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

Percentage Accurate: 88.6% → 98.4%

Time: 10.1s

Alternatives: 18

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{\frac{1}{y - z} \cdot x}{t - z}\\ \mathbf{elif}\;t_1 \leq 10^{+137}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 -2e+212)
     (/ (* (/ 1.0 (- y z)) x) (- t z))
     (if (<= t_1 1e+137) (/ x t_1) (/ (/ x (- y z)) (- t z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = ((1.0 / (y - z)) * x) / (t - z);
	} else if (t_1 <= 1e+137) {
		tmp = x / t_1;
	} else {
		tmp = (x / (y - 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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= (-2d+212)) then
        tmp = ((1.0d0 / (y - z)) * x) / (t - z)
    else if (t_1 <= 1d+137) then
        tmp = x / t_1
    else
        tmp = (x / (y - 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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = ((1.0 / (y - z)) * x) / (t - z);
	} else if (t_1 <= 1e+137) {
		tmp = x / t_1;
	} else {
		tmp = (x / (y - z)) / (t - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -2e+212:
		tmp = ((1.0 / (y - z)) * x) / (t - z)
	elif t_1 <= 1e+137:
		tmp = x / t_1
	else:
		tmp = (x / (y - z)) / (t - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= -2e+212)
		tmp = Float64(Float64(Float64(1.0 / Float64(y - z)) * x) / Float64(t - z));
	elseif (t_1 <= 1e+137)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -2e+212)
		tmp = ((1.0 / (y - z)) * x) / (t - z);
	elseif (t_1 <= 1e+137)
		tmp = x / t_1;
	else
		tmp = (x / (y - 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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+212], N[(N[(N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+137], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -1.9999999999999998e212

   1. Initial program 76.2%

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

      1. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   if -1.9999999999999998e212 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1e137

   1. Initial program 98.9%

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

   if 1e137 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 87.9%

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

      1. associate-/r* 99.0%

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

   3. Simplified 99.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{\frac{1}{y - z} \cdot x}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 10^{+137}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]

Alternative 2: 92.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t}\\ \mathbf{elif}\;t_1 \leq 1.1 \cdot 10^{+306}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 -2e+212)
     (* (/ x (- y z)) (/ 1.0 t))
     (if (<= t_1 1.1e+306) (/ x t_1) (* (/ -1.0 z) (/ x (- t z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = (x / (y - z)) * (1.0 / t);
	} else if (t_1 <= 1.1e+306) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) * (x / (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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= (-2d+212)) then
        tmp = (x / (y - z)) * (1.0d0 / t)
    else if (t_1 <= 1.1d+306) then
        tmp = x / t_1
    else
        tmp = ((-1.0d0) / z) * (x / (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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = (x / (y - z)) * (1.0 / t);
	} else if (t_1 <= 1.1e+306) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) * (x / (t - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -2e+212:
		tmp = (x / (y - z)) * (1.0 / t)
	elif t_1 <= 1.1e+306:
		tmp = x / t_1
	else:
		tmp = (-1.0 / z) * (x / (t - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= -2e+212)
		tmp = Float64(Float64(x / Float64(y - z)) * Float64(1.0 / t));
	elseif (t_1 <= 1.1e+306)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -2e+212)
		tmp = (x / (y - z)) * (1.0 / t);
	elseif (t_1 <= 1.1e+306)
		tmp = x / t_1;
	else
		tmp = (-1.0 / z) * (x / (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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+212], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.1e+306], N[(x / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -1.9999999999999998e212

   1. Initial program 76.2%

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

      1. associate-/r* 99.7%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in t around inf 87.8%

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

   if -1.9999999999999998e212 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1.1e306

   1. Initial program 99.1%

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

   if 1.1e306 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 80.6%

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

      1. *-un-lft-identity 80.6%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around 0 86.5%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 1.1 \cdot 10^{+306}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 3: 96.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{x}{y - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;t_2 \cdot \frac{1}{t}\\ \mathbf{elif}\;t_1 \leq 10^{+137}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))) (t_2 (/ x (- y z))))
   (if (<= t_1 -2e+212)
     (* t_2 (/ 1.0 t))
     (if (<= t_1 1e+137) (/ x t_1) (/ t_2 (- t z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = x / (y - z);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = t_2 * (1.0 / t);
	} else if (t_1 <= 1e+137) {
		tmp = x / t_1;
	} else {
		tmp = t_2 / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    t_2 = x / (y - z)
    if (t_1 <= (-2d+212)) then
        tmp = t_2 * (1.0d0 / t)
    else if (t_1 <= 1d+137) then
        tmp = x / t_1
    else
        tmp = t_2 / (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 t_1 = (y - z) * (t - z);
	double t_2 = x / (y - z);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = t_2 * (1.0 / t);
	} else if (t_1 <= 1e+137) {
		tmp = x / t_1;
	} else {
		tmp = t_2 / (t - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	t_2 = x / (y - z)
	tmp = 0
	if t_1 <= -2e+212:
		tmp = t_2 * (1.0 / t)
	elif t_1 <= 1e+137:
		tmp = x / t_1
	else:
		tmp = t_2 / (t - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	t_2 = Float64(x / Float64(y - z))
	tmp = 0.0
	if (t_1 <= -2e+212)
		tmp = Float64(t_2 * Float64(1.0 / t));
	elseif (t_1 <= 1e+137)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(t_2 / Float64(t - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	t_2 = x / (y - z);
	tmp = 0.0;
	if (t_1 <= -2e+212)
		tmp = t_2 * (1.0 / t);
	elseif (t_1 <= 1e+137)
		tmp = x / t_1;
	else
		tmp = t_2 / (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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+212], N[(t$95$2 * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+137], N[(x / t$95$1), $MachinePrecision], N[(t$95$2 / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -1.9999999999999998e212

