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

Percentage Accurate: 88.7% → 97.7%

Time: 12.9s

Alternatives: 18

Speedup: 0.5×

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: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -1e-299) t_1 (/ (/ x (- t z)) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -1e-299) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= (-1d-299)) then
        tmp = t_1
    else
        tmp = (x / (t - z)) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -1e-299) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -1e-299:
		tmp = t_1
	else:
		tmp = (x / (t - z)) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -1e-299)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -1e-299)
		tmp = t_1;
	else
		tmp = (x / (t - z)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-299], t$95$1, N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -9.99999999999999992e-300

   1. Initial program 99.5%

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

   if -9.99999999999999992e-300 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 84.7%

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

      1. *-un-lft-identity 84.7%

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

      2. times-frac 97.9%

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

      3. *-commutative 97.9%

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

   3. Applied egg-rr 97.9%

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

      1. un-div-inv 97.9%

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

   5. Applied egg-rr 97.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq -1 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \]

Alternative 2: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-152}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+184}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.3e-163)
   (/ (/ x y) (- t z))
   (if (<= t 7e-152)
     (/ (- x) (* z (- y z)))
     (if (<= t 2.7e-78)
       (/ (/ x (- t z)) y)
       (if (<= t 1.4e+21)
         (/ x (* z (- z t)))
         (if (<= t 6.6e+184) (/ x (* (- y z) t)) (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.3e-163) {
		tmp = (x / y) / (t - z);
	} else if (t <= 7e-152) {
		tmp = -x / (z * (y - z));
	} else if (t <= 2.7e-78) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.4e+21) {
		tmp = x / (z * (z - t));
	} else if (t <= 6.6e+184) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.3d-163)) then
        tmp = (x / y) / (t - z)
    else if (t <= 7d-152) then
        tmp = -x / (z * (y - z))
    else if (t <= 2.7d-78) then
        tmp = (x / (t - z)) / y
    else if (t <= 1.4d+21) then
        tmp = x / (z * (z - t))
    else if (t <= 6.6d+184) then
        tmp = x / ((y - z) * t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.3e-163) {
		tmp = (x / y) / (t - z);
	} else if (t <= 7e-152) {
		tmp = -x / (z * (y - z));
	} else if (t <= 2.7e-78) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.4e+21) {
		tmp = x / (z * (z - t));
	} else if (t <= 6.6e+184) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.3e-163:
		tmp = (x / y) / (t - z)
	elif t <= 7e-152:
		tmp = -x / (z * (y - z))
	elif t <= 2.7e-78:
		tmp = (x / (t - z)) / y
	elif t <= 1.4e+21:
		tmp = x / (z * (z - t))
	elif t <= 6.6e+184:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.3e-163)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 7e-152)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	elseif (t <= 2.7e-78)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 1.4e+21)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	elseif (t <= 6.6e+184)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.3e-163)
		tmp = (x / y) / (t - z);
	elseif (t <= 7e-152)
		tmp = -x / (z * (y - z));
	elseif (t <= 2.7e-78)
		tmp = (x / (t - z)) / y;
	elseif (t <= 1.4e+21)
		tmp = x / (z * (z - t));
	elseif (t <= 6.6e+184)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.3e-163], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-152], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-78], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.4e+21], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+184], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.30000000000000001e-163

   1. Initial program 91.6%

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

      1. *-un-lft-identity 91.6%

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

      2. times-frac 96.0%

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

      3. *-commutative 96.0%

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

   3. Applied egg-rr 96.0%

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

   4. Taylor expanded in y around inf 63.0%

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

      1. associate-/r* 63.5%

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

   6. Simplified 63.5%

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

   if -1.30000000000000001e-163 < t < 7.0000000000000002e-152

   1. Initial program 86.0%

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

   2. Taylor expanded in t around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. neg-mul-1 86.0%

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

   4. Simplified 86.0%

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

   if 7.0000000000000002e-152 < t < 2.69999999999999994e-78

   1. Initial program 98.2%

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

      1. *-un-lft-identity 98.2%

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

      2. times-frac 99.6%

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

      3. *-commutative 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-/r* 94.0%

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

   8. Simplified 94.0%

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

   if 2.69999999999999994e-78 < t < 1.4e21

   1. Initial program 91.4%

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

      1. frac-2neg 91.4%

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

      2. div-inv 91.1%

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

      3. distribute-rgt-neg-in 91.1%

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

   3. Applied egg-rr 91.1%

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

      1. distribute-lft-neg-out 91.1%

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

      2. associate-*r/ 91.4%

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

      3. *-rgt-identity 91.4%

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

      4. distribute-neg-frac 91.4%

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

      5. associate-/r* 95.7%

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

      6. neg-sub0 95.7%

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

      7. associate--r- 95.7%

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

      8. neg-sub0 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in y around 0 69.5%

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

   if 1.4e21 < t < 6.5999999999999996e184

   1. Initial program 84.4%

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

   2. Taylor expanded in t around inf 72.4%

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

   if 6.5999999999999996e184 < t

   1. Initial program 76.7%

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

   2. Taylor expanded in t around inf 76.7%

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

      1. associate-/r* 83.3%

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

   4. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y - z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-152}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+184}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 91.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 5e+299) (/ x t_1) (/ (/ x z) (- z t)))))

