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

Percentage Accurate: 88.3% → 97.7%

Time: 12.0s

Alternatives: 20

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.3% 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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -2e-300) t_1 (/ (/ x (- t z)) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2e-300) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= (-2d-300)) then
        tmp = t_1
    else
        tmp = (x / (t - z)) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2e-300) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -2e-300:
		tmp = t_1
	else:
		tmp = (x / (t - z)) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -2e-300)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -2e-300)
		tmp = t_1;
	else
		tmp = (x / (t - z)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-300], t$95$1, N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -2.00000000000000005e-300

   1. Initial program 98.4%

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

   if -2.00000000000000005e-300 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 84.5%

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

      1. associate-/l/ 98.2%

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

   3. Simplified 98.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq -2 \cdot 10^{-300}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \]

Alternative 2: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-1}{z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-29}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -3.8e-73)
     t_1
     (if (<= z 5.6e-197)
       (/ (/ x y) t)
       (if (<= z 1.1e-159)
         (* (/ x y) (/ -1.0 z))
         (if (<= z 5.7e-95)
           (/ (/ x t) y)
           (if (<= z 1.45e-29)
             (/ (- x) (* z t))
             (if (<= z 1.55e-10) (* (/ x t) (/ 1.0 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 <= -3.8e-73) {
		tmp = t_1;
	} else if (z <= 5.6e-197) {
		tmp = (x / y) / t;
	} else if (z <= 1.1e-159) {
		tmp = (x / y) * (-1.0 / z);
	} else if (z <= 5.7e-95) {
		tmp = (x / t) / y;
	} else if (z <= 1.45e-29) {
		tmp = -x / (z * t);
	} else if (z <= 1.55e-10) {
		tmp = (x / t) * (1.0 / 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 <= (-3.8d-73)) then
        tmp = t_1
    else if (z <= 5.6d-197) then
        tmp = (x / y) / t
    else if (z <= 1.1d-159) then
        tmp = (x / y) * ((-1.0d0) / z)
    else if (z <= 5.7d-95) then
        tmp = (x / t) / y
    else if (z <= 1.45d-29) then
        tmp = -x / (z * t)
    else if (z <= 1.55d-10) then
        tmp = (x / t) * (1.0d0 / 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 <= -3.8e-73) {
		tmp = t_1;
	} else if (z <= 5.6e-197) {
		tmp = (x / y) / t;
	} else if (z <= 1.1e-159) {
		tmp = (x / y) * (-1.0 / z);
	} else if (z <= 5.7e-95) {
		tmp = (x / t) / y;
	} else if (z <= 1.45e-29) {
		tmp = -x / (z * t);
	} else if (z <= 1.55e-10) {
		tmp = (x / t) * (1.0 / 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 <= -3.8e-73:
		tmp = t_1
	elif z <= 5.6e-197:
		tmp = (x / y) / t
	elif z <= 1.1e-159:
		tmp = (x / y) * (-1.0 / z)
	elif z <= 5.7e-95:
		tmp = (x / t) / y
	elif z <= 1.45e-29:
		tmp = -x / (z * t)
	elif z <= 1.55e-10:
		tmp = (x / t) * (1.0 / 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 <= -3.8e-73)
		tmp = t_1;
	elseif (z <= 5.6e-197)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 1.1e-159)
		tmp = Float64(Float64(x / y) * Float64(-1.0 / z));
	elseif (z <= 5.7e-95)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.45e-29)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 1.55e-10)
		tmp = Float64(Float64(x / t) * Float64(1.0 / 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 <= -3.8e-73)
		tmp = t_1;
	elseif (z <= 5.6e-197)
		tmp = (x / y) / t;
	elseif (z <= 1.1e-159)
		tmp = (x / y) * (-1.0 / z);
	elseif (z <= 5.7e-95)
		tmp = (x / t) / y;
	elseif (z <= 1.45e-29)
		tmp = -x / (z * t);
	elseif (z <= 1.55e-10)
		tmp = (x / t) * (1.0 / 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, -3.8e-73], t$95$1, If[LessEqual[z, 5.6e-197], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.1e-159], N[(N[(x / y), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-95], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.45e-29], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-10], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.8000000000000003e-73 or 1.55000000000000008e-10 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. unpow2 65.4%

