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

Percentage Accurate: 88.7% → 96.9%

Time: 11.4s

Alternatives: 17

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: 88.7% 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: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{\frac{x}{y - z}}{t - z} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- y z)) (- t z)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return (x / (y - z)) / (t - z)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(y - z)) / Float64(t - z))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (y - z)) / (t - z);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.6%

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

   1. associate-/r* 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 2: 91.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t - z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 2e+286) (/ x t_1) (/ (/ (- x) (- t z)) z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 2e+286) {
		tmp = x / t_1;
	} else {
		tmp = (-x / (t - z)) / z;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 (t_1 <= 2d+286) then
        tmp = x / t_1
    else
        tmp = (-x / (t - z)) / z
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 2e+286) {
		tmp = x / t_1;
	} else {
		tmp = (-x / (t - z)) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 2e+286:
		tmp = x / t_1
	else:
		tmp = (-x / (t - z)) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 2e+286)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(Float64(-x) / Float64(t - z)) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 2e+286)
		tmp = x / t_1;
	else
		tmp = (-x / (t - z)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+286], N[(x / t$95$1), $MachinePrecision], N[(N[((-x) / N[(t - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000007e286

   1. Initial program 95.3%

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

   if 2.00000000000000007e286 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 71.1%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around 0 69.9%

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

      1. *-commutative 69.9%

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

      2. neg-mul-1 69.9%

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

      3. associate-/r* 89.4%

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

      4. distribute-neg-frac 89.4%

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

      5. distribute-frac-neg 89.4%

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

   6. Simplified 89.4%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t - z}}{z}\\ \end{array} \]

Alternative 3: 78.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-68}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.3e-14)
   (/ (/ x y) (- t z))
   (if (<= y -6.8e-68)
     (/ 1.0 (/ z (/ x z)))
     (if (<= y -6.4e-78)
       (/ x (* y (- z)))
       (if (<= y 1.6e-229) (/ x (* z (- z t))) (/ x (* (- y z) t)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.3e-14) {
		tmp = (x / y) / (t - z);
	} else if (y <= -6.8e-68) {
		tmp = 1.0 / (z / (x / z));
	} else if (y <= -6.4e-78) {
		tmp = x / (y * -z);
	} else if (y <= 1.6e-229) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-5.3d-14)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-6.8d-68)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (y <= (-6.4d-78)) then
        tmp = x / (y * -z)
    else if (y <= 1.6d-229) then
        tmp = x / (z * (z - t))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.3e-14) {
		tmp = (x / y) / (t - z);
	} else if (y <= -6.8e-68) {
		tmp = 1.0 / (z / (x / z));
	} else if (y <= -6.4e-78) {
		tmp = x / (y * -z);
	} else if (y <= 1.6e-229) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.3e-14:
		tmp = (x / y) / (t - z)
	elif y <= -6.8e-68:
		tmp = 1.0 / (z / (x / z))
	elif y <= -6.4e-78:
		tmp = x / (y * -z)
	elif y <= 1.6e-229:
		tmp = x / (z * (z - t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.3e-14)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -6.8e-68)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (y <= -6.4e-78)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (y <= 1.6e-229)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.3e-14)
		tmp = (x / y) / (t - z);
	elseif (y <= -6.8e-68)
		tmp = 1.0 / (z / (x / z));
	elseif (y <= -6.4e-78)
		tmp = x / (y * -z);
	elseif (y <= 1.6e-229)
		tmp = x / (z * (z - t));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5.3e-14], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e-68], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.4e-78], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-229], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.3000000000000001e-14

   1. Initial program 86.6%

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

      1. associate-/r* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 86.1%

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

   if -5.3000000000000001e-14 < y < -6.80000000000000037e-68

   1. Initial program 99.7%

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

      1. associate-/r* 99.3%

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

      2. div-inv 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. associate-*l/ 99.6%

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

      2. div-inv 99.7%

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

      3. clear-num 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around inf 43.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 43.7%

