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

Percentage Accurate: 89.3% → 95.9%

Time: 11.0s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.3% 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: 95.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.4%

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

   1. associate-/l/ 95.8%

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

3. Simplified 95.8%

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

   1. clear-num 95.7%

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

   2. inv-pow 95.7%

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

5. Applied egg-rr 95.7%

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

   1. div-inv 95.6%

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

   2. unpow-1 95.6%

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

   3. associate-*l/ 96.2%

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

   4. *-un-lft-identity 96.2%

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

   5. associate-/l* 97.5%

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

   6. clear-num 97.2%

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

   7. inv-pow 97.2%

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

   8. *-un-lft-identity 97.2%

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

   9. times-frac 95.8%

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

   10. clear-num 95.8%

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

   11. /-rgt-identity 95.8%

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

7. Applied egg-rr 95.8%

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

   1. unpow-1 95.8%

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

9. Simplified 95.8%

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

10. Final simplification 95.8%

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

Alternative 2: 92.7% accurate, 0.4× speedup

Math

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

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 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x t) (- y z))
     (if (<= t_1 5e+299) (/ x t_1) (/ (/ (- x) z) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x / t) / (y - z);
	} else if (t_1 <= 5e+299) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (y - z);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / t) / (y - z);
	} else if (t_1 <= 5e+299) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / t) / (y - z)
	elif t_1 <= 5e+299:
		tmp = x / t_1
	else:
		tmp = (-x / z) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (t_1 <= 5e+299)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(Float64(-x) / 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 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / t) / (y - z);
	elseif (t_1 <= 5e+299)
		tmp = x / t_1;
	else
		tmp = (-x / 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[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+299], N[(x / t$95$1), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 61.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 87.9%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5.0000000000000003e299

   1. Initial program 98.5%

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

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

   1. Initial program 83.5%

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

   2. Taylor expanded in t around 0 77.6%

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

      1. associate-*r/ 77.6%

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

      2. neg-mul-1 77.6%

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

      3. *-commutative 77.6%

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

      4. associate-/r* 92.7%

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

   4. Simplified 92.7%

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

4. Final simplification 95.7%

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

Alternative 3: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{y \cdot \left(-z\right)}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -420000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)) (t_2 (/ x (* y (- z)))))
   (if (<= z -1.85e+43)
     t_1
     (if (<= z -420000000000.0)
       t_2
       (if (<= z -3.6e-50)
         t_1
         (if (<= z 2.5e-135) (/ x (* y t)) (if (<= z 1.16e+36) t_2 t_1)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / (y * -z);
	double tmp;
	if (z <= -1.85e+43) {
		tmp = t_1;
	} else if (z <= -420000000000.0) {
		tmp = t_2;
	} else if (z <= -3.6e-50) {
		tmp = t_1;
	} else if (z <= 2.5e-135) {
		tmp = x / (y * t);
	} else if (z <= 1.16e+36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / (y * -z)
    if (z <= (-1.85d+43)) then
        tmp = t_1
    else if (z <= (-420000000000.0d0)) then
        tmp = t_2
    else if (z <= (-3.6d-50)) then
        tmp = t_1
    else if (z <= 2.5d-135) then
        tmp = x / (y * t)
    else if (z <= 1.16d+36) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / (y * -z);
	double tmp;
	if (z <= -1.85e+43) {
		tmp = t_1;
	} else if (z <= -420000000000.0) {
		tmp = t_2;
	} else if (z <= -3.6e-50) {
		tmp = t_1;
	} else if (z <= 2.5e-135) {
		tmp = x / (y * t);
	} else if (z <= 1.16e+36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	t_2 = x / (y * -z)
	tmp = 0
	if z <= -1.85e+43:
		tmp = t_1
	elif z <= -420000000000.0:
		tmp = t_2
	elif z <= -3.6e-50:
		tmp = t_1
	elif z <= 2.5e-135:
		tmp = x / (y * t)
	elif z <= 1.16e+36:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	t_2 = Float64(x / Float64(y * Float64(-z)))
	tmp = 0.0
	if (z <= -1.85e+43)
		tmp = t_1;
	elseif (z <= -420000000000.0)
		tmp = t_2;
	elseif (z <= -3.6e-50)
		tmp = t_1;
	elseif (z <= 2.5e-135)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 1.16e+36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	t_2 = x / (y * -z);
	tmp = 0.0;
	if (z <= -1.85e+43)
		tmp = t_1;
	elseif (z <= -420000000000.0)
		tmp = t_2;
	elseif (z <= -3.6e-50)
		tmp = t_1;
	elseif (z <= 2.5e-135)
		tmp = x / (y * t);
	elseif (z <= 1.16e+36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+43], t$95$1, If[LessEqual[z, -420000000000.0], t$95$2, If[LessEqual[z, -3.6e-50], t$95$1, If[LessEqual[z, 2.5e-135], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e+36], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85e43 or -4.2e11 < z < -3.59999999999999979e-50 or 1.15999999999999998e36 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf 75.9%

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

      1. unpow2 75.9%

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

      2. associate-/r* 80.7%

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

   4. Simplified 80.7%

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

   if -1.85e43 < z < -4.2e11 or 2.5000000000000001e-135 < z < 1.15999999999999998e36