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

      2. associate-/r* 75.2%

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

   4. Simplified 75.2%

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

   if -3.8000000000000003e-73 < z < 5.6000000000000004e-197

   1. Initial program 93.9%

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

      1. associate-/l/ 94.2%

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

      2. div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in z around 0 72.6%

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

      1. associate-/r* 74.2%

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

   6. Simplified 74.2%

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

   if 5.6000000000000004e-197 < z < 1.1e-159

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 37.4%

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

      1. *-commutative 37.4%

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

   4. Simplified 37.4%

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

   5. Taylor expanded in t around 0 28.6%

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

      1. associate-*r/ 28.6%

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

      2. neg-mul-1 28.6%

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

   7. Simplified 28.6%

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

      1. neg-mul-1 28.6%

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

      2. *-commutative 28.6%

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

      3. times-frac 28.9%

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

   9. Applied egg-rr 28.9%

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

   if 1.1e-159 < z < 5.7e-95

   1. Initial program 90.8%

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

      1. associate-/l/ 95.2%

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

      2. div-inv 95.0%

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

   3. Applied egg-rr 95.0%

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

   4. Taylor expanded in t around inf 76.8%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. un-div-inv 76.9%

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

   7. Applied egg-rr 76.9%

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

   if 5.7e-95 < z < 1.45000000000000012e-29

   1. Initial program 99.8%

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

      1. associate-/l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in t around inf 62.7%

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

   5. Taylor expanded in y around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

   7. Simplified 54.8%

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

   if 1.45000000000000012e-29 < z < 1.55000000000000008e-10

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 97.4%

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

      1. *-un-lft-identity 97.4%

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

      2. times-frac 98.0%

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

   4. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-1}{z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-29}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 3: 63.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-159}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 t) y)))
   (if (<= z -3.8e-73)
     t_1
     (if (<= z 5.6e-197)
       (/ (/ x y) t)
       (if (<= z 1.1e-159)
         (/ (- x) (* y z))
         (if (<= z 5.7e-95)
           t_2
           (if (<= z 8.5e-25)
             (/ (- x) (* z t))
             (if (<= z 1.8e-10) 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 / t) / y;
	double tmp;
	if (z <= -3.8e-73) {
		tmp = t_1;
	} else if (z <= 5.6e-197) {
		tmp = (x / y) / t;
	} else if (z <= 1.1e-159) {
		tmp = -x / (y * z);
	} else if (z <= 5.7e-95) {
		tmp = t_2;
	} else if (z <= 8.5e-25) {
		tmp = -x / (z * t);
	} else if (z <= 1.8e-10) {
		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 / t) / y
    if (z <= (-3.8d-73)) then
        tmp = t_1
    else if (z <= 5.6d-197) then
        tmp = (x / y) / t
    else if (z <= 1.1d-159) then
        tmp = -x / (y * z)
    else if (z <= 5.7d-95) then
        tmp = t_2
    else if (z <= 8.5d-25) then
        tmp = -x / (z * t)
    else if (z <= 1.8d-10) 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 / t) / y;
	double tmp;
	if (z <= -3.8e-73) {
		tmp = t_1;
	} else if (z <= 5.6e-197) {
		tmp = (x / y) / t;
	} else if (z <= 1.1e-159) {
		tmp = -x / (y * z);
	} else if (z <= 5.7e-95) {
		tmp = t_2;
	} else if (z <= 8.5e-25) {
		tmp = -x / (z * t);
	} else if (z <= 1.8e-10) {
		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 / t) / y
	tmp = 0
	if z <= -3.8e-73:
		tmp = t_1
	elif z <= 5.6e-197:
		tmp = (x / y) / t
	elif z <= 1.1e-159:
		tmp = -x / (y * z)
	elif z <= 5.7e-95:
		tmp = t_2
	elif z <= 8.5e-25:
		tmp = -x / (z * t)
	elif z <= 1.8e-10:
		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(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -3.8e-73)
		tmp = t_1;
	elseif (z <= 5.6e-197)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 1.1e-159)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (z <= 5.7e-95)
		tmp = t_2;
	elseif (z <= 8.5e-25)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 1.8e-10)
		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 / t) / y;
	tmp = 0.0;
	if (z <= -3.8e-73)
		tmp = t_1;
	elseif (z <= 5.6e-197)
		tmp = (x / y) / t;
	elseif (z <= 1.1e-159)
		tmp = -x / (y * z);
	elseif (z <= 5.7e-95)
		tmp = t_2;
	elseif (z <= 8.5e-25)
		tmp = -x / (z * t);
	elseif (z <= 1.8e-10)
		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[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -3.8e-73], t$95$1, If[LessEqual[z, 5.6e-197], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.1e-159], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-95], t$95$2, If[LessEqual[z, 8.5e-25], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-10], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.8000000000000003e-73 or 1.8e-10 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. unpow2 65.4%

