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

Percentage Accurate: 88.6% → 96.7%

Time: 12.8s

Alternatives: 19

Speedup: 0.7×

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: 88.6% 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: 96.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 4.5 \cdot 10^{+255}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 4.5e+255)
   (/ (/ x (- t z)) (- y z))
   (* (/ x (- y z)) (/ 1.0 (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.5e+255) {
		tmp = (x / (t - z)) / (y - z);
	} else {
		tmp = (x / (y - z)) * (1.0 / (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= 4.5d+255) then
        tmp = (x / (t - z)) / (y - z)
    else
        tmp = (x / (y - z)) * (1.0d0 / (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.5e+255) {
		tmp = (x / (t - z)) / (y - z);
	} else {
		tmp = (x / (y - z)) * (1.0 / (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 4.5e+255:
		tmp = (x / (t - z)) / (y - z)
	else:
		tmp = (x / (y - z)) * (1.0 / (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4.5e+255)
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	else
		tmp = Float64(Float64(x / Float64(y - z)) * Float64(1.0 / Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 4.5e+255)
		tmp = (x / (t - z)) / (y - z);
	else
		tmp = (x / (y - z)) * (1.0 / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 4.5e+255], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.49999999999999964e255

   1. Initial program 90.1%

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

      1. add-sqr-sqrt 43.9%

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

      2. times-frac 47.8%

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

   3. Applied egg-rr 47.8%

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

      1. frac-times 43.9%

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

      2. add-sqr-sqrt 90.1%

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

      3. *-commutative 90.1%

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

      4. associate-/r* 98.1%

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

   5. Applied egg-rr 98.1%

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

   if 4.49999999999999964e255 < t

   1. Initial program 78.9%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.6%

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

   3. Applied egg-rr 99.6%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.5 \cdot 10^{+255}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t - z}\\ \end{array} \]

Alternative 2: 49.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, 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 = (sqrt(x) / (y - z)) * (sqrt(x) / (t - z))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (Math.sqrt(x) / (y - z)) * (Math.sqrt(x) / (t - z));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

   1. add-sqr-sqrt 44.1%

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

   2. times-frac 48.2%

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

3. Applied egg-rr 48.2%

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

4. Final simplification 48.2%

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

Alternative 3: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x t) (- y z))
     (if (<= t_1 2e+290) (/ x t_1) (/ (/ (- x) z) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x / t) / (y - z);
	} else if (t_1 <= 2e+290) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (y - z);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / t) / (y - z);
	} else if (t_1 <= 2e+290) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / t) / (y - z)
	elif t_1 <= 2e+290:
		tmp = x / t_1
	else:
		tmp = (-x / z) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (t_1 <= 2e+290)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / t) / (y - z);
	elseif (t_1 <= 2e+290)
		tmp = x / t_1;
	else
		tmp = (-x / z) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], N[(x / t$95$1), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 56.3%

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

      1. add-sqr-sqrt 28.2%

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

      2. times-frac 47.3%

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

   3. Applied egg-rr 47.3%

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

      1. frac-times 28.2%

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

      2. add-sqr-sqrt 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-/r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around inf 56.3%

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

      1. associate-/r* 95.4%

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

   8. Simplified 95.4%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000012e290

   1. Initial program 98.6%

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

   if 2.00000000000000012e290 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 76.0%

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

      1. add-sqr-sqrt 36.0%

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

      2. times-frac 47.6%

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

   3. Applied egg-rr 47.6%

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

   4. Taylor expanded in t around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/r* 88.7%

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

      3. distribute-neg-frac 88.7%

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

      4. distribute-frac-neg 88.7%

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

   6. Simplified 88.7%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]

Alternative 4: 93.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{y - z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x t) (- y z))
     (if (<= t_1 2e+290) (/ x t_1) (/ (/ -1.0 z) (/ (- y z) x))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x / t) / (y - z);
	} else if (t_1 <= 2e+290) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) / ((y - z) / x);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / t) / (y - z);
	} else if (t_1 <= 2e+290) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) / ((y - z) / x);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / t) / (y - z)
	elif t_1 <= 2e+290:
		tmp = x / t_1
	else:
		tmp = (-1.0 / z) / ((y - z) / x)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (t_1 <= 2e+290)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(y - z) / x));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / t) / (y - z);
	elseif (t_1 <= 2e+290)
		tmp = x / t_1;
	else
		tmp = (-1.0 / z) / ((y - z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], N[(x / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 56.3%

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

      1. add-sqr-sqrt 28.2%

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

      2. times-frac 47.3%

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

   3. Applied egg-rr 47.3%

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

      1. frac-times 28.2%

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

      2. add-sqr-sqrt 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-/r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around inf 56.3%

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

      1. associate-/r* 95.4%

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

   8. Simplified 95.4%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000012e290

   1. Initial program 98.6%

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

   if 2.00000000000000012e290 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 76.0%