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

      2. associate-/l* 43.7%

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

   8. Simplified 43.7%

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

   if -6.80000000000000037e-68 < y < -6.4e-78

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in t around 0 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-rgt-neg-out 50.1%

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

   7. Simplified 50.1%

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

   if -6.4e-78 < y < 1.60000000000000007e-229

   1. Initial program 87.7%

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

      1. frac-2neg 87.7%

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

      2. div-inv 87.7%

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

      3. distribute-rgt-neg-in 87.7%

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

   3. Applied egg-rr 87.7%

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

   4. Taylor expanded in y around 0 79.1%

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

   if 1.60000000000000007e-229 < y

   1. Initial program 86.8%

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

   2. Taylor expanded in t around inf 58.9%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-68}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 4: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 6700000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e+116)
   (* (/ x z) (/ 1.0 z))
   (if (<= z -2.6e-23)
     (/ x (* z (- z t)))
     (if (<= z 6700000000.0) (/ x (* (- y z) t)) (/ (/ x z) z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+116) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -2.6e-23) {
		tmp = x / (z * (z - t));
	} else if (z <= 6700000000.0) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-3.7d+116)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= (-2.6d-23)) then
        tmp = x / (z * (z - t))
    else if (z <= 6700000000.0d0) then
        tmp = x / ((y - z) * t)
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+116) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -2.6e-23) {
		tmp = x / (z * (z - t));
	} else if (z <= 6700000000.0) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e+116:
		tmp = (x / z) * (1.0 / z)
	elif z <= -2.6e-23:
		tmp = x / (z * (z - t))
	elif z <= 6700000000.0:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / z) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e+116)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= -2.6e-23)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	elseif (z <= 6700000000.0)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.7e+116)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= -2.6e-23)
		tmp = x / (z * (z - t));
	elseif (z <= 6700000000.0)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e+116], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-23], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6700000000.0], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7000000000000001e116

   1. Initial program 80.4%

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

   2. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 76.8%

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

   4. Simplified 76.8%

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

      1. *-un-lft-identity 76.8%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. *-commutative 92.9%

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

   8. Simplified 92.9%

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

   if -3.7000000000000001e116 < z < -2.6e-23

   1. Initial program 92.2%

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

      1. frac-2neg 92.2%

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

      2. div-inv 92.2%

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

      3. distribute-rgt-neg-in 92.2%

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

   3. Applied egg-rr 92.2%

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

   4. Taylor expanded in y around 0 77.8%

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

   if -2.6e-23 < z < 6.7e9

   1. Initial program 92.5%

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

   2. Taylor expanded in t around inf 75.2%

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

   if 6.7e9 < z

   1. Initial program 81.9%

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

   2. Taylor expanded in z around inf 71.4%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 71.4%

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

      2. associate-/r* 79.5%

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

   4. Simplified 79.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 6700000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 5: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-258}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 4.45 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.75e+88)
   (* (/ x z) (/ 1.0 z))
   (if (<= z -1.55e-258)
     (/ (/ x t) (- y z))
     (if (<= z 4.45e+18) (/ x (* y (- t z))) (/ (/ x z) z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+88) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -1.55e-258) {
		tmp = (x / t) / (y - z);
	} else if (z <= 4.45e+18) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.75d+88)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= (-1.55d-258)) then
        tmp = (x / t) / (y - z)
    else if (z <= 4.45d+18) then
        tmp = x / (y * (t - z))
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+88) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -1.55e-258) {
		tmp = (x / t) / (y - z);
	} else if (z <= 4.45e+18) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.75e+88:
		tmp = (x / z) * (1.0 / z)
	elif z <= -1.55e-258:
		tmp = (x / t) / (y - z)
	elif z <= 4.45e+18:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / z) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.75e+88)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= -1.55e-258)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 4.45e+18)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.75e+88)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= -1.55e-258)
		tmp = (x / t) / (y - z);
	elseif (z <= 4.45e+18)
		tmp = x / (y * (t - z));
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.75e+88], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-258], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.45e+18], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.75e88