   1. Initial program 97.4%

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

   2. Taylor expanded in y around inf 56.2%

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

      1. *-commutative 56.2%

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

   4. Simplified 56.2%

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

   5. Taylor expanded in t around 0 37.5%

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

      1. mul-1-neg 37.5%

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

      2. distribute-rgt-neg-out 37.5%

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

   7. Simplified 37.5%

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

   if -3.59999999999999979e-50 < z < 2.5000000000000001e-135

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 67.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -420000000000:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 4: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{y \cdot \left(-z\right)}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -310000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-61}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)) (t_2 (/ x (* y (- z)))))
   (if (<= z -5.6e+44)
     t_1
     (if (<= z -310000000.0)
       t_2
       (if (<= z -1.02e-61)
         (/ (- x) (* z t))
         (if (<= z 1.06e-106) (/ x (* y t)) (if (<= z 9e+35) t_2 t_1)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / (y * -z);
	double tmp;
	if (z <= -5.6e+44) {
		tmp = t_1;
	} else if (z <= -310000000.0) {
		tmp = t_2;
	} else if (z <= -1.02e-61) {
		tmp = -x / (z * t);
	} else if (z <= 1.06e-106) {
		tmp = x / (y * t);
	} else if (z <= 9e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / (y * -z)
    if (z <= (-5.6d+44)) then
        tmp = t_1
    else if (z <= (-310000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.02d-61)) then
        tmp = -x / (z * t)
    else if (z <= 1.06d-106) then
        tmp = x / (y * t)
    else if (z <= 9d+35) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / (y * -z);
	double tmp;
	if (z <= -5.6e+44) {
		tmp = t_1;
	} else if (z <= -310000000.0) {
		tmp = t_2;
	} else if (z <= -1.02e-61) {
		tmp = -x / (z * t);
	} else if (z <= 1.06e-106) {
		tmp = x / (y * t);
	} else if (z <= 9e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	t_2 = x / (y * -z)
	tmp = 0
	if z <= -5.6e+44:
		tmp = t_1
	elif z <= -310000000.0:
		tmp = t_2
	elif z <= -1.02e-61:
		tmp = -x / (z * t)
	elif z <= 1.06e-106:
		tmp = x / (y * t)
	elif z <= 9e+35:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	t_2 = Float64(x / Float64(y * Float64(-z)))
	tmp = 0.0
	if (z <= -5.6e+44)
		tmp = t_1;
	elseif (z <= -310000000.0)
		tmp = t_2;
	elseif (z <= -1.02e-61)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 1.06e-106)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 9e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	t_2 = x / (y * -z);
	tmp = 0.0;
	if (z <= -5.6e+44)
		tmp = t_1;
	elseif (z <= -310000000.0)
		tmp = t_2;
	elseif (z <= -1.02e-61)
		tmp = -x / (z * t);
	elseif (z <= 1.06e-106)
		tmp = x / (y * t);
	elseif (z <= 9e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+44], t$95$1, If[LessEqual[z, -310000000.0], t$95$2, If[LessEqual[z, -1.02e-61], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-106], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+35], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.6000000000000002e44 or 8.9999999999999993e35 < z

   1. Initial program 84.6%

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

   2. Taylor expanded in z around inf 80.9%

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

      1. unpow2 80.9%

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

      2. associate-/r* 86.3%

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

   4. Simplified 86.3%

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

   if -5.6000000000000002e44 < z < -3.1e8 or 1.06e-106 < z < 8.9999999999999993e35

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 57.2%

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

      1. *-commutative 57.2%

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

   4. Simplified 57.2%

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

   5. Taylor expanded in t around 0 36.7%

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

      1. mul-1-neg 36.7%

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

      2. distribute-rgt-neg-out 36.7%

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

   7. Simplified 36.7%

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

   if -3.1e8 < z < -1.02e-61

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-frac-neg 59.2%

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

      3. associate-/r* 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in z around 0 29.8%

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

      1. associate-*r/ 29.8%

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

      2. neg-mul-1 29.8%

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

      3. *-commutative 29.8%

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

   7. Simplified 29.8%

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

   if -1.02e-61 < z < 1.06e-106

   1. Initial program 92.8%

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

   2. Taylor expanded in z around 0 67.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -310000000:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-61}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 5: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{y \cdot \left(-z\right)}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -220:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)) (t_2 (/ x (* y (- z)))))
   (if (<= z -1.3e+45)
     t_1
     (if (<= z -220.0)
       t_2
       (if (<= z -2.65e-58)
         (/ (/ (- x) t) z)
         (if (<= z 1.55e-108) (/ x (* y t)) (if (<= z 2.9e+38) t_2 t_1)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / (y * -z);
	double tmp;
	if (z <= -1.3e+45) {
		tmp = t_1;
	} else if (z <= -220.0) {
		tmp = t_2;
	} else if (z <= -2.65e-58) {
		tmp = (-x / t) / z;
	} else if (z <= 1.55e-108) {
		tmp = x / (y * t);
	} else if (z <= 2.9e+38) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / (y * -z)
    if (z <= (-1.3d+45)) then
        tmp = t_1
    else if (z <= (-220.0d0)) then
        tmp = t_2
    else if (z <= (-2.65d-58)) then
        tmp = (-x / t) / z
    else if (z <= 1.55d-108) then
        tmp = x / (y * t)
    else if (z <= 2.9d+38) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / (y * -z);
	double tmp;
	if (z <= -1.3e+45) {
		tmp = t_1;
	} else if (z <= -220.0) {
		tmp = t_2;
	} else if (z <= -2.65e-58) {
		tmp = (-x / t) / z;
	} else if (z <= 1.55e-108) {
		tmp = x / (y * t);
	} else if (z <= 2.9e+38) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	t_2 = x / (y * -z)
	tmp = 0
	if z <= -1.3e+45:
		tmp = t_1
	elif z <= -220.0:
		tmp = t_2
	elif z <= -2.65e-58:
		tmp = (-x / t) / z
	elif z <= 1.55e-108:
		tmp = x / (y * t)
	elif z <= 2.9e+38:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	t_2 = Float64(x / Float64(y * Float64(-z)))
	tmp = 0.0
	if (z <= -1.3e+45)
		tmp = t_1;
	elseif (z <= -220.0)
		tmp = t_2;
	elseif (z <= -2.65e-58)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 1.55e-108)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 2.9e+38)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	t_2 = x / (y * -z);
	tmp = 0.0;
	if (z <= -1.3e+45)
		tmp = t_1;
	elseif (z <= -220.0)
		tmp = t_2;
	elseif (z <= -2.65e-58)
		tmp = (-x / t) / z;
	elseif (z <= 1.55e-108)
		tmp = x / (y * t);
	elseif (z <= 2.9e+38)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+45], t$95$1, If[LessEqual[z, -220.0], t$95$2, If[LessEqual[z, -2.65e-58], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.55e-108], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+38], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.30000000000000004e45 or 2.90000000000000007e38 < z