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

      1. clear-num 76.0%

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

      2. associate-/r/ 76.0%

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

   3. Applied egg-rr 76.0%

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

   4. Taylor expanded in t around 0 73.2%

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

      1. associate-/r* 72.9%

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

   6. Simplified 72.9%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 90.0%

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

   8. Applied egg-rr 90.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{y - z}{x}}\\ \end{array} \]

Alternative 5: 97.8% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 0.0) (/ (/ x (- t z)) (- y z)) t_1)))

C

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

Fortran

NOTE: x, y, z, 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 / ((y - z) * (t - z))
    if (t_1 <= 0.0d0) then
        tmp = (x / (t - z)) / (y - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -0.0

   1. Initial program 84.6%

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

      1. add-sqr-sqrt 38.8%

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

      2. times-frac 45.4%

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

   3. Applied egg-rr 45.4%

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

      1. frac-times 38.8%

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

      2. add-sqr-sqrt 84.6%

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

      3. *-commutative 84.6%

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

      4. associate-/r* 98.1%

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

   5. Applied egg-rr 98.1%

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

   if -0.0 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 99.5%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 6: 50.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+251}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, 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 t))))
   (if (<= t -4.6e-38)
     (/ x (* y t))
     (if (<= t 4.5e-91)
       (/ (- x) (* y z))
       (if (<= t 1.9e+91)
         t_1
         (if (<= t 1.05e+133)
           t_2
           (if (<= t 3.3e+218)
             t_1
             (if (<= t 1.3e+251) t_2 (/ (/ x y) t)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = -x / (z * t);
	double tmp;
	if (t <= -4.6e-38) {
		tmp = x / (y * t);
	} else if (t <= 4.5e-91) {
		tmp = -x / (y * z);
	} else if (t <= 1.9e+91) {
		tmp = t_1;
	} else if (t <= 1.05e+133) {
		tmp = t_2;
	} else if (t <= 3.3e+218) {
		tmp = t_1;
	} else if (t <= 1.3e+251) {
		tmp = t_2;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 * t)
    if (t <= (-4.6d-38)) then
        tmp = x / (y * t)
    else if (t <= 4.5d-91) then
        tmp = -x / (y * z)
    else if (t <= 1.9d+91) then
        tmp = t_1
    else if (t <= 1.05d+133) then
        tmp = t_2
    else if (t <= 3.3d+218) then
        tmp = t_1
    else if (t <= 1.3d+251) then
        tmp = t_2
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = -x / (z * t);
	double tmp;
	if (t <= -4.6e-38) {
		tmp = x / (y * t);
	} else if (t <= 4.5e-91) {
		tmp = -x / (y * z);
	} else if (t <= 1.9e+91) {
		tmp = t_1;
	} else if (t <= 1.05e+133) {
		tmp = t_2;
	} else if (t <= 3.3e+218) {
		tmp = t_1;
	} else if (t <= 1.3e+251) {
		tmp = t_2;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = -x / (z * t)
	tmp = 0
	if t <= -4.6e-38:
		tmp = x / (y * t)
	elif t <= 4.5e-91:
		tmp = -x / (y * z)
	elif t <= 1.9e+91:
		tmp = t_1
	elif t <= 1.05e+133:
		tmp = t_2
	elif t <= 3.3e+218:
		tmp = t_1
	elif t <= 1.3e+251:
		tmp = t_2
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (t <= -4.6e-38)
		tmp = Float64(x / Float64(y * t));
	elseif (t <= 4.5e-91)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (t <= 1.9e+91)
		tmp = t_1;
	elseif (t <= 1.05e+133)
		tmp = t_2;
	elseif (t <= 3.3e+218)
		tmp = t_1;
	elseif (t <= 1.3e+251)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = -x / (z * t);
	tmp = 0.0;
	if (t <= -4.6e-38)
		tmp = x / (y * t);
	elseif (t <= 4.5e-91)
		tmp = -x / (y * z);
	elseif (t <= 1.9e+91)
		tmp = t_1;
	elseif (t <= 1.05e+133)
		tmp = t_2;
	elseif (t <= 3.3e+218)
		tmp = t_1;
	elseif (t <= 1.3e+251)
		tmp = t_2;
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, 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[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e-38], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-91], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+91], t$95$1, If[LessEqual[t, 1.05e+133], t$95$2, If[LessEqual[t, 3.3e+218], t$95$1, If[LessEqual[t, 1.3e+251], t$95$2, N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.60000000000000003e-38

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0 58.2%

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

   if -4.60000000000000003e-38 < t < 4.49999999999999976e-91

   1. Initial program 93.4%

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

   2. Taylor expanded in y around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-/r* 63.8%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in t around 0 54.9%

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

      1. associate-*r/ 54.9%

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

      2. neg-mul-1 54.9%

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

      3. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if 4.49999999999999976e-91 < t < 1.8999999999999999e91 or 1.05e133 < t < 3.29999999999999998e218

