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

Percentage Accurate: 89.4% → 97.0%

Time: 11.1s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

   1. associate-/r* 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 2: 79.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.68 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z (- y z)))))
   (if (<= t -2.8e-184)
     (/ (/ x y) (- t z))
     (if (<= t 1.68e-49)
       t_1
       (if (<= t 6.8e+31)
         (/ x (* (- y z) t))
         (if (<= t 4e+51) t_1 (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (y - z));
	double tmp;
	if (t <= -2.8e-184) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.68e-49) {
		tmp = t_1;
	} else if (t <= 6.8e+31) {
		tmp = x / ((y - z) * t);
	} else if (t <= 4e+51) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (z * (y - z))
    if (t <= (-2.8d-184)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.68d-49) then
        tmp = t_1
    else if (t <= 6.8d+31) then
        tmp = x / ((y - z) * t)
    else if (t <= 4d+51) then
        tmp = t_1
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (y - z));
	double tmp;
	if (t <= -2.8e-184) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.68e-49) {
		tmp = t_1;
	} else if (t <= 6.8e+31) {
		tmp = x / ((y - z) * t);
	} else if (t <= 4e+51) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = -x / (z * (y - z))
	tmp = 0
	if t <= -2.8e-184:
		tmp = (x / y) / (t - z)
	elif t <= 1.68e-49:
		tmp = t_1
	elif t <= 6.8e+31:
		tmp = x / ((y - z) * t)
	elif t <= 4e+51:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * Float64(y - z)))
	tmp = 0.0
	if (t <= -2.8e-184)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.68e-49)
		tmp = t_1;
	elseif (t <= 6.8e+31)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (t <= 4e+51)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * (y - z));
	tmp = 0.0;
	if (t <= -2.8e-184)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.68e-49)
		tmp = t_1;
	elseif (t <= 6.8e+31)
		tmp = x / ((y - z) * t);
	elseif (t <= 4e+51)
		tmp = t_1;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-184], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.68e-49], t$95$1, If[LessEqual[t, 6.8e+31], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+51], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7999999999999998e-184

   1. Initial program 91.7%

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

      1. associate-/r* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 63.2%

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

   if -2.7999999999999998e-184 < t < 1.6800000000000001e-49 or 6.7999999999999996e31 < t < 4e51

   1. Initial program 87.5%

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

   2. Taylor expanded in t around 0 73.5%

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

      1. associate-*r/ 73.5%

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

      2. neg-mul-1 73.5%

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

      3. *-commutative 73.5%

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

   4. Simplified 73.5%

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

   if 1.6800000000000001e-49 < t < 6.7999999999999996e31

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 52.5%

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

   if 4e51 < t

   1. Initial program 89.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 86.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.68 \cdot 10^{-49}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+51}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-253}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{-z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+51}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4e-253)
   (/ x (* y (- t z)))
   (if (<= t 5.4e-49)
     (/ (/ x (- y z)) (- z))
     (if (<= t 5.5e+31)
       (/ x (* (- y z) t))
       (if (<= t 4.4e+51) (/ (- x) (* z (- y z))) (/ (/ x t) (- y z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-253) {
		tmp = x / (y * (t - z));
	} else if (t <= 5.4e-49) {
		tmp = (x / (y - z)) / -z;
	} else if (t <= 5.5e+31) {
		tmp = x / ((y - z) * t);
	} else if (t <= 4.4e+51) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4d-253)) then
        tmp = x / (y * (t - z))
    else if (t <= 5.4d-49) then
        tmp = (x / (y - z)) / -z
    else if (t <= 5.5d+31) then
        tmp = x / ((y - z) * t)
    else if (t <= 4.4d+51) then
        tmp = -x / (z * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-253) {
		tmp = x / (y * (t - z));
	} else if (t <= 5.4e-49) {
		tmp = (x / (y - z)) / -z;
	} else if (t <= 5.5e+31) {
		tmp = x / ((y - z) * t);
	} else if (t <= 4.4e+51) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4e-253:
		tmp = x / (y * (t - z))
	elif t <= 5.4e-49:
		tmp = (x / (y - z)) / -z
	elif t <= 5.5e+31:
		tmp = x / ((y - z) * t)
	elif t <= 4.4e+51:
		tmp = -x / (z * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4e-253)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 5.4e-49)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(-z));
	elseif (t <= 5.5e+31)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (t <= 4.4e+51)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4e-253)
		tmp = x / (y * (t - z));
	elseif (t <= 5.4e-49)
		tmp = (x / (y - z)) / -z;
	elseif (t <= 5.5e+31)
		tmp = x / ((y - z) * t);
	elseif (t <= 4.4e+51)
		tmp = -x / (z * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4e-253], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-49], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[t, 5.5e+31], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+51], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.0000000000000003e-253

