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

Percentage Accurate: 99.1% → 99.1%

Time: 9.8s

Alternatives: 12

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 99.2%

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

3. Final simplification 99.2%

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

Alternative 2: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-94} \lor \neg \left(y \leq 1.02 \cdot 10^{-109}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{\frac{z \cdot t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-94) (not (<= y 1.02e-109)))
   (- 1.0 (/ x (* y (- y t))))
   (+ 1.0 (/ -1.0 (/ (* z t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-94) || !(y <= 1.02e-109)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + (-1.0 / ((z * t) / x));
	}
	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 <= (-5.2d-94)) .or. (.not. (y <= 1.02d-109))) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 + ((-1.0d0) / ((z * t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-94) || !(y <= 1.02e-109)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + (-1.0 / ((z * t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e-94) or not (y <= 1.02e-109):
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 + (-1.0 / ((z * t) / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e-94) || !(y <= 1.02e-109))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(-1.0 / Float64(Float64(z * t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.2e-94) || ~((y <= 1.02e-109)))
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 + (-1.0 / ((z * t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e-94], N[Not[LessEqual[y, 1.02e-109]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999988e-94 or 1.02e-109 < 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 z around 0 89.8%

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

   if -5.19999999999999988e-94 < y < 1.02e-109

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 83.6%

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

      1. clear-num 83.7%

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

      2. inv-pow 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-/l* 81.1%

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

   5. Applied egg-rr 81.1%

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

      1. unpow-1 81.1%

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

      2. associate-*r/ 83.7%

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

      3. *-commutative 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-94} \lor \neg \left(y \leq 1.02 \cdot 10^{-109}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{\frac{z \cdot t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -225000 \lor \neg \left(y \leq 1.1 \cdot 10^{+24}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -225000.0) (not (<= y 1.1e+24)))
   (- 1.0 (/ x (* y t)))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -225000.0) || !(y <= 1.1e+24)) {
		tmp = 1.0 - (x / (y * t));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-225000.0d0)) .or. (.not. (y <= 1.1d+24))) then
        tmp = 1.0d0 - (x / (y * t))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -225000.0) || !(y <= 1.1e+24)) {
		tmp = 1.0 - (x / (y * t));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -225000.0) or not (y <= 1.1e+24):
		tmp = 1.0 - (x / (y * t))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -225000.0) || !(y <= 1.1e+24))
		tmp = Float64(1.0 - Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -225000.0) || ~((y <= 1.1e+24)))
		tmp = 1.0 - (x / (y * t));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -225000.0], N[Not[LessEqual[y, 1.1e+24]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -225000 or 1.10000000000000001e24 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.2%

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

   4. Taylor expanded in y around 0 72.2%

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

      1. associate-*r/ 72.2%

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

      2. mul-1-neg 72.2%

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

   6. Simplified 72.2%

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

      1. div-inv 72.2%

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

      2. add-sqr-sqrt 36.9%

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

      3. sqrt-unprod 55.9%

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

      4. sqr-neg 55.9%

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

      5. sqrt-unprod 34.4%

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

      6. add-sqr-sqrt 70.6%

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

      7. associate-/r* 70.6%

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

   8. Applied egg-rr 70.6%

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

      1. associate-*r/ 70.5%

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

      2. associate-*r/ 70.5%

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

      3. *-rgt-identity 70.5%

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

      4. associate-/r* 70.6%

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

   10. Simplified 70.6%

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

   if -225000 < y < 1.10000000000000001e24

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 69.7%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -225000 \lor \neg \left(y \leq 1.1 \cdot 10^{+24}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -60000000000 \lor \neg \left(y \leq 1.3 \cdot 10^{+14}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -60000000000.0) (not (<= y 1.3e+14)))
   (- 1.0 (/ x (* y z)))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -60000000000.0) || !(y <= 1.3e+14)) {
		tmp = 1.0 - (x / (y * z));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-60000000000.0d0)) .or. (.not. (y <= 1.3d+14))) then
        tmp = 1.0d0 - (x / (y * z))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -60000000000.0) || !(y <= 1.3e+14)) {
		tmp = 1.0 - (x / (y * z));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -60000000000.0) or not (y <= 1.3e+14):
		tmp = 1.0 - (x / (y * z))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -60000000000.0) || !(y <= 1.3e+14))
		tmp = Float64(1.0 - Float64(x / Float64(y * z)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -60000000000.0) || ~((y <= 1.3e+14)))
		tmp = 1.0 - (x / (y * z));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -60000000000.0], N[Not[LessEqual[y, 1.3e+14]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e10 or 1.3e14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 95.5%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. neg-mul-1 71.1%

