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

Percentage Accurate: 99.1% → 98.4%

Time: 10.4s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(1.0 + N[(1.0 / N[(N[(y - z), $MachinePrecision] / N[(x / N[(t - y), $MachinePrecision]), $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. Step-by-step derivation

   1. *-commutative N/A

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

   2. associate-/r* N/A

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

   3. clear-num N/A

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

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

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

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

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

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

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

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

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

   8. --lowering--.f64 99.9%

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

   \[\leadsto 1 + \frac{1}{\frac{y - z}{\frac{x}{t - y}}} \]
6. Add Preprocessing

Alternative 2: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{1}{\frac{y}{\frac{x}{t - y}}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e-50)
   (+ 1.0 (/ (/ x (- y t)) z))
   (if (<= z 1.8e-143)
     (+ 1.0 (/ 1.0 (/ y (/ x (- t y)))))
     (+ 1.0 (/ (/ x (- y z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e-50) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= 1.8e-143) {
		tmp = 1.0 + (1.0 / (y / (x / (t - y))));
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.9d-50)) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    else if (z <= 1.8d-143) then
        tmp = 1.0d0 + (1.0d0 / (y / (x / (t - y))))
    else
        tmp = 1.0d0 + ((x / (y - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e-50) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= 1.8e-143) {
		tmp = 1.0 + (1.0 / (y / (x / (t - y))));
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e-50:
		tmp = 1.0 + ((x / (y - t)) / z)
	elif z <= 1.8e-143:
		tmp = 1.0 + (1.0 / (y / (x / (t - y))))
	else:
		tmp = 1.0 + ((x / (y - z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e-50)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	elseif (z <= 1.8e-143)
		tmp = Float64(1.0 + Float64(1.0 / Float64(y / Float64(x / Float64(t - y)))));
	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 (z <= -2.9e-50)
		tmp = 1.0 + ((x / (y - t)) / z);
	elseif (z <= 1.8e-143)
		tmp = 1.0 + (1.0 / (y / (x / (t - y))));
	else
		tmp = 1.0 + ((x / (y - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e-50], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-143], N[(1.0 + N[(1.0 / N[(y / N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.90000000000000008e-50

   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 96.4%

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

   5. Simplified 96.4%

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

   if -2.90000000000000008e-50 < z < 1.7999999999999999e-143

   1. Initial program 98.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 92.1%

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

   if 1.7999999999999999e-143 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 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 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{1}{\frac{y}{\frac{x}{t - y}}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-144}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.1e-50)
   (+ 1.0 (/ (/ x (- y t)) z))
   (if (<= z 6e-144) (+ 1.0 (/ x (* y (- t y)))) (+ 1.0 (/ (/ x (- y z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e-50) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= 6e-144) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.1d-50)) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    else if (z <= 6d-144) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 + ((x / (y - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e-50) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= 6e-144) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.1e-50:
		tmp = 1.0 + ((x / (y - t)) / z)
	elif z <= 6e-144:
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 + ((x / (y - z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.1e-50)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	elseif (z <= 6e-144)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	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 (z <= -3.1e-50)
		tmp = 1.0 + ((x / (y - t)) / z);
	elseif (z <= 6e-144)
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 + ((x / (y - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.1e-50], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-144], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1000000000000002e-50

   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 96.4%

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

   5. Simplified 96.4%

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

   if -3.1000000000000002e-50 < z < 5.9999999999999997e-144

   1. Initial program 98.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 92.1%

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

   5. Simplified 92.1%

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

   if 5.9999999999999997e-144 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 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 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-144}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-229}:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e-162)
   (+ 1.0 (/ (/ x (- y t)) z))
   (if (<= z -9e-229)
     (+ 1.0 (/ -1.0 (/ (* y y) x)))
     (+ 1.0 (/ (/ x (- y z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e-162) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= -9e-229) {
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.3d-162)) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    else if (z <= (-9d-229)) then
        tmp = 1.0d0 + ((-1.0d0) / ((y * y) / x))
    else
        tmp = 1.0d0 + ((x / (y - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e-162) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= -9e-229) {
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e-162:
		tmp = 1.0 + ((x / (y - t)) / z)
	elif z <= -9e-229:
		tmp = 1.0 + (-1.0 / ((y * y) / x))
	else:
		tmp = 1.0 + ((x / (y - z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e-162)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	elseif (z <= -9e-229)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(Float64(y * y) / x)));
	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 (z <= -3.3e-162)
		tmp = 1.0 + ((x / (y - t)) / z);
	elseif (z <= -9e-229)
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	else
		tmp = 1.0 + ((x / (y - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e-162], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-229], N[(1.0 + N[(-1.0 / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000013e-162

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 89.6%

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

   5. Simplified 89.6%

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

   if -3.30000000000000013e-162 < z < -9.0000000000000004e-229

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{x}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

