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

Percentage Accurate: 89.2% → 96.8%

Time: 9.6s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (x / (t - z)) / (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

   1. associate-/l/ 97.3%

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

3. Simplified 97.3%

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

Alternative 2: 49.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{x}{y \cdot \left(-z\right)}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1150:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-56}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) t)) (t_2 (/ x (* y (- z)))))
   (if (<= y -2.65e+244)
     t_1
     (if (<= y -8.5e+164)
       t_2
       (if (<= y -5e+74)
         t_1
         (if (<= y -1150.0)
           t_2
           (if (<= y -3.4e-46)
             t_1
             (if (<= y 4e-56) (/ (/ x t) (- z)) (/ (/ x t) y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double t_2 = x / (y * -z);
	double tmp;
	if (y <= -2.65e+244) {
		tmp = t_1;
	} else if (y <= -8.5e+164) {
		tmp = t_2;
	} else if (y <= -5e+74) {
		tmp = t_1;
	} else if (y <= -1150.0) {
		tmp = t_2;
	} else if (y <= -3.4e-46) {
		tmp = t_1;
	} else if (y <= 4e-56) {
		tmp = (x / t) / -z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) / t
    t_2 = x / (y * -z)
    if (y <= (-2.65d+244)) then
        tmp = t_1
    else if (y <= (-8.5d+164)) then
        tmp = t_2
    else if (y <= (-5d+74)) then
        tmp = t_1
    else if (y <= (-1150.0d0)) then
        tmp = t_2
    else if (y <= (-3.4d-46)) then
        tmp = t_1
    else if (y <= 4d-56) then
        tmp = (x / t) / -z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double t_2 = x / (y * -z);
	double tmp;
	if (y <= -2.65e+244) {
		tmp = t_1;
	} else if (y <= -8.5e+164) {
		tmp = t_2;
	} else if (y <= -5e+74) {
		tmp = t_1;
	} else if (y <= -1150.0) {
		tmp = t_2;
	} else if (y <= -3.4e-46) {
		tmp = t_1;
	} else if (y <= 4e-56) {
		tmp = (x / t) / -z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) / t
	t_2 = x / (y * -z)
	tmp = 0
	if y <= -2.65e+244:
		tmp = t_1
	elif y <= -8.5e+164:
		tmp = t_2
	elif y <= -5e+74:
		tmp = t_1
	elif y <= -1150.0:
		tmp = t_2
	elif y <= -3.4e-46:
		tmp = t_1
	elif y <= 4e-56:
		tmp = (x / t) / -z
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / t)
	t_2 = Float64(x / Float64(y * Float64(-z)))
	tmp = 0.0
	if (y <= -2.65e+244)
		tmp = t_1;
	elseif (y <= -8.5e+164)
		tmp = t_2;
	elseif (y <= -5e+74)
		tmp = t_1;
	elseif (y <= -1150.0)
		tmp = t_2;
	elseif (y <= -3.4e-46)
		tmp = t_1;
	elseif (y <= 4e-56)
		tmp = Float64(Float64(x / t) / Float64(-z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) / t;
	t_2 = x / (y * -z);
	tmp = 0.0;
	if (y <= -2.65e+244)
		tmp = t_1;
	elseif (y <= -8.5e+164)
		tmp = t_2;
	elseif (y <= -5e+74)
		tmp = t_1;
	elseif (y <= -1150.0)
		tmp = t_2;
	elseif (y <= -3.4e-46)
		tmp = t_1;
	elseif (y <= 4e-56)
		tmp = (x / t) / -z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.65e+244], t$95$1, If[LessEqual[y, -8.5e+164], t$95$2, If[LessEqual[y, -5e+74], t$95$1, If[LessEqual[y, -1150.0], t$95$2, If[LessEqual[y, -3.4e-46], t$95$1, If[LessEqual[y, 4e-56], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6499999999999999e244 or -8.50000000000000027e164 < y < -4.99999999999999963e74 or -1150 < y < -3.39999999999999996e-46

