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

Percentage Accurate: 88.8% → 96.9%

Time: 11.1s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.8% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

   1. associate-/l/ 96.1%

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

3. Simplified 96.1%

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

Alternative 2: 82.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z - t}}{z}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-109}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (- z t)) z)))
   (if (<= y -3.7e+146)
     (/ (/ x y) (- t z))
     (if (<= y -1.25e+18)
       (/ x (* (- t z) y))
       (if (<= y -1.7e-101)
         t_1
         (if (<= y -1.55e-109)
           (/ (/ x t) y)
           (if (<= y 7.6e-44) t_1 (/ (/ x t) (- y z)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / (z - t)) / z;
	double tmp;
	if (y <= -3.7e+146) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.25e+18) {
		tmp = x / ((t - z) * y);
	} else if (y <= -1.7e-101) {
		tmp = t_1;
	} else if (y <= -1.55e-109) {
		tmp = (x / t) / y;
	} else if (y <= 7.6e-44) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (z - t)) / z
    if (y <= (-3.7d+146)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-1.25d+18)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-1.7d-101)) then
        tmp = t_1
    else if (y <= (-1.55d-109)) then
        tmp = (x / t) / y
    else if (y <= 7.6d-44) then
        tmp = t_1
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / (z - t)) / z;
	double tmp;
	if (y <= -3.7e+146) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.25e+18) {
		tmp = x / ((t - z) * y);
	} else if (y <= -1.7e-101) {
		tmp = t_1;
	} else if (y <= -1.55e-109) {
		tmp = (x / t) / y;
	} else if (y <= 7.6e-44) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / (z - t)) / z
	tmp = 0
	if y <= -3.7e+146:
		tmp = (x / y) / (t - z)
	elif y <= -1.25e+18:
		tmp = x / ((t - z) * y)
	elif y <= -1.7e-101:
		tmp = t_1
	elif y <= -1.55e-109:
		tmp = (x / t) / y
	elif y <= 7.6e-44:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(z - t)) / z)
	tmp = 0.0
	if (y <= -3.7e+146)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -1.25e+18)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -1.7e-101)
		tmp = t_1;
	elseif (y <= -1.55e-109)
		tmp = Float64(Float64(x / t) / y);
	elseif (y <= 7.6e-44)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / (z - t)) / z;
	tmp = 0.0;
	if (y <= -3.7e+146)
		tmp = (x / y) / (t - z);
	elseif (y <= -1.25e+18)
		tmp = x / ((t - z) * y);
	elseif (y <= -1.7e-101)
		tmp = t_1;
	elseif (y <= -1.55e-109)
		tmp = (x / t) / y;
	elseif (y <= 7.6e-44)
		tmp = t_1;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -3.7e+146], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e+18], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-101], t$95$1, If[LessEqual[y, -1.55e-109], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7.6e-44], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.70000000000000004e146

   1. Initial program 75.2%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 93.8%

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

   if -3.70000000000000004e146 < y < -1.25e18

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 87.6%

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

      1. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   if -1.25e18 < y < -1.69999999999999995e-101 or -1.55e-109 < y < 7.6000000000000002e-44

   1. Initial program 93.4%

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

      1. associate-/l/ 97.0%

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

      2. div-inv 96.9%

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

   4. Applied egg-rr 96.9%

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

      1. associate-*l/ 93.9%

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

      2. div-inv 94.0%

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

      3. div-inv 94.0%

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

      4. clear-num 93.9%

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

      5. associate-*l/ 94.4%

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

      6. *-un-lft-identity 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in y around 0 75.3%

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

      1. associate-*r/ 75.3%

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

      2. times-frac 78.0%

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

      3. associate-*l/ 78.1%

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

      4. mul-1-neg 78.1%

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

   9. Simplified 78.1%

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

   if -1.69999999999999995e-101 < y < -1.55e-109

   1. Initial program 100.0%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. associate-*l/ 98.4%

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

      2. div-inv 100.0%

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

      3. div-inv 99.2%

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

      4. clear-num 99.2%

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

      5. associate-*l/ 100.0%

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

      6. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 52.0%

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

      1. associate-/r* 52.0%

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

   9. Simplified 52.0%

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

   if 7.6000000000000002e-44 < y

   1. Initial program 93.6%

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

      1. associate-/l/ 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in t around inf 51.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-109}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z t)))))
   (if (<= y -1.75e+146)
     (/ (/ x y) (- t z))
     (if (<= y -2.2e+17)
       (/ x (* (- t z) y))
       (if (<= y -1.7e-101)
         t_1
         (if (<= y -1.25e-106)
           (/ (/ x t) y)
           (if (<= y 5.6e-87) t_1 (/ (/ x t) (- y z)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (y <= -1.75e+146) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.2e+17) {
		tmp = x / ((t - z) * y);
	} else if (y <= -1.7e-101) {
		tmp = t_1;
	} else if (y <= -1.25e-106) {
		tmp = (x / t) / y;
	} else if (y <= 5.6e-87) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z * (z - t))
    if (y <= (-1.75d+146)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-2.2d+17)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-1.7d-101)) then
        tmp = t_1
    else if (y <= (-1.25d-106)) then
        tmp = (x / t) / y
    else if (y <= 5.6d-87) then
        tmp = t_1
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (y <= -1.75e+146) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.2e+17) {
		tmp = x / ((t - z) * y);
	} else if (y <= -1.7e-101) {
		tmp = t_1;
	} else if (y <= -1.25e-106) {
		tmp = (x / t) / y;
	} else if (y <= 5.6e-87) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * (z - t))
	tmp = 0
	if y <= -1.75e+146:
		tmp = (x / y) / (t - z)
	elif y <= -2.2e+17:
		tmp = x / ((t - z) * y)
	elif y <= -1.7e-101:
		tmp = t_1
	elif y <= -1.25e-106:
		tmp = (x / t) / y
	elif y <= 5.6e-87:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - t)))
	tmp = 0.0
	if (y <= -1.75e+146)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -2.2e+17)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -1.7e-101)
		tmp = t_1;
	elseif (y <= -1.25e-106)
		tmp = Float64(Float64(x / t) / y);
	elseif (y <= 5.6e-87)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - t));
	tmp = 0.0;
	if (y <= -1.75e+146)
		tmp = (x / y) / (t - z);
	elseif (y <= -2.2e+17)
		tmp = x / ((t - z) * y);
	elseif (y <= -1.7e-101)
		tmp = t_1;
	elseif (y <= -1.25e-106)
		tmp = (x / t) / y;
	elseif (y <= 5.6e-87)
		tmp = t_1;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e+146], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e+17], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-101], t$95$1, If[LessEqual[y, -1.25e-106], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 5.6e-87], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.7500000000000001e146

   1. Initial program 75.2%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 93.8%

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

   if -1.7500000000000001e146 < y < -2.2e17

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 87.6%

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

      1. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   if -2.2e17 < y < -1.69999999999999995e-101 or -1.24999999999999996e-106 < y < 5.6000000000000002e-87

