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

Percentage Accurate: 99.2% → 99.2%

Time: 9.8s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Final simplification 99.6%

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

Alternative 2: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-187}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.4e-187)
   (+ 1.0 (/ (/ x (- y t)) z))
   (if (<= t 1.16e-139)
     (+ 1.0 (/ (/ x (- z y)) y))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.4e-187) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (t <= 1.16e-139) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.4d-187)) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    else if (t <= 1.16d-139) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.4e-187) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (t <= 1.16e-139) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.4e-187:
		tmp = 1.0 + ((x / (y - t)) / z)
	elif t <= 1.16e-139:
		tmp = 1.0 + ((x / (z - y)) / y)
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.4e-187)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	elseif (t <= 1.16e-139)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.4e-187)
		tmp = 1.0 + ((x / (y - t)) / z);
	elseif (t <= 1.16e-139)
		tmp = 1.0 + ((x / (z - y)) / y);
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.4e-187], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e-139], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.40000000000000016e-187

   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 inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{z \cdot \left(y - t\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{z \cdot \left(y - t\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{z \cdot \left(y - t\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - t}}{\color{blue}{z}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - t}\right), \color{blue}{z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - t\right)\right), z\right)\right) \]

      9. --lowering--.f64 75.2%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), z\right)\right) \]

   5. Simplified 75.2%

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

   if -4.40000000000000016e-187 < t < 1.15999999999999999e-139

   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

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y \cdot \left(y - z\right)}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{x}{\left(y - z\right) \cdot \color{blue}{y}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{y}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), y\right)\right) \]

      6. --lowering--.f64 93.4%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), y\right)\right) \]

   5. Simplified 93.4%

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

   if 1.15999999999999999e-139 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 95.9%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 95.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y - z}}{t}\right), \color{blue}{1}\right) \]

      3. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{t \cdot \left(y - z\right)}\right), 1\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{t}}{y - z}\right), 1\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{t}\right), \left(y - z\right)\right), 1\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(y - z\right)\right), 1\right) \]

      7. --lowering--.f64 94.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{\_.f64}\left(y, z\right)\right), 1\right) \]

   7. Applied egg-rr 94.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-187}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{-190}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-139}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.65e-190)
   (+ 1.0 (/ (/ x (- y t)) z))
   (if (<= t 1.2e-139)
     (+ 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 <= -3.65e-190) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (t <= 1.2e-139) {
		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 <= (-3.65d-190)) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    else if (t <= 1.2d-139) 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 <= -3.65e-190) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (t <= 1.2e-139) {
		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 <= -3.65e-190:
		tmp = 1.0 + ((x / (y - t)) / z)
	elif t <= 1.2e-139:
		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 <= -3.65e-190)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	elseif (t <= 1.2e-139)
		tmp = Float64(1.0 + Float64(Float64(x / 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 <= -3.65e-190)
		tmp = 1.0 + ((x / (y - t)) / z);
	elseif (t <= 1.2e-139)
		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, -3.65e-190], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-139], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.64999999999999988e-190

   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

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{z \cdot \left(y - t\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{z \cdot \left(y - t\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{z \cdot \left(y - t\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - t}}{\color{blue}{z}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - t}\right), \color{blue}{z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - t\right)\right), z\right)\right) \]

      9. --lowering--.f64 75.4%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), z\right)\right) \]

   5. Simplified 75.4%

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

   if -3.64999999999999988e-190 < t < 1.20000000000000007e-139

   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

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y \cdot \left(y - z\right)}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{x}{\left(y - z\right) \cdot \color{blue}{y}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{y}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), y\right)\right) \]

      6. --lowering--.f64 93.3%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), y\right)\right) \]

   5. Simplified 93.3%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{\frac{x}{y - z}}{y}\right)}\right) \]

      2. associate-/l/ N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{x}{\color{blue}{y \cdot \left(y - z\right)}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{\frac{x}{y}}{\color{blue}{y - z}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      6. --lowering--.f64 92.0%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 92.0%