   1. Initial program 76.2%

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

      1. associate-/r* 99.7%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in t around inf 87.8%

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

   if -1.9999999999999998e212 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1e137

   1. Initial program 98.9%

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

   if 1e137 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 87.9%

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

      1. associate-/r* 99.0%

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

   3. Simplified 99.0%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 10^{+137}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y - z}}{t}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (- y z)) t)))
   (if (<= z -2e+157)
     (* (/ x z) (/ 1.0 z))
     (if (<= z -7.6e-134)
       t_1
       (if (<= z 4.1e-7)
         (/ x (* y (- t z)))
         (if (<= z 1.65e+71)
           t_1
           (if (<= z 9.2e+82) (/ (/ x y) (- t z)) (/ (/ x z) z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / (y - z)) / t;
	double tmp;
	if (z <= -2e+157) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -7.6e-134) {
		tmp = t_1;
	} else if (z <= 4.1e-7) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.65e+71) {
		tmp = t_1;
	} else if (z <= 9.2e+82) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / 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) :: t_1
    real(8) :: tmp
    t_1 = (x / (y - z)) / t
    if (z <= (-2d+157)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= (-7.6d-134)) then
        tmp = t_1
    else if (z <= 4.1d-7) then
        tmp = x / (y * (t - z))
    else if (z <= 1.65d+71) then
        tmp = t_1
    else if (z <= 9.2d+82) then
        tmp = (x / y) / (t - z)
    else
        tmp = (x / 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 t_1 = (x / (y - z)) / t;
	double tmp;
	if (z <= -2e+157) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -7.6e-134) {
		tmp = t_1;
	} else if (z <= 4.1e-7) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.65e+71) {
		tmp = t_1;
	} else if (z <= 9.2e+82) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / (y - z)) / t
	tmp = 0
	if z <= -2e+157:
		tmp = (x / z) * (1.0 / z)
	elif z <= -7.6e-134:
		tmp = t_1
	elif z <= 4.1e-7:
		tmp = x / (y * (t - z))
	elif z <= 1.65e+71:
		tmp = t_1
	elif z <= 9.2e+82:
		tmp = (x / y) / (t - z)
	else:
		tmp = (x / z) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(y - z)) / t)
	tmp = 0.0
	if (z <= -2e+157)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= -7.6e-134)
		tmp = t_1;
	elseif (z <= 4.1e-7)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 1.65e+71)
		tmp = t_1;
	elseif (z <= 9.2e+82)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / (y - z)) / t;
	tmp = 0.0;
	if (z <= -2e+157)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= -7.6e-134)
		tmp = t_1;
	elseif (z <= 4.1e-7)
		tmp = x / (y * (t - z));
	elseif (z <= 1.65e+71)
		tmp = t_1;
	elseif (z <= 9.2e+82)
		tmp = (x / y) / (t - z);
	else
		tmp = (x / 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_] := Block[{t$95$1 = N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2e+157], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-134], t$95$1, If[LessEqual[z, 4.1e-7], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+71], t$95$1, If[LessEqual[z, 9.2e+82], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.99999999999999997e157

   1. Initial program 89.4%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. unpow2 89.4%

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

   4. Simplified 89.4%

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

      1. associate-/r* 96.3%

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

      2. div-inv 96.4%

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

   6. Applied egg-rr 96.4%

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

   if -1.99999999999999997e157 < z < -7.60000000000000006e-134 or 4.0999999999999999e-7 < z < 1.6499999999999999e71

   1. Initial program 93.1%

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

   2. Taylor expanded in t around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-/r* 68.9%

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

   4. Simplified 68.9%

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

   if -7.60000000000000006e-134 < z < 4.0999999999999999e-7

   1. Initial program 97.0%

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

   2. Taylor expanded in y around inf 75.9%

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

      1. *-commutative 75.9%

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

   4. Simplified 75.9%

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

   if 1.6499999999999999e71 < z < 9.19999999999999953e82

   1. Initial program 73.7%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. associate-/r* 99.0%

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

   4. Simplified 99.0%

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

   if 9.19999999999999953e82 < z

   1. Initial program 82.5%

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

      1. *-un-lft-identity 82.5%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 98.8%