   1. Initial program 83.0%

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

   2. Taylor expanded in y around inf 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-/r* 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in t around inf 55.7%

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

   if 1.8999999999999999e91 < t < 1.05e133 or 3.29999999999999998e218 < t < 1.3000000000000001e251

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. distribute-lft-out 92.9%

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

      2. mul-1-neg 92.9%

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

      3. distribute-rgt-neg-in 92.9%

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

      4. unsub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in y around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   7. Simplified 86.8%

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

   if 1.3000000000000001e251 < t

   1. Initial program 80.3%

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

   2. Taylor expanded in z around 0 52.1%

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

      1. associate-/r* 61.3%

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

      2. div-inv 61.4%

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

   4. Applied egg-rr 61.4%

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

      1. associate-*l/ 57.9%

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

      2. un-div-inv 58.2%

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

   6. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+133}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+218}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+251}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 7: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, 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 t))))
   (if (<= t -9.5e-37)
     (/ x (* y t))
     (if (<= t 3.1e-93)
       (/ (/ (- x) z) y)
       (if (<= t 1.1e+91)
         t_1
         (if (<= t 1.15e+133)
           t_2
           (if (<= t 2.7e+213)
             t_1
             (if (<= t 1.1e+251) t_2 (/ (/ x y) t)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = -x / (z * t);
	double tmp;
	if (t <= -9.5e-37) {
		tmp = x / (y * t);
	} else if (t <= 3.1e-93) {
		tmp = (-x / z) / y;
	} else if (t <= 1.1e+91) {
		tmp = t_1;
	} else if (t <= 1.15e+133) {
		tmp = t_2;
	} else if (t <= 2.7e+213) {
		tmp = t_1;
	} else if (t <= 1.1e+251) {
		tmp = t_2;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 * t)
    if (t <= (-9.5d-37)) then
        tmp = x / (y * t)
    else if (t <= 3.1d-93) then
        tmp = (-x / z) / y
    else if (t <= 1.1d+91) then
        tmp = t_1
    else if (t <= 1.15d+133) then
        tmp = t_2
    else if (t <= 2.7d+213) then
        tmp = t_1
    else if (t <= 1.1d+251) then
        tmp = t_2
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = -x / (z * t);
	double tmp;
	if (t <= -9.5e-37) {
		tmp = x / (y * t);
	} else if (t <= 3.1e-93) {
		tmp = (-x / z) / y;
	} else if (t <= 1.1e+91) {
		tmp = t_1;
	} else if (t <= 1.15e+133) {
		tmp = t_2;
	} else if (t <= 2.7e+213) {
		tmp = t_1;
	} else if (t <= 1.1e+251) {
		tmp = t_2;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = -x / (z * t)
	tmp = 0
	if t <= -9.5e-37:
		tmp = x / (y * t)
	elif t <= 3.1e-93:
		tmp = (-x / z) / y
	elif t <= 1.1e+91:
		tmp = t_1
	elif t <= 1.15e+133:
		tmp = t_2
	elif t <= 2.7e+213:
		tmp = t_1
	elif t <= 1.1e+251:
		tmp = t_2
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (t <= -9.5e-37)
		tmp = Float64(x / Float64(y * t));
	elseif (t <= 3.1e-93)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 1.1e+91)
		tmp = t_1;
	elseif (t <= 1.15e+133)
		tmp = t_2;
	elseif (t <= 2.7e+213)
		tmp = t_1;
	elseif (t <= 1.1e+251)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = -x / (z * t);
	tmp = 0.0;
	if (t <= -9.5e-37)
		tmp = x / (y * t);
	elseif (t <= 3.1e-93)
		tmp = (-x / z) / y;
	elseif (t <= 1.1e+91)
		tmp = t_1;
	elseif (t <= 1.15e+133)
		tmp = t_2;
	elseif (t <= 2.7e+213)
		tmp = t_1;
	elseif (t <= 1.1e+251)
		tmp = t_2;
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, 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[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-37], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-93], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.1e+91], t$95$1, If[LessEqual[t, 1.15e+133], t$95$2, If[LessEqual[t, 2.7e+213], t$95$1, If[LessEqual[t, 1.1e+251], t$95$2, N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.49999999999999927e-37

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0 58.2%

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

   if -9.49999999999999927e-37 < t < 3.1e-93

   1. Initial program 93.3%

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

   2. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   7. Simplified 57.9%

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

   if 3.1e-93 < t < 1.1e91 or 1.14999999999999995e133 < t < 2.7000000000000001e213

   1. Initial program 83.3%

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

   2. Taylor expanded in y around inf 66.3%

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

      1. *-commutative 66.3%

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

      2. associate-/r* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in t around inf 56.5%

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

   if 1.1e91 < t < 1.14999999999999995e133 or 2.7000000000000001e213 < t < 1.1e251

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. distribute-lft-out 92.9%

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

      2. mul-1-neg 92.9%

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

      3. distribute-rgt-neg-in 92.9%

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

      4. unsub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in y around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   7. Simplified 86.8%

