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

Percentage Accurate: 88.8% → 96.4%

Time: 13.7s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{-1}{\left(y - z\right) \cdot \frac{z - t}{x}} \end{array} \]

FPCore

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

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return -1.0 / ((y - z) * ((z - t) / x));
}

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 = (-1.0d0) / ((y - z) * ((z - t) / x))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return -1.0 / ((y - z) * ((z - t) / x));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return -1.0 / ((y - z) * ((z - t) / x))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(-1.0 / Float64(Float64(y - z) * Float64(Float64(z - t) / x)))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = -1.0 / ((y - z) * ((z - t) / x));
end

Wolfram

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

Derivation

1. Initial program 88.1%

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

   1. clear-num 87.6%

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

   2. inv-pow 87.6%

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

   3. associate-/l* 96.5%

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

4. Applied egg-rr 96.5%

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

   1. unpow-1 96.5%

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

6. Simplified 96.5%

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

7. Final simplification 96.5%

   \[\leadsto \frac{-1}{\left(y - z\right) \cdot \frac{z - t}{x}} \]
8. Add Preprocessing

Alternative 2: 78.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 13600000000:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) (- z t))))
   (if (<= z -1.1e+161)
     t_1
     (if (<= z -4.3e+42)
       (/ x (* z (- z y)))
       (if (<= z -6.5e-40)
         t_1
         (if (<= z 2.15e-128)
           (/ (/ x t) (- y z))
           (if (<= z 13600000000.0) (/ x (* y (- 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 / z) / (z - t);
	double tmp;
	if (z <= -1.1e+161) {
		tmp = t_1;
	} else if (z <= -4.3e+42) {
		tmp = x / (z * (z - y));
	} else if (z <= -6.5e-40) {
		tmp = t_1;
	} else if (z <= 2.15e-128) {
		tmp = (x / t) / (y - z);
	} else if (z <= 13600000000.0) {
		tmp = x / (y * (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 / z) / (z - t)
    if (z <= (-1.1d+161)) then
        tmp = t_1
    else if (z <= (-4.3d+42)) then
        tmp = x / (z * (z - y))
    else if (z <= (-6.5d-40)) then
        tmp = t_1
    else if (z <= 2.15d-128) then
        tmp = (x / t) / (y - z)
    else if (z <= 13600000000.0d0) then
        tmp = x / (y * (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 / z) / (z - t);
	double tmp;
	if (z <= -1.1e+161) {
		tmp = t_1;
	} else if (z <= -4.3e+42) {
		tmp = x / (z * (z - y));
	} else if (z <= -6.5e-40) {
		tmp = t_1;
	} else if (z <= 2.15e-128) {
		tmp = (x / t) / (y - z);
	} else if (z <= 13600000000.0) {
		tmp = x / (y * (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 / z) / (z - t)
	tmp = 0
	if z <= -1.1e+161:
		tmp = t_1
	elif z <= -4.3e+42:
		tmp = x / (z * (z - y))
	elif z <= -6.5e-40:
		tmp = t_1
	elif z <= 2.15e-128:
		tmp = (x / t) / (y - z)
	elif z <= 13600000000.0:
		tmp = x / (y * (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(Float64(x / z) / Float64(z - t))
	tmp = 0.0
	if (z <= -1.1e+161)
		tmp = t_1;
	elseif (z <= -4.3e+42)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (z <= -6.5e-40)
		tmp = t_1;
	elseif (z <= 2.15e-128)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 13600000000.0)
		tmp = Float64(x / Float64(y * 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 / z) / (z - t);
	tmp = 0.0;
	if (z <= -1.1e+161)
		tmp = t_1;
	elseif (z <= -4.3e+42)
		tmp = x / (z * (z - y));
	elseif (z <= -6.5e-40)
		tmp = t_1;
	elseif (z <= 2.15e-128)
		tmp = (x / t) / (y - z);
	elseif (z <= 13600000000.0)
		tmp = x / (y * (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[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+161], t$95$1, If[LessEqual[z, -4.3e+42], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-40], t$95$1, If[LessEqual[z, 2.15e-128], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 13600000000.0], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e161 or -4.2999999999999998e42 < z < -6.4999999999999999e-40 or 1.36e10 < z

   1. Initial program 81.9%

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

      1. associate-/r* 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. neg-sub0 99.8%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.8%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.8%

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

      7. distribute-neg-frac2 99.8%

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

      8. distribute-frac-neg 99.8%

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

      9. distribute-neg-frac2 99.8%

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

      10. sub-neg 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. remove-double-neg 99.8%

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

      13. +-commutative 99.8%

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

      14. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 72.8%

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

      1. associate-/r* 85.1%

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

   7. Simplified 85.1%

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

   if -1.1e161 < z < -4.2999999999999998e42

   1. Initial program 93.1%

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

      1. associate-/r* 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. neg-sub0 99.7%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.7%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.7%

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

      7. distribute-neg-frac2 99.7%

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

      8. distribute-frac-neg 99.7%

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

      9. distribute-neg-frac2 99.7%

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

      10. sub-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. remove-double-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 77.2%