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. neg-mul-1 77.9%

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

   5. Simplified 77.9%

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

   if -1.69999999999999995e-101 < y < -1.24999999999999996e-106

   1. Initial program 100.0%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. associate-*l/ 98.4%

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

      2. div-inv 100.0%

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

      3. div-inv 99.2%

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

      4. clear-num 99.2%

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

      5. associate-*l/ 100.0%

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

      6. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 52.0%

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

      1. associate-/r* 52.0%

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

   9. Simplified 52.0%

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

   if 5.6000000000000002e-87 < y

   1. Initial program 92.7%

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

      1. associate-/l/ 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around inf 55.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{-z}}{t}\\ t_2 := \frac{x}{z \cdot \left(-y\right)}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 205000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (- z)) t)) (t_2 (/ x (* z (- y)))))
   (if (<= z -2.6e+185)
     t_2
     (if (<= z -6e+61)
       t_1
       (if (<= z -1.05e-42)
         t_2
         (if (<= z 205000000000.0)
           (/ (/ x t) y)
           (if (<= z 1.1e+194) t_1 (/ (/ x z) y))))))))

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 t_2 = x / (z * -y);
	double tmp;
	if (z <= -2.6e+185) {
		tmp = t_2;
	} else if (z <= -6e+61) {
		tmp = t_1;
	} else if (z <= -1.05e-42) {
		tmp = t_2;
	} else if (z <= 205000000000.0) {
		tmp = (x / t) / y;
	} else if (z <= 1.1e+194) {
		tmp = t_1;
	} else {
		tmp = (x / z) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / -z) / t
    t_2 = x / (z * -y)
    if (z <= (-2.6d+185)) then
        tmp = t_2
    else if (z <= (-6d+61)) then
        tmp = t_1
    else if (z <= (-1.05d-42)) then
        tmp = t_2
    else if (z <= 205000000000.0d0) then
        tmp = (x / t) / y
    else if (z <= 1.1d+194) then
        tmp = t_1
    else
        tmp = (x / z) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / -z) / t;
	double t_2 = x / (z * -y);
	double tmp;
	if (z <= -2.6e+185) {
		tmp = t_2;
	} else if (z <= -6e+61) {
		tmp = t_1;
	} else if (z <= -1.05e-42) {
		tmp = t_2;
	} else if (z <= 205000000000.0) {
		tmp = (x / t) / y;
	} else if (z <= 1.1e+194) {
		tmp = t_1;
	} else {
		tmp = (x / z) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / -z) / t
	t_2 = x / (z * -y)
	tmp = 0
	if z <= -2.6e+185:
		tmp = t_2
	elif z <= -6e+61:
		tmp = t_1
	elif z <= -1.05e-42:
		tmp = t_2
	elif z <= 205000000000.0:
		tmp = (x / t) / y
	elif z <= 1.1e+194:
		tmp = t_1
	else:
		tmp = (x / z) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(-z)) / t)
	t_2 = Float64(x / Float64(z * Float64(-y)))
	tmp = 0.0
	if (z <= -2.6e+185)
		tmp = t_2;
	elseif (z <= -6e+61)
		tmp = t_1;
	elseif (z <= -1.05e-42)
		tmp = t_2;
	elseif (z <= 205000000000.0)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.1e+194)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / -z) / t;
	t_2 = x / (z * -y);
	tmp = 0.0;
	if (z <= -2.6e+185)
		tmp = t_2;
	elseif (z <= -6e+61)
		tmp = t_1;
	elseif (z <= -1.05e-42)
		tmp = t_2;
	elseif (z <= 205000000000.0)
		tmp = (x / t) / y;
	elseif (z <= 1.1e+194)
		tmp = t_1;
	else
		tmp = (x / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+185], t$95$2, If[LessEqual[z, -6e+61], t$95$1, If[LessEqual[z, -1.05e-42], t$95$2, If[LessEqual[z, 205000000000.0], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.1e+194], t$95$1, N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.60000000000000001e185 or -6e61 < z < -1.05000000000000003e-42

   1. Initial program 93.2%

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

      1. associate-/l/ 95.5%

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

      2. div-inv 95.4%

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

      3. div-inv 95.3%

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

      4. associate-*l* 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around 0 76.6%