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 <= 5e+299) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= 5d+299) then
        tmp = x / t_1
    else
        tmp = (x / z) / (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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+299) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - t);
	}
	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 <= 5e+299:
		tmp = x / t_1
	else:
		tmp = (x / z) / (z - t)
	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 <= 5e+299)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	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 <= 5e+299)
		tmp = x / t_1;
	else
		tmp = (x / z) / (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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+299], N[(x / t$95$1), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 5.0000000000000003e299

   1. Initial program 96.3%

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

   if 5.0000000000000003e299 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 71.3%

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

      1. frac-2neg 71.3%

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

      2. div-inv 71.3%

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

      3. distribute-rgt-neg-in 71.3%

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

   3. Applied egg-rr 71.3%

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

      1. distribute-lft-neg-out 71.3%

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

      2. associate-*r/ 71.3%

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

      3. *-rgt-identity 71.3%

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

      4. distribute-neg-frac 71.3%

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

      5. associate-/r* 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate--r- 99.9%

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

      8. neg-sub0 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 83.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 4: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+83}:\\ \;\;\;\;-\frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-100} \lor \neg \left(y \leq 8500000000000\right) \land y \leq 1.85 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e+83)
   (- (/ x (* y z)))
   (if (or (<= y -8e-100) (and (not (<= y 8500000000000.0)) (<= y 1.85e+151)))
     (/ (/ x t) y)
     (* (/ -1.0 z) (/ x t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e+83) {
		tmp = -(x / (y * z));
	} else if ((y <= -8e-100) || (!(y <= 8500000000000.0) && (y <= 1.85e+151))) {
		tmp = (x / t) / y;
	} else {
		tmp = (-1.0 / z) * (x / 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 (y <= (-3.8d+83)) then
        tmp = -(x / (y * z))
    else if ((y <= (-8d-100)) .or. (.not. (y <= 8500000000000.0d0)) .and. (y <= 1.85d+151)) then
        tmp = (x / t) / y
    else
        tmp = ((-1.0d0) / z) * (x / 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 (y <= -3.8e+83) {
		tmp = -(x / (y * z));
	} else if ((y <= -8e-100) || (!(y <= 8500000000000.0) && (y <= 1.85e+151))) {
		tmp = (x / t) / y;
	} else {
		tmp = (-1.0 / z) * (x / t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e+83:
		tmp = -(x / (y * z))
	elif (y <= -8e-100) or (not (y <= 8500000000000.0) and (y <= 1.85e+151)):
		tmp = (x / t) / y
	else:
		tmp = (-1.0 / z) * (x / t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e+83)
		tmp = Float64(-Float64(x / Float64(y * z)));
	elseif ((y <= -8e-100) || (!(y <= 8500000000000.0) && (y <= 1.85e+151)))
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(-1.0 / z) * Float64(x / t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8e+83)
		tmp = -(x / (y * z));
	elseif ((y <= -8e-100) || (~((y <= 8500000000000.0)) && (y <= 1.85e+151)))
		tmp = (x / t) / y;
	else
		tmp = (-1.0 / z) * (x / 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[LessEqual[y, -3.8e+83], (-N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), If[Or[LessEqual[y, -8e-100], And[N[Not[LessEqual[y, 8500000000000.0]], $MachinePrecision], LessEqual[y, 1.85e+151]]], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e83

   1. Initial program 81.2%

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

   2. Taylor expanded in t around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in z around 0 65.5%

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

      1. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -3.8000000000000002e83 < y < -8.0000000000000002e-100 or 8.5e12 < y < 1.8499999999999999e151

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 47.6%

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

      1. associate-/r* 45.6%

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

   4. Simplified 45.6%

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

   if -8.0000000000000002e-100 < y < 8.5e12 or 1.8499999999999999e151 < y

   1. Initial program 87.3%

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

      1. *-un-lft-identity 87.3%

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

      2. times-frac 94.1%

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

      3. *-commutative 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in y around 0 68.8%

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

   5. Taylor expanded in t around inf 41.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+83}:\\ \;\;\;\;-\frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-100} \lor \neg \left(y \leq 8500000000000\right) \land y \leq 1.85 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \end{array} \]

Alternative 5: 80.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.32e+284)
   (/ (/ x y) (- t z))
   (if (<= y -2.2e-16)
     (/ x (* y (- t z)))
     (if (<= y 1.7e+14) (* (/ x (- t z)) (/ -1.0 z)) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.32e+284) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.2e-16) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.7e+14) {
		tmp = (x / (t - z)) * (-1.0 / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.32d+284)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-2.2d-16)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.7d+14) then
        tmp = (x / (t - z)) * ((-1.0d0) / z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.32e+284) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.2e-16) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.7e+14) {
		tmp = (x / (t - z)) * (-1.0 / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.32e+284:
		tmp = (x / y) / (t - z)
	elif y <= -2.2e-16:
		tmp = x / (y * (t - z))
	elif y <= 1.7e+14:
		tmp = (x / (t - z)) * (-1.0 / z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.32e+284)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -2.2e-16)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.7e+14)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(-1.0 / z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.32e+284)
		tmp = (x / y) / (t - z);
	elseif (y <= -2.2e-16)
		tmp = x / (y * (t - z));
	elseif (y <= 1.7e+14)
		tmp = (x / (t - z)) * (-1.0 / z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.32e+284], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e-16], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+14], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.32e284