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 63.6%

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

      1. *-commutative 63.6%

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

   4. Simplified 63.6%

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

   if -4.0000000000000003e-253 < t < 5.3999999999999999e-49

   1. Initial program 88.6%

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

   2. Taylor expanded in t around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. neg-mul-1 71.7%

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

      3. *-commutative 71.7%

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

   4. Simplified 71.7%

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

      1. neg-mul-1 71.7%

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

      2. times-frac 79.7%

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

   6. Applied egg-rr 79.7%

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

      1. *-commutative 79.7%

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

      2. frac-2neg 79.7%

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

      3. metadata-eval 79.7%

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

      4. un-div-inv 79.8%

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

   8. Applied egg-rr 79.8%

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

   if 5.3999999999999999e-49 < t < 5.50000000000000002e31

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 52.5%

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

   if 5.50000000000000002e31 < t < 4.39999999999999984e51

   1. Initial program 81.5%

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

   2. Taylor expanded in t around 0 71.9%

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

      1. associate-*r/ 71.9%

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

      2. neg-mul-1 71.9%

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

      3. *-commutative 71.9%

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

   4. Simplified 71.9%

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

   if 4.39999999999999984e51 < t

   1. Initial program 89.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 86.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-253}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{-z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+51}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 4: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 4.75 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y (- t z)))))
   (if (<= z -1.5e+46)
     (/ (/ x z) z)
     (if (<= z 4.75e-85)
       t_1
       (if (<= z 4.4e+29)
         (/ x (* (- y z) t))
         (if (<= z 2.7e+62) t_1 (/ 1.0 (* z (/ z x)))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double tmp;
	if (z <= -1.5e+46) {
		tmp = (x / z) / z;
	} else if (z <= 4.75e-85) {
		tmp = t_1;
	} else if (z <= 4.4e+29) {
		tmp = x / ((y - z) * t);
	} else if (z <= 2.7e+62) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * (t - z))
    if (z <= (-1.5d+46)) then
        tmp = (x / z) / z
    else if (z <= 4.75d-85) then
        tmp = t_1
    else if (z <= 4.4d+29) then
        tmp = x / ((y - z) * t)
    else if (z <= 2.7d+62) then
        tmp = t_1
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double tmp;
	if (z <= -1.5e+46) {
		tmp = (x / z) / z;
	} else if (z <= 4.75e-85) {
		tmp = t_1;
	} else if (z <= 4.4e+29) {
		tmp = x / ((y - z) * t);
	} else if (z <= 2.7e+62) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (y * (t - z))
	tmp = 0
	if z <= -1.5e+46:
		tmp = (x / z) / z
	elif z <= 4.75e-85:
		tmp = t_1
	elif z <= 4.4e+29:
		tmp = x / ((y - z) * t)
	elif z <= 2.7e+62:
		tmp = t_1
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (z <= -1.5e+46)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 4.75e-85)
		tmp = t_1;
	elseif (z <= 4.4e+29)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (z <= 2.7e+62)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * (t - z));
	tmp = 0.0;
	if (z <= -1.5e+46)
		tmp = (x / z) / z;
	elseif (z <= 4.75e-85)
		tmp = t_1;
	elseif (z <= 4.4e+29)
		tmp = x / ((y - z) * t);
	elseif (z <= 2.7e+62)
		tmp = t_1;
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+46], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.75e-85], t$95$1, If[LessEqual[z, 4.4e+29], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+62], t$95$1, N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.50000000000000012e46

   1. Initial program 81.8%

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

   2. Taylor expanded in z around inf 67.2%

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

      1. unpow2 67.2%

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

      2. associate-/r* 77.9%

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

   4. Simplified 77.9%

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

   if -1.50000000000000012e46 < z < 4.74999999999999982e-85 or 4.4000000000000003e29 < z < 2.7e62

