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

Percentage Accurate: 89.5% → 97.7%

Time: 14.5s

Alternatives: 22

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.5% 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: 97.7% accurate, 0.5× speedup

Math

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

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 (- y z)) (- t 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 / (y - z)) / (t - 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 / (y - z)) / (t - 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 / (y - z)) / (t - 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 / (y - z)) / (t - 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(y - z)) / Float64(t - 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 / (y - z)) / (t - 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[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - 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 87.2%

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

      1. add-cube-cbrt 86.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 97.2%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 97.2%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 97.2%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 97.9%

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

   5. Applied egg-rr 97.9%

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

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

   1. Initial program 99.8%

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

4. Final simplification 98.3%

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

Alternative 2: 97.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (* (/ (pow (cbrt x) 2.0) (- y z)) (/ (cbrt x) (- t z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (pow(cbrt(x), 2.0) / (y - z)) * (cbrt(x) / (t - z));
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (Math.pow(Math.cbrt(x), 2.0) / (y - z)) * (Math.cbrt(x) / (t - z));
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64((cbrt(x) ^ 2.0) / Float64(y - z)) * Float64(cbrt(x) / Float64(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[Power[N[Power[x, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(N[Power[x, 1/3], $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.3%

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

   1. add-cube-cbrt 89.5%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. times-frac 98.1%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   3. pow2 98.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

3. Applied egg-rr 98.1%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

4. Final simplification 98.1%

   \[\leadsto \frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

Alternative 3: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ t_2 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;t \leq -8 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z y)))) (t_2 (/ x (* y (- t z)))))
   (if (<= t -8e-180)
     t_2
     (if (<= t 1e-223)
       t_1
       (if (<= t 2e-69)
         t_2
         (if (<= t 2e-33)
           t_1
           (if (<= t 4.4e+207) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double t_2 = x / (y * (t - z));
	double tmp;
	if (t <= -8e-180) {
		tmp = t_2;
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 2e-69) {
		tmp = t_2;
	} else if (t <= 2e-33) {
		tmp = t_1;
	} else if (t <= 4.4e+207) {
		tmp = x / ((y - z) * t);
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (z * (z - y))
    t_2 = x / (y * (t - z))
    if (t <= (-8d-180)) then
        tmp = t_2
    else if (t <= 1d-223) then
        tmp = t_1
    else if (t <= 2d-69) then
        tmp = t_2
    else if (t <= 2d-33) then
        tmp = t_1
    else if (t <= 4.4d+207) then
        tmp = x / ((y - z) * t)
    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 t_1 = x / (z * (z - y));
	double t_2 = x / (y * (t - z));
	double tmp;
	if (t <= -8e-180) {
		tmp = t_2;
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 2e-69) {
		tmp = t_2;
	} else if (t <= 2e-33) {
		tmp = t_1;
	} else if (t <= 4.4e+207) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * (z - y))
	t_2 = x / (y * (t - z))
	tmp = 0
	if t <= -8e-180:
		tmp = t_2
	elif t <= 1e-223:
		tmp = t_1
	elif t <= 2e-69:
		tmp = t_2
	elif t <= 2e-33:
		tmp = t_1
	elif t <= 4.4e+207:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - y)))
	t_2 = Float64(x / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (t <= -8e-180)
		tmp = t_2;
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 2e-69)
		tmp = t_2;
	elseif (t <= 2e-33)
		tmp = t_1;
	elseif (t <= 4.4e+207)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	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)
	t_1 = x / (z * (z - y));
	t_2 = x / (y * (t - z));
	tmp = 0.0;
	if (t <= -8e-180)
		tmp = t_2;
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 2e-69)
		tmp = t_2;
	elseif (t <= 2e-33)
		tmp = t_1;
	elseif (t <= 4.4e+207)
		tmp = x / ((y - z) * t);
	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_] := Block[{t$95$1 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e-180], t$95$2, If[LessEqual[t, 1e-223], t$95$1, If[LessEqual[t, 2e-69], t$95$2, If[LessEqual[t, 2e-33], t$95$1, If[LessEqual[t, 4.4e+207], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.0000000000000002e-180 or 9.9999999999999997e-224 < t < 1.9999999999999999e-69

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf 64.2%

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

      1. *-commutative 64.2%

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

   4. Simplified 64.2%

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

   if -8.0000000000000002e-180 < t < 9.9999999999999997e-224 or 1.9999999999999999e-69 < t < 2.0000000000000001e-33

   1. Initial program 95.6%

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

      1. clear-num 95.4%

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

      2. inv-pow 95.4%

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

      3. associate-/l* 97.6%

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

   3. Applied egg-rr 97.6%

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

      1. frac-2neg 97.6%

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

      2. div-inv 97.6%

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

      3. distribute-neg-frac 97.6%

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

   5. Applied egg-rr 97.6%

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

      1. associate-/r/ 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in t around 0 85.2%

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

   if 2.0000000000000001e-33 < t < 4.40000000000000017e207

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 90.7%

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

   if 4.40000000000000017e207 < t

   1. Initial program 79.5%

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

      1. add-cube-cbrt 79.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.4%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.4%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 79.5%

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

      1. associate-/r* 96.5%

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

   8. Simplified 96.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-180}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 4: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z y)))))
   (if (<= t -3.8e-179)
     (/ (/ x y) (- t z))
     (if (<= t 1e-223)
       t_1
       (if (<= t 4.5e-74)
         (/ x (* y (- t z)))
         (if (<= t 2e-34)
           t_1
           (if (<= t 4.3e+207) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double tmp;
	if (t <= -3.8e-179) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 4.5e-74) {
		tmp = x / (y * (t - z));
	} else if (t <= 2e-34) {
		tmp = t_1;
	} else if (t <= 4.3e+207) {
		tmp = x / ((y - z) * t);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (z * (z - y))
    if (t <= (-3.8d-179)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1d-223) then
        tmp = t_1
    else if (t <= 4.5d-74) then
        tmp = x / (y * (t - z))
    else if (t <= 2d-34) then
        tmp = t_1
    else if (t <= 4.3d+207) then
        tmp = x / ((y - z) * t)
    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 t_1 = x / (z * (z - y));
	double tmp;
	if (t <= -3.8e-179) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 4.5e-74) {
		tmp = x / (y * (t - z));
	} else if (t <= 2e-34) {
		tmp = t_1;
	} else if (t <= 4.3e+207) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * (z - y))
	tmp = 0
	if t <= -3.8e-179:
		tmp = (x / y) / (t - z)
	elif t <= 1e-223:
		tmp = t_1
	elif t <= 4.5e-74:
		tmp = x / (y * (t - z))
	elif t <= 2e-34:
		tmp = t_1
	elif t <= 4.3e+207:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (t <= -3.8e-179)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 4.5e-74)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 2e-34)
		tmp = t_1;
	elseif (t <= 4.3e+207)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	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)
	t_1 = x / (z * (z - y));
	tmp = 0.0;
	if (t <= -3.8e-179)
		tmp = (x / y) / (t - z);
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 4.5e-74)
		tmp = x / (y * (t - z));
	elseif (t <= 2e-34)
		tmp = t_1;
	elseif (t <= 4.3e+207)
		tmp = x / ((y - z) * t);
	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_] := Block[{t$95$1 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e-179], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-223], t$95$1, If[LessEqual[t, 4.5e-74], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-34], t$95$1, If[LessEqual[t, 4.3e+207], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.79999999999999974e-179

