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

Percentage Accurate: 88.9% → 96.9%

Time: 11.0s

Alternatives: 21

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: 88.9% 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 90.2%

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

   1. associate-/r* 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 2: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1000000000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (/ (/ x t) y)) (t_2 (/ (/ x z) z)))
   (if (<= z -9.5e+70)
     t_2
     (if (<= z -3e-127)
       (/ x (* z (- t)))
       (if (<= z 3.55e-100)
         t_1
         (if (<= z 1000000000000.0)
           (/ (- x) (* y z))
           (if (<= z 1.1e+58) t_1 t_2)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / z) / z;
	double tmp;
	if (z <= -9.5e+70) {
		tmp = t_2;
	} else if (z <= -3e-127) {
		tmp = x / (z * -t);
	} else if (z <= 3.55e-100) {
		tmp = t_1;
	} else if (z <= 1000000000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 1.1e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / t) / y
    t_2 = (x / z) / z
    if (z <= (-9.5d+70)) then
        tmp = t_2
    else if (z <= (-3d-127)) then
        tmp = x / (z * -t)
    else if (z <= 3.55d-100) then
        tmp = t_1
    else if (z <= 1000000000000.0d0) then
        tmp = -x / (y * z)
    else if (z <= 1.1d+58) then
        tmp = t_1
    else
        tmp = t_2
    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 = (x / t) / y;
	double t_2 = (x / z) / z;
	double tmp;
	if (z <= -9.5e+70) {
		tmp = t_2;
	} else if (z <= -3e-127) {
		tmp = x / (z * -t);
	} else if (z <= 3.55e-100) {
		tmp = t_1;
	} else if (z <= 1000000000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 1.1e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = (x / z) / z
	tmp = 0
	if z <= -9.5e+70:
		tmp = t_2
	elif z <= -3e-127:
		tmp = x / (z * -t)
	elif z <= 3.55e-100:
		tmp = t_1
	elif z <= 1000000000000.0:
		tmp = -x / (y * z)
	elif z <= 1.1e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -9.5e+70)
		tmp = t_2;
	elseif (z <= -3e-127)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (z <= 3.55e-100)
		tmp = t_1;
	elseif (z <= 1000000000000.0)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (z <= 1.1e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = (x / z) / z;
	tmp = 0.0;
	if (z <= -9.5e+70)
		tmp = t_2;
	elseif (z <= -3e-127)
		tmp = x / (z * -t);
	elseif (z <= 3.55e-100)
		tmp = t_1;
	elseif (z <= 1000000000000.0)
		tmp = -x / (y * z);
	elseif (z <= 1.1e+58)
		tmp = t_1;
	else
		tmp = t_2;
	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[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -9.5e+70], t$95$2, If[LessEqual[z, -3e-127], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e-100], t$95$1, If[LessEqual[z, 1000000000000.0], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+58], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5000000000000002e70 or 1.1e58 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 79.1%

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

      1. unpow2 79.1%

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

      2. associate-/r* 83.4%

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

   4. Simplified 83.4%

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

   if -9.5000000000000002e70 < z < -3.00000000000000009e-127

   1. Initial program 94.2%

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

   2. Taylor expanded in t around inf 57.1%

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

   3. Taylor expanded in y around 0 40.4%

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

      1. mul-1-neg 40.4%

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

      2. *-commutative 40.4%

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

      3. distribute-rgt-neg-in 40.4%

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

   5. Simplified 40.4%

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

   if -3.00000000000000009e-127 < z < 3.55e-100 or 1e12 < z < 1.1e58

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 67.3%

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

      1. div-inv 67.2%

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

      2. associate-/r* 68.2%

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

   4. Applied egg-rr 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*l/ 74.6%

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

      3. associate-*r/ 73.7%

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

      4. associate-*l/ 73.8%

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

      5. *-lft-identity 73.8%

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

   6. Simplified 73.8%

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

   if 3.55e-100 < z < 1e12

   1. Initial program 99.3%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 42.0%

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

   5. Taylor expanded in t around 0 31.9%

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

      1. mul-1-neg 31.9%

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

   7. Simplified 31.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{-100}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1000000000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 3: 64.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-130}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 13500000000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (/ (/ x t) y)) (t_2 (/ (/ x z) z)))
   (if (<= z -1.02e+71)
     t_2
     (if (<= z -1.32e-130)
       (/ (/ (- x) t) z)
       (if (<= z 3.6e-101)
         t_1
         (if (<= z 13500000000000.0)
           (/ (- x) (* y z))
           (if (<= z 4e+56) t_1 t_2)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / z) / z;
	double tmp;
	if (z <= -1.02e+71) {
		tmp = t_2;
	} else if (z <= -1.32e-130) {
		tmp = (-x / t) / z;
	} else if (z <= 3.6e-101) {
		tmp = t_1;
	} else if (z <= 13500000000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 4e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / t) / y
    t_2 = (x / z) / z
    if (z <= (-1.02d+71)) then
        tmp = t_2
    else if (z <= (-1.32d-130)) then
        tmp = (-x / t) / z
    else if (z <= 3.6d-101) then
        tmp = t_1
    else if (z <= 13500000000000.0d0) then
        tmp = -x / (y * z)
    else if (z <= 4d+56) then
        tmp = t_1
    else
        tmp = t_2
    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 = (x / t) / y;
	double t_2 = (x / z) / z;
	double tmp;
	if (z <= -1.02e+71) {
		tmp = t_2;
	} else if (z <= -1.32e-130) {
		tmp = (-x / t) / z;
	} else if (z <= 3.6e-101) {
		tmp = t_1;
	} else if (z <= 13500000000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 4e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = (x / z) / z
	tmp = 0
	if z <= -1.02e+71:
		tmp = t_2
	elif z <= -1.32e-130:
		tmp = (-x / t) / z
	elif z <= 3.6e-101:
		tmp = t_1
	elif z <= 13500000000000.0:
		tmp = -x / (y * z)
	elif z <= 4e+56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.02e+71)
		tmp = t_2;
	elseif (z <= -1.32e-130)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 3.6e-101)
		tmp = t_1;
	elseif (z <= 13500000000000.0)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (z <= 4e+56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.02e+71)
		tmp = t_2;
	elseif (z <= -1.32e-130)
		tmp = (-x / t) / z;
	elseif (z <= 3.6e-101)
		tmp = t_1;
	elseif (z <= 13500000000000.0)
		tmp = -x / (y * z);
	elseif (z <= 4e+56)
		tmp = t_1;
	else
		tmp = t_2;
	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[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.02e+71], t$95$2, If[LessEqual[z, -1.32e-130], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.6e-101], t$95$1, If[LessEqual[z, 13500000000000.0], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+56], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.02000000000000003e71 or 4.00000000000000037e56 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 79.1%