   1. Initial program 57.6%

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

      1. *-un-lft-identity 57.6%

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

      2. times-frac 99.6%

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

      3. *-commutative 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around inf 57.6%

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

      1. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

   if -1.32e284 < y < -2.2e-16

   1. Initial program 91.8%

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

   2. Taylor expanded in y around inf 86.9%

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

      1. *-commutative 86.9%

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

   4. Simplified 86.9%

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

   if -2.2e-16 < y < 1.7e14

   1. Initial program 90.8%

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

      1. *-un-lft-identity 90.8%

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

      2. times-frac 96.2%

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

      3. *-commutative 96.2%

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

   3. Applied egg-rr 96.2%

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

   4. Taylor expanded in y around 0 78.7%

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

   if 1.7e14 < y

   1. Initial program 84.8%

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

   2. Taylor expanded in t around inf 56.4%

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

      1. associate-/r* 55.1%

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

   4. Simplified 55.1%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 6: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+83}:\\ \;\;\;\;-\frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-106} \lor \neg \left(y \leq 2150000000000\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.7e+83)
   (- (/ x (* y z)))
   (if (or (<= y -4.8e-106) (not (<= y 2150000000000.0)))
     (/ (/ x t) y)
     (* x (/ (/ -1.0 t) z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.7e+83) {
		tmp = -(x / (y * z));
	} else if ((y <= -4.8e-106) || !(y <= 2150000000000.0)) {
		tmp = (x / t) / y;
	} else {
		tmp = x * ((-1.0 / 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 (y <= (-8.7d+83)) then
        tmp = -(x / (y * z))
    else if ((y <= (-4.8d-106)) .or. (.not. (y <= 2150000000000.0d0))) then
        tmp = (x / t) / y
    else
        tmp = x * (((-1.0d0) / 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 (y <= -8.7e+83) {
		tmp = -(x / (y * z));
	} else if ((y <= -4.8e-106) || !(y <= 2150000000000.0)) {
		tmp = (x / t) / y;
	} else {
		tmp = x * ((-1.0 / t) / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -8.7e+83:
		tmp = -(x / (y * z))
	elif (y <= -4.8e-106) or not (y <= 2150000000000.0):
		tmp = (x / t) / y
	else:
		tmp = x * ((-1.0 / t) / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.7e+83)
		tmp = Float64(-Float64(x / Float64(y * z)));
	elseif ((y <= -4.8e-106) || !(y <= 2150000000000.0))
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x * Float64(Float64(-1.0 / 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 (y <= -8.7e+83)
		tmp = -(x / (y * z));
	elseif ((y <= -4.8e-106) || ~((y <= 2150000000000.0)))
		tmp = (x / t) / y;
	else
		tmp = x * ((-1.0 / 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[y, -8.7e+83], (-N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), If[Or[LessEqual[y, -4.8e-106], N[Not[LessEqual[y, 2150000000000.0]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.7000000000000005e83

   1. Initial program 81.2%

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

   2. Taylor expanded in t around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in z around 0 65.5%

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

      1. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -8.7000000000000005e83 < y < -4.7999999999999995e-106 or 2.15e12 < y

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0 51.0%

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

      1. associate-/r* 49.5%

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

   4. Simplified 49.5%

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

   if -4.7999999999999995e-106 < y < 2.15e12

   1. Initial program 91.1%

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

   2. Taylor expanded in t around inf 60.2%

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

      1. associate-/r* 57.1%

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

   4. Simplified 57.1%

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

      1. associate-/l/ 60.2%

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

      2. div-inv 60.1%

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

      3. *-commutative 60.1%

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

   6. Applied egg-rr 60.1%

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

   7. Taylor expanded in y around 0 49.1%

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

      1. associate-/r* 49.5%

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

   9. Simplified 49.5%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+83}:\\ \;\;\;\;-\frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-106} \lor \neg \left(y \leq 2150000000000\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \end{array} \]

Alternative 7: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e+284)
   (/ (/ x y) (- t z))
   (if (<= y -1.05e-106)
     (/ x (* y (- t z)))
     (if (<= y 1.7e-188) (/ x (* z (- z t))) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+284) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.05e-106) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.7e-188) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1d+284)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-1.05d-106)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.7d-188) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+284) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.05e-106) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.7e-188) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1e+284:
		tmp = (x / y) / (t - z)
	elif y <= -1.05e-106:
		tmp = x / (y * (t - z))
	elif y <= 1.7e-188:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e+284)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -1.05e-106)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.7e-188)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1e+284)
		tmp = (x / y) / (t - z);
	elseif (y <= -1.05e-106)
		tmp = x / (y * (t - z));
	elseif (y <= 1.7e-188)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1e+284], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.05e-106], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-188], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.00000000000000008e284

   1. Initial program 57.6%

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

      1. *-un-lft-identity 57.6%

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

      2. times-frac 99.6%

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

      3. *-commutative 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around inf 57.6%