   1. Initial program 86.1%

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

      1. add-cube-cbrt 85.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.8%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 96.4%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 96.4%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 96.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in y around inf 60.3%

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

      1. associate-/r* 60.7%

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

   8. Simplified 60.7%

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

   if -3.79999999999999974e-179 < t < 9.9999999999999997e-224 or 4.4999999999999999e-74 < t < 1.99999999999999986e-34

   1. Initial program 95.3%

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

      1. clear-num 95.2%

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

      2. inv-pow 95.2%

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

      3. associate-/l* 97.5%

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

   3. Applied egg-rr 97.5%

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

      1. frac-2neg 97.5%

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

      2. div-inv 97.5%

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

      3. distribute-neg-frac 97.5%

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

   5. Applied egg-rr 97.5%

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

      1. associate-/r/ 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in t around 0 88.9%

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

   if 9.9999999999999997e-224 < t < 4.4999999999999999e-74

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

   4. Simplified 77.8%

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

   if 1.99999999999999986e-34 < t < 4.2999999999999997e207

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 91.1%

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

   if 4.2999999999999997e207 < t

   1. Initial program 79.5%

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

      1. add-cube-cbrt 79.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.4%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.4%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 79.5%

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

      1. associate-/r* 96.5%

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

   8. Simplified 96.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 5: 78.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - y}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-178}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.35 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z y))))
   (if (<= t -1.15e-178)
     (/ (/ x y) (- t z))
     (if (<= t 1e-223)
       t_1
       (if (<= t 4e-72)
         (/ x (* y (- t z)))
         (if (<= t 1.4e-33)
           t_1
           (if (<= t 4.35e+207) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - y);
	double tmp;
	if (t <= -1.15e-178) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 4e-72) {
		tmp = x / (y * (t - z));
	} else if (t <= 1.4e-33) {
		tmp = t_1;
	} else if (t <= 4.35e+207) {
		tmp = x / ((y - z) * t);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / (z - y)
    if (t <= (-1.15d-178)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1d-223) then
        tmp = t_1
    else if (t <= 4d-72) then
        tmp = x / (y * (t - z))
    else if (t <= 1.4d-33) then
        tmp = t_1
    else if (t <= 4.35d+207) then
        tmp = x / ((y - z) * t)
    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 t_1 = (x / z) / (z - y);
	double tmp;
	if (t <= -1.15e-178) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 4e-72) {
		tmp = x / (y * (t - z));
	} else if (t <= 1.4e-33) {
		tmp = t_1;
	} else if (t <= 4.35e+207) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / (z - y)
	tmp = 0
	if t <= -1.15e-178:
		tmp = (x / y) / (t - z)
	elif t <= 1e-223:
		tmp = t_1
	elif t <= 4e-72:
		tmp = x / (y * (t - z))
	elif t <= 1.4e-33:
		tmp = t_1
	elif t <= 4.35e+207:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - y))
	tmp = 0.0
	if (t <= -1.15e-178)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 4e-72)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 1.4e-33)
		tmp = t_1;
	elseif (t <= 4.35e+207)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	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)
	t_1 = (x / z) / (z - y);
	tmp = 0.0;
	if (t <= -1.15e-178)
		tmp = (x / y) / (t - z);
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 4e-72)
		tmp = x / (y * (t - z));
	elseif (t <= 1.4e-33)
		tmp = t_1;
	elseif (t <= 4.35e+207)
		tmp = x / ((y - z) * t);
	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_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e-178], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-223], t$95$1, If[LessEqual[t, 4e-72], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-33], t$95$1, If[LessEqual[t, 4.35e+207], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.14999999999999997e-178

   1. Initial program 86.1%

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

      1. add-cube-cbrt 85.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.8%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 96.4%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 96.4%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 96.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in y around inf 60.3%

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

      1. associate-/r* 60.7%

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

   8. Simplified 60.7%

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

   if -1.14999999999999997e-178 < t < 9.9999999999999997e-224 or 3.9999999999999999e-72 < t < 1.4e-33

   1. Initial program 95.3%

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

      1. clear-num 95.2%

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

      2. inv-pow 95.2%

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

      3. associate-/l* 97.5%

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

   3. Applied egg-rr 97.5%

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

      1. frac-2neg 97.5%

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

      2. div-inv 97.5%

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

      3. distribute-neg-frac 97.5%

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

   5. Applied egg-rr 97.5%

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

      1. associate-/r/ 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in t around 0 88.9%

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

      1. associate-/r* 93.2%

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

   10. Simplified 93.2%

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

   if 9.9999999999999997e-224 < t < 3.9999999999999999e-72

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

   4. Simplified 77.8%

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

   if 1.4e-33 < t < 4.35000000000000024e207

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 91.1%

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

   if 4.35000000000000024e207 < t

   1. Initial program 79.5%

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

      1. add-cube-cbrt 79.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.4%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.4%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 79.5%