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 62.7%

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

      1. div-inv 62.6%

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

      2. associate-/r* 62.6%

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

   5. Applied egg-rr 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-*l/ 66.1%

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

      3. associate-*r/ 66.1%

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

      4. associate-*l/ 66.1%

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

      5. *-lft-identity 66.1%

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

   7. Simplified 66.1%

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

   if -2.6499999999999999e244 < y < -8.50000000000000027e164 or -4.99999999999999963e74 < y < -1150

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0 93.9%

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

      1. associate-/l/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 93.0%

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

   7. Taylor expanded in t around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-neg-frac2 69.2%

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

      3. *-commutative 69.2%

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

      4. distribute-rgt-neg-out 69.2%

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

   9. Simplified 69.2%

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

   if -3.39999999999999996e-46 < y < 4.0000000000000002e-56

   1. Initial program 86.8%

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

      1. associate-/l/ 98.3%

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

      2. div-inv 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-/r* 86.7%

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

      3. distribute-neg-frac 86.7%

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

      4. distribute-neg-frac2 86.7%

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

   7. Simplified 86.7%

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

   8. Taylor expanded in z around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. associate-/r* 49.9%

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

      3. distribute-neg-frac2 49.9%

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

   10. Simplified 49.9%

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

   if 4.0000000000000002e-56 < y

   1. Initial program 86.3%

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

      1. associate-/l/ 96.3%

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

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 96.2%

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

      2. associate-/r/ 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in z around 0 43.3%

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

      1. associate-/r* 47.6%

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

   9. Simplified 47.6%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+244}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1150:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-56}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{x}{z \cdot \left(-y\right)}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1550:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) t)) (t_2 (/ x (* z (- y)))))
   (if (<= y -1e+251)
     t_1
     (if (<= y -1.8e+165)
       t_2
       (if (<= y -5.8e+74)
         t_1
         (if (<= y -1550.0)
           t_2
           (if (<= y -2.1e-46)
             t_1
             (if (<= y 2e-56) (/ x (* z (- t))) (/ (/ x t) y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double t_2 = x / (z * -y);
	double tmp;
	if (y <= -1e+251) {
		tmp = t_1;
	} else if (y <= -1.8e+165) {
		tmp = t_2;
	} else if (y <= -5.8e+74) {
		tmp = t_1;
	} else if (y <= -1550.0) {
		tmp = t_2;
	} else if (y <= -2.1e-46) {
		tmp = t_1;
	} else if (y <= 2e-56) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) / t
    t_2 = x / (z * -y)
    if (y <= (-1d+251)) then
        tmp = t_1
    else if (y <= (-1.8d+165)) then
        tmp = t_2
    else if (y <= (-5.8d+74)) then
        tmp = t_1
    else if (y <= (-1550.0d0)) then
        tmp = t_2
    else if (y <= (-2.1d-46)) then
        tmp = t_1
    else if (y <= 2d-56) then
        tmp = x / (z * -t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double t_2 = x / (z * -y);
	double tmp;
	if (y <= -1e+251) {
		tmp = t_1;
	} else if (y <= -1.8e+165) {
		tmp = t_2;
	} else if (y <= -5.8e+74) {
		tmp = t_1;
	} else if (y <= -1550.0) {
		tmp = t_2;
	} else if (y <= -2.1e-46) {
		tmp = t_1;
	} else if (y <= 2e-56) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) / t
	t_2 = x / (z * -y)
	tmp = 0
	if y <= -1e+251:
		tmp = t_1
	elif y <= -1.8e+165:
		tmp = t_2
	elif y <= -5.8e+74:
		tmp = t_1
	elif y <= -1550.0:
		tmp = t_2
	elif y <= -2.1e-46:
		tmp = t_1
	elif y <= 2e-56:
		tmp = x / (z * -t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / t)
	t_2 = Float64(x / Float64(z * Float64(-y)))
	tmp = 0.0
	if (y <= -1e+251)
		tmp = t_1;
	elseif (y <= -1.8e+165)
		tmp = t_2;
	elseif (y <= -5.8e+74)
		tmp = t_1;
	elseif (y <= -1550.0)
		tmp = t_2;
	elseif (y <= -2.1e-46)
		tmp = t_1;
	elseif (y <= 2e-56)
		tmp = Float64(x / Float64(z * Float64(-t)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) / t;
	t_2 = x / (z * -y);
	tmp = 0.0;
	if (y <= -1e+251)
		tmp = t_1;
	elseif (y <= -1.8e+165)
		tmp = t_2;
	elseif (y <= -5.8e+74)
		tmp = t_1;
	elseif (y <= -1550.0)
		tmp = t_2;
	elseif (y <= -2.1e-46)
		tmp = t_1;
	elseif (y <= 2e-56)
		tmp = x / (z * -t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+251], t$95$1, If[LessEqual[y, -1.8e+165], t$95$2, If[LessEqual[y, -5.8e+74], t$95$1, If[LessEqual[y, -1550.0], t$95$2, If[LessEqual[y, -2.1e-46], t$95$1, If[LessEqual[y, 2e-56], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1e251 or -1.7999999999999999e165 < y < -5.8000000000000005e74 or -1550 < y < -2.09999999999999987e-46