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

      3. *-commutative 71.1%

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

   6. Simplified 71.1%

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

      1. div-inv 71.1%

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

      2. add-sqr-sqrt 34.7%

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

      3. sqrt-unprod 54.9%

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

      4. sqr-neg 54.9%

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

      5. sqrt-unprod 36.0%

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

      6. add-sqr-sqrt 70.7%

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

      7. *-commutative 70.7%

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

   8. Applied egg-rr 70.7%

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

      1. associate-*r/ 70.7%

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

      2. *-rgt-identity 70.7%

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

   10. Simplified 70.7%

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

   if -6e10 < y < 1.3e14

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 70.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -60000000000 \lor \neg \left(y \leq 1.3 \cdot 10^{+14}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2500000 \lor \neg \left(y \leq 3000000000000\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2500000.0) (not (<= y 3000000000000.0)))
   (- 1.0 (/ x (* y z)))
   (- 1.0 (/ (/ x t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2500000.0) || !(y <= 3000000000000.0)) {
		tmp = 1.0 - (x / (y * z));
	} 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 ((y <= (-2500000.0d0)) .or. (.not. (y <= 3000000000000.0d0))) then
        tmp = 1.0d0 - (x / (y * z))
    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 ((y <= -2500000.0) || !(y <= 3000000000000.0)) {
		tmp = 1.0 - (x / (y * z));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2500000.0) or not (y <= 3000000000000.0):
		tmp = 1.0 - (x / (y * z))
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2500000.0) || !(y <= 3000000000000.0))
		tmp = Float64(1.0 - Float64(x / Float64(y * z)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2500000.0) || ~((y <= 3000000000000.0)))
		tmp = 1.0 - (x / (y * z));
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2500000.0], N[Not[LessEqual[y, 3000000000000.0]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e6 or 3e12 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 95.5%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. neg-mul-1 71.1%

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

      3. *-commutative 71.1%

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

   6. Simplified 71.1%

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

      1. div-inv 71.1%

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

      2. add-sqr-sqrt 34.7%

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

      3. sqrt-unprod 54.9%

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

      4. sqr-neg 54.9%

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

      5. sqrt-unprod 36.0%

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

      6. add-sqr-sqrt 70.7%

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

      7. *-commutative 70.7%

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

   8. Applied egg-rr 70.7%

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

      1. associate-*r/ 70.7%

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

      2. *-rgt-identity 70.7%

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

   10. Simplified 70.7%

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

   if -2.5e6 < y < 3e12

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 70.3%

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

      1. associate-/r* 68.9%

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

      2. div-inv 68.9%

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

   5. Applied egg-rr 68.9%

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

      1. un-div-inv 68.9%

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

   7. Applied egg-rr 68.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2500000 \lor \neg \left(y \leq 3000000000000\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-128}:\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+122}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.35e-128)
   (- 1.0 (/ x (* y z)))
   (if (<= t 2.7e+122) (- 1.0 (/ x (* z t))) (+ 1.0 (/ x (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e-128) {
		tmp = 1.0 - (x / (y * z));
	} else if (t <= 2.7e+122) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * 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 <= 1.35d-128) then
        tmp = 1.0d0 - (x / (y * z))
    else if (t <= 2.7d+122) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 + (x / (y * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e-128) {
		tmp = 1.0 - (x / (y * z));
	} else if (t <= 2.7e+122) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.35e-128:
		tmp = 1.0 - (x / (y * z))
	elif t <= 2.7e+122:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 + (x / (y * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.35e-128)
		tmp = Float64(1.0 - Float64(x / Float64(y * z)));
	elseif (t <= 2.7e+122)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.35e-128)
		tmp = 1.0 - (x / (y * z));
	elseif (t <= 2.7e+122)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 + (x / (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.35e-128], N[(1.0 - N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+122], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.35000000000000003e-128

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 80.9%

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

   4. Taylor expanded in y around 0 60.2%

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

      1. associate-*r/ 60.2%

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

      2. neg-mul-1 60.2%

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

      3. *-commutative 60.2%

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

   6. Simplified 60.2%

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

      1. div-inv 60.2%

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

      2. add-sqr-sqrt 27.8%

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

      3. sqrt-unprod 49.7%

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

      4. sqr-neg 49.7%

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

      5. sqrt-unprod 29.9%

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

      6. add-sqr-sqrt 56.9%

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

      7. *-commutative 56.9%

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

   8. Applied egg-rr 56.9%

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

      1. associate-*r/ 56.9%

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

      2. *-rgt-identity 56.9%

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

   10. Simplified 56.9%

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

   if 1.35000000000000003e-128 < t < 2.6999999999999998e122

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.7%

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

   if 2.6999999999999998e122 < 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 z around 0 91.4%

