 72.9%

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

   8. Simplified 72.9%

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

      1. add-sqr-sqrt 37.3%

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

      2. sqrt-unprod 61.4%

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

      3. sqr-neg 61.4%

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

      4. sqrt-unprod 34.0%

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

      5. add-sqr-sqrt 66.3%

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

      6. *-un-lft-identity 66.3%

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

      7. *-commutative 66.3%

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

      8. associate-/r* 66.2%

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

   10. Applied egg-rr 66.2%

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

       1. *-lft-identity 66.2%

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

       2. associate-/l/ 66.3%

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

   12. Simplified 66.3%

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

   13. Taylor expanded in x around 0 83.7%

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

   if -2.0999999999999999e-14 < t < 4.79999999999999984e-29

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 90.7%

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

   if 4.79999999999999984e-29 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 87.9%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-29}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-15}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e-13)
   1.0
   (if (<= t 2.1e-15)
     (- 1.0 (/ (/ x (- y z)) y))
     (+ 1.0 (/ x (* y (- t y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-13) {
		tmp = 1.0;
	} else if (t <= 2.1e-15) {
		tmp = 1.0 - ((x / (y - z)) / y);
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.5d-13)) then
        tmp = 1.0d0
    else if (t <= 2.1d-15) then
        tmp = 1.0d0 - ((x / (y - z)) / y)
    else
        tmp = 1.0d0 + (x / (y * (t - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-13) {
		tmp = 1.0;
	} else if (t <= 2.1e-15) {
		tmp = 1.0 - ((x / (y - z)) / y);
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e-13:
		tmp = 1.0
	elif t <= 2.1e-15:
		tmp = 1.0 - ((x / (y - z)) / y)
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e-13)
		tmp = 1.0;
	elseif (t <= 2.1e-15)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - z)) / y));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e-13)
		tmp = 1.0;
	elseif (t <= 2.1e-15)
		tmp = 1.0 - ((x / (y - z)) / y);
	else
		tmp = 1.0 + (x / (y * (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e-13], 1.0, If[LessEqual[t, 2.1e-15], N[(1.0 - N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.49999999999999992e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 94.4%

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

      1. associate-*r/ 94.4%

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

      2. neg-mul-1 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in y around inf 72.9%

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

      1. associate-*r/ 72.9%

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

      2. mul-1-neg 72.9%

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

   8. Simplified 72.9%

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

      1. add-sqr-sqrt 37.3%

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

      2. sqrt-unprod 61.4%

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

      3. sqr-neg 61.4%

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

      4. sqrt-unprod 34.0%

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

      5. add-sqr-sqrt 66.3%

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

      6. *-un-lft-identity 66.3%

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

      7. *-commutative 66.3%

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

      8. associate-/r* 66.2%

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

   10. Applied egg-rr 66.2%

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

       1. *-lft-identity 66.2%

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

       2. associate-/l/ 66.3%

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

   12. Simplified 66.3%

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

   13. Taylor expanded in x around 0 83.7%

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

   if -1.49999999999999992e-13 < t < 2.09999999999999981e-15

   1. Initial program 99.3%

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

      1. clear-num 99.3%

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

      2. associate-/r/ 99.0%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in t around 0 90.9%

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

      1. *-lft-identity 90.9%

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

      2. times-frac 91.0%

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

      3. associate-*l/ 91.0%

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

      4. *-lft-identity 91.0%

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

   7. Simplified 91.0%

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

   if 2.09999999999999981e-15 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 87.3%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-15}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 600000000000:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.25e-13)
   1.0
   (if (<= t 600000000000.0)
     (- 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 <= -1.25e-13) {
		tmp = 1.0;
	} else if (t <= 600000000000.0) {
		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 <= (-1.25d-13)) then
        tmp = 1.0d0
    else if (t <= 600000000000.0d0) 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 <= -1.25e-13) {
		tmp = 1.0;
	} else if (t <= 600000000000.0) {
		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 <= -1.25e-13:
		tmp = 1.0
	elif t <= 600000000000.0:
		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 <= -1.25e-13)
		tmp = 1.0;
	elseif (t <= 600000000000.0)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - 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 <= -1.25e-13)
		tmp = 1.0;
	elseif (t <= 600000000000.0)
		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, -1.25e-13], 1.0, If[LessEqual[t, 600000000000.0], N[(1.0 - N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $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 t < -1.24999999999999997e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 94.4%

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

      1. associate-*r/ 94.4%

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

      2. neg-mul-1 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in y around inf 72.9%