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

      1. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

   if -1.00000000000000008e284 < y < -1.05000000000000002e-106

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. *-commutative 76.3%

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

   4. Simplified 76.3%

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

   if -1.05000000000000002e-106 < y < 1.70000000000000014e-188

   1. Initial program 93.1%

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

      1. frac-2neg 93.1%

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

      2. div-inv 92.9%

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

      3. distribute-rgt-neg-in 92.9%

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

   3. Applied egg-rr 92.9%

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

      1. distribute-lft-neg-out 92.9%

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

      2. associate-*r/ 93.1%

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

      3. *-rgt-identity 93.1%

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

      4. distribute-neg-frac 93.1%

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

      5. associate-/r* 92.3%

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

      6. neg-sub0 92.3%

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

      7. associate--r- 92.3%

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

      8. neg-sub0 92.3%

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

   5. Simplified 92.3%

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

   6. Taylor expanded in y around 0 85.2%

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

   if 1.70000000000000014e-188 < y

   1. Initial program 85.9%

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

   2. Taylor expanded in t around inf 54.1%

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

      1. associate-/r* 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 8: 79.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e+284)
   (/ (/ x y) (- t z))
   (if (<= y -3.3e-16)
     (/ x (* y (- t z)))
     (if (<= y 68000000000000.0) (/ (/ x z) (- z t)) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+284) {
		tmp = (x / y) / (t - z);
	} else if (y <= -3.3e-16) {
		tmp = x / (y * (t - z));
	} else if (y <= 68000000000000.0) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.45d+284)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-3.3d-16)) then
        tmp = x / (y * (t - z))
    else if (y <= 68000000000000.0d0) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+284) {
		tmp = (x / y) / (t - z);
	} else if (y <= -3.3e-16) {
		tmp = x / (y * (t - z));
	} else if (y <= 68000000000000.0) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e+284:
		tmp = (x / y) / (t - z)
	elif y <= -3.3e-16:
		tmp = x / (y * (t - z))
	elif y <= 68000000000000.0:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e+284)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -3.3e-16)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 68000000000000.0)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e+284)
		tmp = (x / y) / (t - z);
	elseif (y <= -3.3e-16)
		tmp = x / (y * (t - z));
	elseif (y <= 68000000000000.0)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e+284], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-16], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 68000000000000.0], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.44999999999999993e284

   1. Initial program 57.6%

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

      1. *-un-lft-identity 57.6%

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

      2. times-frac 99.6%

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

      3. *-commutative 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around inf 57.6%

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

      1. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

   if -1.44999999999999993e284 < y < -3.29999999999999988e-16

   1. Initial program 91.8%

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

   2. Taylor expanded in y around inf 86.9%

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

      1. *-commutative 86.9%

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

   4. Simplified 86.9%

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

   if -3.29999999999999988e-16 < y < 6.8e13

   1. Initial program 90.8%

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

      1. frac-2neg 90.8%

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

      2. div-inv 90.6%

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

      3. distribute-rgt-neg-in 90.6%

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

   3. Applied egg-rr 90.6%

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

      1. distribute-lft-neg-out 90.6%

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

      2. associate-*r/ 90.8%

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

      3. *-rgt-identity 90.8%

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

      4. distribute-neg-frac 90.8%

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

      5. associate-/r* 94.1%

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

      6. neg-sub0 94.1%

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

      7. associate--r- 94.1%

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

      8. neg-sub0 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in y around 0 79.0%

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

   if 6.8e13 < y

   1. Initial program 85.0%

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

   2. Taylor expanded in t around inf 55.7%

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

      1. associate-/r* 54.3%

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

   4. Simplified 54.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+82}:\\ \;\;\;\;-\frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-101} \lor \neg \left(y \leq 2200000000000\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+82)
   (- (/ x (* y z)))
   (if (or (<= y -1.15e-101) (not (<= y 2200000000000.0)))
     (/ (/ x t) y)
     (/ (- x) (* z t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+82) {
		tmp = -(x / (y * z));
	} else if ((y <= -1.15e-101) || !(y <= 2200000000000.0)) {
		tmp = (x / t) / y;
	} else {
		tmp = -x / (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 (y <= (-7.5d+82)) then
        tmp = -(x / (y * z))
    else if ((y <= (-1.15d-101)) .or. (.not. (y <= 2200000000000.0d0))) then
        tmp = (x / t) / y
    else
        tmp = -x / (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 (y <= -7.5e+82) {
		tmp = -(x / (y * z));
	} else if ((y <= -1.15e-101) || !(y <= 2200000000000.0)) {
		tmp = (x / t) / y;
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+82:
		tmp = -(x / (y * z))
	elif (y <= -1.15e-101) or not (y <= 2200000000000.0):
		tmp = (x / t) / y
	else:
		tmp = -x / (z * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+82)
		tmp = Float64(-Float64(x / Float64(y * z)));
	elseif ((y <= -1.15e-101) || !(y <= 2200000000000.0))
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(-x) / Float64(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 (y <= -7.5e+82)
		tmp = -(x / (y * z));
	elseif ((y <= -1.15e-101) || ~((y <= 2200000000000.0)))
		tmp = (x / t) / y;
	else
		tmp = -x / (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[LessEqual[y, -7.5e+82], (-N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), If[Or[LessEqual[y, -1.15e-101], N[Not[LessEqual[y, 2200000000000.0]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999999e82