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

   6. Taylor expanded in z around 0 49.1%

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

      1. mul-1-neg 49.1%

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

      2. distribute-neg-frac2 49.1%

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

      3. *-commutative 49.1%

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

      4. distribute-rgt-neg-out 49.1%

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

   8. Simplified 49.1%

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

   if -2.60000000000000001e185 < z < -6e61 or 2.05e11 < z < 1.1000000000000001e194

   1. Initial program 84.0%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 38.8%

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

   6. Taylor expanded in y around 0 26.6%

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

      1. associate-*r/ 26.6%

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

      2. neg-mul-1 26.6%

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

   8. Simplified 26.6%

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

   9. Taylor expanded in x around 0 26.6%

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

       1. associate-*r/ 26.6%

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

       2. times-frac 41.1%

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

       3. associate-*l/ 41.1%

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

       4. mul-1-neg 41.1%

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

       5. distribute-frac-neg 41.1%

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

   11. Simplified 41.1%

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

   if -1.05000000000000003e-42 < z < 2.05e11

   1. Initial program 93.7%

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

      1. associate-/l/ 93.1%

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

      2. div-inv 93.0%

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

   4. Applied egg-rr 93.0%

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

      1. associate-*l/ 91.7%

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

      2. div-inv 91.9%

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

      3. div-inv 91.9%

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

      4. clear-num 91.8%

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

      5. associate-*l/ 92.3%

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

      6. *-un-lft-identity 92.3%

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

   6. Applied egg-rr 92.3%

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

   7. Taylor expanded in z around 0 57.6%

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

      1. associate-/r* 61.4%

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

   9. Simplified 61.4%

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

   if 1.1000000000000001e194 < z

   1. Initial program 93.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf 56.4%

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

   6. Taylor expanded in t around 0 53.9%

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

      1. associate-*r/ 95.0%

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

      2. neg-mul-1 95.0%

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

   8. Simplified 53.9%

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

      1. un-div-inv 53.9%

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

      2. distribute-frac-neg 53.9%

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

      3. distribute-frac-neg 53.9%

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

      4. distribute-frac-neg2 53.9%

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

      5. add-sqr-sqrt 25.6%

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

      6. sqrt-unprod 37.8%

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

      7. sqr-neg 37.8%

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

      8. sqrt-unprod 28.2%

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

      9. add-sqr-sqrt 50.5%

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

   10. Applied egg-rr 50.5%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq 205000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+194}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-39} \lor \neg \left(z \leq 1.65 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{-1}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (<= z -2.9e+185)
   (/ x (* z (- y)))
   (if (<= z -2.5e+84)
     (/ (/ x (- z)) t)
     (if (or (<= z -1.42e-39) (not (<= z 1.65e-26)))
       (/ -1.0 (* y (/ 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 <= -2.9e+185) {
		tmp = x / (z * -y);
	} else if (z <= -2.5e+84) {
		tmp = (x / -z) / t;
	} else if ((z <= -1.42e-39) || !(z <= 1.65e-26)) {
		tmp = -1.0 / (y * (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 <= (-2.9d+185)) then
        tmp = x / (z * -y)
    else if (z <= (-2.5d+84)) then
        tmp = (x / -z) / t
    else if ((z <= (-1.42d-39)) .or. (.not. (z <= 1.65d-26))) then
        tmp = (-1.0d0) / (y * (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 <= -2.9e+185) {
		tmp = x / (z * -y);
	} else if (z <= -2.5e+84) {
		tmp = (x / -z) / t;
	} else if ((z <= -1.42e-39) || !(z <= 1.65e-26)) {
		tmp = -1.0 / (y * (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 <= -2.9e+185:
		tmp = x / (z * -y)
	elif z <= -2.5e+84:
		tmp = (x / -z) / t
	elif (z <= -1.42e-39) or not (z <= 1.65e-26):
		tmp = -1.0 / (y * (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 <= -2.9e+185)
		tmp = Float64(x / Float64(z * Float64(-y)));
	elseif (z <= -2.5e+84)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif ((z <= -1.42e-39) || !(z <= 1.65e-26))
		tmp = Float64(-1.0 / Float64(y * 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 <= -2.9e+185)
		tmp = x / (z * -y);
	elseif (z <= -2.5e+84)
		tmp = (x / -z) / t;
	elseif ((z <= -1.42e-39) || ~((z <= 1.65e-26)))
		tmp = -1.0 / (y * (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[LessEqual[z, -2.9e+185], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e+84], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, -1.42e-39], N[Not[LessEqual[z, 1.65e-26]], $MachinePrecision]], N[(-1.0 / N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.89999999999999988e185

   1. Initial program 90.2%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*l* 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in t around 0 90.2%

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

   6. Taylor expanded in z around 0 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-neg-frac2 59.9%

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

      3. *-commutative 59.9%

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

      4. distribute-rgt-neg-out 59.9%

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

   8. Simplified 59.9%

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

   if -2.89999999999999988e185 < z < -2.5e84

   1. Initial program 71.4%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 48.0%

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

   6. Taylor expanded in y around 0 27.4%

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

      1. associate-*r/ 27.4%

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

      2. neg-mul-1 27.4%

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

   8. Simplified 27.4%

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

   9. Taylor expanded in x around 0 27.4%

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

       1. associate-*r/ 27.4%

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

       2. times-frac 47.2%

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

       3. associate-*l/ 47.2%

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

       4. mul-1-neg 47.2%

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

       5. distribute-frac-neg 47.2%

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

   11. Simplified 47.2%

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

   if -2.5e84 < z < -1.42000000000000005e-39 or 1.6499999999999999e-26 < z

   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. associate-/l/ 98.1%

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

      2. div-inv 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in y around inf 47.5%

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

   6. Taylor expanded in t around 0 41.4%

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

      1. associate-*r/ 77.8%

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

      2. neg-mul-1 77.8%

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

   8. Simplified 41.4%

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

      1. clear-num 43.1%

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

      2. frac-2neg 43.1%

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

      3. metadata-eval 43.1%

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

      4. frac-times 44.3%

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

      5. metadata-eval 44.3%

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

      6. add-sqr-sqrt 20.2%

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

      7. sqrt-unprod 34.0%

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

      8. sqr-neg 34.0%

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

      9. sqrt-unprod 16.1%

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

      10. add-sqr-sqrt 29.9%

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

      11. add-sqr-sqrt 16.3%

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

      12. sqrt-unprod 27.2%

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

      13. sqr-neg 27.2%

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

      14. sqrt-unprod 19.3%

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

      15. add-sqr-sqrt 44.3%

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

   10. Applied egg-rr 44.3%

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

   if -1.42000000000000005e-39 < z < 1.6499999999999999e-26

   1. Initial program 93.7%

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

      1. associate-/l/ 92.6%

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

      2. div-inv 92.5%

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

   4. Applied egg-rr 92.5%

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

      1. associate-*l/ 91.1%

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

      2. div-inv 91.3%

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

      3. div-inv 91.3%

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

      4. clear-num 91.2%

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

      5. associate-*l/ 91.8%

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

      6. *-un-lft-identity 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in z around 0 61.3%

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

      1. associate-/r* 64.8%

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

   9. Simplified 64.8%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-39} \lor \neg \left(z \leq 1.65 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{-1}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{-z}\\ t_2 := \frac{x}{z \cdot \left(-y\right)}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+61}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- z))) (t_2 (/ x (* z (- y)))))
   (if (<= z -1.05e+185)
     t_2
     (if (<= z -2.15e+61)
       (/ t_1 t)
       (if (<= z -1.42e-39)
         t_2
         (if (<= z 1.65e-26) (/ (/ x t) y) (/ t_1 y)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / -z;
	double t_2 = x / (z * -y);
	double tmp;
	if (z <= -1.05e+185) {
		tmp = t_2;
	} else if (z <= -2.15e+61) {
		tmp = t_1 / t;
	} else if (z <= -1.42e-39) {
		tmp = t_2;
	} else if (z <= 1.65e-26) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1 / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / -z
    t_2 = x / (z * -y)
    if (z <= (-1.05d+185)) then
        tmp = t_2
    else if (z <= (-2.15d+61)) then
        tmp = t_1 / t
    else if (z <= (-1.42d-39)) then
        tmp = t_2
    else if (z <= 1.65d-26) then
        tmp = (x / t) / y
    else
        tmp = t_1 / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / -z;
	double t_2 = x / (z * -y);
	double tmp;
	if (z <= -1.05e+185) {
		tmp = t_2;
	} else if (z <= -2.15e+61) {
		tmp = t_1 / t;
	} else if (z <= -1.42e-39) {
		tmp = t_2;
	} else if (z <= 1.65e-26) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1 / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / -z
	t_2 = x / (z * -y)
	tmp = 0
	if z <= -1.05e+185:
		tmp = t_2
	elif z <= -2.15e+61:
		tmp = t_1 / t
	elif z <= -1.42e-39:
		tmp = t_2
	elif z <= 1.65e-26:
		tmp = (x / t) / y
	else:
		tmp = t_1 / y
	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_2 = Float64(x / Float64(z * Float64(-y)))
	tmp = 0.0
	if (z <= -1.05e+185)
		tmp = t_2;
	elseif (z <= -2.15e+61)
		tmp = Float64(t_1 / t);
	elseif (z <= -1.42e-39)
		tmp = t_2;
	elseif (z <= 1.65e-26)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(t_1 / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / -z;
	t_2 = x / (z * -y);
	tmp = 0.0;
	if (z <= -1.05e+185)
		tmp = t_2;
	elseif (z <= -2.15e+61)
		tmp = t_1 / t;
	elseif (z <= -1.42e-39)
		tmp = t_2;
	elseif (z <= 1.65e-26)
		tmp = (x / t) / y;
	else
		tmp = t_1 / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+185], t$95$2, If[LessEqual[z, -2.15e+61], N[(t$95$1 / t), $MachinePrecision], If[LessEqual[z, -1.42e-39], t$95$2, If[LessEqual[z, 1.65e-26], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(t$95$1 / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05e185 or -2.1500000000000001e61 < z < -1.42000000000000005e-39

   1. Initial program 93.2%

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

      1. associate-/l/ 95.5%

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

      2. div-inv 95.4%

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

      3. div-inv 95.3%

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

      4. associate-*l* 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around 0 76.6%