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

   5. Applied egg-rr 98.8%

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

   6. Taylor expanded in z around inf 82.4%

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

      1. *-rgt-identity 82.4%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{{z}^{2}} \]

      2. unpow2 82.4%

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

      3. times-frac 94.4%

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

      4. associate-*r/ 94.4%

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

      5. *-rgt-identity 94.4%

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

   8. Simplified 94.4%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 5: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+161}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e+157)
   (* (/ x z) (/ 1.0 z))
   (if (<= z -1.3e-133)
     (/ (/ x (- y z)) t)
     (if (<= z 5e-121)
       (/ x (* y (- t z)))
       (if (<= z 2.05e+161) (/ (- x) (* z (- y z))) (/ (/ x z) z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e+157) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -1.3e-133) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 5e-121) {
		tmp = x / (y * (t - z));
	} else if (z <= 2.05e+161) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / 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 <= (-2d+157)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= (-1.3d-133)) then
        tmp = (x / (y - z)) / t
    else if (z <= 5d-121) then
        tmp = x / (y * (t - z))
    else if (z <= 2.05d+161) then
        tmp = -x / (z * (y - z))
    else
        tmp = (x / 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 <= -2e+157) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -1.3e-133) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 5e-121) {
		tmp = x / (y * (t - z));
	} else if (z <= 2.05e+161) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2e+157:
		tmp = (x / z) * (1.0 / z)
	elif z <= -1.3e-133:
		tmp = (x / (y - z)) / t
	elif z <= 5e-121:
		tmp = x / (y * (t - z))
	elif z <= 2.05e+161:
		tmp = -x / (z * (y - z))
	else:
		tmp = (x / z) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e+157)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= -1.3e-133)
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (z <= 5e-121)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 2.05e+161)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) / 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 <= -2e+157)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= -1.3e-133)
		tmp = (x / (y - z)) / t;
	elseif (z <= 5e-121)
		tmp = x / (y * (t - z));
	elseif (z <= 2.05e+161)
		tmp = -x / (z * (y - z));
	else
		tmp = (x / 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, -2e+157], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-133], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5e-121], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+161], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.99999999999999997e157

   1. Initial program 89.4%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. unpow2 89.4%

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

   4. Simplified 89.4%

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

      1. associate-/r* 96.3%

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

      2. div-inv 96.4%

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

   6. Applied egg-rr 96.4%

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

   if -1.99999999999999997e157 < z < -1.3e-133

   1. Initial program 91.5%

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

   2. Taylor expanded in t around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/r* 72.7%

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

   4. Simplified 72.7%

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

   if -1.3e-133 < z < 4.99999999999999989e-121

   1. Initial program 96.0%

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

   2. Taylor expanded in y around inf 82.0%

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

      1. *-commutative 82.0%

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

   4. Simplified 82.0%

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

   if 4.99999999999999989e-121 < z < 2.0500000000000001e161

   1. Initial program 95.6%

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

   2. Taylor expanded in t around 0 73.0%

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

      1. associate-*r/ 73.0%

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

      2. neg-mul-1 73.0%

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

   4. Simplified 73.0%

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

   if 2.0500000000000001e161 < z

   1. Initial program 76.8%

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

      1. *-un-lft-identity 76.8%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in z around inf 76.8%

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

      1. *-rgt-identity 76.8%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{{z}^{2}} \]

      2. unpow2 76.8%

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

      3. times-frac 96.9%

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

      4. associate-*r/ 97.0%

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

      5. *-rgt-identity 97.0%

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

   8. Simplified 97.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+161}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 6: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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)) (t_2 (/ x (* (- y z) t))))
   (if (<= z -4.6e+77)
     t_1
     (if (<= z -4.3e-131)
       t_2
       (if (<= z 3.5e-89) (/ x (* y (- t z))) (if (<= z 9e+82) t_2 t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / ((y - z) * t);
	double tmp;
	if (z <= -4.6e+77) {
		tmp = t_1;
	} else if (z <= -4.3e-131) {
		tmp = t_2;
	} else if (z <= 3.5e-89) {
		tmp = x / (y * (t - z));
	} else if (z <= 9e+82) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / ((y - z) * t)
    if (z <= (-4.6d+77)) then
        tmp = t_1
    else if (z <= (-4.3d-131)) then
        tmp = t_2
    else if (z <= 3.5d-89) then
        tmp = x / (y * (t - z))
    else if (z <= 9d+82) then
        tmp = t_2
    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 t_2 = x / ((y - z) * t);
	double tmp;
	if (z <= -4.6e+77) {
		tmp = t_1;
	} else if (z <= -4.3e-131) {
		tmp = t_2;
	} else if (z <= 3.5e-89) {
		tmp = x / (y * (t - z));
	} else if (z <= 9e+82) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	t_2 = x / ((y - z) * t)
	tmp = 0
	if z <= -4.6e+77:
		tmp = t_1
	elif z <= -4.3e-131:
		tmp = t_2
	elif z <= 3.5e-89:
		tmp = x / (y * (t - z))
	elif z <= 9e+82:
		tmp = t_2
	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)
	t_2 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -4.6e+77)
		tmp = t_1;
	elseif (z <= -4.3e-131)
		tmp = t_2;
	elseif (z <= 3.5e-89)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 9e+82)
		tmp = t_2;
	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;
	t_2 = x / ((y - z) * t);
	tmp = 0.0;
	if (z <= -4.6e+77)
		tmp = t_1;
	elseif (z <= -4.3e-131)
		tmp = t_2;
	elseif (z <= 3.5e-89)
		tmp = x / (y * (t - z));
	elseif (z <= 9e+82)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+77], t$95$1, If[LessEqual[z, -4.3e-131], t$95$2, If[LessEqual[z, 3.5e-89], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+82], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999999e77 or 8.9999999999999993e82 < z