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

   if 1.1e251 < t

   1. Initial program 80.3%

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

   2. Taylor expanded in z around 0 52.1%

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

      1. associate-/r* 61.3%

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

      2. div-inv 61.4%

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

   4. Applied egg-rr 61.4%

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

      1. associate-*l/ 57.9%

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

      2. un-div-inv 58.2%

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

   6. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+133}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 8: 51.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+218}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))))
   (if (<= t -1.95e-37)
     (/ x (* y t))
     (if (<= t 1.2e-93)
       (/ (/ (- x) z) y)
       (if (<= t 1.2e+91)
         (/ (/ x t) y)
         (if (<= t 8.2e+132)
           t_1
           (if (<= t 5.5e+218)
             (* (/ x t) (/ 1.0 y))
             (if (<= t 1.1e+251) t_1 (/ (/ x y) t)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if (t <= -1.95e-37) {
		tmp = x / (y * t);
	} else if (t <= 1.2e-93) {
		tmp = (-x / z) / y;
	} else if (t <= 1.2e+91) {
		tmp = (x / t) / y;
	} else if (t <= 8.2e+132) {
		tmp = t_1;
	} else if (t <= 5.5e+218) {
		tmp = (x / t) * (1.0 / y);
	} else if (t <= 1.1e+251) {
		tmp = t_1;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 * t)
    if (t <= (-1.95d-37)) then
        tmp = x / (y * t)
    else if (t <= 1.2d-93) then
        tmp = (-x / z) / y
    else if (t <= 1.2d+91) then
        tmp = (x / t) / y
    else if (t <= 8.2d+132) then
        tmp = t_1
    else if (t <= 5.5d+218) then
        tmp = (x / t) * (1.0d0 / y)
    else if (t <= 1.1d+251) then
        tmp = t_1
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if (t <= -1.95e-37) {
		tmp = x / (y * t);
	} else if (t <= 1.2e-93) {
		tmp = (-x / z) / y;
	} else if (t <= 1.2e+91) {
		tmp = (x / t) / y;
	} else if (t <= 8.2e+132) {
		tmp = t_1;
	} else if (t <= 5.5e+218) {
		tmp = (x / t) * (1.0 / y);
	} else if (t <= 1.1e+251) {
		tmp = t_1;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -x / (z * t)
	tmp = 0
	if t <= -1.95e-37:
		tmp = x / (y * t)
	elif t <= 1.2e-93:
		tmp = (-x / z) / y
	elif t <= 1.2e+91:
		tmp = (x / t) / y
	elif t <= 8.2e+132:
		tmp = t_1
	elif t <= 5.5e+218:
		tmp = (x / t) * (1.0 / y)
	elif t <= 1.1e+251:
		tmp = t_1
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (t <= -1.95e-37)
		tmp = Float64(x / Float64(y * t));
	elseif (t <= 1.2e-93)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 1.2e+91)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 8.2e+132)
		tmp = t_1;
	elseif (t <= 5.5e+218)
		tmp = Float64(Float64(x / t) * Float64(1.0 / y));
	elseif (t <= 1.1e+251)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	tmp = 0.0;
	if (t <= -1.95e-37)
		tmp = x / (y * t);
	elseif (t <= 1.2e-93)
		tmp = (-x / z) / y;
	elseif (t <= 1.2e+91)
		tmp = (x / t) / y;
	elseif (t <= 8.2e+132)
		tmp = t_1;
	elseif (t <= 5.5e+218)
		tmp = (x / t) * (1.0 / y);
	elseif (t <= 1.1e+251)
		tmp = t_1;
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e-37], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-93], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.2e+91], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 8.2e+132], t$95$1, If[LessEqual[t, 5.5e+218], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+251], t$95$1, N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.94999999999999995e-37

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0 58.2%

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

   if -1.94999999999999995e-37 < t < 1.2000000000000001e-93

   1. Initial program 93.3%

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

   2. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   7. Simplified 57.9%

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

   if 1.2000000000000001e-93 < t < 1.19999999999999991e91

   1. Initial program 92.7%

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

   2. Taylor expanded in y around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-/r* 71.5%

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

   4. Simplified 71.5%

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

   5. Taylor expanded in t around inf 55.4%

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

   if 1.19999999999999991e91 < t < 8.19999999999999983e132 or 5.5000000000000004e218 < t < 1.1e251

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. distribute-lft-out 92.9%

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

      2. mul-1-neg 92.9%

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

      3. distribute-rgt-neg-in 92.9%

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

      4. unsub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in y around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   7. Simplified 86.8%

