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

Percentage Accurate: 99.2% → 99.2%

Time: 8.8s

Alternatives: 15

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 98.6%

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

3. Final simplification 98.6%

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

Alternative 2: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-46} \lor \neg \left(y \leq 3400000\right):\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.8e-46) (not (<= y 3400000.0)))
   (+ 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 ((y <= -2.8e-46) || !(y <= 3400000.0)) {
		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 ((y <= (-2.8d-46)) .or. (.not. (y <= 3400000.0d0))) 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 ((y <= -2.8e-46) || !(y <= 3400000.0)) {
		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 (y <= -2.8e-46) or not (y <= 3400000.0):
		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 ((y <= -2.8e-46) || !(y <= 3400000.0))
		tmp = Float64(1.0 + Float64(Float64(x / 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 ((y <= -2.8e-46) || ~((y <= 3400000.0)))
		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[Or[LessEqual[y, -2.8e-46], N[Not[LessEqual[y, 3400000.0]], $MachinePrecision]], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999998e-46 or 3.4e6 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-/r* 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 95.7%

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

   if -2.7999999999999998e-46 < y < 3.4e6

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. associate-/r* 92.2%

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

      3. distribute-neg-frac2 92.2%

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

      4. sub-neg 92.2%

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

      5. distribute-neg-in 92.2%

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

      6. remove-double-neg 92.2%

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

      7. +-commutative 92.2%

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

      8. sub-neg 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in t around inf 84.5%

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

      1. associate-/r* 86.4%

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

   7. Applied egg-rr 86.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-46} \lor \neg \left(y \leq 3400000\right):\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-205}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e-205)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 2.55e-61)
     (+ 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 <= -3.7e-205) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 2.55e-61) {
		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 <= (-3.7d-205)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 2.55d-61) 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 <= -3.7e-205) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 2.55e-61) {
		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 <= -3.7e-205:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 2.55e-61:
		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 <= -3.7e-205)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 2.55e-61)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.7e-205)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 2.55e-61)
		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, -3.7e-205], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-61], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000001e-205

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. associate-/r* 95.2%

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

      3. distribute-neg-frac2 95.2%

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

      4. sub-neg 95.2%

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

      5. distribute-neg-in 95.2%

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

      6. remove-double-neg 95.2%

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

      7. +-commutative 95.2%

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

      8. sub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. distribute-neg-frac2 76.5%

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

   7. Simplified 76.5%

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

   if -3.7000000000000001e-205 < t < 2.54999999999999984e-61

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 94.5%

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

   if 2.54999999999999984e-61 < t

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-/r* 95.3%

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

      3. distribute-neg-frac2 95.3%

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

      4. sub-neg 95.3%

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

      5. distribute-neg-in 95.3%

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

      6. remove-double-neg 95.3%

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

      7. +-commutative 95.3%

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

      8. sub-neg 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around inf 96.7%

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

      1. associate-/r* 96.8%

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

   7. Applied egg-rr 96.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-205}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-110}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-61}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.95e-110)
   (+ 1.0 (/ x (* (- y z) t)))
   (if (<= t 7.8e-61)
     (+ 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 <= -1.95e-110) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else if (t <= 7.8e-61) {
		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 <= (-1.95d-110)) then
        tmp = 1.0d0 + (x / ((y - z) * t))
    else if (t <= 7.8d-61) 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 <= -1.95e-110) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else if (t <= 7.8e-61) {
		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 <= -1.95e-110:
		tmp = 1.0 + (x / ((y - z) * t))
	elif t <= 7.8e-61:
		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 <= -1.95e-110)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	elseif (t <= 7.8e-61)
		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 <= -1.95e-110)
		tmp = 1.0 + (x / ((y - z) * t));
	elseif (t <= 7.8e-61)
		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, -1.95e-110], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-61], 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 < -1.95e-110