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

      2. associate-/r* 75.2%

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

   4. Simplified 75.2%

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

   if -3.8000000000000003e-73 < z < 5.6000000000000004e-197

   1. Initial program 93.9%

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

      1. associate-/l/ 94.2%

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

      2. div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in z around 0 72.6%

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

      1. associate-/r* 74.2%

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

   6. Simplified 74.2%

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

   if 5.6000000000000004e-197 < z < 1.1e-159

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 37.4%

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

      1. *-commutative 37.4%

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

   4. Simplified 37.4%

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

   5. Taylor expanded in t around 0 28.6%

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

      1. associate-*r/ 28.6%

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

      2. neg-mul-1 28.6%

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

   7. Simplified 28.6%

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

   if 1.1e-159 < z < 5.7e-95 or 8.49999999999999981e-25 < z < 1.8e-10

   1. Initial program 91.5%

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

      1. associate-/l/ 95.5%

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

      2. div-inv 95.4%

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

   3. Applied egg-rr 95.4%

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

   4. Taylor expanded in t around inf 78.8%

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

   5. Taylor expanded in y around inf 78.7%

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

      1. un-div-inv 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 5.7e-95 < z < 8.49999999999999981e-25

   1. Initial program 99.8%

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

      1. associate-/l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in t around inf 62.7%