   1. Initial program 84.9%

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

      1. *-un-lft-identity 84.9%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in z around inf 82.6%

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

      1. *-rgt-identity 82.6%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{{z}^{2}} \]

      2. unpow2 82.6%

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

      3. times-frac 91.4%

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

      4. associate-*r/ 91.4%

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

      5. *-rgt-identity 91.4%

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

   8. Simplified 91.4%

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

   if -4.5999999999999999e77 < z < -4.30000000000000019e-131 or 3.4999999999999997e-89 < z < 8.9999999999999993e82

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf 54.9%

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

   if -4.30000000000000019e-131 < z < 3.4999999999999997e-89

   1. Initial program 96.4%

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

   2. Taylor expanded in y around inf 79.4%

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

      1. *-commutative 79.4%

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

   4. Simplified 79.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 7: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.42e-13)
   (/ (- (/ x z)) (- t z))
   (if (<= z -1.12e-138)
     (/ (/ x (- y z)) t)
     (if (<= z 1.6e-93) (/ x (* y (- t z))) (* (/ -1.0 z) (/ x (- t z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.42e-13) {
		tmp = -(x / z) / (t - z);
	} else if (z <= -1.12e-138) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 1.6e-93) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (-1.0 / z) * (x / (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 <= (-1.42d-13)) then
        tmp = -(x / z) / (t - z)
    else if (z <= (-1.12d-138)) then
        tmp = (x / (y - z)) / t
    else if (z <= 1.6d-93) then
        tmp = x / (y * (t - z))
    else
        tmp = ((-1.0d0) / z) * (x / (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 <= -1.42e-13) {
		tmp = -(x / z) / (t - z);
	} else if (z <= -1.12e-138) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 1.6e-93) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (-1.0 / z) * (x / (t - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.42e-13:
		tmp = -(x / z) / (t - z)
	elif z <= -1.12e-138:
		tmp = (x / (y - z)) / t
	elif z <= 1.6e-93:
		tmp = x / (y * (t - z))
	else:
		tmp = (-1.0 / z) * (x / (t - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.42e-13)
		tmp = Float64(Float64(-Float64(x / z)) / Float64(t - z));
	elseif (z <= -1.12e-138)
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (z <= 1.6e-93)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(-1.0 / z) * Float64(x / 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 <= -1.42e-13)
		tmp = -(x / z) / (t - z);
	elseif (z <= -1.12e-138)
		tmp = (x / (y - z)) / t;
	elseif (z <= 1.6e-93)
		tmp = x / (y * (t - z));
	else
		tmp = (-1.0 / z) * (x / (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, -1.42e-13], N[((-N[(x / z), $MachinePrecision]) / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e-138], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.6e-93], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.42e-13