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 62.7%

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

      1. div-inv 62.6%

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

      2. associate-/r* 62.6%

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

   5. Applied egg-rr 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-*l/ 66.1%

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

      3. associate-*r/ 66.1%

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

      4. associate-*l/ 66.1%

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

      5. *-lft-identity 66.1%

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

   7. Simplified 66.1%

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

   if -1e251 < y < -1.7999999999999999e165 or -5.8000000000000005e74 < y < -1550

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0 93.9%

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

      1. associate-/l/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 93.0%

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

   7. Taylor expanded in t around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-neg-frac2 69.2%

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

      3. *-commutative 69.2%

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

      4. distribute-rgt-neg-out 69.2%

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

   9. Simplified 69.2%

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

   if -2.09999999999999987e-46 < y < 2.0000000000000001e-56

   1. Initial program 86.8%

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

      1. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf 57.4%

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

   6. Taylor expanded in y around 0 46.5%

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

      1. associate-*r/ 46.5%

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

      2. neg-mul-1 46.5%

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

      3. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if 2.0000000000000001e-56 < y

   1. Initial program 86.3%

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

      1. associate-/l/ 96.3%

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

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 96.2%

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

      2. associate-/r/ 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in z around 0 43.3%

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

      1. associate-/r* 47.6%

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

   9. Simplified 47.6%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+251}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+165}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1550:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-234}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (+ t z)))))
   (if (<= t -6.8e-234)
     (/ (/ x y) (- t z))
     (if (<= t 3.9e-244)
       t_1
       (if (<= t 1.45e-111)
         (/ x (* (- t z) y))
         (if (<= t 1.25e-58) t_1 (/ (/ x t) (- y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (t + z));
	double tmp;
	if (t <= -6.8e-234) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.9e-244) {
		tmp = t_1;
	} else if (t <= 1.45e-111) {
		tmp = x / ((t - z) * y);
	} else if (t <= 1.25e-58) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = x / (z * (t + z))
    if (t <= (-6.8d-234)) then
        tmp = (x / y) / (t - z)
    else if (t <= 3.9d-244) then
        tmp = t_1
    else if (t <= 1.45d-111) then
        tmp = x / ((t - z) * y)
    else if (t <= 1.25d-58) then
        tmp = t_1
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (t + z));
	double tmp;
	if (t <= -6.8e-234) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.9e-244) {
		tmp = t_1;
	} else if (t <= 1.45e-111) {
		tmp = x / ((t - z) * y);
	} else if (t <= 1.25e-58) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (t + z))
	tmp = 0
	if t <= -6.8e-234:
		tmp = (x / y) / (t - z)
	elif t <= 3.9e-244:
		tmp = t_1
	elif t <= 1.45e-111:
		tmp = x / ((t - z) * y)
	elif t <= 1.25e-58:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(t + z)))
	tmp = 0.0
	if (t <= -6.8e-234)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 3.9e-244)
		tmp = t_1;
	elseif (t <= 1.45e-111)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (t <= 1.25e-58)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (t + z));
	tmp = 0.0;
	if (t <= -6.8e-234)
		tmp = (x / y) / (t - z);
	elseif (t <= 3.9e-244)
		tmp = t_1;
	elseif (t <= 1.45e-111)
		tmp = x / ((t - z) * y);
	elseif (t <= 1.25e-58)
		tmp = t_1;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-234], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-244], t$95$1, If[LessEqual[t, 1.45e-111], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-58], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.79999999999999971e-234