   1. Initial program 84.6%

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

   2. Taylor expanded in z around inf 80.9%

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

      1. unpow2 80.9%

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

      2. associate-/r* 86.3%

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

   4. Simplified 86.3%

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

   if -1.30000000000000004e45 < z < -220 or 1.55000000000000007e-108 < z < 2.90000000000000007e38

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 57.2%

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

      1. *-commutative 57.2%

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

   4. Simplified 57.2%

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

   5. Taylor expanded in t around 0 36.7%

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

      1. mul-1-neg 36.7%

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

      2. distribute-rgt-neg-out 36.7%

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

   7. Simplified 36.7%

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

   if -220 < z < -2.6500000000000002e-58

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-frac-neg 59.2%

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

      3. associate-/r* 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in z around 0 29.8%

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

      1. associate-*r/ 29.8%

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

      2. neg-mul-1 29.8%

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

      3. *-commutative 29.8%

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

   7. Simplified 29.8%

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

   8. Taylor expanded in x around 0 29.8%

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

      1. mul-1-neg 29.8%

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

      2. associate-/r* 29.7%

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

      3. distribute-neg-frac 29.7%

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

   10. Simplified 29.7%

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

   if -2.6500000000000002e-58 < z < 1.55000000000000007e-108

   1. Initial program 92.8%

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

   2. Taylor expanded in z around 0 67.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -220:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 6: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -2.6e+46)
     t_1
     (if (<= z -8.8)
       (/ (/ (- x) y) z)
       (if (<= z -1.5e-64)
         (/ (/ (- x) t) z)
         (if (<= z 4.2e-106)
           (/ x (* y t))
           (if (<= z 1.65e+34) (/ x (* y (- z))) t_1)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -2.6e+46) {
		tmp = t_1;
	} else if (z <= -8.8) {
		tmp = (-x / y) / z;
	} else if (z <= -1.5e-64) {
		tmp = (-x / t) / z;
	} else if (z <= 4.2e-106) {
		tmp = x / (y * t);
	} else if (z <= 1.65e+34) {
		tmp = x / (y * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-2.6d+46)) then
        tmp = t_1
    else if (z <= (-8.8d0)) then
        tmp = (-x / y) / z
    else if (z <= (-1.5d-64)) then
        tmp = (-x / t) / z
    else if (z <= 4.2d-106) then
        tmp = x / (y * t)
    else if (z <= 1.65d+34) then
        tmp = x / (y * -z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -2.6e+46) {
		tmp = t_1;
	} else if (z <= -8.8) {
		tmp = (-x / y) / z;
	} else if (z <= -1.5e-64) {
		tmp = (-x / t) / z;
	} else if (z <= 4.2e-106) {
		tmp = x / (y * t);
	} else if (z <= 1.65e+34) {
		tmp = x / (y * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -2.6e+46:
		tmp = t_1
	elif z <= -8.8:
		tmp = (-x / y) / z
	elif z <= -1.5e-64:
		tmp = (-x / t) / z
	elif z <= 4.2e-106:
		tmp = x / (y * t)
	elif z <= 1.65e+34:
		tmp = x / (y * -z)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -2.6e+46)
		tmp = t_1;
	elseif (z <= -8.8)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= -1.5e-64)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 4.2e-106)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 1.65e+34)
		tmp = Float64(x / Float64(y * Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -2.6e+46)
		tmp = t_1;
	elseif (z <= -8.8)
		tmp = (-x / y) / z;
	elseif (z <= -1.5e-64)
		tmp = (-x / t) / z;
	elseif (z <= 4.2e-106)
		tmp = x / (y * t);
	elseif (z <= 1.65e+34)
		tmp = x / (y * -z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -2.6e+46], t$95$1, If[LessEqual[z, -8.8], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.5e-64], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.2e-106], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+34], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.60000000000000013e46 or 1.64999999999999994e34 < z