   1. Initial program 91.7%

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

   2. Taylor expanded in y around 0 78.0%

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

      1. mul-1-neg 78.0%

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

      2. distribute-frac-neg 78.0%

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

      3. associate-/r* 79.6%

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

   4. Simplified 79.6%

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

   if -1.42e-13 < z < -1.1199999999999999e-138

   1. Initial program 89.1%

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

   2. Taylor expanded in t around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-/r* 88.9%

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

   4. Simplified 88.9%

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

   if -1.1199999999999999e-138 < z < 1.5999999999999999e-93

   1. Initial program 96.3%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   if 1.5999999999999999e-93 < z

   1. Initial program 88.9%

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

      1. *-un-lft-identity 88.9%

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

      2. times-frac 97.6%

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

   3. Applied egg-rr 97.6%

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

   4. Taylor expanded in y around 0 80.7%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 8: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.55e-13)
   (/ (- (/ x z)) (- t z))
   (if (<= z -9.5e-139)
     (* (/ x (- y z)) (/ 1.0 t))
     (if (<= z 7.2e-92) (/ x (* y (- t z))) (* (/ -1.0 z) (/ x (- t z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e-13) {
		tmp = -(x / z) / (t - z);
	} else if (z <= -9.5e-139) {
		tmp = (x / (y - z)) * (1.0 / t);
	} else if (z <= 7.2e-92) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (-1.0 / z) * (x / (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 <= (-1.55d-13)) then
        tmp = -(x / z) / (t - z)
    else if (z <= (-9.5d-139)) then
        tmp = (x / (y - z)) * (1.0d0 / t)
    else if (z <= 7.2d-92) then
        tmp = x / (y * (t - z))
    else
        tmp = ((-1.0d0) / z) * (x / (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 <= -1.55e-13) {
		tmp = -(x / z) / (t - z);
	} else if (z <= -9.5e-139) {
		tmp = (x / (y - z)) * (1.0 / t);
	} else if (z <= 7.2e-92) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (-1.0 / z) * (x / (t - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e-13:
		tmp = -(x / z) / (t - z)
	elif z <= -9.5e-139:
		tmp = (x / (y - z)) * (1.0 / t)
	elif z <= 7.2e-92:
		tmp = x / (y * (t - z))
	else:
		tmp = (-1.0 / z) * (x / (t - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.55e-13)
		tmp = Float64(Float64(-Float64(x / z)) / Float64(t - z));
	elseif (z <= -9.5e-139)
		tmp = Float64(Float64(x / Float64(y - z)) * Float64(1.0 / t));
	elseif (z <= 7.2e-92)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(-1.0 / z) * Float64(x / 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 <= -1.55e-13)
		tmp = -(x / z) / (t - z);
	elseif (z <= -9.5e-139)
		tmp = (x / (y - z)) * (1.0 / t);
	elseif (z <= 7.2e-92)
		tmp = x / (y * (t - z));
	else
		tmp = (-1.0 / z) * (x / (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, -1.55e-13], N[((-N[(x / z), $MachinePrecision]) / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-139], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-92], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e-13

   1. Initial program 91.7%

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

   2. Taylor expanded in y around 0 78.0%

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

      1. mul-1-neg 78.0%

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

      2. distribute-frac-neg 78.0%

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

      3. associate-/r* 79.6%

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

   4. Simplified 79.6%

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

   if -1.55e-13 < z < -9.5000000000000006e-139

   1. Initial program 89.1%

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

      1. associate-/r* 96.1%

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

      2. div-inv 96.3%

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

   3. Applied egg-rr 96.3%

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

   4. Taylor expanded in t around inf 89.1%

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

   if -9.5000000000000006e-139 < z < 7.20000000000000032e-92

   1. Initial program 96.3%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   if 7.20000000000000032e-92 < z

   1. Initial program 88.9%

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

      1. *-un-lft-identity 88.9%

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

      2. times-frac 97.6%

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

   3. Applied egg-rr 97.6%

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

   4. Taylor expanded in y around 0 80.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 9: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{-\frac{x}{z}}{t - z}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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)) (- t z))))
   (if (<= z -2.3e-12)
     t_1
     (if (<= z -9e-134)
       (/ (/ x (- y z)) t)
       (if (<= z 1.02e-92) (/ x (* y (- t z))) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = -(x / z) / (t - z);
	double tmp;
	if (z <= -2.3e-12) {
		tmp = t_1;
	} else if (z <= -9e-134) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 1.02e-92) {
		tmp = x / (y * (t - z));
	} 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) / (t - z)
    if (z <= (-2.3d-12)) then
        tmp = t_1
    else if (z <= (-9d-134)) then
        tmp = (x / (y - z)) / t
    else if (z <= 1.02d-92) then
        tmp = x / (y * (t - z))
    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) / (t - z);
	double tmp;
	if (z <= -2.3e-12) {
		tmp = t_1;
	} else if (z <= -9e-134) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 1.02e-92) {
		tmp = x / (y * (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = -(x / z) / (t - z)
	tmp = 0
	if z <= -2.3e-12:
		tmp = t_1
	elif z <= -9e-134:
		tmp = (x / (y - z)) / t
	elif z <= 1.02e-92:
		tmp = x / (y * (t - z))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-Float64(x / z)) / Float64(t - z))
	tmp = 0.0
	if (z <= -2.3e-12)
		tmp = t_1;
	elseif (z <= -9e-134)
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (z <= 1.02e-92)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	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) / (t - z);
	tmp = 0.0;
	if (z <= -2.3e-12)
		tmp = t_1;
	elseif (z <= -9e-134)
		tmp = (x / (y - z)) / t;
	elseif (z <= 1.02e-92)
		tmp = x / (y * (t - z));
	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]) / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e-12], t$95$1, If[LessEqual[z, -9e-134], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.02e-92], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999989e-12 or 1.02000000000000005e-92 < z