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 89.2%

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

      1. associate-/l/ 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in y around inf 59.8%

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

   if -6.79999999999999971e-234 < t < 3.8999999999999999e-244 or 1.45000000000000001e-111 < t < 1.24999999999999994e-58

   1. Initial program 92.1%

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

      1. associate-/l/ 96.5%

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

      2. div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in y around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. associate-/r* 73.2%

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

      3. distribute-neg-frac 73.2%

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

      4. distribute-neg-frac2 73.2%

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

   7. Simplified 73.2%

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

      1. *-un-lft-identity 73.2%

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

      2. associate-/l/ 68.8%

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

      3. sub-neg 68.8%

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

      4. add-sqr-sqrt 41.1%

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

      5. sqrt-unprod 58.1%

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

      6. sqr-neg 58.1%

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

      7. sqrt-unprod 17.0%

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

      8. add-sqr-sqrt 35.9%

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

      9. add-sqr-sqrt 19.0%

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

      10. sqrt-unprod 46.6%

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

      11. sqr-neg 46.6%

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

      12. sqrt-unprod 27.6%

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

      13. add-sqr-sqrt 65.2%

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

   9. Applied egg-rr 65.2%

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

       1. *-lft-identity 65.2%

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

       2. *-commutative 65.2%

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

       3. +-commutative 65.2%

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

   11. Simplified 65.2%

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

   if 3.8999999999999999e-244 < t < 1.45000000000000001e-111

   1. Initial program 88.6%

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

   3. Taylor expanded in y around inf 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if 1.24999999999999994e-58 < t

   1. Initial program 84.3%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 81.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-234}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(t + z\right)}\\ t_2 := \frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{-233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (+ t z)))) (t_2 (/ x (* (- t z) y))))
   (if (<= t -3.7e-233)
     t_2
     (if (<= t 8e-244)
       t_1
       (if (<= t 6.8e-108)
         t_2
         (if (<= t 1.55e-60) t_1 (/ (/ x t) (- y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (t + z));
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (t <= -3.7e-233) {
		tmp = t_2;
	} else if (t <= 8e-244) {
		tmp = t_1;
	} else if (t <= 6.8e-108) {
		tmp = t_2;
	} else if (t <= 1.55e-60) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (z * (t + z))
    t_2 = x / ((t - z) * y)
    if (t <= (-3.7d-233)) then
        tmp = t_2
    else if (t <= 8d-244) then
        tmp = t_1
    else if (t <= 6.8d-108) then
        tmp = t_2
    else if (t <= 1.55d-60) then
        tmp = t_1
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (t + z));
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (t <= -3.7e-233) {
		tmp = t_2;
	} else if (t <= 8e-244) {
		tmp = t_1;
	} else if (t <= 6.8e-108) {
		tmp = t_2;
	} else if (t <= 1.55e-60) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (t + z))
	t_2 = x / ((t - z) * y)
	tmp = 0
	if t <= -3.7e-233:
		tmp = t_2
	elif t <= 8e-244:
		tmp = t_1
	elif t <= 6.8e-108:
		tmp = t_2
	elif t <= 1.55e-60:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(t + z)))
	t_2 = Float64(x / Float64(Float64(t - z) * y))
	tmp = 0.0
	if (t <= -3.7e-233)
		tmp = t_2;
	elseif (t <= 8e-244)
		tmp = t_1;
	elseif (t <= 6.8e-108)
		tmp = t_2;
	elseif (t <= 1.55e-60)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (t + z));
	t_2 = x / ((t - z) * y);
	tmp = 0.0;
	if (t <= -3.7e-233)
		tmp = t_2;
	elseif (t <= 8e-244)
		tmp = t_1;
	elseif (t <= 6.8e-108)
		tmp = t_2;
	elseif (t <= 1.55e-60)
		tmp = t_1;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e-233], t$95$2, If[LessEqual[t, 8e-244], t$95$1, If[LessEqual[t, 6.8e-108], t$95$2, If[LessEqual[t, 1.55e-60], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6999999999999998e-233 or 7.9999999999999994e-244 < t < 6.80000000000000004e-108