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

   5. Taylor expanded in y around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

   7. Simplified 54.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-159}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 4: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-159}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-28}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 t) y)))
   (if (<= z -3.8e-73)
     t_1
     (if (<= z 5.6e-197)
       (/ (/ x y) t)
       (if (<= z 1.1e-159)
         (/ (/ (- x) y) z)
         (if (<= z 6.9e-97)
           t_2
           (if (<= z 6e-28)
             (/ (- x) (* z t))
             (if (<= z 1.75e-10) 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 / t) / y;
	double tmp;
	if (z <= -3.8e-73) {
		tmp = t_1;
	} else if (z <= 5.6e-197) {
		tmp = (x / y) / t;
	} else if (z <= 1.1e-159) {
		tmp = (-x / y) / z;
	} else if (z <= 6.9e-97) {
		tmp = t_2;
	} else if (z <= 6e-28) {
		tmp = -x / (z * t);
	} else if (z <= 1.75e-10) {
		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 / t) / y
    if (z <= (-3.8d-73)) then
        tmp = t_1
    else if (z <= 5.6d-197) then
        tmp = (x / y) / t
    else if (z <= 1.1d-159) then
        tmp = (-x / y) / z
    else if (z <= 6.9d-97) then
        tmp = t_2
    else if (z <= 6d-28) then
        tmp = -x / (z * t)
    else if (z <= 1.75d-10) 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 / t) / y;
	double tmp;
	if (z <= -3.8e-73) {
		tmp = t_1;
	} else if (z <= 5.6e-197) {
		tmp = (x / y) / t;
	} else if (z <= 1.1e-159) {
		tmp = (-x / y) / z;
	} else if (z <= 6.9e-97) {
		tmp = t_2;
	} else if (z <= 6e-28) {
		tmp = -x / (z * t);
	} else if (z <= 1.75e-10) {
		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 / t) / y
	tmp = 0
	if z <= -3.8e-73:
		tmp = t_1
	elif z <= 5.6e-197:
		tmp = (x / y) / t
	elif z <= 1.1e-159:
		tmp = (-x / y) / z
	elif z <= 6.9e-97:
		tmp = t_2
	elif z <= 6e-28:
		tmp = -x / (z * t)
	elif z <= 1.75e-10:
		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(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -3.8e-73)
		tmp = t_1;
	elseif (z <= 5.6e-197)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 1.1e-159)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= 6.9e-97)
		tmp = t_2;
	elseif (z <= 6e-28)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 1.75e-10)
		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 / t) / y;
	tmp = 0.0;
	if (z <= -3.8e-73)
		tmp = t_1;
	elseif (z <= 5.6e-197)
		tmp = (x / y) / t;
	elseif (z <= 1.1e-159)
		tmp = (-x / y) / z;
	elseif (z <= 6.9e-97)
		tmp = t_2;
	elseif (z <= 6e-28)
		tmp = -x / (z * t);
	elseif (z <= 1.75e-10)
		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[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -3.8e-73], t$95$1, If[LessEqual[z, 5.6e-197], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.1e-159], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 6.9e-97], t$95$2, If[LessEqual[z, 6e-28], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-10], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.8000000000000003e-73 or 1.7499999999999999e-10 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. unpow2 65.4%

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

      2. associate-/r* 75.2%

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

   4. Simplified 75.2%

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

   if -3.8000000000000003e-73 < z < 5.6000000000000004e-197

   1. Initial program 93.9%

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

      1. associate-/l/ 94.2%

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

      2. div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in z around 0 72.6%

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

      1. associate-/r* 74.2%

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

   6. Simplified 74.2%

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

   if 5.6000000000000004e-197 < z < 1.1e-159

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 37.4%

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

      1. *-commutative 37.4%

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

   4. Simplified 37.4%

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

   5. Taylor expanded in t around 0 28.6%

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

      1. associate-*r/ 28.6%

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

      2. neg-mul-1 28.6%

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

   7. Simplified 28.6%

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

   8. Taylor expanded in x around 0 28.6%

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

      1. associate-*r/ 28.6%

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

      2. associate-/r* 28.9%

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

      3. neg-mul-1 28.9%

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

   10. Simplified 28.9%

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

   if 1.1e-159 < z < 6.8999999999999996e-97 or 6.00000000000000005e-28 < z < 1.7499999999999999e-10

   1. Initial program 91.5%

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

      1. associate-/l/ 95.5%

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

      2. div-inv 95.4%

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

   3. Applied egg-rr 95.4%

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

   4. Taylor expanded in t around inf 78.8%

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

   5. Taylor expanded in y around inf 78.7%

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

      1. un-div-inv 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 6.8999999999999996e-97 < z < 6.00000000000000005e-28

   1. Initial program 99.8%

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

      1. associate-/l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in t around inf 62.7%