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

   4. Simplified 75.3%

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

   if 4.74999999999999982e-85 < z < 4.4000000000000003e29

   1. Initial program 95.3%

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

   2. Taylor expanded in t around inf 48.4%

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

   if 2.7e62 < z

   1. Initial program 86.8%

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

   2. Taylor expanded in z around inf 79.7%

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

      1. unpow2 79.7%

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

   4. Simplified 79.7%

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

      1. associate-/r* 84.6%

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

      2. div-inv 84.6%

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

   6. Applied egg-rr 84.6%

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

      1. clear-num 84.6%

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

      2. frac-times 85.0%

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

      3. metadata-eval 85.0%

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

   8. Applied egg-rr 85.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x} \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 4.75 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 5: 79.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{-z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.36e-17)
   (/ (/ (- x) z) (- t z))
   (if (<= z 3e-146)
     (/ x (* y (- t z)))
     (if (<= z 1.2e+29) (/ (/ x (- t z)) y) (/ (/ x (- y z)) (- z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.36e-17) {
		tmp = (-x / z) / (t - z);
	} else if (z <= 3e-146) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.2e+29) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / (y - z)) / -z;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.36d-17)) then
        tmp = (-x / z) / (t - z)
    else if (z <= 3d-146) then
        tmp = x / (y * (t - z))
    else if (z <= 1.2d+29) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / (y - z)) / -z
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.36e-17) {
		tmp = (-x / z) / (t - z);
	} else if (z <= 3e-146) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.2e+29) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / (y - z)) / -z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.36e-17:
		tmp = (-x / z) / (t - z)
	elif z <= 3e-146:
		tmp = x / (y * (t - z))
	elif z <= 1.2e+29:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / (y - z)) / -z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.36e-17)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	elseif (z <= 3e-146)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 1.2e+29)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(-z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.36e-17)
		tmp = (-x / z) / (t - z);
	elseif (z <= 3e-146)
		tmp = x / (y * (t - z));
	elseif (z <= 1.2e+29)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / (y - z)) / -z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.36e-17], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-146], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+29], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.36e-17

   1. Initial program 84.5%

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

   2. Taylor expanded in y around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. distribute-frac-neg 72.9%

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

      3. associate-/r* 83.3%

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

   4. Simplified 83.3%

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

   if -1.36e-17 < z < 3.00000000000000019e-146

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 81.9%

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

      1. *-commutative 81.9%

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

   4. Simplified 81.9%

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

   if 3.00000000000000019e-146 < z < 1.2e29

   1. Initial program 84.8%

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

   2. Taylor expanded in y around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-/r* 75.0%

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

   4. Simplified 75.0%

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

   if 1.2e29 < z

   1. Initial program 88.4%

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

   2. Taylor expanded in t around 0 83.2%

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

      1. associate-*r/ 83.2%

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

      2. neg-mul-1 83.2%

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

      3. *-commutative 83.2%

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

   4. Simplified 83.2%

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

      1. neg-mul-1 83.2%

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

      2. times-frac 91.8%

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

   6. Applied egg-rr 91.8%

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

      1. *-commutative 91.8%

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

      2. frac-2neg 91.8%

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

      3. metadata-eval 91.8%

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

      4. un-div-inv 91.9%

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

   8. Applied egg-rr 91.9%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{-z}\\ \end{array} \]

Alternative 6: 79.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) z)))
   (if (<= z -1.15e-10)
     (/ t_1 (- t z))
     (if (<= z 5e-149)
       (/ x (* y (- t z)))
       (if (<= z 1.46e+29) (/ (/ x (- t z)) y) (/ t_1 (- y z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (z <= -1.15e-10) {
		tmp = t_1 / (t - z);
	} else if (z <= 5e-149) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.46e+29) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = t_1 / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / z
    if (z <= (-1.15d-10)) then
        tmp = t_1 / (t - z)
    else if (z <= 5d-149) then
        tmp = x / (y * (t - z))
    else if (z <= 1.46d+29) then
        tmp = (x / (t - z)) / y
    else
        tmp = t_1 / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (z <= -1.15e-10) {
		tmp = t_1 / (t - z);
	} else if (z <= 5e-149) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.46e+29) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = t_1 / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = -x / z
	tmp = 0
	if z <= -1.15e-10:
		tmp = t_1 / (t - z)
	elif z <= 5e-149:
		tmp = x / (y * (t - z))
	elif z <= 1.46e+29:
		tmp = (x / (t - z)) / y
	else:
		tmp = t_1 / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -1.15e-10)
		tmp = Float64(t_1 / Float64(t - z));
	elseif (z <= 5e-149)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 1.46e+29)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(t_1 / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / z;
	tmp = 0.0;
	if (z <= -1.15e-10)
		tmp = t_1 / (t - z);
	elseif (z <= 5e-149)
		tmp = x / (y * (t - z));
	elseif (z <= 1.46e+29)
		tmp = (x / (t - z)) / y;
	else
		tmp = t_1 / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -1.15e-10], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-149], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.46e+29], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15000000000000004e-10