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

   if -6.4999999999999999e-40 < z < 2.14999999999999997e-128

   1. Initial program 90.8%

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

   3. Taylor expanded in t around inf 80.1%

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

      1. associate-/r* 81.1%

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

   5. Simplified 81.1%

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

   if 2.14999999999999997e-128 < z < 1.36e10

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 66.5%

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

      1. *-commutative 66.5%

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

   5. Simplified 66.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 13600000000:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot t}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 t))))
   (if (<= z -2.8e+155)
     t_1
     (if (<= z -2.5e-58)
       (/ (/ x y) t)
       (if (<= z 5.2e-283)
         (/ x (* y t))
         (if (<= z 7.6e+78) (/ (/ x t) y) 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 * t);
	double tmp;
	if (z <= -2.8e+155) {
		tmp = t_1;
	} else if (z <= -2.5e-58) {
		tmp = (x / y) / t;
	} else if (z <= 5.2e-283) {
		tmp = x / (y * t);
	} else if (z <= 7.6e+78) {
		tmp = (x / t) / y;
	} 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 / (z * t)
    if (z <= (-2.8d+155)) then
        tmp = t_1
    else if (z <= (-2.5d-58)) then
        tmp = (x / y) / t
    else if (z <= 5.2d-283) then
        tmp = x / (y * t)
    else if (z <= 7.6d+78) then
        tmp = (x / t) / y
    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 * t);
	double tmp;
	if (z <= -2.8e+155) {
		tmp = t_1;
	} else if (z <= -2.5e-58) {
		tmp = (x / y) / t;
	} else if (z <= 5.2e-283) {
		tmp = x / (y * t);
	} else if (z <= 7.6e+78) {
		tmp = (x / t) / y;
	} 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 * t)
	tmp = 0
	if z <= -2.8e+155:
		tmp = t_1
	elif z <= -2.5e-58:
		tmp = (x / y) / t
	elif z <= 5.2e-283:
		tmp = x / (y * t)
	elif z <= 7.6e+78:
		tmp = (x / t) / y
	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(z * t))
	tmp = 0.0
	if (z <= -2.8e+155)
		tmp = t_1;
	elseif (z <= -2.5e-58)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 5.2e-283)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 7.6e+78)
		tmp = Float64(Float64(x / t) / y);
	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 * t);
	tmp = 0.0;
	if (z <= -2.8e+155)
		tmp = t_1;
	elseif (z <= -2.5e-58)
		tmp = (x / y) / t;
	elseif (z <= 5.2e-283)
		tmp = x / (y * t);
	elseif (z <= 7.6e+78)
		tmp = (x / t) / y;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+155], t$95$1, If[LessEqual[z, -2.5e-58], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5.2e-283], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+78], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.80000000000000016e155 or 7.5999999999999998e78 < z

   1. Initial program 79.7%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 77.8%

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

   6. Taylor expanded in z around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. associate-/r* 38.7%

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

      3. distribute-neg-frac2 38.7%

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

   8. Simplified 38.7%

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

      1. associate-/l/ 35.5%

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

      2. add0 35.5%

         \[\leadsto \color{blue}{\frac{x}{\left(-z\right) \cdot t} + 0} \]

      3. add-sqr-sqrt 13.3%

         \[\leadsto \frac{x}{\color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot t} + 0 \]

      4. sqrt-unprod 62.8%

         \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot t} + 0 \]

      5. sqr-neg 62.8%

         \[\leadsto \frac{x}{\sqrt{\color{blue}{z \cdot z}} \cdot t} + 0 \]

      6. sqrt-unprod 20.8%

         \[\leadsto \frac{x}{\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot t} + 0 \]

      7. add-sqr-sqrt 33.9%

         \[\leadsto \frac{x}{\color{blue}{z} \cdot t} + 0 \]

   10. Applied egg-rr 33.9%

       \[\leadsto \color{blue}{\frac{x}{z \cdot t} + 0} \]
   11. Step-by-step derivation

       1. *-commutative 33.9%

          \[\leadsto \frac{x}{\color{blue}{t \cdot z}} + 0 \]

       2. add0 33.9%

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

   12. Simplified 33.9%

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

   if -2.80000000000000016e155 < z < -2.49999999999999989e-58

   1. Initial program 93.8%

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

      1. associate-/r* 98.3%

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

      2. sub-neg 98.3%

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

      3. +-commutative 98.3%

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

      4. neg-sub0 98.3%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 98.3%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 98.3%

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

      7. distribute-neg-frac2 98.3%

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

      8. distribute-frac-neg 98.3%

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

      9. distribute-neg-frac2 98.3%

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

      10. sub-neg 98.3%

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

      11. distribute-neg-in 98.3%

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

      12. remove-double-neg 98.3%

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

      13. +-commutative 98.3%

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

      14. sub-neg 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.2%

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

      2. inv-pow 98.2%

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

      3. div-inv 97.3%

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

      4. clear-num 97.4%

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

   6. Applied egg-rr 97.4%

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

      1. unpow-1 97.4%

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

   8. Simplified 97.4%

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

      1. clear-num 97.3%

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

      2. un-div-inv 98.2%

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

   10. Applied egg-rr 98.2%

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

   11. Taylor expanded in z around 0 22.9%

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

       1. *-rgt-identity 22.9%

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

       2. *-commutative 22.9%

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

       3. times-frac 35.1%

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

       4. associate-*r/ 35.2%

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

       5. *-rgt-identity 35.2%

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

   13. Simplified 35.2%

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

   if -2.49999999999999989e-58 < z < 5.2000000000000002e-283

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 78.9%

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

   if 5.2000000000000002e-283 < z < 7.5999999999999998e78

   1. Initial program 87.9%

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

      1. clear-num 87.3%

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

      2. inv-pow 87.3%

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

      3. associate-/l* 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. unpow-1 96.5%