   1. Initial program 84.6%

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

   2. Taylor expanded in z around inf 80.9%

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

      1. unpow2 80.9%

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

      2. associate-/r* 86.3%

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

   4. Simplified 86.3%

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

   if -2.60000000000000013e46 < z < -8.8000000000000007

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-/r* 49.6%

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

      3. distribute-neg-frac 49.6%

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

      4. distribute-neg-frac 49.6%

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

   7. Simplified 49.6%

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

   if -8.8000000000000007 < z < -1.5e-64

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-frac-neg 59.2%

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

      3. associate-/r* 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in z around 0 29.8%

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

      1. associate-*r/ 29.8%

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

      2. neg-mul-1 29.8%

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

      3. *-commutative 29.8%

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

   7. Simplified 29.8%

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

   8. Taylor expanded in x around 0 29.8%

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

      1. mul-1-neg 29.8%

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

      2. associate-/r* 29.7%

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

      3. distribute-neg-frac 29.7%

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

   10. Simplified 29.7%

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

   if -1.5e-64 < z < 4.20000000000000007e-106

   1. Initial program 92.8%

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

   2. Taylor expanded in z around 0 67.6%

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

   if 4.20000000000000007e-106 < z < 1.64999999999999994e34

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 55.6%

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

      1. *-commutative 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in t around 0 33.8%

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

      1. mul-1-neg 33.8%

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

      2. distribute-rgt-neg-out 33.8%

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

   7. Simplified 33.8%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(-z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -8.8:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 7: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 10^{-106}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -3.2e+45)
     t_1
     (if (<= z -2.4)
       (/ (/ (- x) y) z)
       (if (<= z -4.7e-58)
         (/ (/ (- x) t) z)
         (if (<= z 1e-106)
           (/ 1.0 (/ y (/ x t)))
           (if (<= z 1.7e+38) (/ x (* y (- z))) t_1)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -3.2e+45) {
		tmp = t_1;
	} else if (z <= -2.4) {
		tmp = (-x / y) / z;
	} else if (z <= -4.7e-58) {
		tmp = (-x / t) / z;
	} else if (z <= 1e-106) {
		tmp = 1.0 / (y / (x / t));
	} else if (z <= 1.7e+38) {
		tmp = x / (y * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-3.2d+45)) then
        tmp = t_1
    else if (z <= (-2.4d0)) then
        tmp = (-x / y) / z
    else if (z <= (-4.7d-58)) then
        tmp = (-x / t) / z
    else if (z <= 1d-106) then
        tmp = 1.0d0 / (y / (x / t))
    else if (z <= 1.7d+38) then
        tmp = x / (y * -z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -3.2e+45) {
		tmp = t_1;
	} else if (z <= -2.4) {
		tmp = (-x / y) / z;
	} else if (z <= -4.7e-58) {
		tmp = (-x / t) / z;
	} else if (z <= 1e-106) {
		tmp = 1.0 / (y / (x / t));
	} else if (z <= 1.7e+38) {
		tmp = x / (y * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -3.2e+45:
		tmp = t_1
	elif z <= -2.4:
		tmp = (-x / y) / z
	elif z <= -4.7e-58:
		tmp = (-x / t) / z
	elif z <= 1e-106:
		tmp = 1.0 / (y / (x / t))
	elif z <= 1.7e+38:
		tmp = x / (y * -z)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -3.2e+45)
		tmp = t_1;
	elseif (z <= -2.4)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= -4.7e-58)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 1e-106)
		tmp = Float64(1.0 / Float64(y / Float64(x / t)));
	elseif (z <= 1.7e+38)
		tmp = Float64(x / Float64(y * Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -3.2e+45)
		tmp = t_1;
	elseif (z <= -2.4)
		tmp = (-x / y) / z;
	elseif (z <= -4.7e-58)
		tmp = (-x / t) / z;
	elseif (z <= 1e-106)
		tmp = 1.0 / (y / (x / t));
	elseif (z <= 1.7e+38)
		tmp = x / (y * -z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -3.2e+45], t$95$1, If[LessEqual[z, -2.4], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -4.7e-58], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1e-106], N[(1.0 / N[(y / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+38], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.2000000000000003e45 or 1.69999999999999998e38 < z

   1. Initial program 84.6%

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

   2. Taylor expanded in z around inf 80.9%

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

      1. unpow2 80.9%

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

      2. associate-/r* 86.3%

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

   4. Simplified 86.3%

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

   if -3.2000000000000003e45 < z < -2.39999999999999991

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-/r* 49.6%

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

      3. distribute-neg-frac 49.6%

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

      4. distribute-neg-frac 49.6%

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

   7. Simplified 49.6%

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

   if -2.39999999999999991 < z < -4.69999999999999994e-58

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-frac-neg 59.2%

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

      3. associate-/r* 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in z around 0 29.8%

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

      1. associate-*r/ 29.8%

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

      2. neg-mul-1 29.8%

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

      3. *-commutative 29.8%

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

   7. Simplified 29.8%

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

   8. Taylor expanded in x around 0 29.8%

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

      1. mul-1-neg 29.8%

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

      2. associate-/r* 29.7%

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

      3. distribute-neg-frac 29.7%

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

   10. Simplified 29.7%

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

   if -4.69999999999999994e-58 < z < 9.99999999999999941e-107

   1. Initial program 92.8%

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

      1. associate-/l/ 89.3%

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

   3. Simplified 89.3%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

   5. Applied egg-rr 89.2%

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

      1. div-inv 89.2%

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

      2. unpow-1 89.2%

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

      3. associate-*l/ 89.9%

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

      4. *-un-lft-identity 89.9%

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

      5. associate-/l* 92.8%

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

      6. clear-num 92.9%

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

      7. inv-pow 92.9%

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

      8. *-un-lft-identity 92.9%

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

      9. times-frac 89.8%

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

      10. clear-num 89.8%

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

      11. /-rgt-identity 89.8%

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

   7. Applied egg-rr 89.8%

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

      1. unpow-1 89.8%

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

   9. Simplified 89.8%

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

   10. Taylor expanded in z around 0 67.6%

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

       1. associate-/l* 67.2%

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

   12. Simplified 67.2%

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

   if 9.99999999999999941e-107 < z < 1.69999999999999998e38

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 55.6%

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

      1. *-commutative 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in t around 0 33.8%