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

      1. associate-/r* 96.5%

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

   8. Simplified 96.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-178}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 4.35 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 6: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - y}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z y))))
   (if (<= t -1.05e-179)
     (/ (/ x y) (- t z))
     (if (<= t 1e-223)
       t_1
       (if (<= t 5e-72)
         (/ (/ x (- t z)) y)
         (if (<= t 5e-35)
           t_1
           (if (<= t 4.3e+207) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - y);
	double tmp;
	if (t <= -1.05e-179) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 5e-72) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 5e-35) {
		tmp = t_1;
	} else if (t <= 4.3e+207) {
		tmp = x / ((y - z) * t);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / (z - y)
    if (t <= (-1.05d-179)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1d-223) then
        tmp = t_1
    else if (t <= 5d-72) then
        tmp = (x / (t - z)) / y
    else if (t <= 5d-35) then
        tmp = t_1
    else if (t <= 4.3d+207) then
        tmp = x / ((y - z) * t)
    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 t_1 = (x / z) / (z - y);
	double tmp;
	if (t <= -1.05e-179) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 5e-72) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 5e-35) {
		tmp = t_1;
	} else if (t <= 4.3e+207) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / (z - y)
	tmp = 0
	if t <= -1.05e-179:
		tmp = (x / y) / (t - z)
	elif t <= 1e-223:
		tmp = t_1
	elif t <= 5e-72:
		tmp = (x / (t - z)) / y
	elif t <= 5e-35:
		tmp = t_1
	elif t <= 4.3e+207:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - y))
	tmp = 0.0
	if (t <= -1.05e-179)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 5e-72)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 5e-35)
		tmp = t_1;
	elseif (t <= 4.3e+207)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	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)
	t_1 = (x / z) / (z - y);
	tmp = 0.0;
	if (t <= -1.05e-179)
		tmp = (x / y) / (t - z);
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 5e-72)
		tmp = (x / (t - z)) / y;
	elseif (t <= 5e-35)
		tmp = t_1;
	elseif (t <= 4.3e+207)
		tmp = x / ((y - z) * t);
	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_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-179], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-223], t$95$1, If[LessEqual[t, 5e-72], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 5e-35], t$95$1, If[LessEqual[t, 4.3e+207], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.0499999999999999e-179

   1. Initial program 86.1%

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

      1. add-cube-cbrt 85.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.8%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 96.4%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 96.4%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 96.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in y around inf 60.3%

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

      1. associate-/r* 60.7%

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

   8. Simplified 60.7%

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

   if -1.0499999999999999e-179 < t < 9.9999999999999997e-224 or 4.9999999999999996e-72 < t < 4.99999999999999964e-35

   1. Initial program 95.3%

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

      1. clear-num 95.2%

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

      2. inv-pow 95.2%

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

      3. associate-/l* 97.5%

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

   3. Applied egg-rr 97.5%

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

      1. frac-2neg 97.5%

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

      2. div-inv 97.5%

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

      3. distribute-neg-frac 97.5%

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

   5. Applied egg-rr 97.5%

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

      1. associate-/r/ 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in t around 0 88.9%

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

      1. associate-/r* 93.2%

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

   10. Simplified 93.2%

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

   if 9.9999999999999997e-224 < t < 4.9999999999999996e-72

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-/r* 85.4%

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

   4. Simplified 85.4%

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

   if 4.99999999999999964e-35 < t < 4.2999999999999997e207

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 91.1%

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

   if 4.2999999999999997e207 < t

   1. Initial program 79.5%

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

      1. add-cube-cbrt 79.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.4%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.4%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 79.5%

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

      1. associate-/r* 96.5%

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

   8. Simplified 96.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 7: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ t_2 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z y)))) (t_2 (/ x (* y (- t z)))))
   (if (<= t -8.2e-179)
     t_2
     (if (<= t 1e-223)
       t_1
       (if (<= t 1.6e-73) t_2 (if (<= t 3e-34) t_1 (/ x (* (- y z) t))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double t_2 = x / (y * (t - z));
	double tmp;
	if (t <= -8.2e-179) {
		tmp = t_2;
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 1.6e-73) {
		tmp = t_2;
	} else if (t <= 3e-34) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (z * (z - y))
    t_2 = x / (y * (t - z))
    if (t <= (-8.2d-179)) then
        tmp = t_2
    else if (t <= 1d-223) then
        tmp = t_1
    else if (t <= 1.6d-73) then
        tmp = t_2
    else if (t <= 3d-34) then
        tmp = t_1
    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 t_1 = x / (z * (z - y));
	double t_2 = x / (y * (t - z));
	double tmp;
	if (t <= -8.2e-179) {
		tmp = t_2;
	} else if (t <= 1e-223) {
		tmp = t_1;
	} else if (t <= 1.6e-73) {
		tmp = t_2;
	} else if (t <= 3e-34) {
		tmp = t_1;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * (z - y))
	t_2 = x / (y * (t - z))
	tmp = 0
	if t <= -8.2e-179:
		tmp = t_2
	elif t <= 1e-223:
		tmp = t_1
	elif t <= 1.6e-73:
		tmp = t_2
	elif t <= 3e-34:
		tmp = t_1
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - y)))
	t_2 = Float64(x / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (t <= -8.2e-179)
		tmp = t_2;
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 1.6e-73)
		tmp = t_2;
	elseif (t <= 3e-34)
		tmp = t_1;
	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)
	t_1 = x / (z * (z - y));
	t_2 = x / (y * (t - z));
	tmp = 0.0;
	if (t <= -8.2e-179)
		tmp = t_2;
	elseif (t <= 1e-223)
		tmp = t_1;
	elseif (t <= 1.6e-73)
		tmp = t_2;
	elseif (t <= 3e-34)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-179], t$95$2, If[LessEqual[t, 1e-223], t$95$1, If[LessEqual[t, 1.6e-73], t$95$2, If[LessEqual[t, 3e-34], t$95$1, N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.2e-179 or 9.9999999999999997e-224 < t < 1.59999999999999993e-73

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf 64.2%

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

      1. *-commutative 64.2%

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

   4. Simplified 64.2%

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

   if -8.2e-179 < t < 9.9999999999999997e-224 or 1.59999999999999993e-73 < t < 3e-34

   1. Initial program 95.3%

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

      1. clear-num 95.2%

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

      2. inv-pow 95.2%

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

      3. associate-/l* 97.5%

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

   3. Applied egg-rr 97.5%

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

      1. frac-2neg 97.5%

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

      2. div-inv 97.5%

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

      3. distribute-neg-frac 97.5%

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

   5. Applied egg-rr 97.5%

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

      1. associate-/r/ 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in t around 0 88.9%