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

      1. unpow2 79.1%

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

      2. associate-/r* 83.4%

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

   4. Simplified 83.4%

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

   if -1.02000000000000003e71 < z < -1.3200000000000001e-130

   1. Initial program 94.2%

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

   2. Taylor expanded in t around inf 57.1%

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

   3. Taylor expanded in y around 0 40.4%

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

      1. mul-1-neg 40.4%

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

      2. associate-/r* 40.7%

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

      3. distribute-neg-frac 40.7%

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

      4. distribute-neg-frac 40.7%

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

   5. Simplified 40.7%

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

   if -1.3200000000000001e-130 < z < 3.6e-101 or 1.35e13 < z < 4.00000000000000037e56

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 67.3%

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

      1. div-inv 67.2%

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

      2. associate-/r* 68.2%

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

   4. Applied egg-rr 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*l/ 74.6%

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

      3. associate-*r/ 73.7%

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

      4. associate-*l/ 73.8%

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

      5. *-lft-identity 73.8%

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

   6. Simplified 73.8%

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

   if 3.6e-101 < z < 1.35e13

   1. Initial program 99.3%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 42.0%

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

   5. Taylor expanded in t around 0 31.9%

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

      1. mul-1-neg 31.9%

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

   7. Simplified 31.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-130}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 13500000000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+56}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 4: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2800000000:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (/ (/ x t) y)) (t_2 (/ (/ x z) z)))
   (if (<= z -3.4e+71)
     t_2
     (if (<= z -4.8e-128)
       (/ (/ (- x) t) z)
       (if (<= z 6.8e-100)
         t_1
         (if (<= z 2800000000.0)
           (/ (/ (- x) y) z)
           (if (<= z 8e+56) t_1 t_2)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / z) / z;
	double tmp;
	if (z <= -3.4e+71) {
		tmp = t_2;
	} else if (z <= -4.8e-128) {
		tmp = (-x / t) / z;
	} else if (z <= 6.8e-100) {
		tmp = t_1;
	} else if (z <= 2800000000.0) {
		tmp = (-x / y) / z;
	} else if (z <= 8e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / t) / y
    t_2 = (x / z) / z
    if (z <= (-3.4d+71)) then
        tmp = t_2
    else if (z <= (-4.8d-128)) then
        tmp = (-x / t) / z
    else if (z <= 6.8d-100) then
        tmp = t_1
    else if (z <= 2800000000.0d0) then
        tmp = (-x / y) / z
    else if (z <= 8d+56) then
        tmp = t_1
    else
        tmp = t_2
    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 = (x / t) / y;
	double t_2 = (x / z) / z;
	double tmp;
	if (z <= -3.4e+71) {
		tmp = t_2;
	} else if (z <= -4.8e-128) {
		tmp = (-x / t) / z;
	} else if (z <= 6.8e-100) {
		tmp = t_1;
	} else if (z <= 2800000000.0) {
		tmp = (-x / y) / z;
	} else if (z <= 8e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = (x / z) / z
	tmp = 0
	if z <= -3.4e+71:
		tmp = t_2
	elif z <= -4.8e-128:
		tmp = (-x / t) / z
	elif z <= 6.8e-100:
		tmp = t_1
	elif z <= 2800000000.0:
		tmp = (-x / y) / z
	elif z <= 8e+56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -3.4e+71)
		tmp = t_2;
	elseif (z <= -4.8e-128)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 6.8e-100)
		tmp = t_1;
	elseif (z <= 2800000000.0)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= 8e+56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = (x / z) / z;
	tmp = 0.0;
	if (z <= -3.4e+71)
		tmp = t_2;
	elseif (z <= -4.8e-128)
		tmp = (-x / t) / z;
	elseif (z <= 6.8e-100)
		tmp = t_1;
	elseif (z <= 2800000000.0)
		tmp = (-x / y) / z;
	elseif (z <= 8e+56)
		tmp = t_1;
	else
		tmp = t_2;
	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[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -3.4e+71], t$95$2, If[LessEqual[z, -4.8e-128], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 6.8e-100], t$95$1, If[LessEqual[z, 2800000000.0], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 8e+56], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999998e71 or 8.00000000000000074e56 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 79.1%