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

      1. mul-1-neg 33.8%

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

      2. distribute-rgt-neg-out 33.8%

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

   7. Simplified 33.8%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(-z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -2.4:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 10^{-106}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 8: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1020000000:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-11} \lor \neg \left(z \leq 9.8 \cdot 10^{+32}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -2.5e+43)
     t_1
     (if (<= z -1020000000.0)
       (/ (/ (- x) y) z)
       (if (or (<= z -3.5e-11) (not (<= z 9.8e+32)))
         t_1
         (/ x (* (- y z) t)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -2.5e+43) {
		tmp = t_1;
	} else if (z <= -1020000000.0) {
		tmp = (-x / y) / z;
	} else if ((z <= -3.5e-11) || !(z <= 9.8e+32)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-2.5d+43)) then
        tmp = t_1
    else if (z <= (-1020000000.0d0)) then
        tmp = (-x / y) / z
    else if ((z <= (-3.5d-11)) .or. (.not. (z <= 9.8d+32))) then
        tmp = t_1
    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 t_1 = (x / z) / z;
	double tmp;
	if (z <= -2.5e+43) {
		tmp = t_1;
	} else if (z <= -1020000000.0) {
		tmp = (-x / y) / z;
	} else if ((z <= -3.5e-11) || !(z <= 9.8e+32)) {
		tmp = t_1;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -2.5e+43:
		tmp = t_1
	elif z <= -1020000000.0:
		tmp = (-x / y) / z
	elif (z <= -3.5e-11) or not (z <= 9.8e+32):
		tmp = t_1
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -2.5e+43)
		tmp = t_1;
	elseif (z <= -1020000000.0)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif ((z <= -3.5e-11) || !(z <= 9.8e+32))
		tmp = t_1;
	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)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -2.5e+43)
		tmp = t_1;
	elseif (z <= -1020000000.0)
		tmp = (-x / y) / z;
	elseif ((z <= -3.5e-11) || ~((z <= 9.8e+32)))
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -2.5e+43], t$95$1, If[LessEqual[z, -1020000000.0], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, -3.5e-11], N[Not[LessEqual[z, 9.8e+32]], $MachinePrecision]], t$95$1, N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5000000000000002e43 or -1.02e9 < z < -3.50000000000000019e-11 or 9.8000000000000003e32 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf 79.5%

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

      1. unpow2 79.5%

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

      2. associate-/r* 84.6%

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

   4. Simplified 84.6%

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

   if -2.5000000000000002e43 < z < -1.02e9

   1. Initial program 86.7%

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

   2. Taylor expanded in y around inf 59.6%

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

      1. *-commutative 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in t around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. associate-/r* 56.2%

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

      3. distribute-neg-frac 56.2%

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

      4. distribute-neg-frac 56.2%

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

   7. Simplified 56.2%

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

   if -3.50000000000000019e-11 < z < 9.8000000000000003e32

   1. Initial program 95.3%

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

   2. Taylor expanded in t around inf 70.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1020000000:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-11} \lor \neg \left(z \leq 9.8 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 9: 66.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -118000000:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+24}:\\ \;\;\;\;\frac{1}{\frac{t}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -8.6e+44)
     t_1
     (if (<= z -118000000.0)
       (/ (/ (- x) y) z)
       (if (<= z -7.5e-59)
         (/ (/ (- x) t) z)
         (if (<= z 1.75e+24) (/ 1.0 (/ t (/ x y))) t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -8.6e+44) {
		tmp = t_1;
	} else if (z <= -118000000.0) {
		tmp = (-x / y) / z;
	} else if (z <= -7.5e-59) {
		tmp = (-x / t) / z;
	} else if (z <= 1.75e+24) {
		tmp = 1.0 / (t / (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-8.6d+44)) then
        tmp = t_1
    else if (z <= (-118000000.0d0)) then
        tmp = (-x / y) / z
    else if (z <= (-7.5d-59)) then
        tmp = (-x / t) / z
    else if (z <= 1.75d+24) then
        tmp = 1.0d0 / (t / (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -8.6e+44) {
		tmp = t_1;
	} else if (z <= -118000000.0) {
		tmp = (-x / y) / z;
	} else if (z <= -7.5e-59) {
		tmp = (-x / t) / z;
	} else if (z <= 1.75e+24) {
		tmp = 1.0 / (t / (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -8.6e+44:
		tmp = t_1
	elif z <= -118000000.0:
		tmp = (-x / y) / z
	elif z <= -7.5e-59:
		tmp = (-x / t) / z
	elif z <= 1.75e+24:
		tmp = 1.0 / (t / (x / y))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -8.6e+44)
		tmp = t_1;
	elseif (z <= -118000000.0)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= -7.5e-59)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 1.75e+24)
		tmp = Float64(1.0 / Float64(t / Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -8.6e+44)
		tmp = t_1;
	elseif (z <= -118000000.0)
		tmp = (-x / y) / z;
	elseif (z <= -7.5e-59)
		tmp = (-x / t) / z;
	elseif (z <= 1.75e+24)
		tmp = 1.0 / (t / (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -8.6e+44], t$95$1, If[LessEqual[z, -118000000.0], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -7.5e-59], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.75e+24], N[(1.0 / N[(t / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.59999999999999965e44 or 1.7500000000000001e24 < z