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

   if 1.20000000000000007e-139 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 95.9%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 95.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y - z}}{t}\right), \color{blue}{1}\right) \]

      3. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{t \cdot \left(y - z\right)}\right), 1\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{t}}{y - z}\right), 1\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{t}\right), \left(y - z\right)\right), 1\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(y - z\right)\right), 1\right) \]

      7. --lowering--.f64 94.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{\_.f64}\left(y, z\right)\right), 1\right) \]

   7. Applied egg-rr 94.8%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{-190}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-139}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-103}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-282}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e-103)
   (+ 1.0 (/ (/ x (- y t)) z))
   (if (<= z 2.6e-282)
     (+ 1.0 (/ x (* y (- t y))))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-103) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= 2.6e-282) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.75d-103)) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    else if (z <= 2.6d-282) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-103) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= 2.6e-282) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e-103:
		tmp = 1.0 + ((x / (y - t)) / z)
	elif z <= 2.6e-282:
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e-103)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	elseif (z <= 2.6e-282)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.75e-103)
		tmp = 1.0 + ((x / (y - t)) / z);
	elseif (z <= 2.6e-282)
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e-103], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-282], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75000000000000008e-103

   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

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{z \cdot \left(y - t\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{z \cdot \left(y - t\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{z \cdot \left(y - t\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - t}}{\color{blue}{z}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - t}\right), \color{blue}{z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - t\right)\right), z\right)\right) \]

      9. --lowering--.f64 94.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), z\right)\right) \]

   5. Simplified 94.6%

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

   if -1.75000000000000008e-103 < z < 2.60000000000000012e-282

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y \cdot \left(y - t\right)}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left(y \cdot \left(y - t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(y - t\right)}\right)\right)\right) \]

      4. --lowering--.f64 88.8%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 88.8%

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

   if 2.60000000000000012e-282 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 77.9%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 77.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y - z}}{t}\right), \color{blue}{1}\right) \]

      3. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{t \cdot \left(y - z\right)}\right), 1\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{t}}{y - z}\right), 1\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{t}\right), \left(y - z\right)\right), 1\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(y - z\right)\right), 1\right) \]

      7. --lowering--.f64 77.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{\_.f64}\left(y, z\right)\right), 1\right) \]

   7. Applied egg-rr 77.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-103}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-282}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-72}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+99}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-72) 1.0 (if (<= y 3.2e+99) (+ 1.0 (/ (/ x (- y t)) z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-72) {
		tmp = 1.0;
	} else if (y <= 3.2e+99) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.6d-72)) then
        tmp = 1.0d0
    else if (y <= 3.2d+99) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-72) {
		tmp = 1.0;
	} else if (y <= 3.2e+99) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-72:
		tmp = 1.0
	elif y <= 3.2e+99:
		tmp = 1.0 + ((x / (y - t)) / z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-72)
		tmp = 1.0;
	elseif (y <= 3.2e+99)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e-72)
		tmp = 1.0;
	elseif (y <= 3.2e+99)
		tmp = 1.0 + ((x / (y - t)) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-72], 1.0, If[LessEqual[y, 3.2e+99], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e-72 or 3.19999999999999999e99 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 94.5%

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

   if -1.6e-72 < y < 3.19999999999999999e99

   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 inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{z \cdot \left(y - t\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{z \cdot \left(y - t\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{z \cdot \left(y - t\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - t}}{\color{blue}{z}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - t}\right), \color{blue}{z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - t\right)\right), z\right)\right) \]

      9. --lowering--.f64 83.4%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), z\right)\right) \]