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 64.7%

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

      1. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   if -3.6999999999999998e-233 < t < 7.9999999999999994e-244 or 6.80000000000000004e-108 < t < 1.54999999999999994e-60

   1. Initial program 91.8%

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

      1. associate-/l/ 96.4%

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

      2. div-inv 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/r* 75.7%

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

      3. distribute-neg-frac 75.7%

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

      4. distribute-neg-frac2 75.7%

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

   7. Simplified 75.7%

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

      1. *-un-lft-identity 75.7%

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

      2. associate-/l/ 71.1%

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

      3. sub-neg 71.1%

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

      4. add-sqr-sqrt 42.4%

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

      5. sqrt-unprod 60.1%

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

      6. sqr-neg 60.1%

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

      7. sqrt-unprod 17.6%

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

      8. add-sqr-sqrt 37.2%

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

      9. add-sqr-sqrt 19.6%

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

      10. sqrt-unprod 48.3%

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

      11. sqr-neg 48.3%

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

      12. sqrt-unprod 28.6%

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

      13. add-sqr-sqrt 67.4%

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

   9. Applied egg-rr 67.4%

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

       1. *-lft-identity 67.4%

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

       2. *-commutative 67.4%

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

       3. +-commutative 67.4%

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

   11. Simplified 67.4%

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

   if 1.54999999999999994e-60 < t

   1. Initial program 84.3%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 81.0%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(t + z\right)}\\ t_2 := \frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (+ t z)))) (t_2 (/ x (* (- t z) y))))
   (if (<= t -9.5e-233)
     t_2
     (if (<= t 1.5e-243)
       t_1
       (if (<= t 2.8e-107) t_2 (if (<= t 3.4e-56) t_1 (/ x (* t (- y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (t + z));
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (t <= -9.5e-233) {
		tmp = t_2;
	} else if (t <= 1.5e-243) {
		tmp = t_1;
	} else if (t <= 2.8e-107) {
		tmp = t_2;
	} else if (t <= 3.4e-56) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (z * (t + z))
    t_2 = x / ((t - z) * y)
    if (t <= (-9.5d-233)) then
        tmp = t_2
    else if (t <= 1.5d-243) then
        tmp = t_1
    else if (t <= 2.8d-107) then
        tmp = t_2
    else if (t <= 3.4d-56) then
        tmp = t_1
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (t + z));
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (t <= -9.5e-233) {
		tmp = t_2;
	} else if (t <= 1.5e-243) {
		tmp = t_1;
	} else if (t <= 2.8e-107) {
		tmp = t_2;
	} else if (t <= 3.4e-56) {
		tmp = t_1;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (t + z))
	t_2 = x / ((t - z) * y)
	tmp = 0
	if t <= -9.5e-233:
		tmp = t_2
	elif t <= 1.5e-243:
		tmp = t_1
	elif t <= 2.8e-107:
		tmp = t_2
	elif t <= 3.4e-56:
		tmp = t_1
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(t + z)))
	t_2 = Float64(x / Float64(Float64(t - z) * y))
	tmp = 0.0
	if (t <= -9.5e-233)
		tmp = t_2;
	elseif (t <= 1.5e-243)
		tmp = t_1;
	elseif (t <= 2.8e-107)
		tmp = t_2;
	elseif (t <= 3.4e-56)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (t + z));
	t_2 = x / ((t - z) * y);
	tmp = 0.0;
	if (t <= -9.5e-233)
		tmp = t_2;
	elseif (t <= 1.5e-243)
		tmp = t_1;
	elseif (t <= 2.8e-107)
		tmp = t_2;
	elseif (t <= 3.4e-56)
		tmp = t_1;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-233], t$95$2, If[LessEqual[t, 1.5e-243], t$95$1, If[LessEqual[t, 2.8e-107], t$95$2, If[LessEqual[t, 3.4e-56], t$95$1, N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5000000000000003e-233 or 1.5000000000000001e-243 < t < 2.7999999999999999e-107