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

   6. Taylor expanded in z around 0 49.1%

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

      1. mul-1-neg 49.1%

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

      2. distribute-neg-frac2 49.1%

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

      3. *-commutative 49.1%

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

      4. distribute-rgt-neg-out 49.1%

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

   8. Simplified 49.1%

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

   if -1.05e185 < z < -2.1500000000000001e61

   1. Initial program 77.0%

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

      1. associate-/l/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around inf 47.0%

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

   6. Taylor expanded in y around 0 26.9%

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

      1. associate-*r/ 26.9%

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

      2. neg-mul-1 26.9%

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

   8. Simplified 26.9%

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

   9. Taylor expanded in x around 0 26.9%

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

       1. associate-*r/ 26.9%

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

       2. times-frac 42.7%

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

       3. associate-*l/ 42.8%

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

       4. mul-1-neg 42.8%

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

       5. distribute-frac-neg 42.8%

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

   11. Simplified 42.8%

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

   if -1.42000000000000005e-39 < z < 1.6499999999999999e-26

   1. Initial program 93.7%

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

      1. associate-/l/ 92.6%

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

      2. div-inv 92.5%

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

   4. Applied egg-rr 92.5%

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

      1. associate-*l/ 91.1%

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

      2. div-inv 91.3%

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

      3. div-inv 91.3%

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

      4. clear-num 91.2%

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

      5. associate-*l/ 91.8%

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

      6. *-un-lft-identity 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in z around 0 61.3%

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

      1. associate-/r* 64.8%

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

   9. Simplified 64.8%

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

   if 1.6499999999999999e-26 < z

   1. Initial program 90.1%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

      3. div-inv 99.6%

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

      4. associate-*l* 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in t around 0 80.4%

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

   6. Taylor expanded in z around 0 35.0%

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

      1. mul-1-neg 35.0%

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

      2. distribute-neg-frac2 35.0%

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

      3. *-commutative 35.0%

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

      4. distribute-rgt-neg-out 35.0%

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

   8. Simplified 35.0%

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

   9. Taylor expanded in x around 0 35.0%

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

       1. associate-/l/ 43.1%

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

       2. neg-mul-1 43.1%

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

       3. distribute-frac-neg2 43.1%

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

   11. Simplified 43.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{-z}}{t}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 260000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (- z)) t)))
   (if (<= z -2.7e+185)
     (/ x (* z y))
     (if (<= z -2.7e+24)
       t_1
       (if (<= z 260000000000.0)
         (/ (/ x t) y)
         (if (<= z 2.7e+191) t_1 (/ (/ x z) y)))))))

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 <= -2.7e+185) {
		tmp = x / (z * y);
	} else if (z <= -2.7e+24) {
		tmp = t_1;
	} else if (z <= 260000000000.0) {
		tmp = (x / t) / y;
	} else if (z <= 2.7e+191) {
		tmp = t_1;
	} else {
		tmp = (x / z) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / -z) / t
    if (z <= (-2.7d+185)) then
        tmp = x / (z * y)
    else if (z <= (-2.7d+24)) then
        tmp = t_1
    else if (z <= 260000000000.0d0) then
        tmp = (x / t) / y
    else if (z <= 2.7d+191) then
        tmp = t_1
    else
        tmp = (x / z) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / -z) / t;
	double tmp;
	if (z <= -2.7e+185) {
		tmp = x / (z * y);
	} else if (z <= -2.7e+24) {
		tmp = t_1;
	} else if (z <= 260000000000.0) {
		tmp = (x / t) / y;
	} else if (z <= 2.7e+191) {
		tmp = t_1;
	} else {
		tmp = (x / z) / y;
	}
	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 <= -2.7e+185:
		tmp = x / (z * y)
	elif z <= -2.7e+24:
		tmp = t_1
	elif z <= 260000000000.0:
		tmp = (x / t) / y
	elif z <= 2.7e+191:
		tmp = t_1
	else:
		tmp = (x / z) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(-z)) / t)
	tmp = 0.0
	if (z <= -2.7e+185)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= -2.7e+24)
		tmp = t_1;
	elseif (z <= 260000000000.0)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 2.7e+191)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / -z) / t;
	tmp = 0.0;
	if (z <= -2.7e+185)
		tmp = x / (z * y);
	elseif (z <= -2.7e+24)
		tmp = t_1;
	elseif (z <= 260000000000.0)
		tmp = (x / t) / y;
	elseif (z <= 2.7e+191)
		tmp = t_1;
	else
		tmp = (x / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2.7e+185], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e+24], t$95$1, If[LessEqual[z, 260000000000.0], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.7e+191], t$95$1, N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.70000000000000007e185

   1. Initial program 90.2%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*l* 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in t around 0 90.2%

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

   6. Taylor expanded in z around 0 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-neg-frac2 59.9%

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

      3. *-commutative 59.9%

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

      4. distribute-rgt-neg-out 59.9%

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

   8. Simplified 59.9%

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

      1. frac-2neg 59.9%

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

      2. div-inv 59.9%

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

      3. add-sqr-sqrt 22.4%

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

      4. sqrt-unprod 59.4%

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

      5. sqr-neg 59.4%

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

      6. sqrt-unprod 37.5%

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

      7. add-sqr-sqrt 59.8%

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

      8. distribute-rgt-neg-out 59.8%

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

      9. remove-double-neg 59.8%

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

      10. add-sqr-sqrt 17.0%

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

      11. sqrt-unprod 59.7%

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

      12. sqr-neg 59.7%

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

      13. sqrt-unprod 42.8%

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

      14. add-sqr-sqrt 59.9%

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

      15. *-commutative 59.9%

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

      16. add-sqr-sqrt 42.8%

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

      17. sqrt-unprod 59.7%

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

      18. sqr-neg 59.7%

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

      19. sqrt-unprod 17.0%

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

      20. add-sqr-sqrt 59.8%

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

   10. Applied egg-rr 59.8%

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

       1. associate-*r/ 59.8%

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

       2. *-rgt-identity 59.8%

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

   12. Simplified 59.8%

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

   if -2.70000000000000007e185 < z < -2.7e24 or 2.6e11 < z < 2.69999999999999996e191

   1. Initial program 84.8%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 40.5%

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

   6. Taylor expanded in y around 0 28.6%

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

      1. associate-*r/ 28.6%

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

      2. neg-mul-1 28.6%

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

   8. Simplified 28.6%

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

   9. Taylor expanded in x around 0 28.6%

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

       1. associate-*r/ 28.6%

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

       2. times-frac 41.3%

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

       3. associate-*l/ 41.4%

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

       4. mul-1-neg 41.4%

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

       5. distribute-frac-neg 41.4%

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

   11. Simplified 41.4%

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

   if -2.7e24 < z < 2.6e11

   1. Initial program 94.3%

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

      1. associate-/l/ 92.3%

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

      2. div-inv 92.2%

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

   4. Applied egg-rr 92.2%

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

      1. associate-*l/ 92.5%

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

      2. div-inv 92.7%

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

      3. div-inv 92.7%

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

      4. clear-num 92.6%

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

      5. associate-*l/ 93.1%

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

      6. *-un-lft-identity 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in z around 0 53.7%