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

   5. Taylor expanded in y around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

   7. Simplified 54.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-159}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-28}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 5: 63.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -6 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-1}{z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-26}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 t) y)))
   (if (<= z -6e-74)
     t_1
     (if (<= z 5.6e-197)
       (/ (/ x y) t)
       (if (<= z 1.1e-159)
         (* (/ x y) (/ -1.0 z))
         (if (<= z 5.7e-95)
           t_2
           (if (<= z 1.35e-26)
             (/ (- x) (* z t))
             (if (<= z 1.72e-10) 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 / t) / y;
	double tmp;
	if (z <= -6e-74) {
		tmp = t_1;
	} else if (z <= 5.6e-197) {
		tmp = (x / y) / t;
	} else if (z <= 1.1e-159) {
		tmp = (x / y) * (-1.0 / z);
	} else if (z <= 5.7e-95) {
		tmp = t_2;
	} else if (z <= 1.35e-26) {
		tmp = -x / (z * t);
	} else if (z <= 1.72e-10) {
		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 / t) / y
    if (z <= (-6d-74)) then
        tmp = t_1
    else if (z <= 5.6d-197) then
        tmp = (x / y) / t
    else if (z <= 1.1d-159) then
        tmp = (x / y) * ((-1.0d0) / z)
    else if (z <= 5.7d-95) then
        tmp = t_2
    else if (z <= 1.35d-26) then
        tmp = -x / (z * t)
    else if (z <= 1.72d-10) 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 / t) / y;
	double tmp;
	if (z <= -6e-74) {
		tmp = t_1;
	} else if (z <= 5.6e-197) {
		tmp = (x / y) / t;
	} else if (z <= 1.1e-159) {
		tmp = (x / y) * (-1.0 / z);
	} else if (z <= 5.7e-95) {
		tmp = t_2;
	} else if (z <= 1.35e-26) {
		tmp = -x / (z * t);
	} else if (z <= 1.72e-10) {
		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 / t) / y
	tmp = 0
	if z <= -6e-74:
		tmp = t_1
	elif z <= 5.6e-197:
		tmp = (x / y) / t
	elif z <= 1.1e-159:
		tmp = (x / y) * (-1.0 / z)
	elif z <= 5.7e-95:
		tmp = t_2
	elif z <= 1.35e-26:
		tmp = -x / (z * t)
	elif z <= 1.72e-10:
		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(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -6e-74)
		tmp = t_1;
	elseif (z <= 5.6e-197)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 1.1e-159)
		tmp = Float64(Float64(x / y) * Float64(-1.0 / z));
	elseif (z <= 5.7e-95)
		tmp = t_2;
	elseif (z <= 1.35e-26)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 1.72e-10)
		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 / t) / y;
	tmp = 0.0;
	if (z <= -6e-74)
		tmp = t_1;
	elseif (z <= 5.6e-197)
		tmp = (x / y) / t;
	elseif (z <= 1.1e-159)
		tmp = (x / y) * (-1.0 / z);
	elseif (z <= 5.7e-95)
		tmp = t_2;
	elseif (z <= 1.35e-26)
		tmp = -x / (z * t);
	elseif (z <= 1.72e-10)
		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[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -6e-74], t$95$1, If[LessEqual[z, 5.6e-197], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.1e-159], N[(N[(x / y), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-95], t$95$2, If[LessEqual[z, 1.35e-26], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.72e-10], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.00000000000000014e-74 or 1.72000000000000001e-10 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. unpow2 65.4%

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

      2. associate-/r* 75.2%

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

   4. Simplified 75.2%

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

   if -6.00000000000000014e-74 < z < 5.6000000000000004e-197

   1. Initial program 93.9%

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

      1. associate-/l/ 94.2%

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

      2. div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in z around 0 72.6%

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

      1. associate-/r* 74.2%

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

   6. Simplified 74.2%

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

   if 5.6000000000000004e-197 < z < 1.1e-159

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 37.4%

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

      1. *-commutative 37.4%

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

   4. Simplified 37.4%

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

   5. Taylor expanded in t around 0 28.6%

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

      1. associate-*r/ 28.6%

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

      2. neg-mul-1 28.6%

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

   7. Simplified 28.6%

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

      1. neg-mul-1 28.6%

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

      2. *-commutative 28.6%

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

      3. times-frac 28.9%

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

   9. Applied egg-rr 28.9%

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

   if 1.1e-159 < z < 5.7e-95 or 1.34999999999999991e-26 < z < 1.72000000000000001e-10