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 64.7%

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

      1. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   if -9.5000000000000003e-233 < t < 1.5000000000000001e-243 or 2.7999999999999999e-107 < t < 3.39999999999999982e-56

   1. Initial program 91.8%

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

      1. associate-/l/ 96.4%

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

      2. div-inv 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/r* 75.7%

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

      3. distribute-neg-frac 75.7%

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

      4. distribute-neg-frac2 75.7%

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

   7. Simplified 75.7%

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

      1. *-un-lft-identity 75.7%

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

      2. associate-/l/ 71.1%

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

      3. sub-neg 71.1%

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

      4. add-sqr-sqrt 42.4%

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

      5. sqrt-unprod 60.1%

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

      6. sqr-neg 60.1%

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

      7. sqrt-unprod 17.6%

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

      8. add-sqr-sqrt 37.2%

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

      9. add-sqr-sqrt 19.6%

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

      10. sqrt-unprod 48.3%

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

      11. sqr-neg 48.3%

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

      12. sqrt-unprod 28.6%

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

      13. add-sqr-sqrt 67.4%

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

   9. Applied egg-rr 67.4%

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

       1. *-lft-identity 67.4%

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

       2. *-commutative 67.4%

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

       3. +-commutative 67.4%

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

   11. Simplified 67.4%

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

   if 3.39999999999999982e-56 < t

   1. Initial program 84.3%

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

   3. Taylor expanded in t around inf 73.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-243}:\\ \;\;\;\;\frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e+144)
   (/ (/ x z) (- z y))
   (if (<= z 1.6e+114) (/ x (* (- t z) (- y z))) (/ (/ x z) (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+144) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.6e+114) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (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 <= (-3.5d+144)) then
        tmp = (x / z) / (z - y)
    else if (z <= 1.6d+114) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = (x / z) / (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 <= -3.5e+144) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.6e+114) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e+144:
		tmp = (x / z) / (z - y)
	elif z <= 1.6e+114:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e+144)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 1.6e+114)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e+144)
		tmp = (x / z) / (z - y);
	elseif (z <= 1.6e+114)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e+144], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+114], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999998e144