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

      1. unpow2 79.1%

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

      2. associate-/r* 83.4%

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

   4. Simplified 83.4%

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

   if -3.3999999999999998e71 < z < -4.7999999999999996e-128

   1. Initial program 94.2%

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

   2. Taylor expanded in t around inf 57.1%

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

   3. Taylor expanded in y around 0 40.4%

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

      1. mul-1-neg 40.4%

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

      2. associate-/r* 40.7%

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

      3. distribute-neg-frac 40.7%

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

      4. distribute-neg-frac 40.7%

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

   5. Simplified 40.7%

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

   if -4.7999999999999996e-128 < z < 6.79999999999999953e-100 or 2.8e9 < z < 8.00000000000000074e56

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 67.3%

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

      1. div-inv 67.2%

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

      2. associate-/r* 68.2%

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

   4. Applied egg-rr 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*l/ 74.6%

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

      3. associate-*r/ 73.7%

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

      4. associate-*l/ 73.8%

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

      5. *-lft-identity 73.8%

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

   6. Simplified 73.8%

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

   if 6.79999999999999953e-100 < z < 2.8e9

   1. Initial program 99.3%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 42.0%

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

   5. Taylor expanded in t around 0 31.9%

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

      1. mul-1-neg 31.9%

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

      2. associate-/r* 32.1%

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

      3. distribute-neg-frac 32.1%

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

      4. distribute-neg-frac 32.1%

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

   7. Simplified 32.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-100}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2800000000:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+56}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 5: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ t_2 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;t \leq 3.8 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))) (t_2 (/ x (* y (- t z)))))
   (if (<= t 3.8e-278)
     t_2
     (if (<= t 2.3e-203)
       t_1
       (if (<= t 8.2e-186)
         t_2
         (if (<= t 1.65e-75) t_1 (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double t_2 = x / (y * (t - z));
	double tmp;
	if (t <= 3.8e-278) {
		tmp = t_2;
	} else if (t <= 2.3e-203) {
		tmp = t_1;
	} else if (t <= 8.2e-186) {
		tmp = t_2;
	} else if (t <= 1.65e-75) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) * (1.0d0 / z)
    t_2 = x / (y * (t - z))
    if (t <= 3.8d-278) then
        tmp = t_2
    else if (t <= 2.3d-203) then
        tmp = t_1
    else if (t <= 8.2d-186) then
        tmp = t_2
    else if (t <= 1.65d-75) then
        tmp = t_1
    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 t_1 = (x / z) * (1.0 / z);
	double t_2 = x / (y * (t - z));
	double tmp;
	if (t <= 3.8e-278) {
		tmp = t_2;
	} else if (t <= 2.3e-203) {
		tmp = t_1;
	} else if (t <= 8.2e-186) {
		tmp = t_2;
	} else if (t <= 1.65e-75) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	t_2 = x / (y * (t - z))
	tmp = 0
	if t <= 3.8e-278:
		tmp = t_2
	elif t <= 2.3e-203:
		tmp = t_1
	elif t <= 8.2e-186:
		tmp = t_2
	elif t <= 1.65e-75:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	t_2 = Float64(x / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (t <= 3.8e-278)
		tmp = t_2;
	elseif (t <= 2.3e-203)
		tmp = t_1;
	elseif (t <= 8.2e-186)
		tmp = t_2;
	elseif (t <= 1.65e-75)
		tmp = t_1;
	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)
	t_1 = (x / z) * (1.0 / z);
	t_2 = x / (y * (t - z));
	tmp = 0.0;
	if (t <= 3.8e-278)
		tmp = t_2;
	elseif (t <= 2.3e-203)
		tmp = t_1;
	elseif (t <= 8.2e-186)
		tmp = t_2;
	elseif (t <= 1.65e-75)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 3.8e-278], t$95$2, If[LessEqual[t, 2.3e-203], t$95$1, If[LessEqual[t, 8.2e-186], t$95$2, If[LessEqual[t, 1.65e-75], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 3.7999999999999999e-278 or 2.29999999999999991e-203 < t < 8.2e-186

   1. Initial program 90.5%

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

   2. Taylor expanded in y around inf 55.1%

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

      1. *-commutative 55.1%

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

   4. Simplified 55.1%

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

   if 3.7999999999999999e-278 < t < 2.29999999999999991e-203 or 8.2e-186 < t < 1.65e-75