   1. Initial program 84.5%

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

   2. Taylor expanded in y around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. distribute-frac-neg 72.9%

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

      3. associate-/r* 83.3%

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

   4. Simplified 83.3%

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

   if -1.15000000000000004e-10 < z < 4.99999999999999968e-149

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 81.9%

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

      1. *-commutative 81.9%

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

   4. Simplified 81.9%

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

   if 4.99999999999999968e-149 < z < 1.46e29

   1. Initial program 84.8%

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

   2. Taylor expanded in y around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-/r* 75.0%

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

   4. Simplified 75.0%

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

   if 1.46e29 < z

   1. Initial program 88.4%

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

   2. Taylor expanded in t around 0 83.2%

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

      1. associate-*r/ 83.2%

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

      2. neg-mul-1 83.2%

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

      3. *-commutative 83.2%

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

      4. associate-/r* 91.8%

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

   4. Simplified 91.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]

Alternative 7: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -23000000000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-129}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -23000000000000.0)
   (/ (/ x z) z)
   (if (<= z -1.25e-129)
     (/ (- x) (* z t))
     (if (<= z 9.5e+28) (/ (/ x t) y) (/ 1.0 (* z (/ z x)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -23000000000000.0) {
		tmp = (x / z) / z;
	} else if (z <= -1.25e-129) {
		tmp = -x / (z * t);
	} else if (z <= 9.5e+28) {
		tmp = (x / t) / y;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-23000000000000.0d0)) then
        tmp = (x / z) / z
    else if (z <= (-1.25d-129)) then
        tmp = -x / (z * t)
    else if (z <= 9.5d+28) then
        tmp = (x / t) / y
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -23000000000000.0) {
		tmp = (x / z) / z;
	} else if (z <= -1.25e-129) {
		tmp = -x / (z * t);
	} else if (z <= 9.5e+28) {
		tmp = (x / t) / y;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -23000000000000.0:
		tmp = (x / z) / z
	elif z <= -1.25e-129:
		tmp = -x / (z * t)
	elif z <= 9.5e+28:
		tmp = (x / t) / y
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -23000000000000.0)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= -1.25e-129)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 9.5e+28)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -23000000000000.0)
		tmp = (x / z) / z;
	elseif (z <= -1.25e-129)
		tmp = -x / (z * t);
	elseif (z <= 9.5e+28)
		tmp = (x / t) / y;
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -23000000000000.0], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.25e-129], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+28], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3e13

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 63.7%

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

      1. unpow2 63.7%

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

      2. associate-/r* 73.5%

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

   4. Simplified 73.5%

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

   if -2.3e13 < z < -1.25000000000000007e-129

   1. Initial program 99.7%

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

      1. associate-/l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 66.3%

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

   5. Taylor expanded in y around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. *-commutative 45.3%

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

   7. Simplified 45.3%

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

   if -1.25000000000000007e-129 < z < 9.49999999999999927e28

   1. Initial program 93.5%

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

      1. clear-num 93.3%

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

      2. associate-/r/ 93.4%

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

      3. *-commutative 93.4%

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

      4. associate-/r* 93.6%

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

   3. Applied egg-rr 93.6%

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

      1. div-inv 93.6%

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

      2. associate-*l* 94.2%

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

      3. associate-/r/ 94.3%

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

      4. *-un-lft-identity 94.3%

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

      5. times-frac 94.5%

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

      6. clear-num 94.5%

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

      7. /-rgt-identity 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in z around 0 63.4%