   1. Initial program 83.4%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 94.1%

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

      1. associate-*r/ 94.1%

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

      2. neg-mul-1 94.1%

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

   7. Simplified 94.1%

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

   if -3.4999999999999998e144 < z < 1.6e114

   1. Initial program 93.0%

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

   if 1.6e114 < z

   1. Initial program 68.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. associate-/r* 94.8%

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

      3. distribute-neg-frac 94.8%

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

      4. distribute-neg-frac2 94.8%

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

   7. Simplified 94.8%

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

      1. frac-2neg 94.8%

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

      2. div-inv 94.8%

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

      3. distribute-frac-neg2 94.8%

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

      4. remove-double-neg 94.8%

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

      5. sub-neg 94.8%

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

      6. distribute-neg-in 94.8%

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

      7. remove-double-neg 94.8%

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

   9. Applied egg-rr 94.8%

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

       1. associate-*r/ 94.8%

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

       2. *-rgt-identity 94.8%

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

       3. +-commutative 94.8%

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

       4. unsub-neg 94.8%

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

   11. Simplified 94.8%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10.5 \lor \neg \left(z \leq 0.0008\right):\\ \;\;\;\;\frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -10.5) (not (<= z 0.0008)))
   (/ x (* z (+ t z)))
   (/ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -10.5) || !(z <= 0.0008)) {
		tmp = x / (z * (t + z));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-10.5d0)) .or. (.not. (z <= 0.0008d0))) then
        tmp = x / (z * (t + z))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -10.5) || !(z <= 0.0008)) {
		tmp = x / (z * (t + z));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -10.5) or not (z <= 0.0008):
		tmp = x / (z * (t + z))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -10.5) || !(z <= 0.0008))
		tmp = Float64(x / Float64(z * Float64(t + z)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -10.5) || ~((z <= 0.0008)))
		tmp = x / (z * (t + z));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -10.5], N[Not[LessEqual[z, 0.0008]], $MachinePrecision]], N[(x / N[(z * N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -10.5 or 8.00000000000000038e-4 < z

   1. Initial program 81.1%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. associate-/r* 84.2%

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

      3. distribute-neg-frac 84.2%

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

      4. distribute-neg-frac2 84.2%

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

   7. Simplified 84.2%

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

      1. *-un-lft-identity 84.2%

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

      2. associate-/l/ 72.2%

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

      3. sub-neg 72.2%

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

      4. add-sqr-sqrt 39.4%

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

      5. sqrt-unprod 66.9%

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

      6. sqr-neg 66.9%

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

      7. sqrt-unprod 27.5%

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

      8. add-sqr-sqrt 60.5%

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

      9. add-sqr-sqrt 33.0%

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

      10. sqrt-unprod 65.1%

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

      11. sqr-neg 65.1%

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

      12. sqrt-unprod 32.0%

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

      13. add-sqr-sqrt 68.4%

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

   9. Applied egg-rr 68.4%

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

       1. *-lft-identity 68.4%

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

       2. *-commutative 68.4%

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

       3. +-commutative 68.4%

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

   11. Simplified 68.4%

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

   if -10.5 < z < 8.00000000000000038e-4

   1. Initial program 94.5%

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

   3. Taylor expanded in t around inf 66.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10.5 \lor \neg \left(z \leq 0.0008\right):\\ \;\;\;\;\frac{x}{z \cdot \left(t + z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{-124} \lor \neg \left(t \leq 8.2 \cdot 10^{-156}\right):\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.46e-124) (not (<= t 8.2e-156)))
   (/ x (* t (- y z)))
   (/ x (* y (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.46e-124) || !(t <= 8.2e-156)) {
		tmp = x / (t * (y - z));
	} else {
		tmp = 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 <= (-1.46d-124)) .or. (.not. (t <= 8.2d-156))) then
        tmp = x / (t * (y - z))
    else
        tmp = 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 <= -1.46e-124) || !(t <= 8.2e-156)) {
		tmp = x / (t * (y - z));
	} else {
		tmp = x / (y * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.46e-124) or not (t <= 8.2e-156):
		tmp = x / (t * (y - z))
	else:
		tmp = x / (y * -z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.46e-124) || !(t <= 8.2e-156))
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(x / Float64(y * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.46e-124) || ~((t <= 8.2e-156)))
		tmp = x / (t * (y - z));
	else
		tmp = x / (y * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.46e-124], N[Not[LessEqual[t, 8.2e-156]], $MachinePrecision]], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4599999999999999e-124 or 8.2000000000000004e-156 < t

   1. Initial program 86.9%

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

   3. Taylor expanded in t around inf 69.4%

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

   if -1.4599999999999999e-124 < t < 8.2000000000000004e-156

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 89.8%

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

      1. associate-/l/ 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in y around inf 62.8%

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

   7. Taylor expanded in t around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. distribute-neg-frac2 54.2%

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

      3. *-commutative 54.2%

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

      4. distribute-rgt-neg-out 54.2%

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

   9. Simplified 54.2%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(-y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{-124} \lor \neg \left(t \leq 8.2 \cdot 10^{-156}\right):\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.05e-46)
   (/ (/ x y) (- t z))
   (if (<= y 1.55e-55) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.05e-46) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.55e-55) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (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 <= (-3.05d-46)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.55d-55) then
        tmp = (x / z) / (z - t)
    else
        tmp = (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 <= -3.05e-46) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.55e-55) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.05e-46:
		tmp = (x / y) / (t - z)
	elif y <= 1.55e-55:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.05e-46)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.55e-55)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = 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 <= -3.05e-46)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.55e-55)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.05e-46], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-55], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.05000000000000018e-46