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. associate-/r* 94.0%

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

      3. distribute-neg-frac2 94.0%

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

      4. sub-neg 94.0%

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

      5. distribute-neg-in 94.0%

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

      6. remove-double-neg 94.0%

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

      7. +-commutative 94.0%

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

      8. sub-neg 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around inf 92.0%

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

   if -1.95e-110 < t < 7.80000000000000065e-61

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-/r* 92.5%

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

   5. Applied egg-rr 92.5%

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

   if 7.80000000000000065e-61 < t

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-/r* 95.3%

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

      3. distribute-neg-frac2 95.3%

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

      4. sub-neg 95.3%

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

      5. distribute-neg-in 95.3%

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

      6. remove-double-neg 95.3%

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

      7. +-commutative 95.3%

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

      8. sub-neg 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around inf 96.7%

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

      1. associate-/r* 96.8%

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

   7. Applied egg-rr 96.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-110}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-61}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-108}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-60}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.4e-108)
   (+ 1.0 (/ x (* (- y z) t)))
   (if (<= t 2.35e-60)
     (+ 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 <= -5.4e-108) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else if (t <= 2.35e-60) {
		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 <= (-5.4d-108)) then
        tmp = 1.0d0 + (x / ((y - z) * t))
    else if (t <= 2.35d-60) 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 <= -5.4e-108) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else if (t <= 2.35e-60) {
		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 <= -5.4e-108:
		tmp = 1.0 + (x / ((y - z) * t))
	elif t <= 2.35e-60:
		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 <= -5.4e-108)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	elseif (t <= 2.35e-60)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.4e-108)
		tmp = 1.0 + (x / ((y - z) * t));
	elseif (t <= 2.35e-60)
		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, -5.4e-108], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.35e-60], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4000000000000001e-108

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. associate-/r* 93.9%

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

      3. distribute-neg-frac2 93.9%

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

      4. sub-neg 93.9%

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

      5. distribute-neg-in 93.9%

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

      6. remove-double-neg 93.9%

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

      7. +-commutative 93.9%

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

      8. sub-neg 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in t around inf 93.0%

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

   if -5.4000000000000001e-108 < t < 2.35e-60

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 92.6%

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

   if 2.35e-60 < t

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-/r* 95.3%

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

      3. distribute-neg-frac2 95.3%

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

      4. sub-neg 95.3%

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

      5. distribute-neg-in 95.3%

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

      6. remove-double-neg 95.3%

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

      7. +-commutative 95.3%

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

      8. sub-neg 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around inf 96.7%

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

      1. associate-/r* 96.8%

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

   7. Applied egg-rr 96.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-108}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-60}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-54}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-22)
   (- 1.0 (/ (/ x y) y))
   (if (<= y 7e-54) (+ 1.0 (/ (/ x t) (- y z))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-22) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 7e-54) {
		tmp = 1.0 + ((x / t) / (y - z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d-22)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (y <= 7d-54) then
        tmp = 1.0d0 + ((x / t) / (y - z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-22) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 7e-54) {
		tmp = 1.0 + ((x / t) / (y - z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-22:
		tmp = 1.0 - ((x / y) / y)
	elif y <= 7e-54:
		tmp = 1.0 + ((x / t) / (y - z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-22)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (y <= 7e-54)
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e-22)
		tmp = 1.0 - ((x / y) / y);
	elseif (y <= 7e-54)
		tmp = 1.0 + ((x / t) / (y - z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-22], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-54], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999977e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-/r* 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in y around inf 94.1%

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

   if -2.49999999999999977e-22 < y < 6.99999999999999964e-54

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. associate-/r* 92.1%

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

      3. distribute-neg-frac2 92.1%

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

      4. sub-neg 92.1%

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

      5. distribute-neg-in 92.1%

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

      6. remove-double-neg 92.1%

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

      7. +-commutative 92.1%

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

      8. sub-neg 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in t around inf 85.1%

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

      1. associate-/r* 87.0%

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

   7. Applied egg-rr 87.0%

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

   if 6.99999999999999964e-54 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-/r* 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 86.4%