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

   if 8.19999999999999983e132 < t < 5.5000000000000004e218

   1. Initial program 59.2%

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

   2. Taylor expanded in z around 0 43.5%

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

      1. associate-/r* 59.3%

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

      2. div-inv 59.4%

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

   4. Applied egg-rr 59.4%

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

   if 1.1e251 < t

   1. Initial program 80.3%

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

   2. Taylor expanded in z around 0 52.1%

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

      1. associate-/r* 61.3%

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

      2. div-inv 61.4%

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

   4. Applied egg-rr 61.4%

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

      1. associate-*l/ 57.9%

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

      2. un-div-inv 58.2%

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

   6. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+132}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+218}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 9: 51.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{\frac{1}{t}}{y}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+90}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+218}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))))
   (if (<= t -4.8e-38)
     (* x (/ (/ 1.0 t) y))
     (if (<= t 2.25e-94)
       (/ (/ (- x) z) y)
       (if (<= t 1.52e+90)
         (/ (/ x t) y)
         (if (<= t 2.4e+133)
           t_1
           (if (<= t 1.9e+218)
             (* (/ x t) (/ 1.0 y))
             (if (<= t 1.06e+251) t_1 (/ (/ x y) t)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if (t <= -4.8e-38) {
		tmp = x * ((1.0 / t) / y);
	} else if (t <= 2.25e-94) {
		tmp = (-x / z) / y;
	} else if (t <= 1.52e+90) {
		tmp = (x / t) / y;
	} else if (t <= 2.4e+133) {
		tmp = t_1;
	} else if (t <= 1.9e+218) {
		tmp = (x / t) * (1.0 / y);
	} else if (t <= 1.06e+251) {
		tmp = t_1;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 * t)
    if (t <= (-4.8d-38)) then
        tmp = x * ((1.0d0 / t) / y)
    else if (t <= 2.25d-94) then
        tmp = (-x / z) / y
    else if (t <= 1.52d+90) then
        tmp = (x / t) / y
    else if (t <= 2.4d+133) then
        tmp = t_1
    else if (t <= 1.9d+218) then
        tmp = (x / t) * (1.0d0 / y)
    else if (t <= 1.06d+251) then
        tmp = t_1
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if (t <= -4.8e-38) {
		tmp = x * ((1.0 / t) / y);
	} else if (t <= 2.25e-94) {
		tmp = (-x / z) / y;
	} else if (t <= 1.52e+90) {
		tmp = (x / t) / y;
	} else if (t <= 2.4e+133) {
		tmp = t_1;
	} else if (t <= 1.9e+218) {
		tmp = (x / t) * (1.0 / y);
	} else if (t <= 1.06e+251) {
		tmp = t_1;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -x / (z * t)
	tmp = 0
	if t <= -4.8e-38:
		tmp = x * ((1.0 / t) / y)
	elif t <= 2.25e-94:
		tmp = (-x / z) / y
	elif t <= 1.52e+90:
		tmp = (x / t) / y
	elif t <= 2.4e+133:
		tmp = t_1
	elif t <= 1.9e+218:
		tmp = (x / t) * (1.0 / y)
	elif t <= 1.06e+251:
		tmp = t_1
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (t <= -4.8e-38)
		tmp = Float64(x * Float64(Float64(1.0 / t) / y));
	elseif (t <= 2.25e-94)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 1.52e+90)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 2.4e+133)
		tmp = t_1;
	elseif (t <= 1.9e+218)
		tmp = Float64(Float64(x / t) * Float64(1.0 / y));
	elseif (t <= 1.06e+251)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	tmp = 0.0;
	if (t <= -4.8e-38)
		tmp = x * ((1.0 / t) / y);
	elseif (t <= 2.25e-94)
		tmp = (-x / z) / y;
	elseif (t <= 1.52e+90)
		tmp = (x / t) / y;
	elseif (t <= 2.4e+133)
		tmp = t_1;
	elseif (t <= 1.9e+218)
		tmp = (x / t) * (1.0 / y);
	elseif (t <= 1.06e+251)
		tmp = t_1;
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e-38], N[(x * N[(N[(1.0 / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-94], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.52e+90], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.4e+133], t$95$1, If[LessEqual[t, 1.9e+218], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+251], t$95$1, N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.80000000000000044e-38

   1. Initial program 90.1%

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

      1. clear-num 90.1%

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

      2. associate-/r/ 90.1%

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

   3. Applied egg-rr 90.1%

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

   4. Taylor expanded in z around 0 58.1%

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

      1. associate-/r* 59.0%

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

   6. Simplified 59.0%

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

   if -4.80000000000000044e-38 < t < 2.2500000000000001e-94

   1. Initial program 93.3%

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

   2. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   7. Simplified 57.9%

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

   if 2.2500000000000001e-94 < t < 1.52000000000000009e90

   1. Initial program 92.7%

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

   2. Taylor expanded in y around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-/r* 71.5%

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

   4. Simplified 71.5%

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

   5. Taylor expanded in t around inf 55.4%

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

   if 1.52000000000000009e90 < t < 2.3999999999999999e133 or 1.90000000000000006e218 < t < 1.05999999999999998e251