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

      1. associate-/r* 57.8%

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

   9. Simplified 57.8%

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

   if 2.69999999999999996e191 < z

   1. Initial program 93.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf 56.4%

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

   6. Taylor expanded in t around 0 53.9%

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

      1. associate-*r/ 95.0%

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

      2. neg-mul-1 95.0%

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

   8. Simplified 53.9%

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

      1. un-div-inv 53.9%

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

      2. distribute-frac-neg 53.9%

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

      3. distribute-frac-neg 53.9%

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

      4. distribute-frac-neg2 53.9%

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

      5. add-sqr-sqrt 25.6%

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

      6. sqrt-unprod 37.8%

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

      7. sqr-neg 37.8%

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

      8. sqrt-unprod 28.2%

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

      9. add-sqr-sqrt 50.5%

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

   10. Applied egg-rr 50.5%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq 260000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+129}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z)))))
   (if (<= z -4.8e+136)
     t_1
     (if (<= z 1.4e+48)
       (/ x (* t (- y z)))
       (if (<= z 2e+129) (/ -1.0 (* y (/ z x))) 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 - z));
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t_1;
	} else if (z <= 1.4e+48) {
		tmp = x / (t * (y - z));
	} else if (z <= 2e+129) {
		tmp = -1.0 / (y * (z / x));
	} 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 - z))
    if (z <= (-4.8d+136)) then
        tmp = t_1
    else if (z <= 1.4d+48) then
        tmp = x / (t * (y - z))
    else if (z <= 2d+129) then
        tmp = (-1.0d0) / (y * (z / x))
    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 - z));
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t_1;
	} else if (z <= 1.4e+48) {
		tmp = x / (t * (y - z));
	} else if (z <= 2e+129) {
		tmp = -1.0 / (y * (z / x));
	} 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 - z))
	tmp = 0
	if z <= -4.8e+136:
		tmp = t_1
	elif z <= 1.4e+48:
		tmp = x / (t * (y - z))
	elif z <= 2e+129:
		tmp = -1.0 / (y * (z / x))
	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 * Float64(t - z)))
	tmp = 0.0
	if (z <= -4.8e+136)
		tmp = t_1;
	elseif (z <= 1.4e+48)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 2e+129)
		tmp = Float64(-1.0 / Float64(y * Float64(z / x)));
	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 - z));
	tmp = 0.0;
	if (z <= -4.8e+136)
		tmp = t_1;
	elseif (z <= 1.4e+48)
		tmp = x / (t * (y - z));
	elseif (z <= 2e+129)
		tmp = -1.0 / (y * (z / x));
	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 * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+136], t$95$1, If[LessEqual[z, 1.4e+48], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+129], N[(-1.0 / N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000001e136 or 2e129 < z

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 0 84.5%

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

      1. associate-*r/ 84.5%

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

      2. neg-mul-1 84.5%

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

   5. Simplified 84.5%

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

      1. add-sqr-sqrt 36.7%

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

      2. sqrt-unprod 80.1%

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

      3. sqr-neg 80.1%

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

      4. sqrt-unprod 45.4%

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

      5. add-sqr-sqrt 82.1%

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

      6. *-un-lft-identity 82.1%

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

      7. associate-/r* 81.8%

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

   7. Applied egg-rr 81.8%

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

      1. *-lft-identity 81.8%

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

      2. associate-/r* 82.1%

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

   9. Simplified 82.1%

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

   if -4.8000000000000001e136 < z < 1.40000000000000006e48

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf 60.0%

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

   if 1.40000000000000006e48 < z < 2e129

   1. Initial program 99.5%

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

      1. associate-/l/ 99.6%

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

      2. div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in y around inf 28.5%

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

   6. Taylor expanded in t around 0 28.6%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   8. Simplified 28.6%

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

      1. clear-num 28.6%

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

      2. frac-2neg 28.6%

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

      3. metadata-eval 28.6%

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

      4. frac-times 28.6%

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

      5. metadata-eval 28.6%

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

      6. add-sqr-sqrt 14.2%

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

      7. sqrt-unprod 21.5%

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

      8. sqr-neg 21.5%

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

      9. sqrt-unprod 7.8%

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

      10. add-sqr-sqrt 15.9%

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

      11. add-sqr-sqrt 7.6%

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

      12. sqrt-unprod 8.4%

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

      13. sqr-neg 8.4%

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

      14. sqrt-unprod 7.4%

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

      15. add-sqr-sqrt 28.6%

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

   10. Applied egg-rr 28.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+129}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.1e-46)
   (/ (/ x y) (- t z))
   (if (<= t 3.8e+51) (/ (/ x z) (- z y)) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-46) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.8e+51) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.1d-46)) then
        tmp = (x / y) / (t - z)
    else if (t <= 3.8d+51) then
        tmp = (x / z) / (z - y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-46) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.8e+51) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e-46:
		tmp = (x / y) / (t - z)
	elif t <= 3.8e+51:
		tmp = (x / z) / (z - y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.1e-46)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 3.8e+51)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.1e-46)
		tmp = (x / y) / (t - z);
	elseif (t <= 3.8e+51)
		tmp = (x / z) / (z - y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.1e-46], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+51], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.09999999999999987e-46

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0 93.7%

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

      1. associate-/l/ 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in y around inf 50.7%

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

   if -2.09999999999999987e-46 < t < 3.7999999999999997e51

   1. Initial program 92.4%

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

      1. associate-/l/ 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

   7. Simplified 79.4%

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

   if 3.7999999999999997e51 < t

   1. Initial program 83.5%

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

      1. associate-/l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in t around inf 93.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 (<= t -2.1e-47)
   (/ (/ x t) y)
   (if (<= t 4.5e-141) (/ -1.0 (* y (/ z x))) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-47) {
		tmp = (x / t) / y;
	} else if (t <= 4.5e-141) {
		tmp = -1.0 / (y * (z / x));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.1d-47)) then
        tmp = (x / t) / y
    else if (t <= 4.5d-141) then
        tmp = (-1.0d0) / (y * (z / x))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-47) {
		tmp = (x / t) / y;
	} else if (t <= 4.5e-141) {
		tmp = -1.0 / (y * (z / x));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e-47:
		tmp = (x / t) / y
	elif t <= 4.5e-141:
		tmp = -1.0 / (y * (z / x))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.1e-47)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 4.5e-141)
		tmp = Float64(-1.0 / Float64(y * Float64(z / x)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.1e-47)
		tmp = (x / t) / y;
	elseif (t <= 4.5e-141)
		tmp = -1.0 / (y * (z / x));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.1e-47], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.5e-141], N[(-1.0 / N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1000000000000001e-47

   1. Initial program 93.7%

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

      1. associate-/l/ 96.8%

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

      2. div-inv 96.7%

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

   4. Applied egg-rr 96.7%

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

      1. associate-*l/ 95.2%

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

      2. div-inv 95.3%

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

      3. div-inv 95.3%

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

      4. clear-num 95.2%

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

      5. associate-*l/ 95.1%

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

      6. *-un-lft-identity 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in z around 0 47.5%