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 61.1%

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

      1. unpow2 61.1%

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

   4. Simplified 61.1%

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

      1. associate-/r* 64.2%

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

      2. div-inv 64.3%

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

   6. Applied egg-rr 64.3%

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

   if 1.65e-75 < t

   1. Initial program 87.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 6: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ t_2 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;t \leq 5.2 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))) (t_2 (/ (/ x y) (- t z))))
   (if (<= t 5.2e-278)
     t_2
     (if (<= t 3.5e-206)
       t_1
       (if (<= t 8.8e-184)
         t_2
         (if (<= t 1.25e-75) t_1 (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double t_2 = (x / y) / (t - z);
	double tmp;
	if (t <= 5.2e-278) {
		tmp = t_2;
	} else if (t <= 3.5e-206) {
		tmp = t_1;
	} else if (t <= 8.8e-184) {
		tmp = t_2;
	} else if (t <= 1.25e-75) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) * (1.0d0 / z)
    t_2 = (x / y) / (t - z)
    if (t <= 5.2d-278) then
        tmp = t_2
    else if (t <= 3.5d-206) then
        tmp = t_1
    else if (t <= 8.8d-184) then
        tmp = t_2
    else if (t <= 1.25d-75) then
        tmp = t_1
    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 t_1 = (x / z) * (1.0 / z);
	double t_2 = (x / y) / (t - z);
	double tmp;
	if (t <= 5.2e-278) {
		tmp = t_2;
	} else if (t <= 3.5e-206) {
		tmp = t_1;
	} else if (t <= 8.8e-184) {
		tmp = t_2;
	} else if (t <= 1.25e-75) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	t_2 = (x / y) / (t - z)
	tmp = 0
	if t <= 5.2e-278:
		tmp = t_2
	elif t <= 3.5e-206:
		tmp = t_1
	elif t <= 8.8e-184:
		tmp = t_2
	elif t <= 1.25e-75:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	t_2 = Float64(Float64(x / y) / Float64(t - z))
	tmp = 0.0
	if (t <= 5.2e-278)
		tmp = t_2;
	elseif (t <= 3.5e-206)
		tmp = t_1;
	elseif (t <= 8.8e-184)
		tmp = t_2;
	elseif (t <= 1.25e-75)
		tmp = t_1;
	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)
	t_1 = (x / z) * (1.0 / z);
	t_2 = (x / y) / (t - z);
	tmp = 0.0;
	if (t <= 5.2e-278)
		tmp = t_2;
	elseif (t <= 3.5e-206)
		tmp = t_1;
	elseif (t <= 8.8e-184)
		tmp = t_2;
	elseif (t <= 1.25e-75)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 5.2e-278], t$95$2, If[LessEqual[t, 3.5e-206], t$95$1, If[LessEqual[t, 8.8e-184], t$95$2, If[LessEqual[t, 1.25e-75], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 5.1999999999999997e-278 or 3.49999999999999989e-206 < t < 8.79999999999999967e-184

   1. Initial program 90.5%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 58.6%

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

   if 5.1999999999999997e-278 < t < 3.49999999999999989e-206 or 8.79999999999999967e-184 < t < 1.24999999999999995e-75

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 61.1%

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

      1. unpow2 61.1%

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

   4. Simplified 61.1%

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

      1. associate-/r* 64.2%

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

      2. div-inv 64.3%

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

   6. Applied egg-rr 64.3%

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

   if 1.24999999999999995e-75 < t

   1. Initial program 87.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{-278}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 7: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;t \leq 3.7 \cdot 10^{-278}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-180}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))))
   (if (<= t 3.7e-278)
     (/ (/ x (- t z)) y)
     (if (<= t 8.5e-202)
       t_1
       (if (<= t 1.95e-180)
         (/ (/ x y) (- t z))
         (if (<= t 1.75e-75) t_1 (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (t <= 3.7e-278) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 8.5e-202) {
		tmp = t_1;
	} else if (t <= 1.95e-180) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.75e-75) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) * (1.0d0 / z)
    if (t <= 3.7d-278) then
        tmp = (x / (t - z)) / y
    else if (t <= 8.5d-202) then
        tmp = t_1
    else if (t <= 1.95d-180) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.75d-75) then
        tmp = t_1
    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 t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (t <= 3.7e-278) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 8.5e-202) {
		tmp = t_1;
	} else if (t <= 1.95e-180) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.75e-75) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	tmp = 0
	if t <= 3.7e-278:
		tmp = (x / (t - z)) / y
	elif t <= 8.5e-202:
		tmp = t_1
	elif t <= 1.95e-180:
		tmp = (x / y) / (t - z)
	elif t <= 1.75e-75:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (t <= 3.7e-278)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 8.5e-202)
		tmp = t_1;
	elseif (t <= 1.95e-180)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.75e-75)
		tmp = t_1;
	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)
	t_1 = (x / z) * (1.0 / z);
	tmp = 0.0;
	if (t <= 3.7e-278)
		tmp = (x / (t - z)) / y;
	elseif (t <= 8.5e-202)
		tmp = t_1;
	elseif (t <= 1.95e-180)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.75e-75)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 3.7e-278], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 8.5e-202], t$95$1, If[LessEqual[t, 1.95e-180], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-75], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 3.70000000000000022e-278

   1. Initial program 90.1%

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

   2. Taylor expanded in y around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-/r* 62.3%

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

   4. Simplified 62.3%

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

   if 3.70000000000000022e-278 < t < 8.49999999999999963e-202 or 1.9500000000000001e-180 < t < 1.74999999999999993e-75

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 61.1%

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

      1. unpow2 61.1%

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

   4. Simplified 61.1%

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

      1. associate-/r* 64.2%

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

      2. div-inv 64.3%

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

   6. Applied egg-rr 64.3%

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

   if 8.49999999999999963e-202 < t < 1.9500000000000001e-180

   1. Initial program 99.4%

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

      1. associate-/r* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 81.2%

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

   if 1.74999999999999993e-75 < t

   1. Initial program 87.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{-278}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-180}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 8: 90.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-216}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.2e-98)
   (/ (/ x y) (- t z))
   (if (<= t 1.45e-216)
     (/ (/ (- x) (- y z)) z)
     (if (<= t 4.2e+149) (/ x (* (- y z) (- t z))) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.2e-98) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.45e-216) {
		tmp = (-x / (y - z)) / z;
	} else if (t <= 4.2e+149) {
		tmp = x / ((y - z) * (t - 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 <= (-8.2d-98)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.45d-216) then
        tmp = (-x / (y - z)) / z
    else if (t <= 4.2d+149) then
        tmp = x / ((y - z) * (t - 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 <= -8.2e-98) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.45e-216) {
		tmp = (-x / (y - z)) / z;
	} else if (t <= 4.2e+149) {
		tmp = x / ((y - z) * (t - 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 <= -8.2e-98:
		tmp = (x / y) / (t - z)
	elif t <= 1.45e-216:
		tmp = (-x / (y - z)) / z
	elif t <= 4.2e+149:
		tmp = x / ((y - z) * (t - 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 <= -8.2e-98)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.45e-216)
		tmp = Float64(Float64(Float64(-x) / Float64(y - z)) / z);
	elseif (t <= 4.2e+149)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - 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 <= -8.2e-98)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.45e-216)
		tmp = (-x / (y - z)) / z;
	elseif (t <= 4.2e+149)
		tmp = x / ((y - z) * (t - 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, -8.2e-98], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-216], N[(N[((-x) / N[(y - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 4.2e+149], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.1999999999999996e-98