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

   6. Simplified 96.5%

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

   7. Taylor expanded in z around 0 51.3%

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

      1. associate-/r* 59.5%

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

   9. Simplified 59.5%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-39} \lor \neg \left(z \leq 2 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= z -1.1e+161)
   (/ 1.0 (* z (/ z x)))
   (if (or (<= z -1.04e-39) (not (<= z 2e-62)))
     (/ x (* z (- z t)))
     (/ 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 (z <= -1.1e+161) {
		tmp = 1.0 / (z * (z / x));
	} else if ((z <= -1.04e-39) || !(z <= 2e-62)) {
		tmp = x / (z * (z - t));
	} 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 (z <= (-1.1d+161)) then
        tmp = 1.0d0 / (z * (z / x))
    else if ((z <= (-1.04d-39)) .or. (.not. (z <= 2d-62))) then
        tmp = x / (z * (z - t))
    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 (z <= -1.1e+161) {
		tmp = 1.0 / (z * (z / x));
	} else if ((z <= -1.04e-39) || !(z <= 2e-62)) {
		tmp = x / (z * (z - t));
	} 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 z <= -1.1e+161:
		tmp = 1.0 / (z * (z / x))
	elif (z <= -1.04e-39) or not (z <= 2e-62):
		tmp = x / (z * (z - t))
	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 (z <= -1.1e+161)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	elseif ((z <= -1.04e-39) || !(z <= 2e-62))
		tmp = Float64(x / Float64(z * Float64(z - t)));
	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 (z <= -1.1e+161)
		tmp = 1.0 / (z * (z / x));
	elseif ((z <= -1.04e-39) || ~((z <= 2e-62)))
		tmp = x / (z * (z - t));
	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[z, -1.1e+161], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.04e-39], N[Not[LessEqual[z, 2e-62]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e161

   1. Initial program 72.8%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in t around 0 72.8%

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

       1. associate-*r/ 93.9%

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

   11. Simplified 93.9%

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

   12. Taylor expanded in z around inf 92.3%

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

   if -1.1e161 < z < -1.0400000000000001e-39 or 2.0000000000000001e-62 < z

   1. Initial program 88.8%

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

      1. associate-/r* 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. neg-sub0 99.7%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.7%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.7%

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

      7. distribute-neg-frac2 99.7%

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

      8. distribute-frac-neg 99.7%

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

      9. distribute-neg-frac2 99.7%

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

      10. sub-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. remove-double-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 74.5%

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

   if -1.0400000000000001e-39 < z < 2.0000000000000001e-62

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf 79.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-39} \lor \neg \left(z \leq 2 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-41} \lor \neg \left(z \leq 1.3 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= z -2.6e+161)
   (/ 1.0 (* z (/ z x)))
   (if (or (<= z -7.5e-41) (not (<= z 1.3e-69)))
     (/ 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 (z <= -2.6e+161) {
		tmp = 1.0 / (z * (z / x));
	} else if ((z <= -7.5e-41) || !(z <= 1.3e-69)) {
		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 (z <= (-2.6d+161)) then
        tmp = 1.0d0 / (z * (z / x))
    else if ((z <= (-7.5d-41)) .or. (.not. (z <= 1.3d-69))) 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 (z <= -2.6e+161) {
		tmp = 1.0 / (z * (z / x));
	} else if ((z <= -7.5e-41) || !(z <= 1.3e-69)) {
		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 z <= -2.6e+161:
		tmp = 1.0 / (z * (z / x))
	elif (z <= -7.5e-41) or not (z <= 1.3e-69):
		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 (z <= -2.6e+161)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	elseif ((z <= -7.5e-41) || !(z <= 1.3e-69))
		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 (z <= -2.6e+161)
		tmp = 1.0 / (z * (z / x));
	elseif ((z <= -7.5e-41) || ~((z <= 1.3e-69)))
		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[z, -2.6e+161], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.5e-41], N[Not[LessEqual[z, 1.3e-69]], $MachinePrecision]], 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 z < -2.5999999999999998e161

   1. Initial program 72.8%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in t around 0 72.8%

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

       1. associate-*r/ 93.9%

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

   11. Simplified 93.9%

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

   12. Taylor expanded in z around inf 92.3%

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

   if -2.5999999999999998e161 < z < -7.50000000000000049e-41 or 1.3000000000000001e-69 < z

   1. Initial program 88.9%

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

      1. associate-/r* 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. neg-sub0 99.7%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.7%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.7%

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

      7. distribute-neg-frac2 99.7%

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

      8. distribute-frac-neg 99.7%

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

      9. distribute-neg-frac2 99.7%

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

      10. sub-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. remove-double-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 73.4%

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

   if -7.50000000000000049e-41 < z < 1.3000000000000001e-69

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf 79.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-41} \lor \neg \left(z \leq 1.3 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 9000000000000:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