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

   4. Taylor expanded in y around 0 91.4%

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

      1. associate-*r/ 91.4%

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

      2. mul-1-neg 91.4%

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

   6. Simplified 91.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-128}:\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+122}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-23}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+126}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 5.6e-23)
   (+ 1.0 (/ x (* y z)))
   (if (<= t 6e+126) (- 1.0 (/ (/ x t) z)) (+ 1.0 (/ x (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.6e-23) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 6e+126) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + (x / (y * 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 <= 5.6d-23) then
        tmp = 1.0d0 + (x / (y * z))
    else if (t <= 6d+126) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0 + (x / (y * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.6e-23) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 6e+126) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 5.6e-23:
		tmp = 1.0 + (x / (y * z))
	elif t <= 6e+126:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0 + (x / (y * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 5.6e-23)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif (t <= 6e+126)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 5.6e-23)
		tmp = 1.0 + (x / (y * z));
	elseif (t <= 6e+126)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0 + (x / (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 5.6e-23], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+126], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 5.5999999999999994e-23

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 81.0%

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

   4. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 60.7%

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

      2. neg-mul-1 60.7%

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

      3. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   if 5.5999999999999994e-23 < t < 6.0000000000000005e126

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. associate-/r* 84.6%

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

      2. div-inv 84.6%

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

   5. Applied egg-rr 84.6%

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

      1. un-div-inv 84.6%

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

   7. Applied egg-rr 84.6%

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

   if 6.0000000000000005e126 < 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 z around 0 91.4%

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

   4. Taylor expanded in y around 0 91.4%

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

      1. associate-*r/ 91.4%

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

      2. mul-1-neg 91.4%

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

   6. Simplified 91.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-23}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+126}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+122}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 7.5e-21)
   (+ 1.0 (/ x (* y z)))
   (if (<= t 1.4e+122) (- 1.0 (/ (/ x t) z)) (+ 1.0 (/ (/ x t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.5e-21) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 1.4e+122) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + ((x / 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 <= 7.5d-21) then
        tmp = 1.0d0 + (x / (y * z))
    else if (t <= 1.4d+122) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0 + ((x / 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 <= 7.5e-21) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 1.4e+122) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + ((x / t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 7.5e-21:
		tmp = 1.0 + (x / (y * z))
	elif t <= 1.4e+122:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0 + ((x / t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 7.5e-21)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif (t <= 1.4e+122)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 7.5e-21)
		tmp = 1.0 + (x / (y * z));
	elseif (t <= 1.4e+122)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0 + ((x / t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 7.5e-21], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+122], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 7.50000000000000072e-21

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 81.0%

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

   4. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 60.7%

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

      2. neg-mul-1 60.7%

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

      3. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   if 7.50000000000000072e-21 < t < 1.4e122

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. associate-/r* 84.6%

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

      2. div-inv 84.6%

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

   5. Applied egg-rr 84.6%

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

      1. un-div-inv 84.6%

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

   7. Applied egg-rr 84.6%

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

   if 1.4e122 < 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 z around 0 91.4%

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

   4. Taylor expanded in y around 0 91.4%

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

      1. mul-1-neg 91.4%

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

      2. associate-/r* 91.5%

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

      3. distribute-neg-frac2 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+122}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-22}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+125}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.4e-22)
   (+ 1.0 (/ (/ x z) y))
   (if (<= t 8.8e+125) (- 1.0 (/ (/ x t) z)) (+ 1.0 (/ (/ x t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.4e-22) {
		tmp = 1.0 + ((x / z) / y);
	} else if (t <= 8.8e+125) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + ((x / 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 <= 2.4d-22) then
        tmp = 1.0d0 + ((x / z) / y)
    else if (t <= 8.8d+125) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0 + ((x / 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 <= 2.4e-22) {
		tmp = 1.0 + ((x / z) / y);
	} else if (t <= 8.8e+125) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + ((x / t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.4e-22:
		tmp = 1.0 + ((x / z) / y)
	elif t <= 8.8e+125:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0 + ((x / t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.4e-22)
		tmp = Float64(1.0 + Float64(Float64(x / z) / y));
	elseif (t <= 8.8e+125)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.4e-22)
		tmp = 1.0 + ((x / z) / y);
	elseif (t <= 8.8e+125)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0 + ((x / t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.4e-22], N[(1.0 + N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e+125], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.40000000000000002e-22