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

      1. associate-/r* 53.9%

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

   9. Simplified 53.9%

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

   if -2.1000000000000001e-47 < t < 4.5e-141

   1. Initial program 92.0%

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

      1. associate-/l/ 94.7%

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

      2. div-inv 94.6%

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

   4. Applied egg-rr 94.6%

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

   5. Taylor expanded in y around inf 57.6%

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

   6. Taylor expanded in t around 0 43.2%

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

      1. associate-*r/ 80.2%

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

      2. neg-mul-1 80.2%

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

   8. Simplified 43.2%

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

      1. clear-num 44.2%

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

      2. frac-2neg 44.2%

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

      3. metadata-eval 44.2%

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

      4. frac-times 44.9%

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

      5. metadata-eval 44.9%

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

      6. add-sqr-sqrt 21.3%

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

      7. sqrt-unprod 32.1%

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

      8. sqr-neg 32.1%

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

      9. sqrt-unprod 13.0%

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

      10. add-sqr-sqrt 21.7%

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

      11. add-sqr-sqrt 13.1%

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

      12. sqrt-unprod 28.1%

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

      13. sqr-neg 28.1%

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

      14. sqrt-unprod 23.5%

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

      15. add-sqr-sqrt 44.9%

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

   10. Applied egg-rr 44.9%

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

   if 4.5e-141 < t

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf 62.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+84} \lor \neg \left(z \leq 0.16\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -2.6e+84) (not (<= z 0.16))) (/ x (* z y)) (/ 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 <= -2.6e+84) || !(z <= 0.16)) {
		tmp = x / (z * y);
	} 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 <= (-2.6d+84)) .or. (.not. (z <= 0.16d0))) then
        tmp = x / (z * y)
    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 <= -2.6e+84) || !(z <= 0.16)) {
		tmp = x / (z * y);
	} 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 <= -2.6e+84) or not (z <= 0.16):
		tmp = x / (z * y)
	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 <= -2.6e+84) || !(z <= 0.16))
		tmp = Float64(x / Float64(z * y));
	else
		tmp = Float64(x / Float64(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 <= -2.6e+84) || ~((z <= 0.16)))
		tmp = x / (z * y);
	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, -2.6e+84], N[Not[LessEqual[z, 0.16]], $MachinePrecision]], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000001e84 or 0.160000000000000003 < z

   1. Initial program 86.8%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.8%

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

      3. div-inv 99.7%

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

      4. associate-*l* 89.6%

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

   4. Applied egg-rr 89.6%

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

   5. Taylor expanded in t around 0 79.7%

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

   6. Taylor expanded in z around 0 40.7%

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

      1. mul-1-neg 40.7%

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

      2. distribute-neg-frac2 40.7%

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

      3. *-commutative 40.7%

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

      4. distribute-rgt-neg-out 40.7%

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

   8. Simplified 40.7%

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

      1. frac-2neg 40.7%

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

      2. div-inv 40.7%

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

      3. add-sqr-sqrt 17.3%

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

      4. sqrt-unprod 42.7%

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

      5. sqr-neg 42.7%

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

      6. sqrt-unprod 17.8%

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

      7. add-sqr-sqrt 33.6%

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

      8. distribute-rgt-neg-out 33.6%

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

      9. remove-double-neg 33.6%

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

      10. add-sqr-sqrt 12.6%

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

      11. sqrt-unprod 35.5%

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

      12. sqr-neg 35.5%

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

      13. sqrt-unprod 24.4%

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

      14. add-sqr-sqrt 40.7%

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

      15. *-commutative 40.7%

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

      16. add-sqr-sqrt 24.4%

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

      17. sqrt-unprod 35.5%

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

      18. sqr-neg 35.5%

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

      19. sqrt-unprod 12.6%

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

      20. add-sqr-sqrt 33.6%

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

   10. Applied egg-rr 33.6%

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

       1. associate-*r/ 33.6%

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

       2. *-rgt-identity 33.6%

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

   12. Simplified 33.6%

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

   if -2.6000000000000001e84 < z < 0.160000000000000003

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 51.0%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+84} \lor \neg \left(z \leq 0.16\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

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 -3.8e+121)
   (/ x (* z y))
   (if (<= z 1.4e+53) (/ (/ x t) y) (/ (/ x z) 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+121) {
		tmp = x / (z * y);
	} else if (z <= 1.4e+53) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) / 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+121)) then
        tmp = x / (z * y)
    else if (z <= 1.4d+53) then
        tmp = (x / t) / y
    else
        tmp = (x / z) / 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+121) {
		tmp = x / (z * y);
	} else if (z <= 1.4e+53) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) / 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+121:
		tmp = x / (z * y)
	elif z <= 1.4e+53:
		tmp = (x / t) / y
	else:
		tmp = (x / z) / 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+121)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 1.4e+53)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / z) / 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+121)
		tmp = x / (z * y);
	elseif (z <= 1.4e+53)
		tmp = (x / t) / y;
	else
		tmp = (x / z) / 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, -3.8e+121], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+53], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e121

   1. Initial program 82.8%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*l* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in t around 0 77.9%

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

   6. Taylor expanded in z around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. distribute-neg-frac2 50.4%

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

      3. *-commutative 50.4%

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

      4. distribute-rgt-neg-out 50.4%

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

   8. Simplified 50.4%

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

      1. frac-2neg 50.4%

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

      2. div-inv 50.4%

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

      3. add-sqr-sqrt 16.3%

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

      4. sqrt-unprod 53.0%

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

      5. sqr-neg 53.0%

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

      6. sqrt-unprod 34.2%

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

      7. add-sqr-sqrt 50.7%

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

      8. distribute-rgt-neg-out 50.7%

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

      9. remove-double-neg 50.7%

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

      10. add-sqr-sqrt 13.0%

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

      11. sqrt-unprod 50.1%

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

      12. sqr-neg 50.1%

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

      13. sqrt-unprod 37.5%

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

      14. add-sqr-sqrt 50.4%

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

      15. *-commutative 50.4%

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

      16. add-sqr-sqrt 37.5%

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

      17. sqrt-unprod 50.1%

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

      18. sqr-neg 50.1%

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

      19. sqrt-unprod 13.0%

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

      20. add-sqr-sqrt 50.7%

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

   10. Applied egg-rr 50.7%

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

       1. associate-*r/ 50.7%

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

       2. *-rgt-identity 50.7%

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

   12. Simplified 50.7%

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

   if -3.8e121 < z < 1.4e53

   1. Initial program 93.1%

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

      1. associate-/l/ 93.9%

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

      2. div-inv 93.8%

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

   4. Applied egg-rr 93.8%

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

      1. associate-*l/ 94.0%

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

      2. div-inv 94.2%

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

      3. div-inv 94.1%

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

      4. clear-num 94.1%

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

      5. associate-*l/ 94.5%

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

      6. *-un-lft-identity 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in z around 0 45.1%