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

      1. associate-*r/ 72.9%

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

      2. mul-1-neg 72.9%

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

   8. Simplified 72.9%

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

      1. add-sqr-sqrt 37.3%

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

      2. sqrt-unprod 61.4%

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

      3. sqr-neg 61.4%

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

      4. sqrt-unprod 34.0%

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

      5. add-sqr-sqrt 66.3%

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

      6. *-un-lft-identity 66.3%

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

      7. *-commutative 66.3%

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

      8. associate-/r* 66.2%

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

   10. Applied egg-rr 66.2%

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

       1. *-lft-identity 66.2%

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

       2. associate-/l/ 66.3%

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

   12. Simplified 66.3%

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

   13. Taylor expanded in x around 0 83.7%

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

   if -1.24999999999999997e-13 < t < 6e11

   1. Initial program 99.3%

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

      1. clear-num 99.3%

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

      2. associate-/r/ 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in t around 0 91.3%

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

      1. *-lft-identity 91.3%

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

      2. times-frac 91.3%

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

      3. associate-*l/ 91.3%

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

      4. *-lft-identity 91.3%

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

   7. Simplified 91.3%

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

   if 6e11 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 97.2%

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

      1. associate-*r/ 97.2%

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

      2. neg-mul-1 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 600000000000:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-104}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 330000000000:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.1e-104)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 330000000000.0)
     (- 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 <= -3.1e-104) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 330000000000.0) {
		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 <= (-3.1d-104)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 330000000000.0d0) 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 <= -3.1e-104) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 330000000000.0) {
		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 <= -3.1e-104:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 330000000000.0:
		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 <= -3.1e-104)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 330000000000.0)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - 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 <= -3.1e-104)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 330000000000.0)
		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, -3.1e-104], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 330000000000.0], N[(1.0 - N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $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 t < -3.09999999999999976e-104

   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 inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. associate-/r* 78.0%

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

      3. distribute-neg-frac 78.0%

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

   5. Simplified 78.0%

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

   if -3.09999999999999976e-104 < t < 3.3e11

   1. Initial program 99.2%

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

      1. clear-num 99.2%

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

      2. associate-/r/ 98.9%

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

   4. Applied egg-rr 98.9%

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

   5. Taylor expanded in t around 0 91.7%

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

      1. *-lft-identity 91.7%

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

      2. times-frac 91.7%

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

      3. associate-*l/ 91.8%

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

      4. *-lft-identity 91.8%

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

   7. Simplified 91.8%

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

   if 3.3e11 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 97.2%

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

      1. associate-*r/ 97.2%

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

      2. neg-mul-1 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-104}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 330000000000:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-115}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.9e-115) 1.0 (if (<= t 8.2e-162) (+ 1.0 (/ (/ x z) y)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.9e-115) {
		tmp = 1.0;
	} else if (t <= 8.2e-162) {
		tmp = 1.0 + ((x / z) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.9d-115)) then
        tmp = 1.0d0
    else if (t <= 8.2d-162) then
        tmp = 1.0d0 + ((x / z) / y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.9e-115) {
		tmp = 1.0;
	} else if (t <= 8.2e-162) {
		tmp = 1.0 + ((x / z) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.9e-115:
		tmp = 1.0
	elif t <= 8.2e-162:
		tmp = 1.0 + ((x / z) / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.9e-115)
		tmp = 1.0;
	elseif (t <= 8.2e-162)
		tmp = Float64(1.0 + Float64(Float64(x / z) / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.9e-115)
		tmp = 1.0;
	elseif (t <= 8.2e-162)
		tmp = 1.0 + ((x / z) / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.9e-115], 1.0, If[LessEqual[t, 8.2e-162], N[(1.0 + N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.89999999999999996e-115 or 8.20000000000000039e-162 < t

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf 87.9%

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

      1. associate-*r/ 87.9%

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

      2. neg-mul-1 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in y around inf 69.9%