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

   if 3e-34 < t

   1. Initial program 92.0%

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

   2. Taylor expanded in t around inf 86.7%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 10^{-223}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 8: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-171}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-121}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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) t)) (t_2 (/ (- x) (* z t))))
   (if (<= y -3.1e-50)
     t_1
     (if (<= y -1.7e-94)
       t_2
       (if (<= y -1.95e-171) (/ (/ x t) y) (if (<= y 2.8e-121) t_2 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) / t;
	double t_2 = -x / (z * t);
	double tmp;
	if (y <= -3.1e-50) {
		tmp = t_1;
	} else if (y <= -1.7e-94) {
		tmp = t_2;
	} else if (y <= -1.95e-171) {
		tmp = (x / t) / y;
	} else if (y <= 2.8e-121) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) / t
    t_2 = -x / (z * t)
    if (y <= (-3.1d-50)) then
        tmp = t_1
    else if (y <= (-1.7d-94)) then
        tmp = t_2
    else if (y <= (-1.95d-171)) then
        tmp = (x / t) / y
    else if (y <= 2.8d-121) then
        tmp = t_2
    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) / t;
	double t_2 = -x / (z * t);
	double tmp;
	if (y <= -3.1e-50) {
		tmp = t_1;
	} else if (y <= -1.7e-94) {
		tmp = t_2;
	} else if (y <= -1.95e-171) {
		tmp = (x / t) / y;
	} else if (y <= 2.8e-121) {
		tmp = t_2;
	} 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) / t
	t_2 = -x / (z * t)
	tmp = 0
	if y <= -3.1e-50:
		tmp = t_1
	elif y <= -1.7e-94:
		tmp = t_2
	elif y <= -1.95e-171:
		tmp = (x / t) / y
	elif y <= 2.8e-121:
		tmp = t_2
	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(Float64(x / y) / t)
	t_2 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (y <= -3.1e-50)
		tmp = t_1;
	elseif (y <= -1.7e-94)
		tmp = t_2;
	elseif (y <= -1.95e-171)
		tmp = Float64(Float64(x / t) / y);
	elseif (y <= 2.8e-121)
		tmp = t_2;
	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) / t;
	t_2 = -x / (z * t);
	tmp = 0.0;
	if (y <= -3.1e-50)
		tmp = t_1;
	elseif (y <= -1.7e-94)
		tmp = t_2;
	elseif (y <= -1.95e-171)
		tmp = (x / t) / y;
	elseif (y <= 2.8e-121)
		tmp = t_2;
	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[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e-50], t$95$1, If[LessEqual[y, -1.7e-94], t$95$2, If[LessEqual[y, -1.95e-171], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.8e-121], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000002e-50 or 2.8000000000000001e-121 < y

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0 52.8%

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

      1. *-un-lft-identity 52.8%

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

      2. times-frac 59.9%

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

   4. Applied egg-rr 59.9%

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

      1. associate-*l/ 59.9%

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

      2. *-lft-identity 59.9%

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

   6. Simplified 59.9%

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

   if -3.1000000000000002e-50 < y < -1.6999999999999999e-94 or -1.9499999999999999e-171 < y < 2.8000000000000001e-121

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 68.3%

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

   3. Taylor expanded in y around 0 55.9%

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

      1. associate-*r/ 55.9%

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

      2. neg-mul-1 55.9%

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

      3. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   if -1.6999999999999999e-94 < y < -1.9499999999999999e-171

   1. Initial program 87.9%

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

   2. Taylor expanded in y around inf 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-/r* 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in t around inf 54.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-94}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-171}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-121}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 9: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-121}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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) t)))
   (if (<= y -5e+170)
     t_1
     (if (<= y -2.2e+133)
       (/ (- x) (* y z))
       (if (<= y -5.5e-183)
         (/ (/ x t) y)
         (if (<= y 8.6e-121) (/ (- x) (* z t)) 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) / t;
	double tmp;
	if (y <= -5e+170) {
		tmp = t_1;
	} else if (y <= -2.2e+133) {
		tmp = -x / (y * z);
	} else if (y <= -5.5e-183) {
		tmp = (x / t) / y;
	} else if (y <= 8.6e-121) {
		tmp = -x / (z * t);
	} 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) / t
    if (y <= (-5d+170)) then
        tmp = t_1
    else if (y <= (-2.2d+133)) then
        tmp = -x / (y * z)
    else if (y <= (-5.5d-183)) then
        tmp = (x / t) / y
    else if (y <= 8.6d-121) then
        tmp = -x / (z * t)
    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) / t;
	double tmp;
	if (y <= -5e+170) {
		tmp = t_1;
	} else if (y <= -2.2e+133) {
		tmp = -x / (y * z);
	} else if (y <= -5.5e-183) {
		tmp = (x / t) / y;
	} else if (y <= 8.6e-121) {
		tmp = -x / (z * t);
	} 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) / t
	tmp = 0
	if y <= -5e+170:
		tmp = t_1
	elif y <= -2.2e+133:
		tmp = -x / (y * z)
	elif y <= -5.5e-183:
		tmp = (x / t) / y
	elif y <= 8.6e-121:
		tmp = -x / (z * t)
	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(Float64(x / y) / t)
	tmp = 0.0
	if (y <= -5e+170)
		tmp = t_1;
	elseif (y <= -2.2e+133)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (y <= -5.5e-183)
		tmp = Float64(Float64(x / t) / y);
	elseif (y <= 8.6e-121)
		tmp = Float64(Float64(-x) / Float64(z * t));
	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) / t;
	tmp = 0.0;
	if (y <= -5e+170)
		tmp = t_1;
	elseif (y <= -2.2e+133)
		tmp = -x / (y * z);
	elseif (y <= -5.5e-183)
		tmp = (x / t) / y;
	elseif (y <= 8.6e-121)
		tmp = -x / (z * t);
	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[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[y, -5e+170], t$95$1, If[LessEqual[y, -2.2e+133], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e-183], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.6e-121], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.99999999999999977e170 or 8.5999999999999993e-121 < y