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

      1. *-lft-identity 63.4%

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

      2. times-frac 68.7%

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

      3. associate-*l/ 68.8%

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

      4. *-lft-identity 68.8%

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

   8. Simplified 68.8%

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

   if 9.49999999999999927e28 < z

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 75.1%

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

      1. unpow2 75.1%

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

   4. Simplified 75.1%

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

      1. associate-/r* 79.5%

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

      2. div-inv 79.5%

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

   6. Applied egg-rr 79.5%

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

      1. clear-num 79.4%

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

      2. frac-times 79.8%

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

      3. metadata-eval 79.8%

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

   8. Applied egg-rr 79.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x} \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23000000000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-129}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 8: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.6e+47)
   (/ (/ x z) z)
   (if (<= z 8.2e-145)
     (/ x (* y (- t z)))
     (if (<= z 3.5e+28) (/ (/ x t) (- y z)) (/ 1.0 (* z (/ z x)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e+47) {
		tmp = (x / z) / z;
	} else if (z <= 8.2e-145) {
		tmp = x / (y * (t - z));
	} else if (z <= 3.5e+28) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.6d+47)) then
        tmp = (x / z) / z
    else if (z <= 8.2d-145) then
        tmp = x / (y * (t - z))
    else if (z <= 3.5d+28) then
        tmp = (x / t) / (y - z)
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e+47) {
		tmp = (x / z) / z;
	} else if (z <= 8.2e-145) {
		tmp = x / (y * (t - z));
	} else if (z <= 3.5e+28) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -4.6e+47:
		tmp = (x / z) / z
	elif z <= 8.2e-145:
		tmp = x / (y * (t - z))
	elif z <= 3.5e+28:
		tmp = (x / t) / (y - z)
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.6e+47)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 8.2e-145)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 3.5e+28)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.6e+47)
		tmp = (x / z) / z;
	elseif (z <= 8.2e-145)
		tmp = x / (y * (t - z));
	elseif (z <= 3.5e+28)
		tmp = (x / t) / (y - z);
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -4.6e+47], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 8.2e-145], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+28], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5999999999999997e47

   1. Initial program 81.8%

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

   2. Taylor expanded in z around inf 67.2%

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

      1. unpow2 67.2%

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

      2. associate-/r* 77.9%

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

   4. Simplified 77.9%

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

   if -4.5999999999999997e47 < z < 8.1999999999999995e-145

   1. Initial program 97.9%

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

   2. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

   4. Simplified 79.0%

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

   if 8.1999999999999995e-145 < z < 3.5e28

   1. Initial program 84.8%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 70.6%

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

   if 3.5e28 < z

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 75.1%

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

      1. unpow2 75.1%

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

   4. Simplified 75.1%

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

      1. associate-/r* 79.5%

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

      2. div-inv 79.5%

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

   6. Applied egg-rr 79.5%

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

      1. clear-num 79.4%

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

      2. frac-times 79.8%

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

      3. metadata-eval 79.8%

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

   8. Applied egg-rr 79.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x} \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 9: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+182}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e+46)
   (/ (/ x z) z)
   (if (<= z 2.7e-145)
     (/ x (* y (- t z)))
     (if (<= z 1.3e+182) (/ (/ x (- t z)) y) (/ 1.0 (* z (/ z x)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+46) {
		tmp = (x / z) / z;
	} else if (z <= 2.7e-145) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.3e+182) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.6d+46)) then
        tmp = (x / z) / z
    else if (z <= 2.7d-145) then
        tmp = x / (y * (t - z))
    else if (z <= 1.3d+182) then
        tmp = (x / (t - z)) / y
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+46) {
		tmp = (x / z) / z;
	} else if (z <= 2.7e-145) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.3e+182) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.6e+46:
		tmp = (x / z) / z
	elif z <= 2.7e-145:
		tmp = x / (y * (t - z))
	elif z <= 1.3e+182:
		tmp = (x / (t - z)) / y
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.6e+46)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 2.7e-145)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 1.3e+182)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.6e+46)
		tmp = (x / z) / z;
	elseif (z <= 2.7e-145)
		tmp = x / (y * (t - z));
	elseif (z <= 1.3e+182)
		tmp = (x / (t - z)) / y;
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.6e+46], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.7e-145], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+182], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5999999999999999e46