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf 79.1%

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

      1. unpow2 79.1%

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

      2. associate-/r* 84.3%

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

   4. Simplified 84.3%

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

   if -8.59999999999999965e44 < z < -1.18e8

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-/r* 49.6%

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

      3. distribute-neg-frac 49.6%

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

      4. distribute-neg-frac 49.6%

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

   7. Simplified 49.6%

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

   if -1.18e8 < z < -7.50000000000000019e-59

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-frac-neg 59.2%

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

      3. associate-/r* 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in z around 0 29.8%

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

      1. associate-*r/ 29.8%

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

      2. neg-mul-1 29.8%

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

      3. *-commutative 29.8%

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

   7. Simplified 29.8%

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

   8. Taylor expanded in x around 0 29.8%

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

      1. mul-1-neg 29.8%

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

      2. associate-/r* 29.7%

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

      3. distribute-neg-frac 29.7%

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

   10. Simplified 29.7%

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

   if -7.50000000000000019e-59 < z < 1.7500000000000001e24

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 59.0%

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

      1. clear-num 59.0%

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

      2. inv-pow 59.0%

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

      3. *-commutative 59.0%

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

   4. Applied egg-rr 59.0%

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

      1. unpow-1 59.0%

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

      2. associate-/l* 62.2%

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

   6. Simplified 62.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -118000000:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+24}:\\ \;\;\;\;\frac{1}{\frac{t}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 10: 79.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) (- t z))))
   (if (<= y -1.35e+145)
     t_1
     (if (<= y -9.8e+48)
       (/ x (* y (- t z)))
       (if (<= y -4.8e-26)
         t_1
         (if (<= y 3.4e-98) (/ x (* z (- z t))) (/ x (* (- y z) t))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / (t - z);
	double tmp;
	if (y <= -1.35e+145) {
		tmp = t_1;
	} else if (y <= -9.8e+48) {
		tmp = x / (y * (t - z));
	} else if (y <= -4.8e-26) {
		tmp = t_1;
	} else if (y <= 3.4e-98) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / (t - z)
    if (y <= (-1.35d+145)) then
        tmp = t_1
    else if (y <= (-9.8d+48)) then
        tmp = x / (y * (t - z))
    else if (y <= (-4.8d-26)) then
        tmp = t_1
    else if (y <= 3.4d-98) 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 t_1 = (x / y) / (t - z);
	double tmp;
	if (y <= -1.35e+145) {
		tmp = t_1;
	} else if (y <= -9.8e+48) {
		tmp = x / (y * (t - z));
	} else if (y <= -4.8e-26) {
		tmp = t_1;
	} else if (y <= 3.4e-98) {
		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):
	t_1 = (x / y) / (t - z)
	tmp = 0
	if y <= -1.35e+145:
		tmp = t_1
	elif y <= -9.8e+48:
		tmp = x / (y * (t - z))
	elif y <= -4.8e-26:
		tmp = t_1
	elif y <= 3.4e-98:
		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)
	t_1 = Float64(Float64(x / y) / Float64(t - z))
	tmp = 0.0
	if (y <= -1.35e+145)
		tmp = t_1;
	elseif (y <= -9.8e+48)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -4.8e-26)
		tmp = t_1;
	elseif (y <= 3.4e-98)
		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)
	t_1 = (x / y) / (t - z);
	tmp = 0.0;
	if (y <= -1.35e+145)
		tmp = t_1;
	elseif (y <= -9.8e+48)
		tmp = x / (y * (t - z));
	elseif (y <= -4.8e-26)
		tmp = t_1;
	elseif (y <= 3.4e-98)
		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_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+145], t$95$1, If[LessEqual[y, -9.8e+48], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-26], t$95$1, If[LessEqual[y, 3.4e-98], 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 4 regimes

2. if y < -1.35000000000000011e145 or -9.80000000000000059e48 < y < -4.8000000000000002e-26