   1. Initial program 80.4%

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

   2. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 76.8%

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

   4. Simplified 76.8%

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

      1. *-un-lft-identity 76.8%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. *-commutative 92.9%

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

   8. Simplified 92.9%

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

   if -2.75e88 < z < -1.54999999999999999e-258

   1. Initial program 89.8%

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

      1. associate-/l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 74.7%

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

   if -1.54999999999999999e-258 < z < 4.45e18

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

   4. Simplified 79.1%

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

   if 4.45e18 < z

   1. Initial program 81.5%

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

   2. Taylor expanded in z around inf 72.5%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 72.5%

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

      2. associate-/r* 80.7%

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

   4. Simplified 80.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-258}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 4.45 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 6: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-60}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e-154)
   (/ (/ x y) (- t z))
   (if (<= t 1.35e-60) (/ (- x) (* z (- y z))) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-154) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.35e-60) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-1.8d-154)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.35d-60) then
        tmp = -x / (z * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-154) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.35e-60) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e-154:
		tmp = (x / y) / (t - z)
	elif t <= 1.35e-60:
		tmp = -x / (z * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e-154)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.35e-60)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e-154)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.35e-60)
		tmp = -x / (z * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e-154], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-60], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8000000000000001e-154

   1. Initial program 83.2%

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

      1. associate-/r* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around inf 58.7%

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

   if -1.8000000000000001e-154 < t < 1.35e-60

   1. Initial program 86.6%

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

   2. Taylor expanded in t around 0 65.9%

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

      1. associate-*r/ 65.9%

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

      2. neg-mul-1 65.9%

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

      3. *-commutative 65.9%

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

   4. Simplified 65.9%

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

   if 1.35e-60 < t

   1. Initial program 94.1%

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

      1. associate-/l/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in t around inf 86.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-60}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 7: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e+47)
   (/ (/ x y) (- t z))
   (if (<= y 7.5e-228) (/ (/ (- x) z) (- t z)) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e+47) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7.5e-228) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-2.2d+47)) then
        tmp = (x / y) / (t - z)
    else if (y <= 7.5d-228) then
        tmp = (-x / z) / (t - z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e+47) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7.5e-228) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e+47:
		tmp = (x / y) / (t - z)
	elif y <= 7.5e-228:
		tmp = (-x / z) / (t - z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e+47)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 7.5e-228)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.2e+47)
		tmp = (x / y) / (t - z);
	elseif (y <= 7.5e-228)
		tmp = (-x / z) / (t - z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e+47], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-228], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e47

   1. Initial program 87.6%

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

      1. associate-/r* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 91.8%

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

   if -2.1999999999999999e47 < y < 7.4999999999999999e-228

   1. Initial program 88.8%

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

   2. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-frac-neg 71.2%

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

      3. associate-/r* 80.8%

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

   4. Simplified 80.8%

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

   if 7.4999999999999999e-228 < y

   1. Initial program 86.8%

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

   2. Taylor expanded in t around inf 58.9%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 8: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{-x}{t - z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e+46)
   (/ (/ x y) (- t z))
   (if (<= y 7.5e-228) (/ (/ (- x) (- t z)) z) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e+46) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7.5e-228) {
		tmp = (-x / (t - z)) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-3.6d+46)) then
        tmp = (x / y) / (t - z)
    else if (y <= 7.5d-228) then
        tmp = (-x / (t - z)) / z
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e+46) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7.5e-228) {
		tmp = (-x / (t - z)) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e+46:
		tmp = (x / y) / (t - z)
	elif y <= 7.5e-228:
		tmp = (-x / (t - z)) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e+46)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 7.5e-228)
		tmp = Float64(Float64(Float64(-x) / Float64(t - z)) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.6e+46)
		tmp = (x / y) / (t - z);
	elseif (y <= 7.5e-228)
		tmp = (-x / (t - z)) / z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e+46], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-228], N[(N[((-x) / N[(t - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5999999999999999e46