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

      1. associate-*r/ 69.9%

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

      2. mul-1-neg 69.9%

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

   8. Simplified 69.9%

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

      1. add-sqr-sqrt 35.4%

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

      2. sqrt-unprod 62.0%

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

      3. sqr-neg 62.0%

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

      4. sqrt-unprod 31.2%

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

      5. add-sqr-sqrt 62.9%

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

      6. *-un-lft-identity 62.9%

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

      7. *-commutative 62.9%

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

      8. associate-/r* 62.9%

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

   10. Applied egg-rr 62.9%

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

       1. *-lft-identity 62.9%

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

       2. associate-/l/ 62.9%

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

   12. Simplified 62.9%

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

   13. Taylor expanded in x around 0 83.2%

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

   if -1.89999999999999996e-115 < t < 8.20000000000000039e-162

   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 93.0%

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

   4. Taylor expanded in y around 0 74.1%

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

      1. associate-*r/ 74.1%

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

      2. mul-1-neg 74.1%

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

      3. *-commutative 74.1%

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

   6. Simplified 74.1%

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

      1. div-inv 74.1%

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

      2. cancel-sign-sub 74.1%

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

      3. div-inv 74.1%

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

      4. +-commutative 74.1%

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

      5. associate-/r* 74.1%

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

   8. Applied egg-rr 74.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-115}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-93}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-133}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e-93) 1.0 (if (<= y 1.6e-133) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e-93) {
		tmp = 1.0;
	} else if (y <= 1.6e-133) {
		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 <= (-3.2d-93)) then
        tmp = 1.0d0
    else if (y <= 1.6d-133) 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 <= -3.2e-93) {
		tmp = 1.0;
	} else if (y <= 1.6e-133) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e-93:
		tmp = 1.0
	elif y <= 1.6e-133:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e-93)
		tmp = 1.0;
	elseif (y <= 1.6e-133)
		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 <= -3.2e-93)
		tmp = 1.0;
	elseif (y <= 1.6e-133)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e-93], 1.0, If[LessEqual[y, 1.6e-133], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999999e-93 or 1.60000000000000006e-133 < 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 inf 68.6%

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

      1. associate-*r/ 68.6%

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

      2. neg-mul-1 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in y around inf 62.8%

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

      1. associate-*r/ 62.8%

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

      2. mul-1-neg 62.8%

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

   8. Simplified 62.8%

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

      1. add-sqr-sqrt 30.7%

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

      2. sqrt-unprod 56.2%

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

      3. sqr-neg 56.2%

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

      4. sqrt-unprod 31.0%

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

      5. add-sqr-sqrt 60.8%

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

      6. *-un-lft-identity 60.8%

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

      7. *-commutative 60.8%

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

      8. associate-/r* 60.9%

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

   10. Applied egg-rr 60.9%

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

       1. *-lft-identity 60.9%

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

       2. associate-/l/ 60.8%

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

   12. Simplified 60.8%

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

   13. Taylor expanded in x around 0 84.4%

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

   if -3.1999999999999999e-93 < y < 1.60000000000000006e-133

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 76.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-93}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-133}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-89}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-34}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e-89)
   1.0
   (if (<= y 9.8e-34) (- 1.0 (/ x (* z t))) (- 1.0 (/ (/ x y) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e-89) {
		tmp = 1.0;
	} else if (y <= 9.8e-34) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	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 <= (-3.1d-89)) then
        tmp = 1.0d0
    else if (y <= 9.8d-34) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 - ((x / y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e-89) {
		tmp = 1.0;
	} else if (y <= 9.8e-34) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.1e-89:
		tmp = 1.0
	elif y <= 9.8e-34:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.1e-89)
		tmp = 1.0;
	elseif (y <= 9.8e-34)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.1e-89)
		tmp = 1.0;
	elseif (y <= 9.8e-34)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 - ((x / y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.1e-89], 1.0, If[LessEqual[y, 9.8e-34], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999996e-89

   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 70.1%

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

      1. associate-*r/ 70.1%

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

      2. neg-mul-1 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in y around inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

   8. Simplified 65.3%

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

      1. add-sqr-sqrt 26.9%

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

      2. sqrt-unprod 58.4%

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

      3. sqr-neg 58.4%

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

      4. sqrt-unprod 37.2%

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

      5. add-sqr-sqrt 64.4%

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

      6. *-un-lft-identity 64.4%

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

      7. *-commutative 64.4%

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

      8. associate-/r* 64.4%

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

   10. Applied egg-rr 64.4%

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

       1. *-lft-identity 64.4%

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

       2. associate-/l/ 64.4%

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

   12. Simplified 64.4%

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

   13. Taylor expanded in x around 0 87.6%

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

   if -3.09999999999999996e-89 < y < 9.79999999999999925e-34

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 71.7%

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

   if 9.79999999999999925e-34 < y

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

      1. *-lft-identity 100.0%

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

      2. times-frac 99.9%

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

      3. associate-*l/ 100.0%

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

      4. *-lft-identity 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 90.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-89}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-34}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.0% 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 99.7%

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

3. Taylor expanded in t around inf 74.2%

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

   1. associate-*r/ 74.2%

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

   2. neg-mul-1 74.2%

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

5. Simplified 74.2%

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

6. Taylor expanded in y around inf 56.6%

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

   1. associate-*r/ 56.6%

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

   2. mul-1-neg 56.6%

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

8. Simplified 56.6%

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

   1. add-sqr-sqrt 28.2%

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

   2. sqrt-unprod 53.1%

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

   3. sqr-neg 53.1%

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

   4. sqrt-unprod 27.6%

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

   5. add-sqr-sqrt 52.3%

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

   6. *-un-lft-identity 52.3%

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

   7. *-commutative 52.3%

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

   8. associate-/r* 52.3%

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

10. Applied egg-rr 52.3%

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

    1. *-lft-identity 52.3%

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

    2. associate-/l/ 52.3%

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

12. Simplified 52.3%

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

13. Taylor expanded in x around 0 77.1%

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

14. Final simplification 77.1%

    \[\leadsto 1 \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(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)))))