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 (<= z -8.2e-42)
   (/ (/ x z) (- z y))
   (if (<= z 1.42e-128)
     (/ (/ x t) (- y z))
     (if (<= z 9000000000000.0) (/ x (* y (- t z))) (/ (/ x z) (- z t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e-42) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.42e-128) {
		tmp = (x / t) / (y - z);
	} else if (z <= 9000000000000.0) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / z) / (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 (z <= (-8.2d-42)) then
        tmp = (x / z) / (z - y)
    else if (z <= 1.42d-128) then
        tmp = (x / t) / (y - z)
    else if (z <= 9000000000000.0d0) then
        tmp = x / (y * (t - z))
    else
        tmp = (x / z) / (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 (z <= -8.2e-42) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.42e-128) {
		tmp = (x / t) / (y - z);
	} else if (z <= 9000000000000.0) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -8.2e-42:
		tmp = (x / z) / (z - y)
	elif z <= 1.42e-128:
		tmp = (x / t) / (y - z)
	elif z <= 9000000000000.0:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.2e-42)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 1.42e-128)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 9000000000000.0)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(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 (z <= -8.2e-42)
		tmp = (x / z) / (z - y);
	elseif (z <= 1.42e-128)
		tmp = (x / t) / (y - z);
	elseif (z <= 9000000000000.0)
		tmp = x / (y * (t - z));
	else
		tmp = (x / z) / (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[z, -8.2e-42], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e-128], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9000000000000.0], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2000000000000003e-42

   1. Initial program 85.0%

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

      1. associate-/r* 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. neg-sub0 99.7%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.7%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.7%

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

      7. distribute-neg-frac2 99.7%

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

      8. distribute-frac-neg 99.7%

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

      9. distribute-neg-frac2 99.7%

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

      10. sub-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. remove-double-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. sub-neg 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

      3. div-inv 99.5%

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

      4. clear-num 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in t around 0 73.8%

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

       1. associate-/r* 82.3%

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

   11. Simplified 82.3%

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

   if -8.2000000000000003e-42 < z < 1.4199999999999999e-128

   1. Initial program 90.8%

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

   3. Taylor expanded in t around inf 80.1%

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

      1. associate-/r* 81.1%

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

   5. Simplified 81.1%

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

   if 1.4199999999999999e-128 < z < 9e12

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 66.5%

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

      1. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   if 9e12 < z

   1. Initial program 83.3%

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

      1. associate-/r* 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. neg-sub0 99.8%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.8%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.8%

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

      7. distribute-neg-frac2 99.8%

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

      8. distribute-frac-neg 99.8%

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

      9. distribute-neg-frac2 99.8%

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

      10. sub-neg 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. remove-double-neg 99.8%

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

      13. +-commutative 99.8%

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

      14. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 76.1%

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

      1. associate-/r* 84.8%

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

   7. Simplified 84.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 9000000000000:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+208}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+52} \lor \neg \left(z \leq 2.15 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (<= z -1.75e+208)
   (/ x (* z (- t)))
   (if (or (<= z -6.8e+52) (not (<= z 2.15e+98)))
     (/ 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 <= -1.75e+208) {
		tmp = x / (z * -t);
	} else if ((z <= -6.8e+52) || !(z <= 2.15e+98)) {
		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 <= (-1.75d+208)) then
        tmp = x / (z * -t)
    else if ((z <= (-6.8d+52)) .or. (.not. (z <= 2.15d+98))) 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 <= -1.75e+208) {
		tmp = x / (z * -t);
	} else if ((z <= -6.8e+52) || !(z <= 2.15e+98)) {
		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 <= -1.75e+208:
		tmp = x / (z * -t)
	elif (z <= -6.8e+52) or not (z <= 2.15e+98):
		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 <= -1.75e+208)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif ((z <= -6.8e+52) || !(z <= 2.15e+98))
		tmp = Float64(x / Float64(y * Float64(-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 <= -1.75e+208)
		tmp = x / (z * -t);
	elseif ((z <= -6.8e+52) || ~((z <= 2.15e+98)))
		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[LessEqual[z, -1.75e+208], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.8e+52], N[Not[LessEqual[z, 2.15e+98]], $MachinePrecision]], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75000000000000008e208

   1. Initial program 78.1%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. associate-/r* 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 30.9%