   1. Initial program 90.5%

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

      1. associate-/r* 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around inf 54.2%

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

   if -8.1999999999999996e-98 < t < 1.45e-216

   1. Initial program 90.3%

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

      1. associate-/r* 96.0%

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

      2. div-inv 96.0%

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

   3. Applied egg-rr 96.0%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. associate-/r* 87.8%

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

      3. distribute-neg-frac 87.8%

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

      4. distribute-neg-frac 87.8%

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

   6. Simplified 87.8%

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

   if 1.45e-216 < t < 4.2000000000000003e149

   1. Initial program 96.8%

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

   if 4.2000000000000003e149 < t

   1. Initial program 78.1%

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

      1. associate-/l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around inf 97.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-216}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (/ (/ x z) z)))
   (if (<= z -1.25e+71)
     t_1
     (if (<= z -1.55e-125)
       (/ (/ (- x) t) z)
       (if (<= z 3.55e-100)
         (/ 1.0 (* t (/ y x)))
         (if (<= z 1.9e+44) (/ (/ (- x) y) z) t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.25e+71) {
		tmp = t_1;
	} else if (z <= -1.55e-125) {
		tmp = (-x / t) / z;
	} else if (z <= 3.55e-100) {
		tmp = 1.0 / (t * (y / x));
	} else if (z <= 1.9e+44) {
		tmp = (-x / y) / z;
	} else {
		tmp = t_1;
	}
	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 = (x / z) / z
    if (z <= (-1.25d+71)) then
        tmp = t_1
    else if (z <= (-1.55d-125)) then
        tmp = (-x / t) / z
    else if (z <= 3.55d-100) then
        tmp = 1.0d0 / (t * (y / x))
    else if (z <= 1.9d+44) then
        tmp = (-x / y) / z
    else
        tmp = t_1
    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 = (x / z) / z;
	double tmp;
	if (z <= -1.25e+71) {
		tmp = t_1;
	} else if (z <= -1.55e-125) {
		tmp = (-x / t) / z;
	} else if (z <= 3.55e-100) {
		tmp = 1.0 / (t * (y / x));
	} else if (z <= 1.9e+44) {
		tmp = (-x / y) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -1.25e+71:
		tmp = t_1
	elif z <= -1.55e-125:
		tmp = (-x / t) / z
	elif z <= 3.55e-100:
		tmp = 1.0 / (t * (y / x))
	elif z <= 1.9e+44:
		tmp = (-x / y) / z
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.25e+71)
		tmp = t_1;
	elseif (z <= -1.55e-125)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 3.55e-100)
		tmp = Float64(1.0 / Float64(t * Float64(y / x)));
	elseif (z <= 1.9e+44)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.25e+71)
		tmp = t_1;
	elseif (z <= -1.55e-125)
		tmp = (-x / t) / z;
	elseif (z <= 3.55e-100)
		tmp = 1.0 / (t * (y / x));
	elseif (z <= 1.9e+44)
		tmp = (-x / y) / z;
	else
		tmp = t_1;
	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[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.25e+71], t$95$1, If[LessEqual[z, -1.55e-125], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.55e-100], N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+44], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.24999999999999993e71 or 1.9000000000000001e44 < z