   1. Initial program 89.9%

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

   2. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-frac-neg 75.5%

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

      3. associate-/r* 80.3%

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

   4. Simplified 80.3%

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

   if -2.29999999999999989e-12 < z < -9.000000000000001e-134

   1. Initial program 89.1%

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

   2. Taylor expanded in t around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-/r* 88.9%

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

   4. Simplified 88.9%

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

   if -9.000000000000001e-134 < z < 1.02000000000000005e-92

   1. Initial program 96.3%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \end{array} \]

Alternative 10: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.85e+139)
   (* (/ x z) (/ 1.0 z))
   (if (<= z -2.1e-134)
     (/ (/ x t) (- y z))
     (if (<= z 9.2e+82) (/ x (* y (- t z))) (/ (/ x z) z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+139) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -2.1e-134) {
		tmp = (x / t) / (y - z);
	} else if (z <= 9.2e+82) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / 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 <= (-1.85d+139)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= (-2.1d-134)) then
        tmp = (x / t) / (y - z)
    else if (z <= 9.2d+82) then
        tmp = x / (y * (t - z))
    else
        tmp = (x / 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 <= -1.85e+139) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -2.1e-134) {
		tmp = (x / t) / (y - z);
	} else if (z <= 9.2e+82) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.85e+139:
		tmp = (x / z) * (1.0 / z)
	elif z <= -2.1e-134:
		tmp = (x / t) / (y - z)
	elif z <= 9.2e+82:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / z) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.85e+139)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= -2.1e-134)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 9.2e+82)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / 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 <= -1.85e+139)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= -2.1e-134)
		tmp = (x / t) / (y - z);
	elseif (z <= 9.2e+82)
		tmp = x / (y * (t - z));
	else
		tmp = (x / 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, -1.85e+139], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-134], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+82], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.84999999999999996e139

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 88.4%

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

      1. unpow2 88.4%

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

   4. Simplified 88.4%

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

      1. associate-/r* 94.0%

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

      2. div-inv 94.1%

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

   6. Applied egg-rr 94.1%

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

   if -1.84999999999999996e139 < z < -2.0999999999999999e-134

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 60.3%

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

      1. associate-/r* 65.9%

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

   4. Simplified 65.9%

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

   if -2.0999999999999999e-134 < z < 9.19999999999999953e82

   1. Initial program 96.7%

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

   2. Taylor expanded in y around inf 71.8%

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

      1. *-commutative 71.8%

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

   4. Simplified 71.8%

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

   if 9.19999999999999953e82 < z

   1. Initial program 82.5%

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

      1. *-un-lft-identity 82.5%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 98.8%

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

   5. Applied egg-rr 98.8%

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

   6. Taylor expanded in z around inf 82.4%

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

      1. *-rgt-identity 82.4%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{{z}^{2}} \]

      2. unpow2 82.4%

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

      3. times-frac 94.4%

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

      4. associate-*r/ 94.4%

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

      5. *-rgt-identity 94.4%

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

   8. Simplified 94.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 11: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-98}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+82}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -7e-15)
     t_1
     (if (<= z 9e-98) (/ (/ x t) y) (if (<= z 9e+82) (/ (- x) (* z t)) 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 <= -7e-15) {
		tmp = t_1;
	} else if (z <= 9e-98) {
		tmp = (x / t) / y;
	} else if (z <= 9e+82) {
		tmp = -x / (z * t);
	} 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 <= (-7d-15)) then
        tmp = t_1
    else if (z <= 9d-98) then
        tmp = (x / t) / y
    else if (z <= 9d+82) then
        tmp = -x / (z * t)
    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 <= -7e-15) {
		tmp = t_1;
	} else if (z <= 9e-98) {
		tmp = (x / t) / y;
	} else if (z <= 9e+82) {
		tmp = -x / (z * t);
	} 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 <= -7e-15:
		tmp = t_1
	elif z <= 9e-98:
		tmp = (x / t) / y
	elif z <= 9e+82:
		tmp = -x / (z * t)
	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 <= -7e-15)
		tmp = t_1;
	elseif (z <= 9e-98)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 9e+82)
		tmp = Float64(Float64(-x) / Float64(z * t));
	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 <= -7e-15)
		tmp = t_1;
	elseif (z <= 9e-98)
		tmp = (x / t) / y;
	elseif (z <= 9e+82)
		tmp = -x / (z * t);
	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, -7e-15], t$95$1, If[LessEqual[z, 9e-98], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 9e+82], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000001e-15 or 8.9999999999999993e82 < z

   1. Initial program 87.2%

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

      1. *-un-lft-identity 87.2%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 98.7%

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

   5. Applied egg-rr 98.7%

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

   6. Taylor expanded in z around inf 75.8%

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

      1. *-rgt-identity 75.8%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{{z}^{2}} \]