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

      1. associate-*r/ 30.9%

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

      2. neg-mul-1 30.9%

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

      3. *-commutative 30.9%

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

   10. Simplified 30.9%

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

   if -1.75000000000000008e208 < z < -6.8e52 or 2.1500000000000001e98 < z

   1. Initial program 83.7%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 77.6%

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

   6. Taylor expanded in z around 0 38.5%

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

      1. associate-*r/ 38.5%

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

      2. neg-mul-1 38.5%

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

      3. *-commutative 38.5%

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

   8. Simplified 38.5%

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

   if -6.8e52 < z < 2.1500000000000001e98

   1. Initial program 91.9%

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

      1. clear-num 91.1%

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

      2. inv-pow 91.1%

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

      3. associate-/l* 94.5%

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

   4. Applied egg-rr 94.5%

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

      1. unpow-1 94.5%

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

   6. Simplified 94.5%

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

   7. Taylor expanded in z around 0 55.4%

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

      1. associate-/r* 57.7%

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

   9. Simplified 57.7%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+208}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+52} \lor \neg \left(z \leq 2.15 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+52} \lor \neg \left(z \leq 5.4 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (<= z -1.35e+208)
   (/ (/ x t) (- z))
   (if (or (<= z -6.5e+52) (not (<= z 5.4e+96)))
     (/ 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 <= -1.35e+208) {
		tmp = (x / t) / -z;
	} else if ((z <= -6.5e+52) || !(z <= 5.4e+96)) {
		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 <= (-1.35d+208)) then
        tmp = (x / t) / -z
    else if ((z <= (-6.5d+52)) .or. (.not. (z <= 5.4d+96))) 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 <= -1.35e+208) {
		tmp = (x / t) / -z;
	} else if ((z <= -6.5e+52) || !(z <= 5.4e+96)) {
		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 <= -1.35e+208:
		tmp = (x / t) / -z
	elif (z <= -6.5e+52) or not (z <= 5.4e+96):
		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 <= -1.35e+208)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif ((z <= -6.5e+52) || !(z <= 5.4e+96))
		tmp = Float64(x / Float64(y * Float64(-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 <= -1.35e+208)
		tmp = (x / t) / -z;
	elseif ((z <= -6.5e+52) || ~((z <= 5.4e+96)))
		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[LessEqual[z, -1.35e+208], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[Or[LessEqual[z, -6.5e+52], N[Not[LessEqual[z, 5.4e+96]], $MachinePrecision]], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e208

   1. Initial program 78.1%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 78.1%

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

   6. Taylor expanded in z around 0 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-/r* 39.3%

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

      3. distribute-neg-frac2 39.3%

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

   8. Simplified 39.3%

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

   if -1.35e208 < z < -6.49999999999999996e52 or 5.40000000000000044e96 < z

   1. Initial program 83.7%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 77.6%

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

   6. Taylor expanded in z around 0 38.5%

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

      1. associate-*r/ 38.5%

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

      2. neg-mul-1 38.5%

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

      3. *-commutative 38.5%

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

   8. Simplified 38.5%

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

   if -6.49999999999999996e52 < z < 5.40000000000000044e96

   1. Initial program 91.9%

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

      1. clear-num 91.1%

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

      2. inv-pow 91.1%

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

      3. associate-/l* 94.5%

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

   4. Applied egg-rr 94.5%

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

      1. unpow-1 94.5%

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

   6. Simplified 94.5%

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

   7. Taylor expanded in z around 0 55.4%

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

      1. associate-/r* 57.7%

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

   9. Simplified 57.7%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+52} \lor \neg \left(z \leq 5.4 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+161} \lor \neg \left(z \leq 10^{+144}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

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 -1.1e+161) (not (<= z 1e+144)))
   (/ (/ x z) (- z t))
   (/ 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 <= -1.1e+161) || !(z <= 1e+144)) {
		tmp = (x / z) / (z - t);
	} 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 <= (-1.1d+161)) .or. (.not. (z <= 1d+144))) then
        tmp = (x / z) / (z - t)
    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 <= -1.1e+161) || !(z <= 1e+144)) {
		tmp = (x / z) / (z - t);
	} 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 <= -1.1e+161) or not (z <= 1e+144):
		tmp = (x / z) / (z - t)
	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 <= -1.1e+161) || !(z <= 1e+144))
		tmp = Float64(Float64(x / z) / Float64(z - t));
	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 <= -1.1e+161) || ~((z <= 1e+144)))
		tmp = (x / z) / (z - t);
	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, -1.1e+161], N[Not[LessEqual[z, 1e+144]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / N[(z - t), $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 < -1.1e161 or 1.00000000000000002e144 < z

   1. Initial program 75.6%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 74.7%

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

      1. associate-/r* 95.2%

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

   7. Simplified 95.2%

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

   if -1.1e161 < z < 1.00000000000000002e144

   1. Initial program 92.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+161} \lor \neg \left(z \leq 10^{+144}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-39} \lor \neg \left(z \leq 1.68 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -3.2e-39) (not (<= z 1.68e+22)))
   (/ 1.0 (* z (/ z x)))
   (/ (/ 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 <= -3.2e-39) || !(z <= 1.68e+22)) {
		tmp = 1.0 / (z * (z / x));
	} 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 <= (-3.2d-39)) .or. (.not. (z <= 1.68d+22))) then
        tmp = 1.0d0 / (z * (z / x))
    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 <= -3.2e-39) || !(z <= 1.68e+22)) {
		tmp = 1.0 / (z * (z / x));
	} 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 <= -3.2e-39) or not (z <= 1.68e+22):
		tmp = 1.0 / (z * (z / x))
	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 <= -3.2e-39) || !(z <= 1.68e+22))
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	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 <= -3.2e-39) || ~((z <= 1.68e+22)))
		tmp = 1.0 / (z * (z / x));
	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, -3.2e-39], N[Not[LessEqual[z, 1.68e+22]], $MachinePrecision]], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999998e-39 or 1.68e22 < z

   1. Initial program 84.1%

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

      1. associate-/r* 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. neg-sub0 99.8%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.8%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.8%

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

      7. distribute-neg-frac2 99.8%

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

      8. distribute-frac-neg 99.8%

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

      9. distribute-neg-frac2 99.8%

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

      10. sub-neg 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. remove-double-neg 99.8%

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

      13. +-commutative 99.8%

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

      14. sub-neg 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.5%

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

      2. inv-pow 99.5%

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

      3. div-inv 99.4%

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

      4. clear-num 99.5%

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

   6. Applied egg-rr 99.5%

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

      1. unpow-1 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in t around 0 76.1%