   1. Initial program 85.0%

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

   2. Taylor expanded in z around inf 77.6%

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

      1. unpow2 77.6%

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

      2. associate-/r* 81.9%

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

   4. Simplified 81.9%

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

   if -1.24999999999999993e71 < z < -1.55000000000000006e-125

   1. Initial program 94.2%

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

   2. Taylor expanded in t around inf 57.1%

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

   3. Taylor expanded in y around 0 40.4%

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

      1. mul-1-neg 40.4%

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

      2. associate-/r* 40.7%

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

      3. distribute-neg-frac 40.7%

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

      4. distribute-neg-frac 40.7%

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

   5. Simplified 40.7%

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

   if -1.55000000000000006e-125 < z < 3.55e-100

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 74.5%

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

      1. clear-num 74.4%

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

      2. inv-pow 74.4%

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

      3. associate-/l* 75.5%

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

   4. Applied egg-rr 75.5%

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

      1. unpow-1 75.5%

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

      2. associate-/r/ 76.7%

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

   6. Simplified 76.7%

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

   if 3.55e-100 < z < 1.9000000000000001e44

   1. Initial program 92.9%

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

      1. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 42.6%

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

   5. Taylor expanded in t around 0 28.4%

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

      1. mul-1-neg 28.4%

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

      2. associate-/r* 28.5%

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

      3. distribute-neg-frac 28.5%

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

      4. distribute-neg-frac 28.5%

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

   7. Simplified 28.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 10: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e+35)
   (/ (/ x y) (- t z))
   (if (<= y -8.5e-52)
     (/ (- x) (* z (- y z)))
     (if (<= y 2.5e-117) (/ (/ (- x) z) (- t z)) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e+35) {
		tmp = (x / y) / (t - z);
	} else if (y <= -8.5e-52) {
		tmp = -x / (z * (y - z));
	} else if (y <= 2.5e-117) {
		tmp = (-x / z) / (t - 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 (y <= (-6d+35)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-8.5d-52)) then
        tmp = -x / (z * (y - z))
    else if (y <= 2.5d-117) then
        tmp = (-x / z) / (t - 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 (y <= -6e+35) {
		tmp = (x / y) / (t - z);
	} else if (y <= -8.5e-52) {
		tmp = -x / (z * (y - z));
	} else if (y <= 2.5e-117) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -6e+35:
		tmp = (x / y) / (t - z)
	elif y <= -8.5e-52:
		tmp = -x / (z * (y - z))
	elif y <= 2.5e-117:
		tmp = (-x / z) / (t - 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 (y <= -6e+35)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -8.5e-52)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	elseif (y <= 2.5e-117)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - 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 (y <= -6e+35)
		tmp = (x / y) / (t - z);
	elseif (y <= -8.5e-52)
		tmp = -x / (z * (y - z));
	elseif (y <= 2.5e-117)
		tmp = (-x / z) / (t - 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[y, -6e+35], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-52], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-117], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.99999999999999981e35

   1. Initial program 84.1%

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

      1. associate-/r* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around inf 95.5%

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

   if -5.99999999999999981e35 < y < -8.50000000000000006e-52

   1. Initial program 89.1%

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

   2. Taylor expanded in t around 0 67.4%

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

      1. associate-*r/ 67.4%

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

      2. neg-mul-1 67.4%

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

      3. *-commutative 67.4%

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

   4. Simplified 67.4%

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

   if -8.50000000000000006e-52 < y < 2.5e-117

   1. Initial program 92.0%

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

   2. Taylor expanded in y around 0 81.5%

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

      1. mul-1-neg 81.5%

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

      2. distribute-frac-neg 81.5%

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

      3. associate-/r* 84.1%

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

   4. Simplified 84.1%

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

   if 2.5e-117 < y

   1. Initial program 91.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. Taylor expanded in t around inf 64.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.5e+35)
   (/ (/ x y) (- t z))
   (if (<= y -6e-52)
     (/ (/ (- x) (- y z)) z)
     (if (<= y 2e-116) (/ (/ (- x) z) (- t z)) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e+35) {
		tmp = (x / y) / (t - z);
	} else if (y <= -6e-52) {
		tmp = (-x / (y - z)) / z;
	} else if (y <= 2e-116) {
		tmp = (-x / z) / (t - 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 (y <= (-4.5d+35)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-6d-52)) then
        tmp = (-x / (y - z)) / z
    else if (y <= 2d-116) then
        tmp = (-x / z) / (t - 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 (y <= -4.5e+35) {
		tmp = (x / y) / (t - z);
	} else if (y <= -6e-52) {
		tmp = (-x / (y - z)) / z;
	} else if (y <= 2e-116) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.5e+35:
		tmp = (x / y) / (t - z)
	elif y <= -6e-52:
		tmp = (-x / (y - z)) / z
	elif y <= 2e-116:
		tmp = (-x / z) / (t - 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 (y <= -4.5e+35)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -6e-52)
		tmp = Float64(Float64(Float64(-x) / Float64(y - z)) / z);
	elseif (y <= 2e-116)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - 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 (y <= -4.5e+35)
		tmp = (x / y) / (t - z);
	elseif (y <= -6e-52)
		tmp = (-x / (y - z)) / z;
	elseif (y <= 2e-116)
		tmp = (-x / z) / (t - 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[y, -4.5e+35], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-52], N[(N[((-x) / N[(y - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2e-116], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4999999999999997e35

   1. Initial program 84.1%

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

      1. associate-/r* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around inf 95.5%

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

   if -4.4999999999999997e35 < y < -6e-52

   1. Initial program 89.1%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in t around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. associate-/r* 72.9%

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

      3. distribute-neg-frac 72.9%

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

      4. distribute-neg-frac 72.9%

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

   6. Simplified 72.9%

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

   if -6e-52 < y < 2e-116

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-frac-neg 81.7%

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

      3. associate-/r* 84.3%

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

   4. Simplified 84.3%

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

   if 2e-116 < y

   1. Initial program 91.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. Taylor expanded in t around inf 63.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 12: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1020000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (/ (/ x z) z)) (t_2 (/ (/ x t) y)))
   (if (<= z -2.3e+35)
     t_1
     (if (<= z 7.2e-100)
       t_2
       (if (<= z 1020000000.0)
         (/ (- x) (* y z))
         (if (<= z 4.5e+56) t_2 t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -2.3e+35) {
		tmp = t_1;
	} else if (z <= 7.2e-100) {
		tmp = t_2;
	} else if (z <= 1020000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 4.5e+56) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = (x / t) / y
    if (z <= (-2.3d+35)) then
        tmp = t_1
    else if (z <= 7.2d-100) then
        tmp = t_2
    else if (z <= 1020000000.0d0) then
        tmp = -x / (y * z)
    else if (z <= 4.5d+56) then
        tmp = t_2
    else
        tmp = t_1
    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 = (x / z) / z;
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -2.3e+35) {
		tmp = t_1;
	} else if (z <= 7.2e-100) {
		tmp = t_2;
	} else if (z <= 1020000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 4.5e+56) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	t_2 = (x / t) / y
	tmp = 0
	if z <= -2.3e+35:
		tmp = t_1
	elif z <= 7.2e-100:
		tmp = t_2
	elif z <= 1020000000.0:
		tmp = -x / (y * z)
	elif z <= 4.5e+56:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	t_2 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -2.3e+35)
		tmp = t_1;
	elseif (z <= 7.2e-100)
		tmp = t_2;
	elseif (z <= 1020000000.0)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (z <= 4.5e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	t_2 = (x / t) / y;
	tmp = 0.0;
	if (z <= -2.3e+35)
		tmp = t_1;
	elseif (z <= 7.2e-100)
		tmp = t_2;
	elseif (z <= 1020000000.0)
		tmp = -x / (y * z);
	elseif (z <= 4.5e+56)
		tmp = t_2;
	else
		tmp = t_1;
	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[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -2.3e+35], t$95$1, If[LessEqual[z, 7.2e-100], t$95$2, If[LessEqual[z, 1020000000.0], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+56], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2999999999999998e35 or 4.5000000000000003e56 < z