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 81.0%

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

   4. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 60.7%

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

      2. neg-mul-1 60.7%

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

      3. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in x around 0 60.7%

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

      1. neg-mul-1 60.7%

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

      2. distribute-neg-frac2 60.7%

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

      3. *-commutative 60.7%

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

      4. distribute-rgt-neg-out 60.7%

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

      5. associate-/r* 60.8%

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

   9. Simplified 60.8%

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

   if 2.40000000000000002e-22 < t < 8.79999999999999964e125

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. associate-/r* 84.6%

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

      2. div-inv 84.6%

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

   5. Applied egg-rr 84.6%

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

      1. un-div-inv 84.6%

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

   7. Applied egg-rr 84.6%

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

   if 8.79999999999999964e125 < 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 z around 0 91.4%

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

   4. Taylor expanded in y around 0 91.4%

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

      1. mul-1-neg 91.4%

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

      2. associate-/r* 91.5%

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

      3. distribute-neg-frac2 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-22}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+125}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+122}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.7e-6)
   (+ 1.0 (/ x (* y (- z y))))
   (if (<= t 4e+122) (- 1.0 (/ (/ x t) z)) (+ 1.0 (/ (/ x t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.7e-6) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else if (t <= 4e+122) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + ((x / 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 <= 3.7d-6) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else if (t <= 4d+122) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0 + ((x / 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 <= 3.7e-6) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else if (t <= 4e+122) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + ((x / t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3.7e-6:
		tmp = 1.0 + (x / (y * (z - y)))
	elif t <= 4e+122:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0 + ((x / t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.7e-6)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	elseif (t <= 4e+122)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3.7e-6)
		tmp = 1.0 + (x / (y * (z - y)));
	elseif (t <= 4e+122)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0 + ((x / t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3.7e-6], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+122], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 3.7000000000000002e-6

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 81.3%

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

   if 3.7000000000000002e-6 < t < 4.00000000000000006e122

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 91.2%

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

      1. associate-/r* 91.3%

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

      2. div-inv 91.2%

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

   5. Applied egg-rr 91.2%

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

      1. un-div-inv 91.3%

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

   7. Applied egg-rr 91.3%

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

   if 4.00000000000000006e122 < 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 z around 0 91.4%

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

   4. Taylor expanded in y around 0 91.4%

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

      1. mul-1-neg 91.4%

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

      2. associate-/r* 91.5%

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

      3. distribute-neg-frac2 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+122}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.2 \cdot 10^{-21}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.2e-21) (+ 1.0 (/ x (* y (- z y)))) (+ 1.0 (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.2e-21) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 3.2d-21) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.2e-21) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3.2e-21:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.2e-21)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3.2e-21)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3.2e-21], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.2000000000000002e-21

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 81.0%

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

   if 3.2000000000000002e-21 < t

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. times-frac 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. associate-/r* 98.7%

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

      3. distribute-neg-frac2 98.7%

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

      4. sub-neg 98.7%

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

      5. neg-mul-1 98.7%

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

      6. +-commutative 98.7%

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

      7. distribute-neg-in 98.7%

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

      8. neg-mul-1 98.7%

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

      9. remove-double-neg 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in x around 0 98.6%

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

      1. associate-/r* 98.7%

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

   10. Simplified 98.7%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.2 \cdot 10^{-21}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in z around 0 75.4%

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

4. Taylor expanded in y around 0 57.1%

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

   1. associate-*r/ 57.1%

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

   2. mul-1-neg 57.1%

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

6. Simplified 57.1%

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

   1. div-inv 57.1%

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

   2. add-sqr-sqrt 29.0%

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

   3. sqrt-unprod 46.8%

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

   4. sqr-neg 46.8%

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

   5. sqrt-unprod 24.3%

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

   6. add-sqr-sqrt 50.3%

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

   7. associate-/r* 50.3%

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

8. Applied egg-rr 50.3%

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

   1. associate-*r/ 50.3%

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

   2. associate-*r/ 50.3%

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

   3. *-rgt-identity 50.3%

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

   4. associate-/r* 50.3%

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

10. Simplified 50.3%

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

11. Final simplification 50.3%

    \[\leadsto 1 - \frac{x}{y \cdot t} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024078 
(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)))))