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

   6. Taylor expanded in x around 0 92.9%

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

Alternative 7: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e-22)
   (- 1.0 (/ (/ x y) y))
   (if (<= y 2.7e-56) (+ 1.0 (/ x (* (- y z) t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-22) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 2.7e-56) {
		tmp = 1.0 + (x / ((y - 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 <= (-2.8d-22)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (y <= 2.7d-56) then
        tmp = 1.0d0 + (x / ((y - 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 <= -2.8e-22) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 2.7e-56) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e-22:
		tmp = 1.0 - ((x / y) / y)
	elif y <= 2.7e-56:
		tmp = 1.0 + (x / ((y - z) * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e-22)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (y <= 2.7e-56)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e-22)
		tmp = 1.0 - ((x / y) / y);
	elseif (y <= 2.7e-56)
		tmp = 1.0 + (x / ((y - z) * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e-22], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-56], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999995e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-/r* 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in y around inf 94.1%

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

   if -2.79999999999999995e-22 < y < 2.69999999999999995e-56

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. associate-/r* 92.1%

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

      3. distribute-neg-frac2 92.1%

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

      4. sub-neg 92.1%

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

      5. distribute-neg-in 92.1%

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

      6. remove-double-neg 92.1%

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

      7. +-commutative 92.1%

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

      8. sub-neg 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in t around inf 85.1%

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

   if 2.69999999999999995e-56 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-/r* 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 86.4%

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

   6. Taylor expanded in x around 0 92.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-169} \lor \neg \left(z \leq 7.9 \cdot 10^{-109}\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.4e-169) (not (<= z 7.9e-109))) 1.0 (+ 1.0 (/ x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4e-169) || !(z <= 7.9e-109)) {
		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 <= (-4.4d-169)) .or. (.not. (z <= 7.9d-109))) 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 <= -4.4e-169) || !(z <= 7.9e-109)) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.4e-169) or not (z <= 7.9e-109):
		tmp = 1.0
	else:
		tmp = 1.0 + (x / (y * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.4e-169) || !(z <= 7.9e-109))
		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 <= -4.4e-169) || ~((z <= 7.9e-109)))
		tmp = 1.0;
	else
		tmp = 1.0 + (x / (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.4e-169], N[Not[LessEqual[z, 7.9e-109]], $MachinePrecision]], 1.0, N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000015e-169 or 7.8999999999999997e-109 < z

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. associate-/r* 98.5%

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

      3. distribute-neg-frac2 98.5%

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

      4. sub-neg 98.5%

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

      5. distribute-neg-in 98.5%

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

      6. remove-double-neg 98.5%

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

      7. +-commutative 98.5%

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

      8. sub-neg 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around inf 61.7%

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

   6. Taylor expanded in x around 0 79.5%

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

   if -4.40000000000000015e-169 < z < 7.8999999999999997e-109

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. associate-/r* 89.9%

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

      3. distribute-neg-frac2 89.9%

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

      4. sub-neg 89.9%

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

      5. distribute-neg-in 89.9%

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

      6. remove-double-neg 89.9%

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

      7. +-commutative 89.9%

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

      8. sub-neg 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 83.8%

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

   6. Taylor expanded in t around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

   8. Simplified 71.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-169} \lor \neg \left(z \leq 7.9 \cdot 10^{-109}\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-130} \lor \neg \left(t \leq 8.4 \cdot 10^{-223}\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.5e-130) (not (<= t 8.4e-223))) 1.0 (+ 1.0 (/ x (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.5e-130) || !(t <= 8.4e-223)) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (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 <= (-7.5d-130)) .or. (.not. (t <= 8.4d-223))) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + (x / (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 <= -7.5e-130) || !(t <= 8.4e-223)) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.5e-130) or not (t <= 8.4e-223):
		tmp = 1.0
	else:
		tmp = 1.0 + (x / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.5e-130) || !(t <= 8.4e-223))
		tmp = 1.0;
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7.5e-130) || ~((t <= 8.4e-223)))
		tmp = 1.0;
	else
		tmp = 1.0 + (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.5e-130], N[Not[LessEqual[t, 8.4e-223]], $MachinePrecision]], 1.0, N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4999999999999994e-130 or 8.39999999999999929e-223 < t