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. distribute-lft-out 92.9%

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

      2. mul-1-neg 92.9%

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

      3. distribute-rgt-neg-in 92.9%

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

      4. unsub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in y around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   7. Simplified 86.8%

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

   if 2.3999999999999999e133 < t < 1.90000000000000006e218

   1. Initial program 59.2%

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

   2. Taylor expanded in z around 0 43.5%

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

      1. associate-/r* 59.3%

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

      2. div-inv 59.4%

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

   4. Applied egg-rr 59.4%

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

   if 1.05999999999999998e251 < t

   1. Initial program 80.3%

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

   2. Taylor expanded in z around 0 52.1%

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

      1. associate-/r* 61.3%

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

      2. div-inv 61.4%

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

   4. Applied egg-rr 61.4%

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

      1. associate-*l/ 57.9%

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

      2. un-div-inv 58.2%

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

   6. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{\frac{1}{t}}{y}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+90}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+133}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+218}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+251}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 10: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{\frac{1}{t}}{y}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+89}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+214}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))))
   (if (<= t -5.5e-37)
     (* x (/ (/ 1.0 t) y))
     (if (<= t 3.3e-97)
       (/ (/ (- x) z) y)
       (if (<= t 3e+89)
         (/ (/ x t) y)
         (if (<= t 4e+133)
           t_1
           (if (<= t 3e+214)
             (/ 1.0 (/ y (/ x t)))
             (if (<= t 1.05e+251) t_1 (/ (/ x y) t)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if (t <= -5.5e-37) {
		tmp = x * ((1.0 / t) / y);
	} else if (t <= 3.3e-97) {
		tmp = (-x / z) / y;
	} else if (t <= 3e+89) {
		tmp = (x / t) / y;
	} else if (t <= 4e+133) {
		tmp = t_1;
	} else if (t <= 3e+214) {
		tmp = 1.0 / (y / (x / t));
	} else if (t <= 1.05e+251) {
		tmp = t_1;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 * t)
    if (t <= (-5.5d-37)) then
        tmp = x * ((1.0d0 / t) / y)
    else if (t <= 3.3d-97) then
        tmp = (-x / z) / y
    else if (t <= 3d+89) then
        tmp = (x / t) / y
    else if (t <= 4d+133) then
        tmp = t_1
    else if (t <= 3d+214) then
        tmp = 1.0d0 / (y / (x / t))
    else if (t <= 1.05d+251) then
        tmp = t_1
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if (t <= -5.5e-37) {
		tmp = x * ((1.0 / t) / y);
	} else if (t <= 3.3e-97) {
		tmp = (-x / z) / y;
	} else if (t <= 3e+89) {
		tmp = (x / t) / y;
	} else if (t <= 4e+133) {
		tmp = t_1;
	} else if (t <= 3e+214) {
		tmp = 1.0 / (y / (x / t));
	} else if (t <= 1.05e+251) {
		tmp = t_1;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -x / (z * t)
	tmp = 0
	if t <= -5.5e-37:
		tmp = x * ((1.0 / t) / y)
	elif t <= 3.3e-97:
		tmp = (-x / z) / y
	elif t <= 3e+89:
		tmp = (x / t) / y
	elif t <= 4e+133:
		tmp = t_1
	elif t <= 3e+214:
		tmp = 1.0 / (y / (x / t))
	elif t <= 1.05e+251:
		tmp = t_1
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (t <= -5.5e-37)
		tmp = Float64(x * Float64(Float64(1.0 / t) / y));
	elseif (t <= 3.3e-97)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 3e+89)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 4e+133)
		tmp = t_1;
	elseif (t <= 3e+214)
		tmp = Float64(1.0 / Float64(y / Float64(x / t)));
	elseif (t <= 1.05e+251)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	tmp = 0.0;
	if (t <= -5.5e-37)
		tmp = x * ((1.0 / t) / y);
	elseif (t <= 3.3e-97)
		tmp = (-x / z) / y;
	elseif (t <= 3e+89)
		tmp = (x / t) / y;
	elseif (t <= 4e+133)
		tmp = t_1;
	elseif (t <= 3e+214)
		tmp = 1.0 / (y / (x / t));
	elseif (t <= 1.05e+251)
		tmp = t_1;
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-37], N[(x * N[(N[(1.0 / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-97], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 3e+89], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4e+133], t$95$1, If[LessEqual[t, 3e+214], N[(1.0 / N[(y / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+251], t$95$1, N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.4999999999999998e-37

   1. Initial program 90.1%

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

      1. clear-num 90.1%

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

      2. associate-/r/ 90.1%

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

   3. Applied egg-rr 90.1%

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

   4. Taylor expanded in z around 0 58.1%

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

      1. associate-/r* 59.0%

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

   6. Simplified 59.0%

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

   if -5.4999999999999998e-37 < t < 3.3000000000000001e-97

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-/r* 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in t around 0 57.5%