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

       1. associate-*r/ 84.1%

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

   11. Simplified 84.1%

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

   12. Taylor expanded in z around inf 73.9%

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

   if -3.1999999999999998e-39 < z < 1.68e22

   1. Initial program 92.7%

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

      1. clear-num 91.7%

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

      2. inv-pow 91.7%

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

      3. associate-/l* 93.1%

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

   4. Applied egg-rr 93.1%

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

      1. unpow-1 93.1%

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

   6. Simplified 93.1%

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

   7. Taylor expanded in z around 0 66.4%

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

      1. associate-/r* 66.4%

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

   9. Simplified 66.4%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-39} \lor \neg \left(z \leq 1.68 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-7} \lor \neg \left(z \leq 1.95 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (or (<= z -2.1e-7) (not (<= z 1.95e+16)))
   (/ 1.0 (* z (/ z x)))
   (/ 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 ((z <= -2.1e-7) || !(z <= 1.95e+16)) {
		tmp = 1.0 / (z * (z / x));
	} 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 ((z <= (-2.1d-7)) .or. (.not. (z <= 1.95d+16))) then
        tmp = 1.0d0 / (z * (z / x))
    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 ((z <= -2.1e-7) || !(z <= 1.95e+16)) {
		tmp = 1.0 / (z * (z / x));
	} 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 (z <= -2.1e-7) or not (z <= 1.95e+16):
		tmp = 1.0 / (z * (z / x))
	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 ((z <= -2.1e-7) || !(z <= 1.95e+16))
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	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 ((z <= -2.1e-7) || ~((z <= 1.95e+16)))
		tmp = 1.0 / (z * (z / x));
	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[Or[LessEqual[z, -2.1e-7], N[Not[LessEqual[z, 1.95e+16]], $MachinePrecision]], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e-7 or 1.95e16 < z

   1. Initial program 83.8%

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

      1. associate-/r* 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. neg-sub0 99.8%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.8%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.8%

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

      7. distribute-neg-frac2 99.8%

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

      8. distribute-frac-neg 99.8%

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

      9. distribute-neg-frac2 99.8%

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

      10. sub-neg 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. remove-double-neg 99.8%

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

      13. +-commutative 99.8%

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

      14. sub-neg 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.5%

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

      2. inv-pow 99.5%

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

      3. div-inv 99.4%

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

      4. clear-num 99.5%

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

   6. Applied egg-rr 99.5%

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

      1. unpow-1 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in t around 0 76.3%

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

       1. associate-*r/ 84.5%

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

   11. Simplified 84.5%

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

   12. Taylor expanded in z around inf 75.1%

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

   if -2.1e-7 < z < 1.95e16

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf 76.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-7} \lor \neg \left(z \leq 1.95 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e-46)
   (/ x (* y (- t z)))
   (if (<= y 1.1e-195) (/ x (* z (- z t))) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-46) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.1e-195) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.4d-46)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.1d-195) then
        tmp = x / (z * (z - t))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-46) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.1e-195) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e-46:
		tmp = x / (y * (t - z))
	elif y <= 1.1e-195:
		tmp = x / (z * (z - t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e-46)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.1e-195)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e-46)
		tmp = x / (y * (t - z));
	elseif (y <= 1.1e-195)
		tmp = x / (z * (z - t));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e-46], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-195], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4000000000000002e-46

   1. Initial program 87.7%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   if -4.4000000000000002e-46 < y < 1.10000000000000003e-195

   1. Initial program 92.8%

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

      1. associate-/r* 97.4%

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

      2. sub-neg 97.4%

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

      3. +-commutative 97.4%

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

      4. neg-sub0 97.4%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 97.4%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 97.4%

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

      7. distribute-neg-frac2 97.4%

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

      8. distribute-frac-neg 97.4%

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

      9. distribute-neg-frac2 97.4%

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

      10. sub-neg 97.4%

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

      11. distribute-neg-in 97.4%

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

      12. remove-double-neg 97.4%

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

      13. +-commutative 97.4%

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

      14. sub-neg 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 76.6%

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

   if 1.10000000000000003e-195 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf 52.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 79.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -1.04e-45)
   (/ x (* y (- t z)))
   (if (<= y 1.7e-194) (/ x (* z (- 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 tmp;
	if (y <= -1.04e-45) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.7e-194) {
		tmp = x / (z * (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) :: tmp
    if (y <= (-1.04d-45)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.7d-194) then
        tmp = x / (z * (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 tmp;
	if (y <= -1.04e-45) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.7e-194) {
		tmp = x / (z * (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):
	tmp = 0
	if y <= -1.04e-45:
		tmp = x / (y * (t - z))
	elif y <= 1.7e-194:
		tmp = x / (z * (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)
	tmp = 0.0
	if (y <= -1.04e-45)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.7e-194)
		tmp = Float64(x / Float64(z * Float64(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)
	tmp = 0.0;
	if (y <= -1.04e-45)
		tmp = x / (y * (t - z));
	elseif (y <= 1.7e-194)
		tmp = x / (z * (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_] := If[LessEqual[y, -1.04e-45], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-194], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0400000000000001e-45

   1. Initial program 87.7%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   if -1.0400000000000001e-45 < y < 1.70000000000000005e-194