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. associate-/r* 95.5%

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

      3. distribute-neg-frac2 95.5%

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

      4. sub-neg 95.5%

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

      5. distribute-neg-in 95.5%

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

      6. remove-double-neg 95.5%

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

      7. +-commutative 95.5%

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

      8. sub-neg 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 67.3%

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

   6. Taylor expanded in x around 0 76.9%

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

   if -7.4999999999999994e-130 < t < 8.39999999999999929e-223

   1. Initial program 95.9%

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

      1. sub-neg 95.9%

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

      2. associate-/r* 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. distribute-neg-frac2 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in t around 0 77.8%

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

      1. *-commutative 77.8%

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

   10. Simplified 77.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-130} \lor \neg \left(t \leq 8.4 \cdot 10^{-223}\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-56}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-99) 1.0 (if (<= y 1.3e-56) (- 1.0 (/ (/ x t) z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-99) {
		tmp = 1.0;
	} else if (y <= 1.3e-56) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.6d-99)) then
        tmp = 1.0d0
    else if (y <= 1.3d-56) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-99) {
		tmp = 1.0;
	} else if (y <= 1.3e-56) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-99:
		tmp = 1.0
	elif y <= 1.3e-56:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-99)
		tmp = 1.0;
	elseif (y <= 1.3e-56)
		tmp = Float64(1.0 - Float64(Float64(x / 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-99)
		tmp = 1.0;
	elseif (y <= 1.3e-56)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-99], 1.0, If[LessEqual[y, 1.3e-56], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e-99 or 1.29999999999999998e-56 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-/r* 98.8%

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

      3. distribute-neg-frac2 98.8%

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

      4. sub-neg 98.8%

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

      5. distribute-neg-in 98.8%

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

      6. remove-double-neg 98.8%

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

      7. +-commutative 98.8%

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

      8. sub-neg 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around inf 88.6%

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

   6. Taylor expanded in x around 0 89.5%

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

   if -1.6e-99 < y < 1.29999999999999998e-56

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 74.3%

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

      1. associate-/r* 75.8%

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

   5. Applied egg-rr 75.8%

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

Alternative 11: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-57}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e-99) 1.0 (if (<= y 6.8e-57) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-99) {
		tmp = 1.0;
	} else if (y <= 6.8e-57) {
		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 <= (-5.2d-99)) then
        tmp = 1.0d0
    else if (y <= 6.8d-57) 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 <= -5.2e-99) {
		tmp = 1.0;
	} else if (y <= 6.8e-57) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e-99:
		tmp = 1.0
	elif y <= 6.8e-57:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e-99)
		tmp = 1.0;
	elseif (y <= 6.8e-57)
		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 <= -5.2e-99)
		tmp = 1.0;
	elseif (y <= 6.8e-57)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e-99], 1.0, If[LessEqual[y, 6.8e-57], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000001e-99 or 6.80000000000000032e-57 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-/r* 98.8%

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

      3. distribute-neg-frac2 98.8%

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

      4. sub-neg 98.8%

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

      5. distribute-neg-in 98.8%

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

      6. remove-double-neg 98.8%

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

      7. +-commutative 98.8%

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

      8. sub-neg 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around inf 88.6%

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

   6. Taylor expanded in x around 0 89.5%

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

   if -5.2000000000000001e-99 < y < 6.80000000000000032e-57

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 74.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-57}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-167}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-109}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e-167) 1.0 (if (<= z 3.5e-109) (+ 1.0 (/ (/ x t) y)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-167) {
		tmp = 1.0;
	} else if (z <= 3.5e-109) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.2d-167)) then
        tmp = 1.0d0
    else if (z <= 3.5d-109) then
        tmp = 1.0d0 + ((x / t) / y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-167) {
		tmp = 1.0;
	} else if (z <= 3.5e-109) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e-167:
		tmp = 1.0
	elif z <= 3.5e-109:
		tmp = 1.0 + ((x / t) / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e-167)
		tmp = 1.0;
	elseif (z <= 3.5e-109)
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e-167)
		tmp = 1.0;
	elseif (z <= 3.5e-109)
		tmp = 1.0 + ((x / t) / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e-167], 1.0, If[LessEqual[z, 3.5e-109], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000035e-167 or 3.5e-109 < z