   1. Initial program 87.6%

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

      1. associate-/r* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 91.8%

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

   if -3.5999999999999999e46 < y < 7.4999999999999999e-228

   1. Initial program 88.8%

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

      1. associate-/r* 96.4%

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

      2. div-inv 96.4%

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

   3. Applied egg-rr 96.4%

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

   4. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. neg-mul-1 71.2%

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

      3. associate-/r* 81.0%

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

      4. distribute-neg-frac 81.0%

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

      5. distribute-frac-neg 81.0%

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

   6. Simplified 81.0%

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

   if 7.4999999999999999e-228 < y

   1. Initial program 86.8%

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

   2. Taylor expanded in t around inf 58.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{-x}{t - z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 9: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -57 \lor \neg \left(z \leq 6400000000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -57.0) (not (<= z 6400000000.0)))
   (/ (/ x z) z)
   (* (/ x t) (/ 1.0 y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -57.0) || !(z <= 6400000000.0)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) * (1.0 / y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-57.0d0)) .or. (.not. (z <= 6400000000.0d0))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) * (1.0d0 / y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -57.0) || !(z <= 6400000000.0)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) * (1.0 / y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -57.0) or not (z <= 6400000000.0):
		tmp = (x / z) / z
	else:
		tmp = (x / t) * (1.0 / y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -57.0) || !(z <= 6400000000.0))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -57.0) || ~((z <= 6400000000.0)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -57.0], N[Not[LessEqual[z, 6400000000.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -57 or 6.4e9 < z

   1. Initial program 82.1%

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

   2. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 69.3%

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

      2. associate-/r* 79.6%

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

   4. Simplified 79.6%

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

   if -57 < z < 6.4e9

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 60.4%

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

      1. *-un-lft-identity 60.4%

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

      2. times-frac 62.8%

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

   4. Applied egg-rr 62.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -57 \lor \neg \left(z \leq 6400000000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \end{array} \]

Alternative 10: 66.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1500:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 460000000:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1500.0)
   (* (/ x z) (/ 1.0 z))
   (if (<= z 460000000.0) (* (/ x t) (/ 1.0 y)) (/ (/ x z) z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1500.0) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 460000000.0) {
		tmp = (x / t) * (1.0 / y);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-1500.0d0)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 460000000.0d0) then
        tmp = (x / t) * (1.0d0 / y)
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1500.0) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 460000000.0) {
		tmp = (x / t) * (1.0 / y);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1500.0:
		tmp = (x / z) * (1.0 / z)
	elif z <= 460000000.0:
		tmp = (x / t) * (1.0 / y)
	else:
		tmp = (x / z) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1500.0)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 460000000.0)
		tmp = Float64(Float64(x / t) * Float64(1.0 / y));
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1500.0)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 460000000.0)
		tmp = (x / t) * (1.0 / y);
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1500.0], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 460000000.0], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1500

   1. Initial program 82.3%

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

   2. Taylor expanded in z around inf 67.6%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 67.6%

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

   4. Simplified 67.6%

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

      1. *-un-lft-identity 67.6%

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

      2. times-frac 79.8%

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

   6. Applied egg-rr 79.8%

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

      1. *-commutative 79.8%

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

   8. Simplified 79.8%

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

   if -1500 < z < 4.6e8

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 60.4%

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

      1. *-un-lft-identity 60.4%

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

      2. times-frac 62.8%

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

   4. Applied egg-rr 62.8%

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

   if 4.6e8 < z

   1. Initial program 81.9%

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

   2. Taylor expanded in z around inf 71.4%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 71.4%

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

      2. associate-/r* 79.5%

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

   4. Simplified 79.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1500:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 460000000:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 11: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 44000000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.6e+94)
   (* (/ x z) (/ 1.0 z))
   (if (<= z 44000000000.0) (/ x (* (- y z) t)) (/ (/ x z) z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+94) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 44000000000.0) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-6.6d+94)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 44000000000.0d0) then
        tmp = x / ((y - z) * t)
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+94) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 44000000000.0) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.6e+94:
		tmp = (x / z) * (1.0 / z)
	elif z <= 44000000000.0:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / z) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.6e+94)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 44000000000.0)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.6e+94)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 44000000000.0)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -6.6e+94], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 44000000000.0], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6e94