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

      1. associate-/r* 50.1%

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

   9. Simplified 50.1%

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

   if 1.4e53 < z

   1. Initial program 89.0%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 47.6%

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

   6. Taylor expanded in t around 0 46.3%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   8. Simplified 46.3%

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

      1. un-div-inv 46.3%

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

      2. distribute-frac-neg 46.3%

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

      3. distribute-frac-neg 46.3%

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

      4. distribute-frac-neg2 46.3%

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

      5. add-sqr-sqrt 26.7%

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

      6. sqrt-unprod 31.2%

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

      7. sqr-neg 31.2%

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

      8. sqrt-unprod 19.8%

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

      9. add-sqr-sqrt 41.8%

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

   10. Applied egg-rr 41.8%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

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 -6.5e+121)
   (/ x (* z y))
   (if (<= z 4.4e+45) (/ (/ x t) y) (/ (/ x z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+121) {
		tmp = x / (z * y);
	} else if (z <= 4.4e+45) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / 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 <= (-6.5d+121)) then
        tmp = x / (z * y)
    else if (z <= 4.4d+45) then
        tmp = (x / t) / y
    else
        tmp = (x / 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 <= -6.5e+121) {
		tmp = x / (z * y);
	} else if (z <= 4.4e+45) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e+121:
		tmp = x / (z * y)
	elif z <= 4.4e+45:
		tmp = (x / t) / y
	else:
		tmp = (x / 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 <= -6.5e+121)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 4.4e+45)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / 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 <= -6.5e+121)
		tmp = x / (z * y);
	elseif (z <= 4.4e+45)
		tmp = (x / t) / y;
	else
		tmp = (x / 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, -6.5e+121], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+45], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.50000000000000019e121

   1. Initial program 82.8%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*l* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in t around 0 77.9%

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

   6. Taylor expanded in z around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. distribute-neg-frac2 50.4%

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

      3. *-commutative 50.4%

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

      4. distribute-rgt-neg-out 50.4%

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

   8. Simplified 50.4%

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

      1. frac-2neg 50.4%

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

      2. div-inv 50.4%

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

      3. add-sqr-sqrt 16.3%

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

      4. sqrt-unprod 53.0%

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

      5. sqr-neg 53.0%

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

      6. sqrt-unprod 34.2%

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

      7. add-sqr-sqrt 50.7%

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

      8. distribute-rgt-neg-out 50.7%

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

      9. remove-double-neg 50.7%

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

      10. add-sqr-sqrt 13.0%

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

      11. sqrt-unprod 50.1%

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

      12. sqr-neg 50.1%

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

      13. sqrt-unprod 37.5%

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

      14. add-sqr-sqrt 50.4%

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

      15. *-commutative 50.4%

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

      16. add-sqr-sqrt 37.5%

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

      17. sqrt-unprod 50.1%

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

      18. sqr-neg 50.1%

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

      19. sqrt-unprod 13.0%

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

      20. add-sqr-sqrt 50.7%

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

   10. Applied egg-rr 50.7%

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

       1. associate-*r/ 50.7%

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

       2. *-rgt-identity 50.7%

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

   12. Simplified 50.7%

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

   if -6.50000000000000019e121 < z < 4.4000000000000001e45

   1. Initial program 93.0%

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

      1. associate-/l/ 93.8%

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

      2. div-inv 93.7%

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

   4. Applied egg-rr 93.7%

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

      1. associate-*l/ 93.9%

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

      2. div-inv 94.1%

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

      3. div-inv 94.0%

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

      4. clear-num 94.0%

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

      5. associate-*l/ 94.4%

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

      6. *-un-lft-identity 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in z around 0 46.2%

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

      1. associate-/r* 51.4%

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

   9. Simplified 51.4%

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

   if 4.4000000000000001e45 < z

   1. Initial program 89.6%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 42.3%

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

   6. Taylor expanded in y around 0 39.3%

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

      1. associate-*r/ 39.3%

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

      2. neg-mul-1 39.3%

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

   8. Simplified 39.3%

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

      1. add-sqr-sqrt 18.1%

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

      2. sqrt-unprod 42.6%

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

      3. sqr-neg 42.6%

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

      4. sqrt-unprod 17.9%

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

      5. add-sqr-sqrt 33.1%

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

      6. *-un-lft-identity 33.1%

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

      7. associate-/r* 31.6%

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

   10. Applied egg-rr 31.6%

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

       1. *-lft-identity 31.6%

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

       2. associate-/r* 33.1%

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

       3. *-lft-identity 33.1%

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

       4. times-frac 41.5%

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

       5. associate-*l/ 41.5%

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

       6. *-lft-identity 41.5%

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

   12. Simplified 41.5%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \end{array} \]

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 (<= z -4.2e+122)
   (/ x (* z y))
   (if (<= z 1.15e+45) (/ (/ x t) y) (/ x (* t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+122) {
		tmp = x / (z * y);
	} else if (z <= 1.15e+45) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (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 <= (-4.2d+122)) then
        tmp = x / (z * y)
    else if (z <= 1.15d+45) then
        tmp = (x / t) / y
    else
        tmp = x / (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 <= -4.2e+122) {
		tmp = x / (z * y);
	} else if (z <= 1.15e+45) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (t * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e+122:
		tmp = x / (z * y)
	elif z <= 1.15e+45:
		tmp = (x / t) / y
	else:
		tmp = x / (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 <= -4.2e+122)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 1.15e+45)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / 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 <= -4.2e+122)
		tmp = x / (z * y);
	elseif (z <= 1.15e+45)
		tmp = (x / t) / y;
	else
		tmp = x / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e+122], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+45], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000032e122

   1. Initial program 82.8%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*l* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in t around 0 77.9%

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

   6. Taylor expanded in z around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. distribute-neg-frac2 50.4%

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

      3. *-commutative 50.4%

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

      4. distribute-rgt-neg-out 50.4%

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

   8. Simplified 50.4%

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

      1. frac-2neg 50.4%

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

      2. div-inv 50.4%

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

      3. add-sqr-sqrt 16.3%

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

      4. sqrt-unprod 53.0%

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

      5. sqr-neg 53.0%

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

      6. sqrt-unprod 34.2%

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

      7. add-sqr-sqrt 50.7%

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

      8. distribute-rgt-neg-out 50.7%

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

      9. remove-double-neg 50.7%

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

      10. add-sqr-sqrt 13.0%

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

      11. sqrt-unprod 50.1%

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

      12. sqr-neg 50.1%

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

      13. sqrt-unprod 37.5%

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

      14. add-sqr-sqrt 50.4%

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

      15. *-commutative 50.4%

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

      16. add-sqr-sqrt 37.5%

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

      17. sqrt-unprod 50.1%

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

      18. sqr-neg 50.1%

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

      19. sqrt-unprod 13.0%

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

      20. add-sqr-sqrt 50.7%

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

   10. Applied egg-rr 50.7%

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

       1. associate-*r/ 50.7%

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

       2. *-rgt-identity 50.7%

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

   12. Simplified 50.7%

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

   if -4.20000000000000032e122 < z < 1.15000000000000006e45

   1. Initial program 93.0%

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

      1. associate-/l/ 93.8%

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

      2. div-inv 93.7%

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

   4. Applied egg-rr 93.7%

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

      1. associate-*l/ 93.9%

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

      2. div-inv 94.1%

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

      3. div-inv 94.0%

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

      4. clear-num 94.0%

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

      5. associate-*l/ 94.4%

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

      6. *-un-lft-identity 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in z around 0 46.2%