   1. Initial program 84.7%

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

      1. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 90.1%

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

   if -1.35000000000000011e145 < y < -9.80000000000000059e48

   1. Initial program 84.6%

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

   2. Taylor expanded in y around inf 79.4%

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

      1. *-commutative 79.4%

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

   4. Simplified 79.4%

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

   if -4.8000000000000002e-26 < y < 3.4000000000000001e-98

   1. Initial program 94.1%

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

      1. associate-/l/ 95.6%

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

   3. Simplified 95.6%

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

      1. clear-num 95.5%

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

      2. inv-pow 95.5%

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

   5. Applied egg-rr 95.5%

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

      1. div-inv 95.5%

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

      2. unpow-1 95.5%

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

      3. associate-*l/ 95.6%

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

      4. *-un-lft-identity 95.6%

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

      5. associate-/l* 97.5%

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

      6. clear-num 96.7%

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

      7. inv-pow 96.7%

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

      8. *-un-lft-identity 96.7%

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

      9. times-frac 94.6%

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

      10. clear-num 94.7%

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

      11. /-rgt-identity 94.7%

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

   7. Applied egg-rr 94.7%

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

      1. unpow-1 94.7%

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

   9. Simplified 94.7%

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

       1. frac-2neg 94.7%

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

       2. div-inv 94.6%

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

       3. add-sqr-sqrt 51.3%

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

       4. sqrt-unprod 52.0%

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

       5. sqr-neg 52.0%

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

       6. sqrt-unprod 13.2%

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

       7. add-sqr-sqrt 33.5%

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

       8. frac-2neg 33.5%

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

       9. metadata-eval 33.5%

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

       10. add-sqr-sqrt 20.2%

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

       11. sqrt-unprod 50.9%

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

       12. sqr-neg 50.9%

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

       13. sqrt-unprod 43.2%

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

       14. add-sqr-sqrt 94.6%

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

   11. Applied egg-rr 94.6%

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

   12. Taylor expanded in y around 0 88.4%

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

   if 3.4000000000000001e-98 < y

   1. Initial program 92.5%

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

   2. Taylor expanded in t around inf 57.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+145}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 11: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e-25)
   (/ (/ x (- t z)) y)
   (if (<= y 6.5e-97) (/ (/ (- x) z) (- t z)) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e-25) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 6.5e-97) {
		tmp = (-x / z) / (t - 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 (y <= (-7.6d-25)) then
        tmp = (x / (t - z)) / y
    else if (y <= 6.5d-97) then
        tmp = (-x / z) / (t - 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 (y <= -7.6e-25) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 6.5e-97) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -7.6e-25:
		tmp = (x / (t - z)) / y
	elif y <= 6.5e-97:
		tmp = (-x / z) / (t - 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 (y <= -7.6e-25)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 6.5e-97)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - 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 (y <= -7.6e-25)
		tmp = (x / (t - z)) / y;
	elseif (y <= 6.5e-97)
		tmp = (-x / z) / (t - 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[y, -7.6e-25], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6.5e-97], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5999999999999996e-25

   1. Initial program 84.7%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/r* 83.8%

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

   4. Simplified 83.8%

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

   if -7.5999999999999996e-25 < y < 6.5000000000000004e-97

   1. Initial program 94.1%

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

   2. Taylor expanded in y around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. distribute-frac-neg 88.4%

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

      3. associate-/r* 91.0%

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

   4. Simplified 91.0%

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

   if 6.5000000000000004e-97 < y

   1. Initial program 92.5%

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

   2. Taylor expanded in t around inf 57.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 12: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-305}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-25)
   (/ x (* y (- t z)))
   (if (<= y 7.5e-305) (/ (/ x z) z) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-25) {
		tmp = x / (y * (t - z));
	} else if (y <= 7.5e-305) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d-25)) then
        tmp = x / (y * (t - z))
    else if (y <= 7.5d-305) then
        tmp = (x / z) / z
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-25) {
		tmp = x / (y * (t - z));
	} else if (y <= 7.5e-305) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-25:
		tmp = x / (y * (t - z))
	elif y <= 7.5e-305:
		tmp = (x / z) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-25)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 7.5e-305)
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-25)
		tmp = x / (y * (t - z));
	elseif (y <= 7.5e-305)
		tmp = (x / z) / z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-25], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-305], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000002e-25

   1. Initial program 84.7%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -3.40000000000000002e-25 < y < 7.5000000000000003e-305

   1. Initial program 93.9%

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

   2. Taylor expanded in z around inf 68.9%

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

      1. unpow2 68.9%

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

      2. associate-/r* 73.3%

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

   4. Simplified 73.3%

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

   if 7.5000000000000003e-305 < y

   1. Initial program 93.1%

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

   2. Taylor expanded in t around inf 58.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-305}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 13: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e-25)
   (/ x (* y (- t z)))
   (if (<= y 1.5e-99) (/ 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 <= -4.2e-25) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.5e-99) {
		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 <= (-4.2d-25)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.5d-99) 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 <= -4.2e-25) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.5e-99) {
		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 <= -4.2e-25:
		tmp = x / (y * (t - z))
	elif y <= 1.5e-99:
		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 <= -4.2e-25)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.5e-99)
		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 <= -4.2e-25)
		tmp = x / (y * (t - z));
	elseif (y <= 1.5e-99)
		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, -4.2e-25], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-99], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.20000000000000005e-25

   1. Initial program 84.7%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -4.20000000000000005e-25 < y < 1.50000000000000003e-99