   1. Initial program 81.2%

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

   2. Taylor expanded in t around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in z around 0 65.5%

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

      1. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -7.4999999999999999e82 < y < -1.15e-101 or 2.2e12 < y

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0 51.4%

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

      1. associate-/r* 49.9%

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

   4. Simplified 49.9%

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

   if -1.15e-101 < y < 2.2e12

   1. Initial program 91.1%

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

   2. Taylor expanded in t around inf 60.5%

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

      1. associate-/r* 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in y around 0 49.7%

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

      1. associate-*r/ 49.7%

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

      2. neg-mul-1 49.7%

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

   7. Simplified 49.7%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+82}:\\ \;\;\;\;-\frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-101} \lor \neg \left(y \leq 2200000000000\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]

Alternative 10: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0245 \lor \neg \left(z \leq 1.05 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.0245) (not (<= z 1.05e-71)))
   (/ x (* z (- z t)))
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0245) || !(z <= 1.05e-71)) {
		tmp = x / (z * (z - t));
	} 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 <= (-0.0245d0)) .or. (.not. (z <= 1.05d-71))) then
        tmp = x / (z * (z - t))
    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 <= -0.0245) || !(z <= 1.05e-71)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -0.0245) or not (z <= 1.05e-71):
		tmp = x / (z * (z - t))
	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 <= -0.0245) || !(z <= 1.05e-71))
		tmp = Float64(x / Float64(z * Float64(z - t)));
	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 <= -0.0245) || ~((z <= 1.05e-71)))
		tmp = x / (z * (z - t));
	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, -0.0245], N[Not[LessEqual[z, 1.05e-71]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.024500000000000001 or 1.0500000000000001e-71 < z

   1. Initial program 81.8%

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

      1. frac-2neg 81.8%

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

      2. div-inv 81.7%

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

      3. distribute-rgt-neg-in 81.7%

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

   3. Applied egg-rr 81.7%

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

      1. distribute-lft-neg-out 81.7%

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

      2. associate-*r/ 81.8%

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

      3. *-rgt-identity 81.8%

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

      4. distribute-neg-frac 81.8%

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

      5. associate-/r* 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate--r- 99.8%

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

      8. neg-sub0 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 66.2%

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

   if -0.024500000000000001 < z < 1.0500000000000001e-71

   1. Initial program 97.1%

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

   2. Taylor expanded in t around inf 77.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0245 \lor \neg \left(z \leq 1.05 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 11: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-90}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-187}:\\ \;\;\;\;-\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.1e-90)
   (/ (/ x y) t)
   (if (<= t 6.2e-187) (- (/ x (* y z))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-90) {
		tmp = (x / y) / t;
	} else if (t <= 6.2e-187) {
		tmp = -(x / (y * 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 (t <= (-2.1d-90)) then
        tmp = (x / y) / t
    else if (t <= 6.2d-187) then
        tmp = -(x / (y * 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 (t <= -2.1e-90) {
		tmp = (x / y) / t;
	} else if (t <= 6.2e-187) {
		tmp = -(x / (y * z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e-90:
		tmp = (x / y) / t
	elif t <= 6.2e-187:
		tmp = -(x / (y * 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 (t <= -2.1e-90)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 6.2e-187)
		tmp = Float64(-Float64(x / Float64(y * 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 (t <= -2.1e-90)
		tmp = (x / y) / t;
	elseif (t <= 6.2e-187)
		tmp = -(x / (y * 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[LessEqual[t, -2.1e-90], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 6.2e-187], (-N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e-90

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0 51.5%

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

      1. *-un-lft-identity 51.5%

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

      2. times-frac 52.1%

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

   4. Applied egg-rr 52.1%

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

      1. associate-*l/ 52.1%

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

      2. *-un-lft-identity 52.1%

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

   6. Applied egg-rr 52.1%

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

   if -2.0999999999999999e-90 < t < 6.20000000000000039e-187

   1. Initial program 89.1%

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

   2. Taylor expanded in t around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

   4. Simplified 84.1%

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

   5. Taylor expanded in z around 0 54.2%

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

      1. *-commutative 54.2%

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

   7. Simplified 54.2%

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

   if 6.20000000000000039e-187 < t

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 64.1%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-90}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-187}:\\ \;\;\;\;-\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 12: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.06e-106)
   (/ x (* y (- t z)))
   (if (<= y 2.5e-34) (/ x (* z (- z t))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.06e-106) {
		tmp = x / (y * (t - z));
	} else if (y <= 2.5e-34) {
		tmp = x / (z * (z - t));
	} 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 (y <= (-1.06d-106)) then
        tmp = x / (y * (t - z))
    else if (y <= 2.5d-34) then
        tmp = x / (z * (z - t))
    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 (y <= -1.06e-106) {
		tmp = x / (y * (t - z));
	} else if (y <= 2.5e-34) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.06e-106:
		tmp = x / (y * (t - z))
	elif y <= 2.5e-34:
		tmp = x / (z * (z - t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.06e-106)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 2.5e-34)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	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 (y <= -1.06e-106)
		tmp = x / (y * (t - z));
	elseif (y <= 2.5e-34)
		tmp = x / (z * (z - t));
	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[LessEqual[y, -1.06e-106], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-34], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e-106