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

      1. associate-/r* 51.4%

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

   9. Simplified 51.4%

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

   if 1.15000000000000006e45 < z

   1. Initial program 89.6%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 42.3%

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

   6. Taylor expanded in y around 0 39.3%

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

      1. associate-*r/ 39.3%

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

      2. neg-mul-1 39.3%

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

   8. Simplified 39.3%

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

      1. add-sqr-sqrt 18.1%

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

      2. sqrt-unprod 42.6%

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

      3. sqr-neg 42.6%

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

      4. sqrt-unprod 17.9%

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

      5. add-sqr-sqrt 33.1%

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

      6. *-un-lft-identity 33.1%

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

      7. associate-/r* 31.6%

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

   10. Applied egg-rr 31.6%

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

       1. *-lft-identity 31.6%

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

       2. associate-/l/ 33.1%

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

   12. Simplified 33.1%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \end{array} \]

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 (<= z -2.6e+84)
   (/ x (* z y))
   (if (<= z 2.4e+46) (/ x (* t y)) (/ x (* t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e+84) {
		tmp = x / (z * y);
	} else if (z <= 2.4e+46) {
		tmp = x / (t * y);
	} else {
		tmp = x / (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 <= (-2.6d+84)) then
        tmp = x / (z * y)
    else if (z <= 2.4d+46) then
        tmp = x / (t * y)
    else
        tmp = x / (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 <= -2.6e+84) {
		tmp = x / (z * y);
	} else if (z <= 2.4e+46) {
		tmp = x / (t * y);
	} else {
		tmp = x / (t * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.6e+84:
		tmp = x / (z * y)
	elif z <= 2.4e+46:
		tmp = x / (t * y)
	else:
		tmp = x / (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 <= -2.6e+84)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 2.4e+46)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = Float64(x / 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 <= -2.6e+84)
		tmp = x / (z * y);
	elseif (z <= 2.4e+46)
		tmp = x / (t * y);
	else
		tmp = x / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.6e+84], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+46], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6000000000000001e84

   1. Initial program 80.0%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

      3. div-inv 99.9%

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

      4. associate-*l* 84.8%

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

   4. Applied egg-rr 84.8%

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

   5. Taylor expanded in t around 0 75.8%

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

   6. Taylor expanded in z around 0 50.9%

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

      1. mul-1-neg 50.9%

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

      2. distribute-neg-frac2 50.9%

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

      3. *-commutative 50.9%

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

      4. distribute-rgt-neg-out 50.9%

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

   8. Simplified 50.9%

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

      1. frac-2neg 50.9%

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

      2. div-inv 50.9%

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

      3. add-sqr-sqrt 16.8%

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

      4. sqrt-unprod 48.9%

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

      5. sqr-neg 48.9%

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

      6. sqrt-unprod 30.0%

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

      7. add-sqr-sqrt 47.0%

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

      8. distribute-rgt-neg-out 47.0%

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

      9. remove-double-neg 47.0%

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

      10. add-sqr-sqrt 14.0%

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

      11. sqrt-unprod 46.5%

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

      12. sqr-neg 46.5%

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

      13. sqrt-unprod 32.7%

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

      14. add-sqr-sqrt 50.9%

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

      15. *-commutative 50.9%

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

      16. add-sqr-sqrt 32.7%

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

      17. sqrt-unprod 46.5%

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

      18. sqr-neg 46.5%

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

      19. sqrt-unprod 14.0%

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

      20. add-sqr-sqrt 47.0%

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

   10. Applied egg-rr 47.0%

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

       1. associate-*r/ 47.0%

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

       2. *-rgt-identity 47.0%

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

   12. Simplified 47.0%

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

   if -2.6000000000000001e84 < z < 2.40000000000000008e46

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 47.0%

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

   if 2.40000000000000008e46 < z

   1. Initial program 89.6%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 42.3%

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

   6. Taylor expanded in y around 0 39.3%

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

      1. associate-*r/ 39.3%

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

      2. neg-mul-1 39.3%

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

   8. Simplified 39.3%

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

      1. add-sqr-sqrt 18.1%

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

      2. sqrt-unprod 42.6%

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

      3. sqr-neg 42.6%

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

      4. sqrt-unprod 17.9%

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

      5. add-sqr-sqrt 33.1%

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

      6. *-un-lft-identity 33.1%

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

      7. associate-/r* 31.6%

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

   10. Applied egg-rr 31.6%

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

       1. *-lft-identity 31.6%

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

       2. associate-/l/ 33.1%

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

   12. Simplified 33.1%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 90.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{+204}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 6e+204) (/ x (* (- t z) (- y z))) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6e+204) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 6d+204) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6e+204) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 6e+204:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6e+204)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6e+204)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 6e+204], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.99999999999999965e204

   1. Initial program 93.0%

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

   if 5.99999999999999965e204 < t

   1. Initial program 68.5%

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

      1. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf 98.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{+204}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.4e+40) (/ (/ x (- t z)) y) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e+40) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.4d+40) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e+40) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.4e+40:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.4e+40)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.4e+40)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.4e+40], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.4000000000000001e40

   1. Initial program 93.3%

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

      1. associate-/l/ 96.0%

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

      2. div-inv 95.9%

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

   4. Applied egg-rr 95.9%

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

      1. associate-*l/ 97.5%

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

      2. div-inv 97.7%

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

      3. div-inv 97.6%

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

      4. clear-num 97.6%

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

      5. associate-*l/ 97.6%

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

      6. *-un-lft-identity 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around inf 54.5%

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

      1. associate-/l/ 56.9%

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

   9. Simplified 56.9%

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

   if 1.4000000000000001e40 < t

   1. Initial program 82.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 96.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 92.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 72.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.2e-69) (/ (/ x y) (- t z)) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.2e-69) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.2d-69) then
        tmp = (x / y) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.2e-69) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.2e-69:
		tmp = (x / y) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.2e-69)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.2e-69)
		tmp = (x / y) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.2e-69], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.2000000000000001e-69

   1. Initial program 92.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.8%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-/l/ 97.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   5. Simplified 97.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   6. Taylor expanded in y around inf 55.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{t - z} \]

   if 1.2000000000000001e-69 < t

   1. Initial program 86.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 97.7%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 6.5e-68) (/ x (* (- t z) y)) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.5e-68) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 6.5d-68) then
        tmp = x / ((t - z) * y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.5e-68) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 6.5e-68:
		tmp = x / ((t - z) * y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6.5e-68)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6.5e-68)
		tmp = x / ((t - z) * y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 6.5e-68], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.4999999999999997e-68

   1. Initial program 92.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 55.6%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 55.6%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 55.6%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   if 6.4999999999999997e-68 < t

   1. Initial program 86.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 97.7%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 (<= y -1.3e+18) (/ x (* (- t z) y)) (/ x (* t (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+18) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.3d+18)) then
        tmp = x / ((t - z) * y)
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+18) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e+18:
		tmp = x / ((t - z) * y)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e+18)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(x / Float64(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 <= -1.3e+18)
		tmp = x / ((t - z) * y);
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e+18], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e18

   1. Initial program 82.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.9%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 81.9%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 81.9%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   if -1.3e18 < y

   1. Initial program 93.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 53.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 39.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{t \cdot y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* t y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (t * y)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / (t * y)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / Float64(t * y))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (t * y);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.8%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 36.6%

   \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
4. Add Preprocessing

Developer target: 87.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024107 
(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))))