      2. unpow2 75.8%

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

      3. times-frac 83.1%

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

      4. associate-*r/ 83.1%

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

      5. *-rgt-identity 83.1%

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

   8. Simplified 83.1%

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

   if -7.0000000000000001e-15 < z < 8.99999999999999994e-98

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 71.2%

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

      1. associate-/r* 71.0%

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

   4. Simplified 71.0%

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

   if 8.99999999999999994e-98 < z < 8.9999999999999993e82

   1. Initial program 97.7%

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

      1. *-un-lft-identity 97.7%

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

      2. times-frac 93.0%

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

   3. Applied egg-rr 93.0%

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

   4. Taylor expanded in y around 0 57.4%

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

   5. Taylor expanded in z around 0 36.0%

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

      1. associate-*r/ 36.0%

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

      2. neg-mul-1 36.0%

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

      3. *-commutative 36.0%

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

   7. Simplified 36.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-98}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+82}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 12: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+82}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -1.3e-11)
     t_1
     (if (<= z 5e-121)
       (/ (/ x t) y)
       (if (<= z 9e+82) (/ (- x) (* y z)) 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 <= -1.3e-11) {
		tmp = t_1;
	} else if (z <= 5e-121) {
		tmp = (x / t) / y;
	} else if (z <= 9e+82) {
		tmp = -x / (y * z);
	} 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 <= (-1.3d-11)) then
        tmp = t_1
    else if (z <= 5d-121) then
        tmp = (x / t) / y
    else if (z <= 9d+82) then
        tmp = -x / (y * z)
    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 <= -1.3e-11) {
		tmp = t_1;
	} else if (z <= 5e-121) {
		tmp = (x / t) / y;
	} else if (z <= 9e+82) {
		tmp = -x / (y * z);
	} 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 <= -1.3e-11:
		tmp = t_1
	elif z <= 5e-121:
		tmp = (x / t) / y
	elif z <= 9e+82:
		tmp = -x / (y * z)
	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 <= -1.3e-11)
		tmp = t_1;
	elseif (z <= 5e-121)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 9e+82)
		tmp = Float64(Float64(-x) / Float64(y * z));
	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 <= -1.3e-11)
		tmp = t_1;
	elseif (z <= 5e-121)
		tmp = (x / t) / y;
	elseif (z <= 9e+82)
		tmp = -x / (y * z);
	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, -1.3e-11], t$95$1, If[LessEqual[z, 5e-121], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 9e+82], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e-11 or 8.9999999999999993e82 < z

   1. Initial program 87.2%

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

      1. *-un-lft-identity 87.2%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 98.7%

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

   5. Applied egg-rr 98.7%

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

   6. Taylor expanded in z around inf 75.8%

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

      1. *-rgt-identity 75.8%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{{z}^{2}} \]

      2. unpow2 75.8%

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

      3. times-frac 83.1%

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

      4. associate-*r/ 83.1%

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

      5. *-rgt-identity 83.1%

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

   8. Simplified 83.1%

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

   if -1.3e-11 < z < 4.99999999999999989e-121

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 72.2%

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

      1. associate-/r* 72.0%

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

   4. Simplified 72.0%

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

   if 4.99999999999999989e-121 < z < 8.9999999999999993e82

   1. Initial program 97.8%

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

   2. Taylor expanded in t around 0 64.5%

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

      1. associate-*r/ 64.5%

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

      2. neg-mul-1 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in z around 0 44.3%

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

      1. *-commutative 44.3%

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

   7. Simplified 44.3%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+82}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 13: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+80} \lor \neg \left(z \leq 9 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -1.15e+80) (not (<= z 9e+82)))
   (/ (/ x z) z)
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+80) || !(z <= 9e+82)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * 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 <= (-1.15d+80)) .or. (.not. (z <= 9d+82))) then
        tmp = (x / z) / z
    else
        tmp = x / ((y - z) * 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 <= -1.15e+80) || !(z <= 9e+82)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e+80) or not (z <= 9e+82):
		tmp = (x / z) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e+80) || !(z <= 9e+82))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * 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 <= -1.15e+80) || ~((z <= 9e+82)))
		tmp = (x / z) / z;
	else
		tmp = x / ((y - z) * 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, -1.15e+80], N[Not[LessEqual[z, 9e+82]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000002e80 or 8.9999999999999993e82 < z

   1. Initial program 84.9%

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

      1. *-un-lft-identity 84.9%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in z around inf 82.6%

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

      1. *-rgt-identity 82.6%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{{z}^{2}} \]

      2. unpow2 82.6%

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

      3. times-frac 91.4%

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

      4. associate-*r/ 91.4%

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

      5. *-rgt-identity 91.4%

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

   8. Simplified 91.4%

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

   if -1.15000000000000002e80 < z < 8.9999999999999993e82

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 71.7%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+80} \lor \neg \left(z \leq 9 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 14: 46.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+121} \lor \neg \left(z \leq 4.3 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -3.6e+121) (not (<= z 4.3e+67))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e+121) || !(z <= 4.3e+67)) {
		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 <= (-3.6d+121)) .or. (.not. (z <= 4.3d+67))) 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 <= -3.6e+121) || !(z <= 4.3e+67)) {
		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 <= -3.6e+121) or not (z <= 4.3e+67):
		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 <= -3.6e+121) || !(z <= 4.3e+67))
		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 <= -3.6e+121) || ~((z <= 4.3e+67)))
		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, -3.6e+121], N[Not[LessEqual[z, 4.3e+67]], $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 < -3.59999999999999981e121 or 4.3000000000000001e67 < z