   1. Initial program 81.8%

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

   2. Taylor expanded in z around inf 67.2%

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

      1. unpow2 67.2%

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

      2. associate-/r* 77.9%

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

   4. Simplified 77.9%

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

   if -3.5999999999999999e46 < z < 2.7e-145

   1. Initial program 97.9%

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

   2. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

   4. Simplified 79.0%

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

   if 2.7e-145 < z < 1.3e182

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. associate-/r* 70.2%

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

   4. Simplified 70.2%

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

   if 1.3e182 < z

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf 91.3%

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

      1. unpow2 91.3%

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

   4. Simplified 91.3%

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

      1. associate-/r* 99.5%

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

      2. div-inv 99.5%

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

   6. Applied egg-rr 99.5%

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

      1. clear-num 99.4%

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

      2. frac-times 100.0%

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

      3. metadata-eval 100.0%

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

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x} \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+182}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 10: 93.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{-z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.4e+110)
   (/ (/ x (- y z)) (- z))
   (if (<= z 4.2e+131) (/ x (* (- y z) (- t z))) (/ (/ (- x) z) (- t z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.4e+110) {
		tmp = (x / (y - z)) / -z;
	} else if (z <= 4.2e+131) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.4d+110)) then
        tmp = (x / (y - z)) / -z
    else if (z <= 4.2d+131) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (-x / z) / (t - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.4e+110) {
		tmp = (x / (y - z)) / -z;
	} else if (z <= 4.2e+131) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.4e+110:
		tmp = (x / (y - z)) / -z
	elif z <= 4.2e+131:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (-x / z) / (t - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.4e+110)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(-z));
	elseif (z <= 4.2e+131)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.4e+110)
		tmp = (x / (y - z)) / -z;
	elseif (z <= 4.2e+131)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (-x / z) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.4e+110], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 4.2e+131], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000001e110

   1. Initial program 72.1%

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

   2. Taylor expanded in t around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

      3. *-commutative 72.3%

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

   4. Simplified 72.3%

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

      1. neg-mul-1 72.3%

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

      2. times-frac 97.3%

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

   6. Applied egg-rr 97.3%

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

      1. *-commutative 97.3%

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

      2. frac-2neg 97.3%

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

      3. metadata-eval 97.3%

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

      4. un-div-inv 97.3%

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

   8. Applied egg-rr 97.3%

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

   if -3.4000000000000001e110 < z < 4.19999999999999971e131

   1. Initial program 96.0%

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

   if 4.19999999999999971e131 < z

   1. Initial program 82.2%

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

   2. Taylor expanded in y around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. distribute-frac-neg 82.2%

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

      3. associate-/r* 91.6%

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

   4. Simplified 91.6%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{-z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \]

Alternative 11: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -1.4e+14)
     t_1
     (if (<= z -6.5e-130)
       (/ (- x) (* z t))
       (if (<= z 3.6e+28) (/ (/ x t) y) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.4e+14) {
		tmp = t_1;
	} else if (z <= -6.5e-130) {
		tmp = -x / (z * t);
	} else if (z <= 3.6e+28) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-1.4d+14)) then
        tmp = t_1
    else if (z <= (-6.5d-130)) then
        tmp = -x / (z * t)
    else if (z <= 3.6d+28) then
        tmp = (x / t) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.4e+14) {
		tmp = t_1;
	} else if (z <= -6.5e-130) {
		tmp = -x / (z * t);
	} else if (z <= 3.6e+28) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -1.4e+14:
		tmp = t_1
	elif z <= -6.5e-130:
		tmp = -x / (z * t)
	elif z <= 3.6e+28:
		tmp = (x / t) / y
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.4e+14)
		tmp = t_1;
	elseif (z <= -6.5e-130)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 3.6e+28)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.4e+14)
		tmp = t_1;
	elseif (z <= -6.5e-130)
		tmp = -x / (z * t);
	elseif (z <= 3.6e+28)
		tmp = (x / t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.4e+14], t$95$1, If[LessEqual[z, -6.5e-130], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+28], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e14 or 3.5999999999999999e28 < z