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0 51.4%

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

      1. *-un-lft-identity 51.4%

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

      2. times-frac 58.5%

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

   4. Applied egg-rr 58.5%

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

      1. associate-*l/ 58.4%

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

      2. *-lft-identity 58.4%

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

   6. Simplified 58.4%

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

   if -4.99999999999999977e170 < y < -2.2e133

   1. Initial program 87.4%

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

   2. Taylor expanded in y around inf 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-/r* 87.9%

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

   4. Simplified 87.9%

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

   5. Taylor expanded in t around 0 55.7%

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

      1. associate-*r/ 55.7%

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

      2. neg-mul-1 55.7%

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

      3. *-commutative 55.7%

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

   7. Simplified 55.7%

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

   if -2.2e133 < y < -5.4999999999999999e-183

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-/r* 75.5%

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

   4. Simplified 75.5%

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

   5. Taylor expanded in t around inf 62.0%

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

   if -5.4999999999999999e-183 < y < 8.5999999999999993e-121

   1. Initial program 88.5%

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

   2. Taylor expanded in t around inf 65.8%

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

   3. Taylor expanded in y around 0 54.7%

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

      1. associate-*r/ 54.7%

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

      2. neg-mul-1 54.7%

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

      3. *-commutative 54.7%

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

   5. Simplified 54.7%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+170}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-121}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 10: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+181}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (<= t -7e-179)
   (/ (/ x y) t)
   (if (<= t 3.9e-91)
     (/ (/ (- x) z) y)
     (if (<= t 7.2e+78)
       (/ x (* y t))
       (if (<= t 5.5e+181) (/ (- 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 (t <= -7e-179) {
		tmp = (x / y) / t;
	} else if (t <= 3.9e-91) {
		tmp = (-x / z) / y;
	} else if (t <= 7.2e+78) {
		tmp = x / (y * t);
	} else if (t <= 5.5e+181) {
		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 (t <= (-7d-179)) then
        tmp = (x / y) / t
    else if (t <= 3.9d-91) then
        tmp = (-x / z) / y
    else if (t <= 7.2d+78) then
        tmp = x / (y * t)
    else if (t <= 5.5d+181) 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 (t <= -7e-179) {
		tmp = (x / y) / t;
	} else if (t <= 3.9e-91) {
		tmp = (-x / z) / y;
	} else if (t <= 7.2e+78) {
		tmp = x / (y * t);
	} else if (t <= 5.5e+181) {
		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 t <= -7e-179:
		tmp = (x / y) / t
	elif t <= 3.9e-91:
		tmp = (-x / z) / y
	elif t <= 7.2e+78:
		tmp = x / (y * t)
	elif t <= 5.5e+181:
		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 (t <= -7e-179)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 3.9e-91)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 7.2e+78)
		tmp = Float64(x / Float64(y * t));
	elseif (t <= 5.5e+181)
		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 (t <= -7e-179)
		tmp = (x / y) / t;
	elseif (t <= 3.9e-91)
		tmp = (-x / z) / y;
	elseif (t <= 7.2e+78)
		tmp = x / (y * t);
	elseif (t <= 5.5e+181)
		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[t, -7e-179], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 3.9e-91], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 7.2e+78], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+181], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.00000000000000049e-179

   1. Initial program 86.1%

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

   2. Taylor expanded in z around 0 52.0%

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

      1. *-un-lft-identity 52.0%

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

      2. times-frac 55.8%

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

   4. Applied egg-rr 55.8%

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

      1. associate-*l/ 55.8%

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

      2. *-lft-identity 55.8%

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

   6. Simplified 55.8%

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

   if -7.00000000000000049e-179 < t < 3.89999999999999994e-91

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-/r* 73.5%

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

   4. Simplified 73.5%

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

   5. Taylor expanded in t around 0 61.7%

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

      1. associate-*r/ 61.7%

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

      2. neg-mul-1 61.7%

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

   7. Simplified 61.7%

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

   if 3.89999999999999994e-91 < t < 7.20000000000000039e78

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 63.9%

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

   if 7.20000000000000039e78 < t < 5.49999999999999991e181

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 88.4%

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

   3. Taylor expanded in y around 0 62.3%

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

      1. associate-*r/ 62.3%

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

      2. neg-mul-1 62.3%

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

      3. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if 5.49999999999999991e181 < t

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. associate-/r* 73.9%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in t around inf 73.9%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+181}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 11: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-143}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+181}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* t (/ y x)))))
   (if (<= t -5.1e-193)
     t_1
     (if (<= t 1.25e-143)
       (/ (/ (- x) z) y)
       (if (<= t 7.2e+78)
         t_1
         (if (<= t 2.95e+181) (/ (- 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 t_1 = 1.0 / (t * (y / x));
	double tmp;
	if (t <= -5.1e-193) {
		tmp = t_1;
	} else if (t <= 1.25e-143) {
		tmp = (-x / z) / y;
	} else if (t <= 7.2e+78) {
		tmp = t_1;
	} else if (t <= 2.95e+181) {
		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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (t * (y / x))
    if (t <= (-5.1d-193)) then
        tmp = t_1
    else if (t <= 1.25d-143) then
        tmp = (-x / z) / y
    else if (t <= 7.2d+78) then
        tmp = t_1
    else if (t <= 2.95d+181) 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 t_1 = 1.0 / (t * (y / x));
	double tmp;
	if (t <= -5.1e-193) {
		tmp = t_1;
	} else if (t <= 1.25e-143) {
		tmp = (-x / z) / y;
	} else if (t <= 7.2e+78) {
		tmp = t_1;
	} else if (t <= 2.95e+181) {
		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):
	t_1 = 1.0 / (t * (y / x))
	tmp = 0
	if t <= -5.1e-193:
		tmp = t_1
	elif t <= 1.25e-143:
		tmp = (-x / z) / y
	elif t <= 7.2e+78:
		tmp = t_1
	elif t <= 2.95e+181:
		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)
	t_1 = Float64(1.0 / Float64(t * Float64(y / x)))
	tmp = 0.0
	if (t <= -5.1e-193)
		tmp = t_1;
	elseif (t <= 1.25e-143)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 7.2e+78)
		tmp = t_1;
	elseif (t <= 2.95e+181)
		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)
	t_1 = 1.0 / (t * (y / x));
	tmp = 0.0;
	if (t <= -5.1e-193)
		tmp = t_1;
	elseif (t <= 1.25e-143)
		tmp = (-x / z) / y;
	elseif (t <= 7.2e+78)
		tmp = t_1;
	elseif (t <= 2.95e+181)
		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_] := Block[{t$95$1 = N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e-193], t$95$1, If[LessEqual[t, 1.25e-143], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 7.2e+78], t$95$1, If[LessEqual[t, 2.95e+181], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.0999999999999998e-193 or 1.2500000000000001e-143 < t < 7.20000000000000039e78

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0 53.1%

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

      1. clear-num 53.9%

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

      2. inv-pow 53.9%

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

      3. *-commutative 53.9%

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

      4. associate-/l* 55.8%

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

   4. Applied egg-rr 55.8%

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

      1. unpow-1 55.8%

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

      2. associate-/r/ 57.5%

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

   6. Simplified 57.5%

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

   if -5.0999999999999998e-193 < t < 1.2500000000000001e-143

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-/r* 75.9%

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

   4. Simplified 75.9%

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

   5. Taylor expanded in t around 0 69.6%

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

      1. associate-*r/ 69.6%

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

      2. neg-mul-1 69.6%

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

   7. Simplified 69.6%

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

   if 7.20000000000000039e78 < t < 2.9499999999999999e181

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 88.4%

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

   3. Taylor expanded in y around 0 62.3%

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

      1. associate-*r/ 62.3%

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

      2. neg-mul-1 62.3%

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

      3. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if 2.9499999999999999e181 < t