   1. Initial program 92.8%

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

      1. associate-/r* 97.4%

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

      2. sub-neg 97.4%

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

      3. +-commutative 97.4%

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

      4. neg-sub0 97.4%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 97.4%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 97.4%

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

      7. distribute-neg-frac2 97.4%

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

      8. distribute-frac-neg 97.4%

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

      9. distribute-neg-frac2 97.4%

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

      10. sub-neg 97.4%

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

      11. distribute-neg-in 97.4%

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

      12. remove-double-neg 97.4%

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

      13. +-commutative 97.4%

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

      14. sub-neg 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 76.6%

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

   if 1.70000000000000005e-194 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf 52.6%

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

      1. associate-/r* 58.1%

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

   5. Simplified 58.1%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -4.8e-73)
   (/ (/ x y) t)
   (if (<= y 1.15e-62) (/ x (* z (- t))) (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-73) {
		tmp = (x / y) / t;
	} else if (y <= 1.15e-62) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.8d-73)) then
        tmp = (x / y) / t
    else if (y <= 1.15d-62) then
        tmp = x / (z * -t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-73) {
		tmp = (x / y) / t;
	} else if (y <= 1.15e-62) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-73:
		tmp = (x / y) / t
	elif y <= 1.15e-62:
		tmp = x / (z * -t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-73)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 1.15e-62)
		tmp = Float64(x / Float64(z * Float64(-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 <= -4.8e-73)
		tmp = (x / y) / t;
	elseif (y <= 1.15e-62)
		tmp = x / (z * -t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-73], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 1.15e-62], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000011e-73

   1. Initial program 89.2%

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

      1. associate-/r* 97.4%

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

      2. sub-neg 97.4%

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

      3. +-commutative 97.4%

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

      4. neg-sub0 97.4%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 97.4%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 97.4%

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

      7. distribute-neg-frac2 97.4%

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

      8. distribute-frac-neg 97.4%

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

      9. distribute-neg-frac2 97.4%

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

      10. sub-neg 97.4%

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

      11. distribute-neg-in 97.4%

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

      12. remove-double-neg 97.4%

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

      13. +-commutative 97.4%

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

      14. sub-neg 97.4%

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

   3. Simplified 97.4%

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

      1. clear-num 96.9%

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

      2. inv-pow 96.9%

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

      3. div-inv 96.9%

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

      4. clear-num 96.8%

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

   6. Applied egg-rr 96.8%

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

      1. unpow-1 96.8%

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

   8. Simplified 96.8%

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

      1. clear-num 96.9%

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

      2. un-div-inv 96.9%

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

   10. Applied egg-rr 96.9%

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

   11. Taylor expanded in z around 0 56.8%

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

       1. *-rgt-identity 56.8%

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

       2. *-commutative 56.8%

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

       3. times-frac 61.3%

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

       4. associate-*r/ 61.3%

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

       5. *-rgt-identity 61.3%

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

   13. Simplified 61.3%

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

   if -4.80000000000000011e-73 < y < 1.15e-62

   1. Initial program 90.6%

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

      1. associate-/r* 95.4%

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

      2. sub-neg 95.4%

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

      3. +-commutative 95.4%

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

      4. neg-sub0 95.4%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 95.4%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 95.4%

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

      7. distribute-neg-frac2 95.4%

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

      8. distribute-frac-neg 95.4%

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

      9. distribute-neg-frac2 95.4%

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

      10. sub-neg 95.4%

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

      11. distribute-neg-in 95.4%

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

      12. remove-double-neg 95.4%

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

      13. +-commutative 95.4%

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

      14. sub-neg 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around 0 72.6%

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

      1. associate-/r* 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in z around 0 38.5%

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

      1. associate-*r/ 38.5%

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

      2. neg-mul-1 38.5%

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

      3. *-commutative 38.5%

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

   10. Simplified 38.5%

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

   if 1.15e-62 < y

   1. Initial program 84.6%

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

      1. clear-num 84.6%

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

      2. inv-pow 84.6%

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

      3. associate-/l* 96.2%

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

   4. Applied egg-rr 96.2%

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

      1. unpow-1 96.2%

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

   6. Simplified 96.2%

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

   7. Taylor expanded in z around 0 47.6%

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

      1. associate-/r* 52.4%

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

   9. Simplified 52.4%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+89} \lor \neg \left(z \leq 14500000000000\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -1.12e+89) (not (<= z 14500000000000.0)))
   (/ x (* z t))
   (/ 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 <= -1.12e+89) || !(z <= 14500000000000.0)) {
		tmp = x / (z * t);
	} 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 <= (-1.12d+89)) .or. (.not. (z <= 14500000000000.0d0))) then
        tmp = x / (z * t)
    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 <= -1.12e+89) || !(z <= 14500000000000.0)) {
		tmp = x / (z * t);
	} 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 <= -1.12e+89) or not (z <= 14500000000000.0):
		tmp = x / (z * t)
	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 <= -1.12e+89) || !(z <= 14500000000000.0))
		tmp = Float64(x / Float64(z * t));
	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 <= -1.12e+89) || ~((z <= 14500000000000.0)))
		tmp = x / (z * t);
	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, -1.12e+89], N[Not[LessEqual[z, 14500000000000.0]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.11999999999999995e89 or 1.45e13 < z