   1. Initial program 80.4%

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

   2. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 76.8%

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

   4. Simplified 76.8%

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

      1. *-un-lft-identity 76.8%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. *-commutative 92.9%

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

   8. Simplified 92.9%

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

   if -6.6e94 < z < 4.4e10

   1. Initial program 92.5%

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

   2. Taylor expanded in t around inf 71.6%

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

   if 4.4e10 < z

   1. Initial program 81.9%

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

   2. Taylor expanded in z around inf 71.4%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 71.4%

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

      2. associate-/r* 79.5%

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

   4. Simplified 79.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 44000000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 12: 45.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+78} \lor \neg \left(z \leq 8.6 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.75e+78) (not (<= z 8.6e+113))) (/ x (* z t)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.75e+78) || !(z <= 8.6e+113)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.75d+78)) .or. (.not. (z <= 8.6d+113))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.75e+78) || !(z <= 8.6e+113)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.75e+78) or not (z <= 8.6e+113):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.75e+78) || !(z <= 8.6e+113))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.75e+78) || ~((z <= 8.6e+113)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.75e+78], N[Not[LessEqual[z, 8.6e+113]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7499999999999999e78 or 8.6000000000000007e113 < z

   1. Initial program 79.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. Taylor expanded in t around inf 44.6%

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

   5. Taylor expanded in y around 0 44.8%

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

      1. mul-1-neg 44.8%

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

      2. associate-/r* 44.6%

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

      3. distribute-neg-frac 44.6%

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

      4. distribute-neg-frac 44.6%

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

   7. Simplified 44.6%

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

      1. expm1-log1p-u 44.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{t}}{z}\right)\right)} \]

      2. expm1-udef 58.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{t}}{z}\right)} - 1} \]

      3. associate-/l/ 58.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot t}}\right)} - 1 \]

      4. add-sqr-sqrt 22.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      5. sqrt-unprod 55.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      6. sqr-neg 55.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      7. sqrt-unprod 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      8. add-sqr-sqrt 58.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   9. Applied egg-rr 58.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 43.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

       2. expm1-log1p 43.2%

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

   11. Simplified 43.2%

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

   if -2.7499999999999999e78 < z < 8.6000000000000007e113

   1. Initial program 92.2%

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

   2. Taylor expanded in z around 0 52.9%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+78} \lor \neg \left(z \leq 8.6 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 13: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -410 \lor \neg \left(z \leq 90000000000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -410.0) (not (<= z 90000000000.0)))
   (/ x (* z z))
   (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -410.0) || !(z <= 90000000000.0)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-410.0d0)) .or. (.not. (z <= 90000000000.0d0))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -410.0) || !(z <= 90000000000.0)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -410.0) or not (z <= 90000000000.0):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -410.0) || !(z <= 90000000000.0))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -410.0) || ~((z <= 90000000000.0)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -410.0], N[Not[LessEqual[z, 90000000000.0]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -410 or 9e10 < z

   1. Initial program 82.1%

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

   2. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 69.3%

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

   4. Simplified 69.3%

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

   if -410 < z < 9e10

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 60.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -410 \lor \neg \left(z \leq 90000000000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -850 \lor \neg \left(z \leq 95000000000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -850.0) (not (<= z 95000000000.0)))
   (/ (/ x z) z)
   (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -850.0) || !(z <= 95000000000.0)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-850.0d0)) .or. (.not. (z <= 95000000000.0d0))) then
        tmp = (x / z) / z
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -850.0) || !(z <= 95000000000.0)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -850.0) or not (z <= 95000000000.0):
		tmp = (x / z) / z
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -850.0) || !(z <= 95000000000.0))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -850.0) || ~((z <= 95000000000.0)))
		tmp = (x / z) / z;
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -850.0], N[Not[LessEqual[z, 95000000000.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -850 or 9.5e10 < z