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 69.5%

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

      1. unpow2 69.5%

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

      2. associate-/r* 76.6%

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

   4. Simplified 76.6%

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

   if -1.4e14 < z < -6.5000000000000002e-130

   1. Initial program 99.7%

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

      1. associate-/l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 66.3%

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

   5. Taylor expanded in y around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. *-commutative 45.3%

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

   7. Simplified 45.3%

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

   if -6.5000000000000002e-130 < z < 3.5999999999999999e28

   1. Initial program 93.5%

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

      1. clear-num 93.3%

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

      2. associate-/r/ 93.4%

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

      3. *-commutative 93.4%

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

      4. associate-/r* 93.6%

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

   3. Applied egg-rr 93.6%

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

      1. div-inv 93.6%

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

      2. associate-*l* 94.2%

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

      3. associate-/r/ 94.3%

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

      4. *-un-lft-identity 94.3%

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

      5. times-frac 94.5%

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

      6. clear-num 94.5%

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

      7. /-rgt-identity 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in z around 0 63.4%

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

      1. *-lft-identity 63.4%

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

      2. times-frac 68.7%

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

      3. associate-*l/ 68.8%

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

      4. *-lft-identity 68.8%

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

   8. Simplified 68.8%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 12: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+47)
   (/ (/ x z) z)
   (if (<= z 3.5e+29) (/ x (* (- y z) t)) (/ 1.0 (* z (/ z x))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+47) {
		tmp = (x / z) / z;
	} else if (z <= 3.5e+29) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.25d+47)) then
        tmp = (x / z) / z
    else if (z <= 3.5d+29) then
        tmp = x / ((y - z) * t)
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+47) {
		tmp = (x / z) / z;
	} else if (z <= 3.5e+29) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+47:
		tmp = (x / z) / z
	elif z <= 3.5e+29:
		tmp = x / ((y - z) * t)
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.25e+47)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 3.5e+29)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.25e+47)
		tmp = (x / z) / z;
	elseif (z <= 3.5e+29)
		tmp = x / ((y - z) * t);
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.25e+47], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.5e+29], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e47

   1. Initial program 81.8%

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

   2. Taylor expanded in z around inf 67.2%

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

      1. unpow2 67.2%

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

      2. associate-/r* 77.9%

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

   4. Simplified 77.9%

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

   if -2.2499999999999999e47 < z < 3.49999999999999979e29

   1. Initial program 94.8%

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

   2. Taylor expanded in t around inf 73.3%

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

   if 3.49999999999999979e29 < z

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 75.1%

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

      1. unpow2 75.1%

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

   4. Simplified 75.1%

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

      1. associate-/r* 79.5%

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

      2. div-inv 79.5%

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

   6. Applied egg-rr 79.5%

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

      1. clear-num 79.4%

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

      2. frac-times 79.8%

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

      3. metadata-eval 79.8%

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

   8. Applied egg-rr 79.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 13: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+47} \lor \neg \left(z \leq 2.25 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.1e+47) (not (<= z 2.25e+55))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e+47) || !(z <= 2.25e+55)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.1d+47)) .or. (.not. (z <= 2.25d+55))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e+47) || !(z <= 2.25e+55)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.1e+47) or not (z <= 2.25e+55):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.1e+47) || !(z <= 2.25e+55))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.1e+47) || ~((z <= 2.25e+55)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.1e+47], N[Not[LessEqual[z, 2.25e+55]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e47 or 2.24999999999999999e55 < z

   1. Initial program 84.5%

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

   2. Taylor expanded in y around inf 42.9%

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

      1. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in t around 0 40.0%

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

      1. mul-1-neg 40.0%

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

      2. associate-/r* 40.3%

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

      3. distribute-neg-frac 40.3%

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

      4. distribute-neg-frac 40.3%

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

   7. Simplified 40.3%

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

      1. expm1-log1p-u 40.1%

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

      2. expm1-udef 59.9%

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

      3. associate-/l/ 60.0%

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

      4. add-sqr-sqrt 37.7%

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

      5. sqrt-unprod 58.6%

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

      6. sqr-neg 58.6%

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

      7. sqrt-unprod 22.2%

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

      8. add-sqr-sqrt 59.9%

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

   9. Applied egg-rr 59.9%

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

       1. expm1-def 37.0%

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

       2. expm1-log1p 37.4%

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

       3. *-commutative 37.4%

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

   11. Simplified 37.4%

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

   if -1.1e47 < z < 2.24999999999999999e55

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 55.0%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+47} \lor \neg \left(z \leq 2.25 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -96000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -96000000000.0) (not (<= z 5.5e+22)))
   (/ x (* z z))
   (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -96000000000.0) || !(z <= 5.5e+22)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-96000000000.0d0)) .or. (.not. (z <= 5.5d+22))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -96000000000.0) || !(z <= 5.5e+22)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -96000000000.0) or not (z <= 5.5e+22):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -96000000000.0) || !(z <= 5.5e+22))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -96000000000.0) || ~((z <= 5.5e+22)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -96000000000.0], N[Not[LessEqual[z, 5.5e+22]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.6e10 or 5.50000000000000021e22 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 68.5%