   1. Initial program 82.8%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 78.6%

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

   6. Taylor expanded in z around 0 32.4%

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

      1. mul-1-neg 32.4%

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

      2. associate-/r* 34.0%

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

      3. distribute-neg-frac2 34.0%

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

   8. Simplified 34.0%

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

      1. associate-/l/ 32.4%

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

      2. add0 32.4%

         \[\leadsto \color{blue}{\frac{x}{\left(-z\right) \cdot t} + 0} \]

      3. add-sqr-sqrt 12.5%

         \[\leadsto \frac{x}{\color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot t} + 0 \]

      4. sqrt-unprod 52.3%

         \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot t} + 0 \]

      5. sqr-neg 52.3%

         \[\leadsto \frac{x}{\sqrt{\color{blue}{z \cdot z}} \cdot t} + 0 \]

      6. sqrt-unprod 17.9%

         \[\leadsto \frac{x}{\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot t} + 0 \]

      7. add-sqr-sqrt 30.4%

         \[\leadsto \frac{x}{\color{blue}{z} \cdot t} + 0 \]

   10. Applied egg-rr 30.4%

       \[\leadsto \color{blue}{\frac{x}{z \cdot t} + 0} \]
   11. Step-by-step derivation

       1. *-commutative 30.4%

          \[\leadsto \frac{x}{\color{blue}{t \cdot z}} + 0 \]

       2. add0 30.4%

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

   12. Simplified 30.4%

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

   if -1.11999999999999995e89 < z < 1.45e13

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 58.2%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+89} \lor \neg \left(z \leq 14500000000000\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+87} \lor \neg \left(z \leq 2.6 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (or (<= z -3.8e+87) (not (<= z 2.6e+79))) (/ 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 ((z <= -3.8e+87) || !(z <= 2.6e+79)) {
		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 ((z <= (-3.8d+87)) .or. (.not. (z <= 2.6d+79))) 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 ((z <= -3.8e+87) || !(z <= 2.6e+79)) {
		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 (z <= -3.8e+87) or not (z <= 2.6e+79):
		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 ((z <= -3.8e+87) || !(z <= 2.6e+79))
		tmp = 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 ((z <= -3.8e+87) || ~((z <= 2.6e+79)))
		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[Or[LessEqual[z, -3.8e+87], N[Not[LessEqual[z, 2.6e+79]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000011e87 or 2.60000000000000015e79 < z

   1. Initial program 82.5%

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

      1. associate-/r* 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. neg-sub0 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. sub-neg 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 80.9%

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

   6. Taylor expanded in z around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. associate-/r* 35.8%

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

      3. distribute-neg-frac2 35.8%

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

   8. Simplified 35.8%

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

      1. associate-/l/ 33.0%

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

      2. add0 33.0%

         \[\leadsto \color{blue}{\frac{x}{\left(-z\right) \cdot t} + 0} \]

      3. add-sqr-sqrt 14.0%

         \[\leadsto \frac{x}{\color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot t} + 0 \]

      4. sqrt-unprod 56.4%

         \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot t} + 0 \]

      5. sqr-neg 56.4%

         \[\leadsto \frac{x}{\sqrt{\color{blue}{z \cdot z}} \cdot t} + 0 \]

      6. sqrt-unprod 17.8%

         \[\leadsto \frac{x}{\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot t} + 0 \]

      7. add-sqr-sqrt 31.8%

         \[\leadsto \frac{x}{\color{blue}{z} \cdot t} + 0 \]

   10. Applied egg-rr 31.8%

       \[\leadsto \color{blue}{\frac{x}{z \cdot t} + 0} \]
   11. Step-by-step derivation

       1. *-commutative 31.8%

          \[\leadsto \frac{x}{\color{blue}{t \cdot z}} + 0 \]

       2. add0 31.8%

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

   12. Simplified 31.8%

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

   if -3.80000000000000011e87 < z < 2.60000000000000015e79

   1. Initial program 91.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. 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* 94.7%

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

   4. Applied egg-rr 94.7%

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

      1. unpow-1 94.7%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in z around 0 55.3%

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

      1. associate-/r* 58.1%

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

   9. Simplified 58.1%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+87} \lor \neg \left(z \leq 2.6 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 96.8% accurate, 1.0× speedup

Math

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

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 (- z y)) (- z t)))

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 88.1%

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

   1. associate-/r* 97.0%

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

   2. sub-neg 97.0%

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

   3. +-commutative 97.0%

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

   4. neg-sub0 97.0%

      \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

   5. associate-+l- 97.0%

      \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

   6. neg-sub0 97.0%

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

   7. distribute-neg-frac2 97.0%

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

   8. distribute-frac-neg 97.0%

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

   9. distribute-neg-frac2 97.0%

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

   10. sub-neg 97.0%

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

   11. distribute-neg-in 97.0%

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

   12. remove-double-neg 97.0%

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

   13. +-commutative 97.0%

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

   14. sub-neg 97.0%

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

3. Simplified 97.0%

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

5. Final simplification 97.0%

   \[\leadsto \frac{\frac{x}{z - y}}{z - t} \]
6. Add Preprocessing

Alternative 18: 39.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (y * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.1%

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

3. Taylor expanded in z around 0 42.0%

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

4. Final simplification 42.0%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer target: 87.5% 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 2024046 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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