   1. Initial program 91.5%

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

      1. associate-/l/ 95.5%

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

      2. div-inv 95.4%

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

   3. Applied egg-rr 95.4%

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

   4. Taylor expanded in t around inf 78.8%

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

   5. Taylor expanded in y around inf 78.7%

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

      1. un-div-inv 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 5.7e-95 < z < 1.34999999999999991e-26

   1. Initial program 99.8%

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

      1. associate-/l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in t around inf 62.7%

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

   5. Taylor expanded in y around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

   7. Simplified 54.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-1}{z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-26}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 6: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+151}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -1.9e+19)
     t_1
     (if (<= z 1.4e-91)
       (/ (/ x (- t z)) y)
       (if (<= z 1.35e-10)
         (/ x (* (- y z) t))
         (if (<= z 9e+151) (/ (- x) (* z (- y z))) t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.9e+19) {
		tmp = t_1;
	} else if (z <= 1.4e-91) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 1.35e-10) {
		tmp = x / ((y - z) * t);
	} else if (z <= 9e+151) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-1.9d+19)) then
        tmp = t_1
    else if (z <= 1.4d-91) then
        tmp = (x / (t - z)) / y
    else if (z <= 1.35d-10) then
        tmp = x / ((y - z) * t)
    else if (z <= 9d+151) then
        tmp = -x / (z * (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.9e+19) {
		tmp = t_1;
	} else if (z <= 1.4e-91) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 1.35e-10) {
		tmp = x / ((y - z) * t);
	} else if (z <= 9e+151) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -1.9e+19:
		tmp = t_1
	elif z <= 1.4e-91:
		tmp = (x / (t - z)) / y
	elif z <= 1.35e-10:
		tmp = x / ((y - z) * t)
	elif z <= 9e+151:
		tmp = -x / (z * (y - z))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.9e+19)
		tmp = t_1;
	elseif (z <= 1.4e-91)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (z <= 1.35e-10)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (z <= 9e+151)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.9e+19)
		tmp = t_1;
	elseif (z <= 1.4e-91)
		tmp = (x / (t - z)) / y;
	elseif (z <= 1.35e-10)
		tmp = x / ((y - z) * t);
	elseif (z <= 9e+151)
		tmp = -x / (z * (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.9e+19], t$95$1, If[LessEqual[z, 1.4e-91], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.35e-10], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+151], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9e19 or 8.9999999999999997e151 < z