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

      1. unpow2 68.5%

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

   4. Simplified 68.5%

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

   if -9.6e10 < z < 5.50000000000000021e22

   1. Initial program 95.2%

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

   2. Taylor expanded in z around 0 58.8%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -96000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -22000000000000 \lor \neg \left(z \leq 1.46 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -22000000000000.0) (not (<= z 1.46e+29)))
   (/ x (* z z))
   (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -22000000000000.0) || !(z <= 1.46e+29)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-22000000000000.0d0)) .or. (.not. (z <= 1.46d+29))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -22000000000000.0) || !(z <= 1.46e+29)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -22000000000000.0) or not (z <= 1.46e+29):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -22000000000000.0) || !(z <= 1.46e+29))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -22000000000000.0) || ~((z <= 1.46e+29)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -22000000000000.0], N[Not[LessEqual[z, 1.46e+29]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e13 or 1.46e29 < z

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 69.5%

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

      1. unpow2 69.5%

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

   4. Simplified 69.5%

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

   if -2.2e13 < z < 1.46e29

   1. Initial program 94.6%

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

      1. clear-num 94.5%

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

      2. associate-/r/ 94.5%

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

      3. *-commutative 94.5%

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

      4. associate-/r* 94.7%

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

   3. Applied egg-rr 94.7%

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

      1. div-inv 94.7%

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

      2. associate-*l* 94.4%

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

      3. associate-/r/ 94.4%

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

      4. *-un-lft-identity 94.4%

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

      5. times-frac 94.7%

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

      6. clear-num 94.7%

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

      7. /-rgt-identity 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in z around 0 58.0%

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

      1. *-lft-identity 58.0%

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

      2. times-frac 63.0%

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

      3. associate-*l/ 63.1%

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

      4. *-lft-identity 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22000000000000 \lor \neg \left(z \leq 1.46 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 16: 67.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -780000000000 \lor \neg \left(z \leq 4.2 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -780000000000.0) (not (<= z 4.2e+28)))
   (/ (/ x z) z)
   (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -780000000000.0) || !(z <= 4.2e+28)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-780000000000.0d0)) .or. (.not. (z <= 4.2d+28))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -780000000000.0) || !(z <= 4.2e+28)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -780000000000.0) or not (z <= 4.2e+28):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -780000000000.0) || !(z <= 4.2e+28))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -780000000000.0) || ~((z <= 4.2e+28)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -780000000000.0], N[Not[LessEqual[z, 4.2e+28]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e11 or 4.19999999999999978e28 < z

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 69.5%

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

      1. unpow2 69.5%

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

      2. associate-/r* 76.6%

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

   4. Simplified 76.6%

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

   if -7.8e11 < z < 4.19999999999999978e28

   1. Initial program 94.6%

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

      1. clear-num 94.5%

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

      2. associate-/r/ 94.5%

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

      3. *-commutative 94.5%

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

      4. associate-/r* 94.7%

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

   3. Applied egg-rr 94.7%

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

      1. div-inv 94.7%

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

      2. associate-*l* 94.4%

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

      3. associate-/r/ 94.4%

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

      4. *-un-lft-identity 94.4%

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

      5. times-frac 94.7%

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

      6. clear-num 94.7%

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

      7. /-rgt-identity 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in z around 0 58.0%

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

      1. *-lft-identity 58.0%

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

      2. times-frac 63.0%

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

      3. associate-*l/ 63.1%

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

      4. *-lft-identity 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -780000000000 \lor \neg \left(z \leq 4.2 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 17: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

   1. associate-/l/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 18: 39.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

2. Taylor expanded in z around 0 40.3%

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

3. Final simplification 40.3%

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

Developer target: 88.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))