   1. Initial program 88.3%

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

   2. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

   4. Simplified 74.7%

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

   if -1.06e-106 < y < 2.5000000000000001e-34

   1. Initial program 91.5%

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

      1. frac-2neg 91.5%

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

      2. div-inv 91.3%

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

      3. distribute-rgt-neg-in 91.3%

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

   3. Applied egg-rr 91.3%

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

      1. distribute-lft-neg-out 91.3%

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

      2. associate-*r/ 91.5%

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

      3. *-rgt-identity 91.5%

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

      4. distribute-neg-frac 91.5%

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

      5. associate-/r* 93.6%

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

      6. neg-sub0 93.6%

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

      7. associate--r- 93.6%

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

      8. neg-sub0 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in y around 0 79.7%

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

   if 2.5000000000000001e-34 < y

   1. Initial program 85.1%

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

   2. Taylor expanded in t around inf 56.0%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 13: 77.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.06e-106)
   (/ x (* y (- t z)))
   (if (<= y 1.7e-188) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.06e-106) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.7e-188) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.06d-106)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.7d-188) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.06e-106) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.7e-188) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.06e-106:
		tmp = x / (y * (t - z))
	elif y <= 1.7e-188:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.06e-106)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.7e-188)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.06e-106)
		tmp = x / (y * (t - z));
	elseif (y <= 1.7e-188)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.06e-106], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-188], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e-106

   1. Initial program 88.3%

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

   2. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

   4. Simplified 74.7%

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

   if -1.06e-106 < y < 1.70000000000000014e-188

   1. Initial program 93.1%

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

      1. frac-2neg 93.1%

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

      2. div-inv 92.9%

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

      3. distribute-rgt-neg-in 92.9%

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

   3. Applied egg-rr 92.9%

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

      1. distribute-lft-neg-out 92.9%

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

      2. associate-*r/ 93.1%

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

      3. *-rgt-identity 93.1%

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

      4. distribute-neg-frac 93.1%

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

      5. associate-/r* 92.3%

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

      6. neg-sub0 92.3%

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

      7. associate--r- 92.3%

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

      8. neg-sub0 92.3%

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

   5. Simplified 92.3%

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

   6. Taylor expanded in y around 0 85.2%

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

   if 1.70000000000000014e-188 < y

   1. Initial program 85.9%

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

   2. Taylor expanded in t around inf 54.1%

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

      1. associate-/r* 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 14: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 3000000000000:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e-83)
   (/ (/ x y) t)
   (if (<= y 3000000000000.0) (/ (- x) (* z t)) (/ (/ x t) y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-83) {
		tmp = (x / y) / t;
	} else if (y <= 3000000000000.0) {
		tmp = -x / (z * t);
	} 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 (y <= (-3d-83)) then
        tmp = (x / y) / t
    else if (y <= 3000000000000.0d0) then
        tmp = -x / (z * t)
    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 (y <= -3e-83) {
		tmp = (x / y) / t;
	} else if (y <= 3000000000000.0) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3e-83:
		tmp = (x / y) / t
	elif y <= 3000000000000.0:
		tmp = -x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e-83)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 3000000000000.0)
		tmp = Float64(Float64(-x) / Float64(z * t));
	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 (y <= -3e-83)
		tmp = (x / y) / t;
	elseif (y <= 3000000000000.0)
		tmp = -x / (z * t);
	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[LessEqual[y, -3e-83], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 3000000000000.0], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000001e-83

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 40.4%

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

      1. *-un-lft-identity 40.4%

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

      2. times-frac 44.5%

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

   4. Applied egg-rr 44.5%

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

      1. associate-*l/ 44.6%

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

      2. *-un-lft-identity 44.6%

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

   6. Applied egg-rr 44.6%

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

   if -3.0000000000000001e-83 < y < 3e12

   1. Initial program 91.3%

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

   2. Taylor expanded in t around inf 59.4%

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

      1. associate-/r* 56.5%

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

   4. Simplified 56.5%

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

   5. Taylor expanded in y around 0 48.7%

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

      1. associate-*r/ 48.7%

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

      2. neg-mul-1 48.7%

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

   7. Simplified 48.7%

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

   if 3e12 < y

   1. Initial program 85.0%

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

   2. Taylor expanded in z around 0 53.0%

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

      1. associate-/r* 50.7%

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

   4. Simplified 50.7%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 3000000000000:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 15: 46.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+48} \lor \neg \left(z \leq 3.9 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -2.85e+48) (not (<= z 3.9e-14))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.85e+48) || !(z <= 3.9e-14)) {
		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 <= (-2.85d+48)) .or. (.not. (z <= 3.9d-14))) 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 <= -2.85e+48) || !(z <= 3.9e-14)) {
		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 <= -2.85e+48) or not (z <= 3.9e-14):
		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 <= -2.85e+48) || !(z <= 3.9e-14))
		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 <= -2.85e+48) || ~((z <= 3.9e-14)))
		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, -2.85e+48], N[Not[LessEqual[z, 3.9e-14]], $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 < -2.84999999999999984e48 or 3.8999999999999998e-14 < z