   1. Initial program 82.1%

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

   2. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 69.3%

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

      2. associate-/r* 79.6%

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

   4. Simplified 79.6%

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

   if -850 < z < 9.5e10

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 60.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -850 \lor \neg \left(z \leq 95000000000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 45.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+80)
   (/ x (* z t))
   (if (<= z 3.2e+118) (/ x (* y t)) (/ x (* y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+80) {
		tmp = x / (z * t);
	} else if (z <= 3.2e+118) {
		tmp = x / (y * t);
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.2d+80)) then
        tmp = x / (z * t)
    else if (z <= 3.2d+118) then
        tmp = x / (y * t)
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+80) {
		tmp = x / (z * t);
	} else if (z <= 3.2e+118) {
		tmp = x / (y * t);
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+80:
		tmp = x / (z * t)
	elif z <= 3.2e+118:
		tmp = x / (y * t)
	else:
		tmp = x / (y * z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+80)
		tmp = Float64(x / Float64(z * t));
	elseif (z <= 3.2e+118)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e+80)
		tmp = x / (z * t);
	elseif (z <= 3.2e+118)
		tmp = x / (y * t);
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+80], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+118], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000003e80

   1. Initial program 81.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. Taylor expanded in t around inf 47.2%

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

   5. Taylor expanded in y around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. associate-/r* 47.1%

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

      3. distribute-neg-frac 47.1%

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

      4. distribute-neg-frac 47.1%

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

   7. Simplified 47.1%

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

      1. expm1-log1p-u 46.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{t}}{z}\right)\right)} \]

      2. expm1-udef 64.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{t}}{z}\right)} - 1} \]

      3. associate-/l/ 64.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot t}}\right)} - 1 \]

      4. add-sqr-sqrt 26.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      5. sqrt-unprod 62.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      6. sqr-neg 62.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      7. sqrt-unprod 38.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      8. add-sqr-sqrt 65.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   9. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 46.1%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

       2. expm1-log1p 46.2%

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

   11. Simplified 46.2%

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

   if -2.20000000000000003e80 < z < 3.20000000000000016e118

   1. Initial program 91.8%

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

   2. Taylor expanded in z around 0 52.9%

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

   if 3.20000000000000016e118 < z

   1. Initial program 77.1%

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

   2. Taylor expanded in y around inf 42.0%

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

      1. *-commutative 42.0%

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

   4. Simplified 42.0%

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

   5. Taylor expanded in t around 0 42.0%

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

      1. mul-1-neg 42.0%

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

      2. associate-/r* 40.5%

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

      3. distribute-neg-frac 40.5%

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

      4. distribute-neg-frac 40.5%

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

   7. Simplified 40.5%

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

      1. expm1-log1p-u 40.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{y}}{z}\right)\right)} \]

      2. expm1-udef 58.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{y}}{z}\right)} - 1} \]

      3. associate-/l/ 58.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot y}}\right)} - 1 \]

      4. add-sqr-sqrt 19.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot y}\right)} - 1 \]

      5. sqrt-unprod 54.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot y}\right)} - 1 \]

      6. sqr-neg 54.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot y}\right)} - 1 \]

      7. sqrt-unprod 39.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot y}\right)} - 1 \]

      8. add-sqr-sqrt 58.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot y}\right)} - 1 \]

   9. Applied egg-rr 58.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot y}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 41.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot y}\right)\right)} \]

       2. expm1-log1p 42.1%

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

   11. Simplified 42.1%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]

Alternative 16: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- t z)) (- y z)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return (x / (t - z)) / (y - z)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(t - z)) / Float64(y - z))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (t - z)) / (y - z);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.6%

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

   1. associate-/l/ 96.4%

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

3. Simplified 96.4%

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

4. Final simplification 96.4%

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

Alternative 17: 39.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{x}{y \cdot t} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* y t)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 * t)
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return x / (y * t)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(x / Float64(y * t))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (y * t);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.6%

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

2. Taylor expanded in z around 0 43.2%

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

3. Final simplification 43.2%

   \[\leadsto \frac{x}{y \cdot t} \]

Developer target: 87.7% 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 2023238 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (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))))