   5. Simplified 83.4%

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

Alternative 6: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-122}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e-73) 1.0 (if (<= y 6.5e-122) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-73) {
		tmp = 1.0;
	} else if (y <= 6.5e-122) {
		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 <= (-4.8d-73)) then
        tmp = 1.0d0
    else if (y <= 6.5d-122) 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 <= -4.8e-73) {
		tmp = 1.0;
	} else if (y <= 6.5e-122) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-73:
		tmp = 1.0
	elif y <= 6.5e-122:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-73)
		tmp = 1.0;
	elseif (y <= 6.5e-122)
		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 <= -4.8e-73)
		tmp = 1.0;
	elseif (y <= 6.5e-122)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-73], 1.0, If[LessEqual[y, 6.5e-122], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000011e-73 or 6.49999999999999965e-122 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 89.5%

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

   if -4.80000000000000011e-73 < y < 6.49999999999999965e-122

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 82.6%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 82.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-122}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8.5 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 8.5e-143) (+ 1.0 (/ (/ x (- y t)) z)) (+ 1.0 (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 8.5e-143) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} 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 <= 8.5d-143) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    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 <= 8.5e-143) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 8.5e-143:
		tmp = 1.0 + ((x / (y - t)) / z)
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 8.5e-143)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	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 <= 8.5e-143)
		tmp = 1.0 + ((x / (y - t)) / z);
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 8.5e-143], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $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 < 8.50000000000000072e-143

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{z \cdot \left(y - t\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{z \cdot \left(y - t\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{z \cdot \left(y - t\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - t}}{\color{blue}{z}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - t}\right), \color{blue}{z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - t\right)\right), z\right)\right) \]

      9. --lowering--.f64 80.5%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), z\right)\right) \]

   5. Simplified 80.5%

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

   if 8.50000000000000072e-143 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 95.0%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 95.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y - z}}{t}\right), \color{blue}{1}\right) \]

      3. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{t \cdot \left(y - z\right)}\right), 1\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{t}}{y - z}\right), 1\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{t}\right), \left(y - z\right)\right), 1\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(y - z\right)\right), 1\right) \]

      7. --lowering--.f64 93.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{\_.f64}\left(y, z\right)\right), 1\right) \]

   7. Applied egg-rr 93.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.5 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.7 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 6.7e-143) (+ 1.0 (/ (/ x (- y t)) z)) (+ 1.0 (/ (/ x (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.7e-143) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} 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 <= 6.7d-143) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    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 <= 6.7e-143) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 6.7e-143:
		tmp = 1.0 + ((x / (y - t)) / z)
	else:
		tmp = 1.0 + ((x / (y - z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6.7e-143)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	else
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6.7e-143)
		tmp = 1.0 + ((x / (y - t)) / z);
	else
		tmp = 1.0 + ((x / (y - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 6.7e-143], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.7000000000000004e-143

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{z \cdot \left(y - t\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{z \cdot \left(y - t\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{z \cdot \left(y - t\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - t}}{\color{blue}{z}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - t}\right), \color{blue}{z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - t\right)\right), z\right)\right) \]

      9. --lowering--.f64 80.5%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), z\right)\right) \]

   5. Simplified 80.5%

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

   if 6.7000000000000004e-143 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 95.0%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 95.0%

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

Alternative 9: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-249}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.05e-249) 1.0 (+ 1.0 (/ (/ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.05e-249) {
		tmp = 1.0;
	} 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 (z <= (-2.05d-249)) then
        tmp = 1.0d0
    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 (z <= -2.05e-249) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + ((x / y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.05e-249:
		tmp = 1.0
	else:
		tmp = 1.0 + ((x / y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.05e-249)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + Float64(Float64(x / y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.05e-249)
		tmp = 1.0;
	else
		tmp = 1.0 + ((x / y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.05e-249], 1.0, N[(1.0 + N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05000000000000002e-249

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 78.8%

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

   if -2.05000000000000002e-249 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 76.7%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 76.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{y}\right)}, t\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 59.7%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), t\right)\right) \]

   8. Simplified 59.7%

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

Alternative 10: 75.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Simplified 78.0%

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

Reproduce

herbie shell --seed 2024161 
(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)))))