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. associate-/r* 73.9%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in t around inf 73.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-193}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-143}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+181}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 12: 80.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-60}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= y -9e-60)
   (/ (/ x (- t z)) y)
   (if (<= y -6.2e-138)
     (/ (/ x z) (- z y))
     (if (<= y 7.2e-137) (/ (- x) (* z (- 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 (y <= -9e-60) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -6.2e-138) {
		tmp = (x / z) / (z - y);
	} else if (y <= 7.2e-137) {
		tmp = -x / (z * (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 (y <= (-9d-60)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-6.2d-138)) then
        tmp = (x / z) / (z - y)
    else if (y <= 7.2d-137) then
        tmp = -x / (z * (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 (y <= -9e-60) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -6.2e-138) {
		tmp = (x / z) / (z - y);
	} else if (y <= 7.2e-137) {
		tmp = -x / (z * (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 y <= -9e-60:
		tmp = (x / (t - z)) / y
	elif y <= -6.2e-138:
		tmp = (x / z) / (z - y)
	elif y <= 7.2e-137:
		tmp = -x / (z * (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 (y <= -9e-60)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -6.2e-138)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (y <= 7.2e-137)
		tmp = Float64(Float64(-x) / Float64(z * 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 (y <= -9e-60)
		tmp = (x / (t - z)) / y;
	elseif (y <= -6.2e-138)
		tmp = (x / z) / (z - y);
	elseif (y <= 7.2e-137)
		tmp = -x / (z * (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[y, -9e-60], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -6.2e-138], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-137], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.00000000000000001e-60

   1. Initial program 90.1%

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

   2. Taylor expanded in y around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-/r* 87.2%

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

   4. Simplified 87.2%

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

   if -9.00000000000000001e-60 < y < -6.1999999999999996e-138

   1. Initial program 99.7%

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

      1. clear-num 97.9%

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

      2. inv-pow 97.9%

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

      3. associate-/l* 98.1%

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

   3. Applied egg-rr 98.1%

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

      1. frac-2neg 98.1%

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

      2. div-inv 98.0%

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

      3. distribute-neg-frac 98.0%

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

   5. Applied egg-rr 98.0%

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

      1. associate-/r/ 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in t around 0 50.1%

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

      1. associate-/r* 50.2%

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

   10. Simplified 50.2%

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

   if -6.1999999999999996e-138 < y < 7.20000000000000013e-137

   1. Initial program 86.9%

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

   2. Taylor expanded in y around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. neg-mul-1 73.9%

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

   4. Simplified 73.9%

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

   if 7.20000000000000013e-137 < y

   1. Initial program 91.0%

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

      1. add-cube-cbrt 90.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.0%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.0%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 95.1%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 95.1%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 95.1%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in t around inf 61.6%

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

      1. associate-/r* 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-60}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 13: 50.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{y}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-243}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 z) y)) (t_2 (/ (/ x t) y)))
   (if (<= z -1.7e+104)
     t_1
     (if (<= z -2.7e-79)
       t_2
       (if (<= z 1.26e-243) (/ (/ x y) t) (if (<= z 1.02e+91) t_2 t_1))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / y;
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -1.7e+104) {
		tmp = t_1;
	} else if (z <= -2.7e-79) {
		tmp = t_2;
	} else if (z <= 1.26e-243) {
		tmp = (x / y) / t;
	} else if (z <= 1.02e+91) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / y
    t_2 = (x / t) / y
    if (z <= (-1.7d+104)) then
        tmp = t_1
    else if (z <= (-2.7d-79)) then
        tmp = t_2
    else if (z <= 1.26d-243) then
        tmp = (x / y) / t
    else if (z <= 1.02d+91) then
        tmp = t_2
    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 / z) / y;
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -1.7e+104) {
		tmp = t_1;
	} else if (z <= -2.7e-79) {
		tmp = t_2;
	} else if (z <= 1.26e-243) {
		tmp = (x / y) / t;
	} else if (z <= 1.02e+91) {
		tmp = t_2;
	} 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 / z) / y
	t_2 = (x / t) / y
	tmp = 0
	if z <= -1.7e+104:
		tmp = t_1
	elif z <= -2.7e-79:
		tmp = t_2
	elif z <= 1.26e-243:
		tmp = (x / y) / t
	elif z <= 1.02e+91:
		tmp = t_2
	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(Float64(x / z) / y)
	t_2 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -1.7e+104)
		tmp = t_1;
	elseif (z <= -2.7e-79)
		tmp = t_2;
	elseif (z <= 1.26e-243)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 1.02e+91)
		tmp = t_2;
	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 / z) / y;
	t_2 = (x / t) / y;
	tmp = 0.0;
	if (z <= -1.7e+104)
		tmp = t_1;
	elseif (z <= -2.7e-79)
		tmp = t_2;
	elseif (z <= 1.26e-243)
		tmp = (x / y) / t;
	elseif (z <= 1.02e+91)
		tmp = t_2;
	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[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.7e+104], t$95$1, If[LessEqual[z, -2.7e-79], t$95$2, If[LessEqual[z, 1.26e-243], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.02e+91], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6999999999999998e104 or 1.01999999999999992e91 < z

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-/r* 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in t around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   7. Simplified 51.6%

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

      1. expm1-log1p-u 51.4%

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

      2. expm1-udef 63.2%

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

      3. associate-/l/ 63.2%

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

      4. add-sqr-sqrt 32.6%

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

      5. sqrt-unprod 61.7%

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

      6. sqr-neg 61.7%

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

      7. sqrt-unprod 30.7%

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

      8. add-sqr-sqrt 63.2%

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

   9. Applied egg-rr 63.2%

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

       1. expm1-def 42.4%

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

       2. expm1-log1p 42.7%

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

       3. *-commutative 42.7%

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

   11. Simplified 42.7%

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

       1. div-inv 42.7%

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

       2. *-commutative 42.7%

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

       3. associate-/r* 42.7%

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

   13. Applied egg-rr 42.7%

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

       1. associate-*r/ 39.4%

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

       2. associate-*l/ 47.7%

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

       3. associate-*r/ 47.7%

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

       4. *-rgt-identity 47.7%

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

   15. Simplified 47.7%

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

   if -1.6999999999999998e104 < z < -2.7000000000000002e-79 or 1.2599999999999999e-243 < z < 1.01999999999999992e91

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-/r* 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in t around inf 46.3%