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. associate-/r* 98.5%

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

      3. distribute-neg-frac2 98.5%

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

      4. sub-neg 98.5%

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

      5. distribute-neg-in 98.5%

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

      6. remove-double-neg 98.5%

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

      7. +-commutative 98.5%

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

      8. sub-neg 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around inf 61.7%

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

   6. Taylor expanded in x around 0 79.5%

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

   if -4.20000000000000035e-167 < z < 3.5e-109

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. associate-/r* 89.9%

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

      3. distribute-neg-frac2 89.9%

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

      4. sub-neg 89.9%

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

      5. distribute-neg-in 89.9%

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

      6. remove-double-neg 89.9%

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

      7. +-commutative 89.9%

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

      8. sub-neg 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 83.8%

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

   6. Taylor expanded in t around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

   8. Simplified 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-/r* 73.2%

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

   10. Applied egg-rr 73.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-167}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-109}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-134}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-221}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.5e-134) 1.0 (if (<= t 5.2e-221) (+ 1.0 (/ (/ x z) y)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.5e-134) {
		tmp = 1.0;
	} else if (t <= 5.2e-221) {
		tmp = 1.0 + ((x / z) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.5d-134)) then
        tmp = 1.0d0
    else if (t <= 5.2d-221) then
        tmp = 1.0d0 + ((x / z) / y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.5e-134) {
		tmp = 1.0;
	} else if (t <= 5.2e-221) {
		tmp = 1.0 + ((x / z) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.5e-134:
		tmp = 1.0
	elif t <= 5.2e-221:
		tmp = 1.0 + ((x / z) / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.5e-134)
		tmp = 1.0;
	elseif (t <= 5.2e-221)
		tmp = Float64(1.0 + Float64(Float64(x / z) / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.5e-134)
		tmp = 1.0;
	elseif (t <= 5.2e-221)
		tmp = 1.0 + ((x / z) / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.5e-134], 1.0, If[LessEqual[t, 5.2e-221], N[(1.0 + N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5000000000000002e-134 or 5.2000000000000004e-221 < t

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. associate-/r* 95.6%

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

      3. distribute-neg-frac2 95.6%

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

      4. sub-neg 95.6%

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

      5. distribute-neg-in 95.6%

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

      6. remove-double-neg 95.6%

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

      7. +-commutative 95.6%

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

      8. sub-neg 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around inf 67.9%

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

   6. Taylor expanded in x around 0 77.3%

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

   if -2.5000000000000002e-134 < t < 5.2000000000000004e-221

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. associate-/r* 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-neg-frac2 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in t around 0 75.9%

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

      1. *-commutative 75.9%

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

   10. Simplified 75.9%

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

   11. Taylor expanded in x around 0 75.9%

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

       1. associate-/l/ 76.0%

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

   13. Simplified 76.0%

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

Alternative 14: 98.5% accurate, 1.0× speedup

Math

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

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(Float64(x / 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[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.6%

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

   1. sub-neg 98.6%

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

   2. associate-/r* 96.3%

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

   3. distribute-neg-frac2 96.3%

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

   4. sub-neg 96.3%

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

   5. distribute-neg-in 96.3%

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

   6. remove-double-neg 96.3%

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

   7. +-commutative 96.3%

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

   8. sub-neg 96.3%

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

3. Simplified 96.3%

   \[\leadsto \color{blue}{1 + \frac{\frac{x}{y - z}}{t - y}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 15: 76.2% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. sub-neg 98.6%

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

   2. associate-/r* 96.3%

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

   3. distribute-neg-frac2 96.3%

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

   4. sub-neg 96.3%

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

   5. distribute-neg-in 96.3%

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

   6. remove-double-neg 96.3%

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

   7. +-commutative 96.3%

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

   8. sub-neg 96.3%

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

3. Simplified 96.3%

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

5. Taylor expanded in y around inf 67.3%

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

6. Taylor expanded in x around 0 74.4%

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

Reproduce

herbie shell --seed 2024096 
(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)))))