   1. Initial program 83.6%

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

   2. Taylor expanded in t around 0 82.6%

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

      1. associate-*r/ 82.6%

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

      2. neg-mul-1 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in z around 0 42.0%

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

      1. *-commutative 42.0%

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

   7. Simplified 42.0%

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

      1. expm1-log1p-u 41.7%

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

      2. expm1-udef 63.1%

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

      3. add-sqr-sqrt 32.0%

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

      4. sqrt-unprod 61.5%

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

      5. sqr-neg 61.5%

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

      6. sqrt-unprod 31.3%

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

      7. add-sqr-sqrt 63.3%

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

      8. associate-/r* 63.3%

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

   9. Applied egg-rr 63.3%

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

       1. expm1-def 48.5%

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

       2. expm1-log1p 48.7%

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

       3. associate-/l/ 40.9%

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

   11. Simplified 40.9%

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

   if -3.59999999999999981e121 < z < 4.3000000000000001e67

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 53.7%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+121} \lor \neg \left(z \leq 4.3 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-17} \lor \neg \left(z \leq 3.3 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -3e-17) (not (<= z 3.3e-95))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e-17) || !(z <= 3.3e-95)) {
		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 <= (-3d-17)) .or. (.not. (z <= 3.3d-95))) 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 <= -3e-17) || !(z <= 3.3e-95)) {
		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 <= -3e-17) or not (z <= 3.3e-95):
		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 <= -3e-17) || !(z <= 3.3e-95))
		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 <= -3e-17) || ~((z <= 3.3e-95)))
		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, -3e-17], N[Not[LessEqual[z, 3.3e-95]], $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 < -3.00000000000000006e-17 or 3.3e-95 < z

   1. Initial program 90.0%

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

   2. Taylor expanded in z around inf 63.3%

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

      1. unpow2 63.3%

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

   4. Simplified 63.3%

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

   if -3.00000000000000006e-17 < z < 3.3e-95

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 70.0%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-17} \lor \neg \left(z \leq 3.3 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 16: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-11} \lor \neg \left(z \leq 3.3 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -1.02e-11) (not (<= z 3.3e-95))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e-11) || !(z <= 3.3e-95)) {
		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 <= (-1.02d-11)) .or. (.not. (z <= 3.3d-95))) 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 <= -1.02e-11) || !(z <= 3.3e-95)) {
		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 <= -1.02e-11) or not (z <= 3.3e-95):
		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 <= -1.02e-11) || !(z <= 3.3e-95))
		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 <= -1.02e-11) || ~((z <= 3.3e-95)))
		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, -1.02e-11], N[Not[LessEqual[z, 3.3e-95]], $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 < -1.01999999999999994e-11 or 3.3e-95 < z

   1. Initial program 90.0%

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

   2. Taylor expanded in z around inf 63.3%

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

      1. unpow2 63.3%

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

   4. Simplified 63.3%

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

   if -1.01999999999999994e-11 < z < 3.3e-95

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 70.0%

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

      1. associate-/r* 69.8%

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

   4. Simplified 69.8%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-11} \lor \neg \left(z \leq 3.3 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 17: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-13} \lor \neg \left(z \leq 3.3 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -4.6e-13) (not (<= z 3.3e-95))) (/ (/ x z) z) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e-13) || !(z <= 3.3e-95)) {
		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 <= (-4.6d-13)) .or. (.not. (z <= 3.3d-95))) 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 <= -4.6e-13) || !(z <= 3.3e-95)) {
		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 <= -4.6e-13) or not (z <= 3.3e-95):
		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 <= -4.6e-13) || !(z <= 3.3e-95))
		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 <= -4.6e-13) || ~((z <= 3.3e-95)))
		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, -4.6e-13], N[Not[LessEqual[z, 3.3e-95]], $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 < -4.59999999999999958e-13 or 3.3e-95 < z

   1. Initial program 90.0%

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

      1. *-un-lft-identity 90.0%

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

      2. times-frac 97.9%

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

   3. Applied egg-rr 97.9%

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

      1. associate-*l/ 98.0%

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

      2. associate-/l* 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in z around inf 63.3%

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

      1. *-rgt-identity 63.3%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{{z}^{2}} \]

      2. unpow2 63.3%

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

      3. times-frac 68.7%

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

      4. associate-*r/ 68.7%

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

      5. *-rgt-identity 68.7%

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

   8. Simplified 68.7%

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

   if -4.59999999999999958e-13 < z < 3.3e-95

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 70.0%

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

      1. associate-/r* 69.8%

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

   4. Simplified 69.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-13} \lor \neg \left(z \leq 3.3 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 18: 39.1% 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 91.9%

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

2. Taylor expanded in z around 0 39.7%

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

3. Final simplification 39.7%

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

Developer target: 87.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(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))))