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

   if -2.7000000000000002e-79 < z < 1.2599999999999999e-243

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 80.9%

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

      1. *-un-lft-identity 80.9%

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

      2. times-frac 79.3%

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

   4. Applied egg-rr 79.3%

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

      1. associate-*l/ 79.1%

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

      2. *-lft-identity 79.1%

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

   6. Simplified 79.1%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-243}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 14: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+79} \lor \neg \left(z \leq 1.7 \cdot 10^{+132}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

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 (or (<= z -6e+79) (not (<= z 1.7e+132)))
   (/ (/ x z) (- z y))
   (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+79) || !(z <= 1.7e+132)) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = x / ((y - z) * (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 ((z <= (-6d+79)) .or. (.not. (z <= 1.7d+132))) then
        tmp = (x / z) / (z - y)
    else
        tmp = x / ((y - z) * (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 ((z <= -6e+79) || !(z <= 1.7e+132)) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -6e+79) or not (z <= 1.7e+132):
		tmp = (x / z) / (z - y)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e+79) || !(z <= 1.7e+132))
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(x / Float64(Float64(y - z) * 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 ((z <= -6e+79) || ~((z <= 1.7e+132)))
		tmp = (x / z) / (z - y);
	else
		tmp = x / ((y - z) * (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[Or[LessEqual[z, -6e+79], N[Not[LessEqual[z, 1.7e+132]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999948e79 or 1.70000000000000013e132 < z

   1. Initial program 76.2%

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

      1. clear-num 75.8%

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

      2. inv-pow 75.8%

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

      3. associate-/l* 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. frac-2neg 99.5%

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

      2. div-inv 99.4%

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

      3. distribute-neg-frac 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. associate-/r/ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in t around 0 74.9%

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

      1. associate-/r* 89.2%

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

   10. Simplified 89.2%

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

   if -5.99999999999999948e79 < z < 1.70000000000000013e132

   1. Initial program 96.1%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+79} \lor \neg \left(z \leq 1.7 \cdot 10^{+132}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 15: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-136}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= y -9.2e-73)
   (/ (/ x (- t z)) y)
   (if (<= y 1.3e-136) (/ (/ (- x) z) (- 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 (y <= -9.2e-73) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 1.3e-136) {
		tmp = (-x / z) / (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 (y <= (-9.2d-73)) then
        tmp = (x / (t - z)) / y
    else if (y <= 1.3d-136) then
        tmp = (-x / z) / (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 (y <= -9.2e-73) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 1.3e-136) {
		tmp = (-x / z) / (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 y <= -9.2e-73:
		tmp = (x / (t - z)) / y
	elif y <= 1.3e-136:
		tmp = (-x / z) / (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 (y <= -9.2e-73)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 1.3e-136)
		tmp = Float64(Float64(Float64(-x) / z) / 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 (y <= -9.2e-73)
		tmp = (x / (t - z)) / y;
	elseif (y <= 1.3e-136)
		tmp = (-x / z) / (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[y, -9.2e-73], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.3e-136], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.19999999999999953e-73

   1. Initial program 90.6%

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

   2. Taylor expanded in y around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-/r* 87.8%

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

   4. Simplified 87.8%

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

   if -9.19999999999999953e-73 < y < 1.29999999999999998e-136

   1. Initial program 89.0%

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

      1. add-cube-cbrt 88.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 97.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 97.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 97.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 96.5%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 96.5%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 96.5%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in y around 0 73.3%

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

      1. associate-/r* 83.8%

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

      2. associate-*r/ 83.8%

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

      3. associate-*r/ 83.8%

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

      4. neg-mul-1 83.8%

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

   8. Simplified 83.8%

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

   if 1.29999999999999998e-136 < y

   1. Initial program 91.0%

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

      1. add-cube-cbrt 90.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.0%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.0%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 95.1%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 95.1%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 95.1%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in t around inf 61.6%

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

      1. associate-/r* 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-136}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 16: 64.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-193}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-191}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -3.6e-193)
   (/ 1.0 (* t (/ y x)))
   (if (<= t 3e-191) (/ (/ (- 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 <= -3.6e-193) {
		tmp = 1.0 / (t * (y / x));
	} else if (t <= 3e-191) {
		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 <= (-3.6d-193)) then
        tmp = 1.0d0 / (t * (y / x))
    else if (t <= 3d-191) 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 <= -3.6e-193) {
		tmp = 1.0 / (t * (y / x));
	} else if (t <= 3e-191) {
		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 <= -3.6e-193:
		tmp = 1.0 / (t * (y / x))
	elif t <= 3e-191:
		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 <= -3.6e-193)
		tmp = Float64(1.0 / Float64(t * Float64(y / x)));
	elseif (t <= 3e-191)
		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 <= -3.6e-193)
		tmp = 1.0 / (t * (y / x));
	elseif (t <= 3e-191)
		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, -3.6e-193], N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-191], 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 < -3.5999999999999999e-193

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 50.3%

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

      1. clear-num 50.8%

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

      2. inv-pow 50.8%

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

      3. *-commutative 50.8%

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

      4. associate-/l* 54.3%

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

   4. Applied egg-rr 54.3%

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

      1. unpow-1 54.3%

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

      2. associate-/r/ 55.0%

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

   6. Simplified 55.0%

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

   if -3.5999999999999999e-193 < t < 3.0000000000000001e-191

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-/r* 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in t around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

   7. Simplified 71.0%

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

   if 3.0000000000000001e-191 < t

   1. Initial program 92.6%

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

   2. Taylor expanded in t around inf 74.3%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-193}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-191}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 17: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -3.9e-84)
   (/ 1.0 (* t (/ y x)))
   (if (<= t 1.15e-34) (/ x (* z (- 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 <= -3.9e-84) {
		tmp = 1.0 / (t * (y / x));
	} else if (t <= 1.15e-34) {
		tmp = x / (z * (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 <= (-3.9d-84)) then
        tmp = 1.0d0 / (t * (y / x))
    else if (t <= 1.15d-34) then
        tmp = x / (z * (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 <= -3.9e-84) {
		tmp = 1.0 / (t * (y / x));
	} else if (t <= 1.15e-34) {
		tmp = x / (z * (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 <= -3.9e-84:
		tmp = 1.0 / (t * (y / x))
	elif t <= 1.15e-34:
		tmp = x / (z * (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 <= -3.9e-84)
		tmp = Float64(1.0 / Float64(t * Float64(y / x)));
	elseif (t <= 1.15e-34)
		tmp = Float64(x / Float64(z * Float64(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 <= -3.9e-84)
		tmp = 1.0 / (t * (y / x));
	elseif (t <= 1.15e-34)
		tmp = x / (z * (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, -3.9e-84], N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-34], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.90000000000000023e-84