   1. Initial program 78.6%

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

   2. Taylor expanded in z around inf 72.6%

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

      1. unpow2 72.6%

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

      2. associate-/r* 86.8%

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

   4. Simplified 86.8%

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

   if -1.9e19 < z < 1.4e-91

   1. Initial program 93.8%

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

      1. associate-/l/ 94.6%

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

      2. div-inv 94.5%

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

   3. Applied egg-rr 94.5%

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

      1. frac-times 93.8%

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

      2. clear-num 92.7%

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

      3. *-rgt-identity 92.7%

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

      4. associate-*r/ 92.0%

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

      5. associate-/r* 92.1%

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

   5. Applied egg-rr 92.1%

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

      1. *-un-lft-identity 92.1%

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

      2. div-inv 91.9%

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

      3. times-frac 94.4%

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

   7. Applied egg-rr 94.4%

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

   8. Taylor expanded in y around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/r* 78.4%

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

   10. Simplified 78.4%

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

   if 1.4e-91 < z < 1.35e-10

   1. Initial program 99.7%

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

   2. Taylor expanded in t around inf 78.8%

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

   if 1.35e-10 < z < 8.9999999999999997e151

   1. Initial program 90.8%

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

   2. Taylor expanded in t around 0 69.3%

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

      1. associate-*r/ 69.3%

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

      2. neg-mul-1 69.3%

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

      3. *-commutative 69.3%

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

   4. Simplified 69.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+151}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 7: 77.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{-x}{z}}{y - z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-10}:\\ \;\;\;\;\frac{1}{\frac{\left(y - z\right) \cdot t}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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) (- y z))))
   (if (<= z -3.1e-93)
     t_1
     (if (<= z 1.5e-92)
       (/ (/ x (- t z)) y)
       (if (<= z 1.25e-10) (/ 1.0 (/ (* (- y z) t) x)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / (y - z);
	double tmp;
	if (z <= -3.1e-93) {
		tmp = t_1;
	} else if (z <= 1.5e-92) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 1.25e-10) {
		tmp = 1.0 / (((y - z) * t) / x);
	} 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) / (y - z)
    if (z <= (-3.1d-93)) then
        tmp = t_1
    else if (z <= 1.5d-92) then
        tmp = (x / (t - z)) / y
    else if (z <= 1.25d-10) then
        tmp = 1.0d0 / (((y - z) * t) / x)
    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) / (y - z);
	double tmp;
	if (z <= -3.1e-93) {
		tmp = t_1;
	} else if (z <= 1.5e-92) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 1.25e-10) {
		tmp = 1.0 / (((y - z) * t) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (-x / z) / (y - z)
	tmp = 0
	if z <= -3.1e-93:
		tmp = t_1
	elif z <= 1.5e-92:
		tmp = (x / (t - z)) / y
	elif z <= 1.25e-10:
		tmp = 1.0 / (((y - z) * t) / x)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / z) / Float64(y - z))
	tmp = 0.0
	if (z <= -3.1e-93)
		tmp = t_1;
	elseif (z <= 1.5e-92)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (z <= 1.25e-10)
		tmp = Float64(1.0 / Float64(Float64(Float64(y - z) * t) / x));
	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) / (y - z);
	tmp = 0.0;
	if (z <= -3.1e-93)
		tmp = t_1;
	elseif (z <= 1.5e-92)
		tmp = (x / (t - z)) / y;
	elseif (z <= 1.25e-10)
		tmp = 1.0 / (((y - z) * t) / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e-93], t$95$1, If[LessEqual[z, 1.5e-92], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.25e-10], N[(1.0 / N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e-93 or 1.25000000000000008e-10 < z

   1. Initial program 83.6%

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

   2. Taylor expanded in t around 0 72.9%

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

      1. associate-*r/ 72.9%

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

      2. neg-mul-1 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-/r* 86.8%

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

      5. distribute-frac-neg 86.8%

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

   4. Simplified 86.8%

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

   if -3.1e-93 < z < 1.50000000000000007e-92

   1. Initial program 93.0%

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

      1. associate-/l/ 94.0%

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

      2. div-inv 93.9%

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

   3. Applied egg-rr 93.9%

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

      1. frac-times 93.0%

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

      2. clear-num 91.8%

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

      3. *-rgt-identity 91.8%

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

      4. associate-*r/ 91.0%

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

      5. associate-/r* 91.1%

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

   5. Applied egg-rr 91.1%

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

      1. *-un-lft-identity 91.1%

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

      2. div-inv 90.9%

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

      3. times-frac 93.8%

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

   7. Applied egg-rr 93.8%

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

   8. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/r* 80.7%

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

   10. Simplified 80.7%

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

   if 1.50000000000000007e-92 < z < 1.25000000000000008e-10

   1. Initial program 99.7%

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

      1. associate-/l/ 86.0%

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

      2. div-inv 86.3%

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

   3. Applied egg-rr 86.3%

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

   4. Taylor expanded in t around inf 72.4%

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

      1. div-inv 72.2%

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

      2. associate-/l/ 78.8%

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

      3. clear-num 78.9%

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

      4. *-commutative 78.9%

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

   6. Applied egg-rr 78.9%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-10}:\\ \;\;\;\;\frac{1}{\frac{\left(y - z\right) \cdot t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]