   1. Initial program 86.5%

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

   2. Taylor expanded in z around inf 76.0%

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

      1. unpow2 76.0%

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

      2. associate-/r* 80.1%

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

   4. Simplified 80.1%

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

   if -2.2999999999999998e35 < z < 7.1999999999999997e-100 or 1.02e9 < z < 4.5000000000000003e56

   1. Initial program 91.9%

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

   2. Taylor expanded in z around 0 55.6%

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

      1. div-inv 55.5%

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

      2. associate-/r* 56.2%

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

   4. Applied egg-rr 56.2%

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

      1. *-commutative 56.2%

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

      2. associate-*l/ 62.5%

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

      3. associate-*r/ 62.7%

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

      4. associate-*l/ 62.8%

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

      5. *-lft-identity 62.8%

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

   6. Simplified 62.8%

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

   if 7.1999999999999997e-100 < z < 1.02e9

   1. Initial program 99.3%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 42.0%

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

   5. Taylor expanded in t around 0 31.9%

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

      1. mul-1-neg 31.9%

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

   7. Simplified 31.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-100}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1020000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 13: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-130}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-75}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.3e-130)
   (/ (/ x y) (- t z))
   (if (<= t 1.72e-75) (/ (- 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 <= -3.3e-130) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.72e-75) {
		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 <= (-3.3d-130)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.72d-75) 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 <= -3.3e-130) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.72e-75) {
		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 <= -3.3e-130:
		tmp = (x / y) / (t - z)
	elif t <= 1.72e-75:
		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 <= -3.3e-130)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.72e-75)
		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 <= -3.3e-130)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.72e-75)
		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, -3.3e-130], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.72e-75], 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 < -3.2999999999999998e-130

   1. Initial program 90.0%

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

      1. associate-/r* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around inf 54.6%

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

   if -3.2999999999999998e-130 < t < 1.72e-75

   1. Initial program 93.5%

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

   2. Taylor expanded in t around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. neg-mul-1 83.7%

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

      3. *-commutative 83.7%

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

   4. Simplified 83.7%

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

   if 1.72e-75 < t

   1. Initial program 87.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-130}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-75}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 14: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+70} \lor \neg \left(z \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e+70) (not (<= z 2.3e+71)))
   (/ (/ x z) z)
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+70) || !(z <= 2.3e+71)) {
		tmp = (x / 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 ((z <= (-9.5d+70)) .or. (.not. (z <= 2.3d+71))) then
        tmp = (x / 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 ((z <= -9.5e+70) || !(z <= 2.3e+71)) {
		tmp = (x / 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 (z <= -9.5e+70) or not (z <= 2.3e+71):
		tmp = (x / 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 ((z <= -9.5e+70) || !(z <= 2.3e+71))
		tmp = Float64(Float64(x / 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 ((z <= -9.5e+70) || ~((z <= 2.3e+71)))
		tmp = (x / 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[Or[LessEqual[z, -9.5e+70], N[Not[LessEqual[z, 2.3e+71]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000002e70 or 2.3000000000000002e71 < z

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf 80.4%

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

      1. unpow2 80.4%

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

      2. associate-/r* 84.9%

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

   4. Simplified 84.9%

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

   if -9.5000000000000002e70 < z < 2.3000000000000002e71

   1. Initial program 93.3%

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

   2. Taylor expanded in t around inf 68.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+70} \lor \neg \left(z \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 15: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.82e-37)
   (/ x (* y (- t z)))
   (if (<= y -1.52e-87) (/ (/ x z) z) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.82e-37) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.52e-87) {
		tmp = (x / 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 <= (-1.82d-37)) then
        tmp = x / (y * (t - z))
    else if (y <= (-1.52d-87)) then
        tmp = (x / 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 <= -1.82e-37) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.52e-87) {
		tmp = (x / 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 <= -1.82e-37:
		tmp = x / (y * (t - z))
	elif y <= -1.52e-87:
		tmp = (x / 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 <= -1.82e-37)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -1.52e-87)
		tmp = Float64(Float64(x / 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 <= -1.82e-37)
		tmp = x / (y * (t - z));
	elseif (y <= -1.52e-87)
		tmp = (x / 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, -1.82e-37], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.52e-87], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.82000000000000002e-37

   1. Initial program 84.5%

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

   2. Taylor expanded in y around inf 80.1%

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

      1. *-commutative 80.1%

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

   4. Simplified 80.1%

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

   if -1.82000000000000002e-37 < y < -1.52000000000000004e-87

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 87.3%

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

      1. unpow2 87.3%

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

      2. associate-/r* 87.3%

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

   4. Simplified 87.3%

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

   if -1.52000000000000004e-87 < y

   1. Initial program 91.7%

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

   2. Taylor expanded in t around inf 61.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 16: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+113} \lor \neg \left(z \leq 2.3 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -1.3e+113) (not (<= z 2.3e+47))) (/ x (* z t)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e+113) || !(z <= 2.3e+47)) {
		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 <= (-1.3d+113)) .or. (.not. (z <= 2.3d+47))) 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 <= -1.3e+113) || !(z <= 2.3e+47)) {
		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 <= -1.3e+113) or not (z <= 2.3e+47):
		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 <= -1.3e+113) || !(z <= 2.3e+47))
		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 <= -1.3e+113) || ~((z <= 2.3e+47)))
		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, -1.3e+113], N[Not[LessEqual[z, 2.3e+47]], $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 < -1.3e113 or 2.2999999999999999e47 < z