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 53.8%

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

      1. clear-num 54.5%

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

      2. inv-pow 54.5%

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

      3. *-commutative 54.5%

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

      4. associate-/l* 59.0%

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

   4. Applied egg-rr 59.0%

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

      1. unpow-1 59.0%

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

      2. associate-/r/ 58.8%

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

   6. Simplified 58.8%

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

   if -3.90000000000000023e-84 < t < 1.15000000000000006e-34

   1. Initial program 91.0%

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

      1. clear-num 90.8%

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

      2. inv-pow 90.8%

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

      3. associate-/l* 98.7%

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

   3. Applied egg-rr 98.7%

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

      1. frac-2neg 98.7%

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

      2. div-inv 98.6%

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

      3. distribute-neg-frac 98.6%

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

   5. Applied egg-rr 98.6%

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

      1. associate-/r/ 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in t around 0 70.2%

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

   if 1.15000000000000006e-34 < t

   1. Initial program 92.0%

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

   2. Taylor expanded in t around inf 86.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 18: 46.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+78} \lor \neg \left(z \leq 1.45 \cdot 10^{+69}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 (or (<= z -8.5e+78) (not (<= z 1.45e+69))) (/ x (* y z)) (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+78) || !(z <= 1.45e+69)) {
		tmp = x / (y * z);
	} 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) :: tmp
    if ((z <= (-8.5d+78)) .or. (.not. (z <= 1.45d+69))) then
        tmp = x / (y * z)
    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 tmp;
	if ((z <= -8.5e+78) || !(z <= 1.45e+69)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e+78) or not (z <= 1.45e+69):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e+78) || !(z <= 1.45e+69))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(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)
	tmp = 0.0;
	if ((z <= -8.5e+78) || ~((z <= 1.45e+69)))
		tmp = x / (y * z);
	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_] := If[Or[LessEqual[z, -8.5e+78], N[Not[LessEqual[z, 1.45e+69]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000079e78 or 1.4499999999999999e69 < z

   1. Initial program 81.2%

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

   2. Taylor expanded in y around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-/r* 56.0%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in t around 0 51.1%

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

      1. associate-*r/ 51.1%

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

      2. neg-mul-1 51.1%

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

   7. Simplified 51.1%

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

      1. expm1-log1p-u 49.9%

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

      2. expm1-udef 60.9%

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

      3. associate-/l/ 60.9%

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

      4. add-sqr-sqrt 31.3%

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

      5. sqrt-unprod 59.6%

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

      6. sqr-neg 59.6%

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

      7. sqrt-unprod 29.7%

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

      8. add-sqr-sqrt 60.9%

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

   9. Applied egg-rr 60.9%

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

       1. expm1-def 40.3%

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

       2. expm1-log1p 40.7%

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

       3. *-commutative 40.7%

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

   11. Simplified 40.7%

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

   if -8.50000000000000079e78 < z < 1.4499999999999999e69

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 57.2%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+78} \lor \neg \left(z \leq 1.45 \cdot 10^{+69}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 19: 48.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+105} \lor \neg \left(z \leq 8.4 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (or (<= z -4.8e+105) (not (<= z 8.4e+86))) (/ x (* y z)) (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+105) || !(z <= 8.4e+86)) {
		tmp = x / (y * z);
	} 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 ((z <= (-4.8d+105)) .or. (.not. (z <= 8.4d+86))) then
        tmp = x / (y * z)
    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 ((z <= -4.8e+105) || !(z <= 8.4e+86)) {
		tmp = x / (y * z);
	} 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 (z <= -4.8e+105) or not (z <= 8.4e+86):
		tmp = x / (y * z)
	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 ((z <= -4.8e+105) || !(z <= 8.4e+86))
		tmp = Float64(x / Float64(y * z));
	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 ((z <= -4.8e+105) || ~((z <= 8.4e+86)))
		tmp = x / (y * z);
	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[Or[LessEqual[z, -4.8e+105], N[Not[LessEqual[z, 8.4e+86]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7999999999999995e105 or 8.3999999999999996e86 < z

   1. Initial program 80.6%

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

   2. Taylor expanded in y around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/r* 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in t around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   7. Simplified 51.6%

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

      1. expm1-log1p-u 51.4%

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

      2. expm1-udef 62.9%

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

      3. associate-/l/ 62.9%

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

      4. add-sqr-sqrt 31.9%

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

      5. sqrt-unprod 61.4%

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

      6. sqr-neg 61.4%

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

      7. sqrt-unprod 31.1%

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

      8. add-sqr-sqrt 62.8%

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

   9. Applied egg-rr 62.8%

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

       1. expm1-def 42.5%

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

       2. expm1-log1p 42.9%

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

       3. *-commutative 42.9%

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

   11. Simplified 42.9%

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

   if -4.7999999999999995e105 < z < 8.3999999999999996e86

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-/r* 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in t around inf 59.1%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+105} \lor \neg \left(z \leq 8.4 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 20: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 90.3%

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

   1. add-cube-cbrt 89.5%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. times-frac 98.1%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   3. pow2 98.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

3. Applied egg-rr 98.1%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
4. Step-by-step derivation

   1. frac-times 89.5%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(y - z\right) \cdot \left(t - z\right)}} \]

   2. unpow2 89.5%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   3. add-cube-cbrt 90.3%

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

   4. associate-/l/ 97.7%

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

5. Applied egg-rr 97.7%

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

6. Final simplification 97.7%

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

Alternative 21: 44.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -5.5e+61) (/ (/ x y) 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 <= -5.5e+61) {
		tmp = (x / y) / 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 <= (-5.5d+61)) then
        tmp = (x / y) / 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 <= -5.5e+61) {
		tmp = (x / y) / 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 <= -5.5e+61:
		tmp = (x / y) / 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 <= -5.5e+61)
		tmp = Float64(Float64(x / y) / 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 <= -5.5e+61)
		tmp = (x / y) / 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, -5.5e+61], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000036e61

   1. Initial program 88.5%

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

   2. Taylor expanded in z around 0 51.2%

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

      1. *-un-lft-identity 51.2%

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

      2. times-frac 63.8%

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

   4. Applied egg-rr 63.8%

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

      1. associate-*l/ 63.8%

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

      2. *-lft-identity 63.8%

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

   6. Simplified 63.8%

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

   if -5.50000000000000036e61 < y

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/r* 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in t around inf 47.4%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 22: 39.0% 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 90.3%

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

2. Taylor expanded in z around 0 44.4%

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

3. Final simplification 44.4%

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

Developer target: 88.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023335 
(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))))