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

      1. associate-*r/ 57.5%

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

      2. neg-mul-1 57.5%

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

   7. Simplified 57.5%

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

   if 3.3000000000000001e-97 < t < 3.00000000000000013e89

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-/r* 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in t around inf 54.2%

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

   if 3.00000000000000013e89 < t < 4.0000000000000001e133 or 3.0000000000000001e214 < t < 1.05e251

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. distribute-lft-out 92.9%

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

      2. mul-1-neg 92.9%

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

      3. distribute-rgt-neg-in 92.9%

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

      4. unsub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in y around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   7. Simplified 86.8%

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

   if 4.0000000000000001e133 < t < 3.0000000000000001e214

   1. Initial program 59.2%

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

   2. Taylor expanded in z around 0 43.5%

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

      1. clear-num 52.4%

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

      2. inv-pow 52.4%

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

      3. *-commutative 52.4%

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

   4. Applied egg-rr 52.4%

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

      1. unpow-1 52.4%

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

      2. associate-/l* 63.7%

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

   6. Simplified 63.7%

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

   if 1.05e251 < t

   1. Initial program 80.3%

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

   2. Taylor expanded in z around 0 52.1%

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

      1. associate-/r* 61.3%

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

      2. div-inv 61.4%

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

   4. Applied egg-rr 61.4%

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

      1. associate-*l/ 57.9%

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

      2. un-div-inv 58.2%

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

   6. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{\frac{1}{t}}{y}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+89}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+133}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+214}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+251}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 11: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-214}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-17)
   (/ (/ x (- t z)) y)
   (if (<= y 3.4e-214) (/ (- x) (* z (- t z))) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-17) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 3.4e-214) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-5d-17)) then
        tmp = (x / (t - z)) / y
    else if (y <= 3.4d-214) then
        tmp = -x / (z * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-17) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 3.4e-214) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5e-17:
		tmp = (x / (t - z)) / y
	elif y <= 3.4e-214:
		tmp = -x / (z * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-17)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 3.4e-214)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e-17)
		tmp = (x / (t - z)) / y;
	elseif (y <= 3.4e-214)
		tmp = -x / (z * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5e-17], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.4e-214], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999999e-17

   1. Initial program 83.2%

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

   2. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/r* 86.0%

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

   4. Simplified 86.0%

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

   if -4.9999999999999999e-17 < y < 3.3999999999999999e-214

   1. Initial program 91.2%

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

   2. Taylor expanded in y around 0 74.1%

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

      1. associate-*r/ 74.1%

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

      2. neg-mul-1 74.1%

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

   4. Simplified 74.1%

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

   if 3.3999999999999999e-214 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf 62.4%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-214}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 12: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-214}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.25e-17)
   (/ (/ x (- t z)) y)
   (if (<= y 2.3e-214) (/ (/ (- x) z) (- t z)) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-17) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 2.3e-214) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.25d-17)) then
        tmp = (x / (t - z)) / y
    else if (y <= 2.3d-214) then
        tmp = (-x / z) / (t - z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-17) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 2.3e-214) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.25e-17:
		tmp = (x / (t - z)) / y
	elif y <= 2.3e-214:
		tmp = (-x / z) / (t - z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-17)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 2.3e-214)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-17)
		tmp = (x / (t - z)) / y;
	elseif (y <= 2.3e-214)
		tmp = (-x / z) / (t - z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.25e-17], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.3e-214], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.24999999999999989e-17

   1. Initial program 83.2%

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

   2. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/r* 86.0%

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

   4. Simplified 86.0%

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

   if -2.24999999999999989e-17 < y < 2.30000000000000011e-214

   1. Initial program 91.2%

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

      1. add-sqr-sqrt 39.7%

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

      2. times-frac 43.9%

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

   3. Applied egg-rr 43.9%

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

   4. Taylor expanded in y around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. associate-/r* 79.4%

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

      3. distribute-neg-frac 79.4%

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

      4. distribute-frac-neg 79.4%

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

   6. Simplified 79.4%

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

   if 2.30000000000000011e-214 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf 62.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-214}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 13: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{\frac{1}{t}}{y}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.6e-38)
   (* x (/ (/ 1.0 t) y))
   (if (<= t 5.5e-94) (/ (/ (- x) z) y) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e-38) {
		tmp = x * ((1.0 / t) / y);
	} else if (t <= 5.5e-94) {
		tmp = (-x / z) / y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-4.6d-38)) then
        tmp = x * ((1.0d0 / t) / y)
    else if (t <= 5.5d-94) then
        tmp = (-x / z) / y
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e-38) {
		tmp = x * ((1.0 / t) / y);
	} else if (t <= 5.5e-94) {
		tmp = (-x / z) / y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.6e-38:
		tmp = x * ((1.0 / t) / y)
	elif t <= 5.5e-94:
		tmp = (-x / z) / y
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.6e-38)
		tmp = Float64(x * Float64(Float64(1.0 / t) / y));
	elseif (t <= 5.5e-94)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.6e-38)
		tmp = x * ((1.0 / t) / y);
	elseif (t <= 5.5e-94)
		tmp = (-x / z) / y;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.6e-38], N[(x * N[(N[(1.0 / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-94], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.60000000000000003e-38