      5. unpow2 N/A

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

      6. *-lowering-*.f64 89.3%

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

   5. Simplified 89.3%

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

      1. clear-num N/A

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

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

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

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

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

      4. *-lowering-*.f64 89.3%

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

   7. Applied egg-rr 89.3%

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

   if -9.0000000000000004e-229 < z

   1. Initial program 98.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-229}:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-161}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-229}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e-161)
   (+ 1.0 (/ (/ x (- y t)) z))
   (if (<= z -3.8e-229) (- 1.0 (/ x (* y y))) (+ 1.0 (/ (/ x (- y z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-161) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= -3.8e-229) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2d-161)) then
        tmp = 1.0d0 + ((x / (y - t)) / z)
    else if (z <= (-3.8d-229)) then
        tmp = 1.0d0 - (x / (y * y))
    else
        tmp = 1.0d0 + ((x / (y - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-161) {
		tmp = 1.0 + ((x / (y - t)) / z);
	} else if (z <= -3.8e-229) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 + ((x / (y - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2e-161:
		tmp = 1.0 + ((x / (y - t)) / z)
	elif z <= -3.8e-229:
		tmp = 1.0 - (x / (y * y))
	else:
		tmp = 1.0 + ((x / (y - z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e-161)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	elseif (z <= -3.8e-229)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	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 (z <= -2e-161)
		tmp = 1.0 + ((x / (y - t)) / z);
	elseif (z <= -3.8e-229)
		tmp = 1.0 - (x / (y * y));
	else
		tmp = 1.0 + ((x / (y - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2e-161], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-229], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000006e-161

   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 89.6%

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

   5. Simplified 89.6%

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

   if -2.00000000000000006e-161 < z < -3.8000000000000002e-229

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{x}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

      5. unpow2 N/A

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

      6. *-lowering-*.f64 89.3%

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

   5. Simplified 89.3%

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

   if -3.8000000000000002e-229 < z

   1. Initial program 98.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 81.4%

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

   5. Simplified 81.4%

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

Alternative 6: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{\frac{x}{y - t}}{z}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-204}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ (/ x (- y t)) z))))
   (if (<= z -4.1e-162) t_1 (if (<= z 5.6e-204) (- 1.0 (/ (/ x y) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / (y - t)) / z);
	double tmp;
	if (z <= -4.1e-162) {
		tmp = t_1;
	} else if (z <= 5.6e-204) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + ((x / (y - t)) / z)
    if (z <= (-4.1d-162)) then
        tmp = t_1
    else if (z <= 5.6d-204) then
        tmp = 1.0d0 - ((x / y) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / (y - t)) / z);
	double tmp;
	if (z <= -4.1e-162) {
		tmp = t_1;
	} else if (z <= 5.6e-204) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + ((x / (y - t)) / z)
	tmp = 0
	if z <= -4.1e-162:
		tmp = t_1
	elif z <= 5.6e-204:
		tmp = 1.0 - ((x / y) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z))
	tmp = 0.0
	if (z <= -4.1e-162)
		tmp = t_1;
	elseif (z <= 5.6e-204)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((x / (y - t)) / z);
	tmp = 0.0;
	if (z <= -4.1e-162)
		tmp = t_1;
	elseif (z <= 5.6e-204)
		tmp = 1.0 - ((x / y) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e-162], t$95$1, If[LessEqual[z, 5.6e-204], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000019e-162 or 5.60000000000000001e-204 < z

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1 + \frac{x}{z \cdot \left(y - t\right)}} \]
   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 89.0%

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

   5. Simplified 89.0%

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

   if -4.10000000000000019e-162 < z < 5.60000000000000001e-204

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{x}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

      5. unpow2 N/A

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

      6. *-lowering-*.f64 76.6%

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

   5. Simplified 76.6%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 76.6%

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

   7. Applied egg-rr 76.6%

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

Alternative 7: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-96}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.9e-15) 1.0 (if (<= y 6.5e-96) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e-15) {
		tmp = 1.0;
	} else if (y <= 6.5e-96) {
		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 <= (-2.9d-15)) then
        tmp = 1.0d0
    else if (y <= 6.5d-96) 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 <= -2.9e-15) {
		tmp = 1.0;
	} else if (y <= 6.5e-96) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.9e-15:
		tmp = 1.0
	elif y <= 6.5e-96:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.9e-15)
		tmp = 1.0;
	elseif (y <= 6.5e-96)
		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 <= -2.9e-15)
		tmp = 1.0;
	elseif (y <= 6.5e-96)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.9e-15], 1.0, If[LessEqual[y, 6.5e-96], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.90000000000000019e-15 or 6.50000000000000001e-96 < 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 x around 0

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

   5. Simplified 90.8%

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

   if -2.90000000000000019e-15 < y < 6.50000000000000001e-96

   1. Initial program 98.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 76.1%

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

   5. Simplified 76.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-96}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-129}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e-129) 1.0 (+ 1.0 (/ x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e-129) {
		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 <= (-2.3d-129)) 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 <= -2.3e-129) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e-129:
		tmp = 1.0
	else:
		tmp = 1.0 + (x / (y * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e-129)
		tmp = 1.0;
	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 (z <= -2.3e-129)
		tmp = 1.0;
	else
		tmp = 1.0 + (x / (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e-129], 1.0, N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e-129

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 83.5%

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

   if -2.3e-129 < z

   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 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 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in y around inf

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

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

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

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

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

      3. *-lowering-*.f64 62.9%

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

   8. Simplified 62.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-129}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 10: 75.4% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

5. Simplified 74.2%

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

Reproduce

herbie shell --seed 2024160 
(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)))))