   1. Initial program 79.3%

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

   2. Taylor expanded in y around inf 45.4%

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

      1. *-commutative 45.4%

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

   4. Simplified 45.4%

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

   5. Taylor expanded in t around 0 42.5%

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

      1. associate-/r* 43.9%

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

      2. associate-*r/ 43.9%

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

      3. mul-1-neg 43.9%

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

   7. Simplified 43.9%

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

      1. distribute-frac-neg 43.9%

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

      2. neg-sub0 43.9%

         \[\leadsto \color{blue}{0 - \frac{\frac{x}{y}}{z}} \]

      3. add-sqr-sqrt 29.7%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{\frac{x}{y}} \cdot \sqrt{\frac{x}{y}}}}{z} \]

      4. sqrt-unprod 39.4%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{\frac{x}{y} \cdot \frac{x}{y}}}}{z} \]

      5. sqr-neg 39.4%

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

      6. sqrt-unprod 18.3%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{-\frac{x}{y}} \cdot \sqrt{-\frac{x}{y}}}}{z} \]

      7. add-sqr-sqrt 33.9%

         \[\leadsto 0 - \frac{\color{blue}{-\frac{x}{y}}}{z} \]

      8. distribute-frac-neg 33.9%

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

      9. neg-sub0 33.9%

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

      10. add-sqr-sqrt 23.2%

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

      11. sqrt-unprod 37.8%

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

      12. sqr-neg 37.8%

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

      13. sqrt-unprod 21.7%

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

      14. add-sqr-sqrt 43.9%

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

      15. associate--r- 43.9%

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

      16. metadata-eval 43.9%

          \[\leadsto \color{blue}{0} + \frac{-\frac{x}{y}}{z} \]

   9. Applied egg-rr 37.4%

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

       1. +-lft-identity 37.4%

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

   11. Simplified 37.4%

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

   if -2.84999999999999984e48 < z < 3.8999999999999998e-14

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 51.2%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+48} \lor \neg \left(z \leq 3.9 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 16: 48.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+76} \lor \neg \left(z \leq 2.45 \cdot 10^{+165}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -2.8e+76) (not (<= z 2.45e+165))) (/ x (* y z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+76) || !(z <= 2.45e+165)) {
		tmp = x / (y * 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 <= (-2.8d+76)) .or. (.not. (z <= 2.45d+165))) then
        tmp = x / (y * 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 <= -2.8e+76) || !(z <= 2.45e+165)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+76) or not (z <= 2.45e+165):
		tmp = x / (y * 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 <= -2.8e+76) || !(z <= 2.45e+165))
		tmp = Float64(x / Float64(y * 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 <= -2.8e+76) || ~((z <= 2.45e+165)))
		tmp = x / (y * 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, -2.8e+76], N[Not[LessEqual[z, 2.45e+165]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e76 or 2.44999999999999993e165 < z

   1. Initial program 73.0%

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

   2. Taylor expanded in y around inf 41.6%

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

      1. *-commutative 41.6%

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

   4. Simplified 41.6%

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

   5. Taylor expanded in t around 0 41.5%

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

      1. associate-/r* 42.2%

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

      2. associate-*r/ 42.2%

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

      3. mul-1-neg 42.2%

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

   7. Simplified 42.2%

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

      1. distribute-frac-neg 42.2%

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

      2. neg-sub0 42.2%

         \[\leadsto \color{blue}{0 - \frac{\frac{x}{y}}{z}} \]

      3. add-sqr-sqrt 29.8%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{\frac{x}{y}} \cdot \sqrt{\frac{x}{y}}}}{z} \]

      4. sqrt-unprod 40.7%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{\frac{x}{y} \cdot \frac{x}{y}}}}{z} \]

      5. sqr-neg 40.7%

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

      6. sqrt-unprod 16.4%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{-\frac{x}{y}} \cdot \sqrt{-\frac{x}{y}}}}{z} \]

      7. add-sqr-sqrt 36.3%

         \[\leadsto 0 - \frac{\color{blue}{-\frac{x}{y}}}{z} \]

      8. distribute-frac-neg 36.3%

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

      9. neg-sub0 36.3%

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

      10. add-sqr-sqrt 23.9%

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

      11. sqrt-unprod 36.0%

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

      12. sqr-neg 36.0%

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

      13. sqrt-unprod 16.4%

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

      14. add-sqr-sqrt 42.2%

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

      15. associate--r- 42.2%

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

      16. metadata-eval 42.2%

          \[\leadsto \color{blue}{0} + \frac{-\frac{x}{y}}{z} \]