   1. Initial program 85.5%

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

   2. Taylor expanded in t around inf 44.2%

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

   3. Taylor expanded in y around 0 42.1%

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

      1. mul-1-neg 42.1%

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

      2. *-commutative 42.1%

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

      3. distribute-rgt-neg-in 42.1%

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

   5. Simplified 42.1%

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

      1. expm1-log1p-u 41.8%

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

      2. expm1-udef 69.6%

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

      3. remove-double-neg 69.6%

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

      4. distribute-rgt-neg-out 69.6%

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

      5. frac-2neg 69.6%

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

      6. associate-/l/ 69.6%

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

      7. add-sqr-sqrt 34.1%

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

      8. sqrt-unprod 67.3%

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

      9. sqr-neg 67.3%

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

      10. sqrt-unprod 35.6%

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

      11. add-sqr-sqrt 69.9%

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

   7. Applied egg-rr 69.9%

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

      1. expm1-def 39.2%

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

      2. expm1-log1p 39.3%

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

      3. associate-/l/ 42.2%

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

   9. Simplified 42.2%

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

   if -1.3e113 < z < 2.2999999999999999e47

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 47.0%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+113} \lor \neg \left(z \leq 2.3 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 17: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+34} \lor \neg \left(z \leq 1.42 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -1e+34) (not (<= z 1.42e-27))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+34) || !(z <= 1.42e-27)) {
		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 <= (-1d+34)) .or. (.not. (z <= 1.42d-27))) 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 <= -1e+34) || !(z <= 1.42e-27)) {
		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 <= -1e+34) or not (z <= 1.42e-27):
		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 <= -1e+34) || !(z <= 1.42e-27))
		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 <= -1e+34) || ~((z <= 1.42e-27)))
		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, -1e+34], N[Not[LessEqual[z, 1.42e-27]], $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 < -9.99999999999999946e33 or 1.41999999999999996e-27 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf 67.0%

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

      1. unpow2 67.0%

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

   4. Simplified 67.0%

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

   if -9.99999999999999946e33 < z < 1.41999999999999996e-27

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 55.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+34} \lor \neg \left(z \leq 1.42 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 18: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+39} \lor \neg \left(z \leq 2.4 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -6.4e+39) (not (<= z 2.4e+56))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.4e+39) || !(z <= 2.4e+56)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / 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 <= (-6.4d+39)) .or. (.not. (z <= 2.4d+56))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / 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 <= -6.4e+39) || !(z <= 2.4e+56)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -6.4e+39) or not (z <= 2.4e+56):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.4e+39) || !(z <= 2.4e+56))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / 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 <= -6.4e+39) || ~((z <= 2.4e+56)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / 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, -6.4e+39], N[Not[LessEqual[z, 2.4e+56]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.39999999999999986e39 or 2.40000000000000013e56 < z

   1. Initial program 86.5%

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

   2. Taylor expanded in z around inf 76.0%

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

      1. unpow2 76.0%

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

   4. Simplified 76.0%

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

   if -6.39999999999999986e39 < z < 2.40000000000000013e56

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 50.1%

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

      1. div-inv 50.1%

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

      2. associate-/r* 50.6%

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

   4. Applied egg-rr 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*l/ 56.0%

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

      3. associate-*r/ 56.2%

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

      4. associate-*l/ 56.3%

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

      5. *-lft-identity 56.3%

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

   6. Simplified 56.3%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+39} \lor \neg \left(z \leq 2.4 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 19: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+33} \lor \neg \left(z \leq 3.8 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -1.26e+33) (not (<= z 3.8e+56))) (/ (/ x z) z) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.26e+33) || !(z <= 3.8e+56)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / 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 <= (-1.26d+33)) .or. (.not. (z <= 3.8d+56))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / 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 <= -1.26e+33) || !(z <= 3.8e+56)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.26e+33) or not (z <= 3.8e+56):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.26e+33) || !(z <= 3.8e+56))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / 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 <= -1.26e+33) || ~((z <= 3.8e+56)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / 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, -1.26e+33], N[Not[LessEqual[z, 3.8e+56]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.26e33 or 3.79999999999999996e56 < z

   1. Initial program 86.5%

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

   2. Taylor expanded in z around inf 76.0%

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

      1. unpow2 76.0%

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

      2. associate-/r* 80.1%

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

   4. Simplified 80.1%

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

   if -1.26e33 < z < 3.79999999999999996e56

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 50.1%

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

      1. div-inv 50.1%

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

      2. associate-/r* 50.6%

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

   4. Applied egg-rr 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*l/ 56.0%

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

      3. associate-*r/ 56.2%

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

      4. associate-*l/ 56.3%

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

      5. *-lft-identity 56.3%

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

   6. Simplified 56.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+33} \lor \neg \left(z \leq 3.8 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 20: 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 90.2%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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. Final simplification 98.1%

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

Alternative 21: 40.5% 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 90.2%

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

2. Taylor expanded in z around 0 37.8%

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

3. Final simplification 37.8%

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

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 2023230 
(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))))