   1. Initial program 90.1%

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

      1. clear-num 90.1%

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

      2. associate-/r/ 90.1%

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

   3. Applied egg-rr 90.1%

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

   4. Taylor expanded in z around 0 58.1%

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

      1. associate-/r* 59.0%

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

   6. Simplified 59.0%

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

   if -4.60000000000000003e-38 < t < 5.49999999999999989e-94

   1. Initial program 93.3%

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

   2. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   7. Simplified 57.9%

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

   if 5.49999999999999989e-94 < t

   1. Initial program 84.5%

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

   2. Taylor expanded in t around inf 74.4%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{\frac{1}{t}}{y}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 14: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e-52)
   (/ (/ x y) t)
   (if (<= y 6.4e-84) (/ (- x) (* z t)) (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e-52) {
		tmp = (x / y) / t;
	} else if (y <= 6.4e-84) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-1.02d-52)) then
        tmp = (x / y) / t
    else if (y <= 6.4d-84) then
        tmp = -x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e-52) {
		tmp = (x / y) / t;
	} else if (y <= 6.4e-84) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e-52:
		tmp = (x / y) / t
	elif y <= 6.4e-84:
		tmp = -x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e-52)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 6.4e-84)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.02e-52)
		tmp = (x / y) / t;
	elseif (y <= 6.4e-84)
		tmp = -x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e-52], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 6.4e-84], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02000000000000009e-52

   1. Initial program 84.8%

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

   2. Taylor expanded in z around 0 39.9%

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

      1. associate-/r* 42.8%

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

      2. div-inv 42.8%

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

   4. Applied egg-rr 42.8%

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

      1. associate-*l/ 45.0%

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

      2. un-div-inv 45.0%

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

   6. Applied egg-rr 45.0%

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

   if -1.02000000000000009e-52 < y < 6.3999999999999999e-84

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0 67.0%

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

      1. distribute-lft-out 67.0%

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

      2. mul-1-neg 67.0%

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

      3. distribute-rgt-neg-in 67.0%

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

      4. unsub-neg 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in y around 0 49.5%

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

      1. associate-*r/ 49.5%

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

      2. neg-mul-1 49.5%

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

   7. Simplified 49.5%

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

   if 6.3999999999999999e-84 < y

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-/r* 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in t around inf 58.1%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 15: 70.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 8.2e-79) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 8.2e-79) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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-79) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 8.2e-79) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 8.2e-79:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 8.2e-79)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 8.2e-79)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 8.2e-79], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.19999999999999987e-79

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

   4. Simplified 61.2%

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

   if 8.19999999999999987e-79 < t

   1. Initial program 83.1%

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

   2. Taylor expanded in t around inf 75.7%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 16: 72.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.85e-79) (/ x (* y (- t z))) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.85e-79) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.85d-79) then
        tmp = x / (y * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.85e-79) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.85e-79:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.85e-79)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.85e-79)
		tmp = x / (y * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.85e-79], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.85000000000000009e-79

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

   4. Simplified 61.2%

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

   if 1.85000000000000009e-79 < t

   1. Initial program 83.1%

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

      1. add-sqr-sqrt 40.2%

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

      2. times-frac 47.5%

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

   3. Applied egg-rr 47.5%

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

      1. frac-times 40.2%

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

      2. add-sqr-sqrt 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-/r* 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in t around inf 75.7%

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

      1. associate-/r* 78.3%

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

   8. Simplified 78.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 17: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 7.5e-79) (/ (/ x (- t z)) y) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.5e-79) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= 7.5d-79) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.5e-79) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 7.5e-79:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 7.5e-79)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 7.5e-79)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 7.5e-79], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.49999999999999969e-79

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-/r* 64.1%

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

   4. Simplified 64.1%

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

   if 7.49999999999999969e-79 < t

   1. Initial program 83.1%

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

      1. add-sqr-sqrt 40.2%

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

      2. times-frac 47.5%

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

   3. Applied egg-rr 47.5%

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

      1. frac-times 40.2%

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

      2. add-sqr-sqrt 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-/r* 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in t around inf 75.7%

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

      1. associate-/r* 78.3%

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

   8. Simplified 78.3%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 18: 39.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, 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 89.5%

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

2. Taylor expanded in z around 0 38.1%

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

3. Final simplification 38.1%

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

Alternative 19: 42.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, 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) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

2. Taylor expanded in y around inf 59.1%

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

   1. *-commutative 59.1%

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

   2. associate-/r* 63.7%

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

4. Simplified 63.7%

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

5. Taylor expanded in t around inf 40.2%

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

6. Final simplification 40.2%

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

Developer target: 87.4% 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 2023319 
(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))))