   1. Initial program 94.1%

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

      1. associate-/l/ 95.6%

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

   3. Simplified 95.6%

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

      1. clear-num 95.5%

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

      2. inv-pow 95.5%

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

   5. Applied egg-rr 95.5%

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

      1. div-inv 95.5%

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

      2. unpow-1 95.5%

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

      3. associate-*l/ 95.6%

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

      4. *-un-lft-identity 95.6%

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

      5. associate-/l* 97.5%

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

      6. clear-num 96.7%

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

      7. inv-pow 96.7%

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

      8. *-un-lft-identity 96.7%

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

      9. times-frac 94.6%

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

      10. clear-num 94.7%

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

      11. /-rgt-identity 94.7%

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

   7. Applied egg-rr 94.7%

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

      1. unpow-1 94.7%

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

   9. Simplified 94.7%

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

       1. frac-2neg 94.7%

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

       2. div-inv 94.6%

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

       3. add-sqr-sqrt 51.3%

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

       4. sqrt-unprod 52.0%

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

       5. sqr-neg 52.0%

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

       6. sqrt-unprod 13.2%

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

       7. add-sqr-sqrt 33.5%

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

       8. frac-2neg 33.5%

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

       9. metadata-eval 33.5%

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

       10. add-sqr-sqrt 20.2%

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

       11. sqrt-unprod 50.9%

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

       12. sqr-neg 50.9%

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

       13. sqrt-unprod 43.2%

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

       14. add-sqr-sqrt 94.6%

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

   11. Applied egg-rr 94.6%

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

   12. Taylor expanded in y around 0 88.4%

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

   if 1.50000000000000003e-99 < y

   1. Initial program 92.5%

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

   2. Taylor expanded in t around inf 57.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 14: 78.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e-26)
   (/ (/ x (- t z)) y)
   (if (<= y 1.32e-99) (/ 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 <= -4.6e-26) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 1.32e-99) {
		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 <= (-4.6d-26)) then
        tmp = (x / (t - z)) / y
    else if (y <= 1.32d-99) 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 <= -4.6e-26) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 1.32e-99) {
		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 <= -4.6e-26:
		tmp = (x / (t - z)) / y
	elif y <= 1.32e-99:
		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 <= -4.6e-26)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 1.32e-99)
		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 <= -4.6e-26)
		tmp = (x / (t - z)) / y;
	elseif (y <= 1.32e-99)
		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, -4.6e-26], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.32e-99], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000018e-26

   1. Initial program 84.7%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/r* 83.8%

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

   4. Simplified 83.8%

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

   if -4.60000000000000018e-26 < y < 1.31999999999999999e-99

   1. Initial program 94.1%

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

      1. associate-/l/ 95.6%

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

   3. Simplified 95.6%

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

      1. clear-num 95.5%

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

      2. inv-pow 95.5%

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

   5. Applied egg-rr 95.5%

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

      1. div-inv 95.5%

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

      2. unpow-1 95.5%

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

      3. associate-*l/ 95.6%

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

      4. *-un-lft-identity 95.6%

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

      5. associate-/l* 97.5%

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

      6. clear-num 96.7%

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

      7. inv-pow 96.7%

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

      8. *-un-lft-identity 96.7%

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

      9. times-frac 94.6%

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

      10. clear-num 94.7%

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

      11. /-rgt-identity 94.7%

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

   7. Applied egg-rr 94.7%

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

      1. unpow-1 94.7%

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

   9. Simplified 94.7%

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

       1. frac-2neg 94.7%

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

       2. div-inv 94.6%

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

       3. add-sqr-sqrt 51.3%

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

       4. sqrt-unprod 52.0%

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

       5. sqr-neg 52.0%

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

       6. sqrt-unprod 13.2%

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

       7. add-sqr-sqrt 33.5%

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

       8. frac-2neg 33.5%

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

       9. metadata-eval 33.5%

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

       10. add-sqr-sqrt 20.2%

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

       11. sqrt-unprod 50.9%

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

       12. sqr-neg 50.9%

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

       13. sqrt-unprod 43.2%

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

       14. add-sqr-sqrt 94.6%

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

   11. Applied egg-rr 94.6%

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

   12. Taylor expanded in y around 0 88.4%

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

   if 1.31999999999999999e-99 < y

   1. Initial program 92.5%

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

   2. Taylor expanded in t around inf 57.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 15: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-50} \lor \neg \left(z \leq 0.017\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.6e-50) (not (<= z 0.017))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-50) || !(z <= 0.017)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.6d-50)) .or. (.not. (z <= 0.017d0))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-50) || !(z <= 0.017)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.6e-50) or not (z <= 0.017):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.6e-50) || !(z <= 0.017))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.6e-50) || ~((z <= 0.017)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.6e-50], N[Not[LessEqual[z, 0.017]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999979e-50 or 0.017000000000000001 < z

   1. Initial program 87.6%

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

   2. Taylor expanded in z around inf 69.0%

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

      1. unpow2 69.0%

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

   4. Simplified 69.0%

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

   if -3.59999999999999979e-50 < z < 0.017000000000000001

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 62.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-50} \lor \neg \left(z \leq 0.017\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 16: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-50} \lor \neg \left(z \leq 0.000325\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -2.6e-50) (not (<= z 0.000325))) (/ (/ x z) z) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e-50) || !(z <= 0.000325)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.6d-50)) .or. (.not. (z <= 0.000325d0))) then
        tmp = (x / z) / z
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e-50) || !(z <= 0.000325)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e-50) or not (z <= 0.000325):
		tmp = (x / z) / z
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.6e-50) || !(z <= 0.000325))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.6e-50) || ~((z <= 0.000325)))
		tmp = (x / z) / z;
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.6e-50], N[Not[LessEqual[z, 0.000325]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000001e-50 or 3.2499999999999999e-4 < z

   1. Initial program 87.6%

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

   2. Taylor expanded in z around inf 69.0%

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

      1. unpow2 69.0%

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

      2. associate-/r* 73.1%

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

   4. Simplified 73.1%

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

   if -2.6000000000000001e-50 < z < 3.2499999999999999e-4

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 62.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-50} \lor \neg \left(z \leq 0.000325\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 17: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.4%

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

   1. associate-/l/ 95.8%

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

3. Simplified 95.8%

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

4. Final simplification 95.8%

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

Alternative 18: 40.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.4%

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

2. Taylor expanded in z around 0 36.8%

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

3. Final simplification 36.8%

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

Developer target: 88.1% 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 2023224 
(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))))