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 90.4%

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

      1. associate-/l/ 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in y around inf 88.0%

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

   if -3.05000000000000018e-46 < y < 1.54999999999999998e-55

   1. Initial program 86.8%

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

      1. associate-/l/ 98.3%

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

      2. div-inv 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-/r* 86.7%

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

      3. distribute-neg-frac 86.7%

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

      4. distribute-neg-frac2 86.7%

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

   7. Simplified 86.7%

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

      1. frac-2neg 86.7%

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

      2. div-inv 86.6%

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

      3. distribute-frac-neg2 86.6%

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

      4. remove-double-neg 86.6%

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

      5. sub-neg 86.6%

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

      6. distribute-neg-in 86.6%

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

      7. remove-double-neg 86.6%

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

   9. Applied egg-rr 86.6%

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

       1. associate-*r/ 86.7%

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

       2. *-rgt-identity 86.7%

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

       3. +-commutative 86.7%

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

       4. unsub-neg 86.7%

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

   11. Simplified 86.7%

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

   if 1.54999999999999998e-55 < y

   1. Initial program 86.3%

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

      1. associate-/l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf 51.2%

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

Alternative 11: 42.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.7e-59) (/ x (* y (- z))) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.7e-59) {
		tmp = x / (y * -z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 2.7d-59) then
        tmp = x / (y * -z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.7e-59) {
		tmp = x / (y * -z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.7e-59:
		tmp = x / (y * -z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.7e-59)
		tmp = Float64(x / Float64(y * Float64(-z)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.7e-59)
		tmp = x / (y * -z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.7e-59], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.6999999999999999e-59

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 89.6%

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

      1. associate-/l/ 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in y around inf 59.0%

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

   7. Taylor expanded in t around 0 40.9%

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

      1. mul-1-neg 40.9%

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

      2. distribute-neg-frac2 40.9%

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

      3. *-commutative 40.9%

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

      4. distribute-rgt-neg-out 40.9%

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

   9. Simplified 40.9%

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

   if 2.6999999999999999e-59 < t

   1. Initial program 84.3%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 51.1%

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

      1. associate-/r* 60.2%

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

   9. Simplified 60.2%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 6.5e-134) (/ (/ x y) t) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.5e-134) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 6.5d-134) then
        tmp = (x / y) / t
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.5e-134) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 6.5e-134:
		tmp = (x / y) / t
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6.5e-134)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6.5e-134)
		tmp = (x / y) / t;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 6.5e-134], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.4999999999999998e-134

   1. Initial program 89.4%

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

   3. Taylor expanded in z around 0 29.9%

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

      1. div-inv 29.8%

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

      2. associate-/r* 29.8%

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

   5. Applied egg-rr 29.8%

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

      1. *-commutative 29.8%

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

      2. associate-*l/ 31.9%

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

      3. associate-*r/ 30.7%

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

      4. associate-*l/ 30.7%

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

      5. *-lft-identity 30.7%

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

   7. Simplified 30.7%

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

   if 6.4999999999999998e-134 < t

   1. Initial program 85.1%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 47.0%

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

      1. associate-/r* 55.1%

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

   9. Simplified 55.1%

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

Alternative 13: 43.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (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 = (x / t) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

   1. associate-/l/ 97.3%

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

3. Simplified 97.3%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. clear-num 97.1%

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

   2. associate-/r/ 97.3%

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

6. Applied egg-rr 97.3%

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

7. Taylor expanded in z around 0 36.6%

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

   1. associate-/r* 41.1%

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

9. Simplified 41.1%

   \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
10. Add Preprocessing

Alternative 14: 40.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

3. Taylor expanded in z around 0 36.6%

   \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
4. Add Preprocessing

Developer target: 88.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / 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 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024102 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))