   9. Applied egg-rr 41.7%

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

       1. +-lft-identity 41.7%

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

   11. Simplified 41.7%

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

   if -2.7999999999999999e76 < z < 2.44999999999999993e165

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 43.7%

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

      1. associate-/r* 46.4%

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

   4. Simplified 46.4%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+76} \lor \neg \left(z \leq 2.45 \cdot 10^{+165}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 17: 49.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e+80)
   (/ x (* y z))
   (if (<= z 3.6e+48) (/ (/ x t) y) (/ (/ x z) y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+80) {
		tmp = x / (y * z);
	} else if (z <= 3.6e+48) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) / 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 <= (-2.9d+80)) then
        tmp = x / (y * z)
    else if (z <= 3.6d+48) then
        tmp = (x / t) / y
    else
        tmp = (x / z) / 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 <= -2.9e+80) {
		tmp = x / (y * z);
	} else if (z <= 3.6e+48) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e+80:
		tmp = x / (y * z)
	elif z <= 3.6e+48:
		tmp = (x / t) / y
	else:
		tmp = (x / z) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e+80)
		tmp = Float64(x / Float64(y * z));
	elseif (z <= 3.6e+48)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / z) / 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 <= -2.9e+80)
		tmp = x / (y * z);
	elseif (z <= 3.6e+48)
		tmp = (x / t) / y;
	else
		tmp = (x / z) / 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[LessEqual[z, -2.9e+80], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+48], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999986e80

   1. Initial program 75.5%

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

   2. Taylor expanded in y around inf 44.0%

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

      1. *-commutative 44.0%

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

   4. Simplified 44.0%

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

   5. Taylor expanded in t around 0 43.9%

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

      1. associate-/r* 42.9%

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

      2. associate-*r/ 42.9%

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

      3. mul-1-neg 42.9%

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

   7. Simplified 42.9%

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

      1. distribute-frac-neg 42.9%

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

      2. neg-sub0 42.9%

         \[\leadsto \color{blue}{0 - \frac{\frac{x}{y}}{z}} \]

      3. add-sqr-sqrt 31.9%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{\frac{x}{y}} \cdot \sqrt{\frac{x}{y}}}}{z} \]

      4. sqrt-unprod 40.8%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{\frac{x}{y} \cdot \frac{x}{y}}}}{z} \]

      5. sqr-neg 40.8%

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

      6. sqrt-unprod 15.6%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{-\frac{x}{y}} \cdot \sqrt{-\frac{x}{y}}}}{z} \]

      7. add-sqr-sqrt 34.9%

         \[\leadsto 0 - \frac{\color{blue}{-\frac{x}{y}}}{z} \]

      8. distribute-frac-neg 34.9%

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

      9. neg-sub0 34.9%

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

      10. add-sqr-sqrt 23.9%

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

      11. sqrt-unprod 34.6%

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

      12. sqr-neg 34.6%

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

      13. sqrt-unprod 15.5%

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

      14. add-sqr-sqrt 42.9%

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

      15. associate--r- 42.9%

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

      16. metadata-eval 42.9%

          \[\leadsto \color{blue}{0} + \frac{-\frac{x}{y}}{z} \]

   9. Applied egg-rr 44.1%

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

       1. +-lft-identity 44.1%

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

   11. Simplified 44.1%

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

   if -2.89999999999999986e80 < z < 3.59999999999999983e48

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 47.4%

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

      1. associate-/r* 48.7%

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

   4. Simplified 48.7%

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

   if 3.59999999999999983e48 < z

   1. Initial program 78.2%

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

   2. Taylor expanded in y around inf 41.8%

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

      1. *-commutative 41.8%

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

   4. Simplified 41.8%

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

   5. Taylor expanded in t around 0 40.0%

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

      1. associate-/r* 42.2%

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

      2. associate-*r/ 42.2%

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

      3. mul-1-neg 42.2%

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

   7. Simplified 42.2%

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

      1. distribute-frac-neg 42.2%

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

      2. neg-sub0 42.2%

         \[\leadsto \color{blue}{0 - \frac{\frac{x}{y}}{z}} \]

      3. add-sqr-sqrt 27.2%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{\frac{x}{y}} \cdot \sqrt{\frac{x}{y}}}}{z} \]

      4. sqrt-unprod 39.4%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{\frac{x}{y} \cdot \frac{x}{y}}}}{z} \]

      5. sqr-neg 39.4%

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

      6. sqrt-unprod 18.4%

         \[\leadsto 0 - \frac{\color{blue}{\sqrt{-\frac{x}{y}} \cdot \sqrt{-\frac{x}{y}}}}{z} \]

      7. add-sqr-sqrt 36.6%

         \[\leadsto 0 - \frac{\color{blue}{-\frac{x}{y}}}{z} \]

      8. distribute-frac-neg 36.6%

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

      9. neg-sub0 36.6%

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

      10. add-sqr-sqrt 25.7%

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

      11. sqrt-unprod 41.5%

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

      12. sqr-neg 41.5%

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

      13. sqrt-unprod 22.5%

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

      14. add-sqr-sqrt 42.2%

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

      15. associate--r- 42.2%

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

      16. metadata-eval 42.2%

          \[\leadsto \color{blue}{0} + \frac{-\frac{x}{y}}{z} \]

   9. Applied egg-rr 36.8%

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

       1. +-lft-identity 36.8%

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

   11. Simplified 36.8%

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

   12. Taylor expanded in x around 0 36.8%

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

       1. *-commutative 36.8%

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

       2. associate-/r* 43.7%

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

   14. Simplified 43.7%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]

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 88.4%

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

2. Taylor expanded in z around 0 35.6%

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

3. Final simplification 35.6%

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

Developer target: 87.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(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))))