Alternative 8: 77.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{-x}{z}}{y - z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) z) (- y z))))
   (if (<= z -3.1e-93)
     t_1
     (if (<= z 1.9e-91)
       (/ (/ x (- t z)) y)
       (if (<= z 1.35e-10) (/ x (* (- y z) t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / (y - z);
	double tmp;
	if (z <= -3.1e-93) {
		tmp = t_1;
	} else if (z <= 1.9e-91) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 1.35e-10) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-x / z) / (y - z)
    if (z <= (-3.1d-93)) then
        tmp = t_1
    else if (z <= 1.9d-91) then
        tmp = (x / (t - z)) / y
    else if (z <= 1.35d-10) then
        tmp = x / ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / (y - z);
	double tmp;
	if (z <= -3.1e-93) {
		tmp = t_1;
	} else if (z <= 1.9e-91) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 1.35e-10) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (-x / z) / (y - z)
	tmp = 0
	if z <= -3.1e-93:
		tmp = t_1
	elif z <= 1.9e-91:
		tmp = (x / (t - z)) / y
	elif z <= 1.35e-10:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / z) / Float64(y - z))
	tmp = 0.0
	if (z <= -3.1e-93)
		tmp = t_1;
	elseif (z <= 1.9e-91)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (z <= 1.35e-10)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (-x / z) / (y - z);
	tmp = 0.0;
	if (z <= -3.1e-93)
		tmp = t_1;
	elseif (z <= 1.9e-91)
		tmp = (x / (t - z)) / y;
	elseif (z <= 1.35e-10)
		tmp = x / ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e-93], t$95$1, If[LessEqual[z, 1.9e-91], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.35e-10], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e-93 or 1.35e-10 < z

   1. Initial program 83.6%

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

   2. Taylor expanded in t around 0 72.9%

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

      1. associate-*r/ 72.9%

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

      2. neg-mul-1 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-/r* 86.8%

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

      5. distribute-frac-neg 86.8%

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

   4. Simplified 86.8%

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

   if -3.1e-93 < z < 1.89999999999999989e-91

   1. Initial program 93.0%

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

      1. associate-/l/ 94.0%

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

      2. div-inv 93.9%

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

   3. Applied egg-rr 93.9%

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

      1. frac-times 93.0%

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

      2. clear-num 91.8%

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

      3. *-rgt-identity 91.8%

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

      4. associate-*r/ 91.0%

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

      5. associate-/r* 91.1%

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

   5. Applied egg-rr 91.1%

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

      1. *-un-lft-identity 91.1%

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

      2. div-inv 90.9%

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

      3. times-frac 93.8%

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

   7. Applied egg-rr 93.8%

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

   8. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/r* 80.7%

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

   10. Simplified 80.7%

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

   if 1.89999999999999989e-91 < z < 1.35e-10

   1. Initial program 99.7%

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

   2. Taylor expanded in t around inf 78.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]

Alternative 9: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 t) y)))
   (if (<= z -1.45e-73)
     t_1
     (if (<= z 5.7e-95)
       t_2
       (if (<= z 5.2e-22) (/ (- x) (* z t)) (if (<= z 1.46e-10) 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 / t) / y;
	double tmp;
	if (z <= -1.45e-73) {
		tmp = t_1;
	} else if (z <= 5.7e-95) {
		tmp = t_2;
	} else if (z <= 5.2e-22) {
		tmp = -x / (z * t);
	} else if (z <= 1.46e-10) {
		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 / t) / y
    if (z <= (-1.45d-73)) then
        tmp = t_1
    else if (z <= 5.7d-95) then
        tmp = t_2
    else if (z <= 5.2d-22) then
        tmp = -x / (z * t)
    else if (z <= 1.46d-10) 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 / t) / y;
	double tmp;
	if (z <= -1.45e-73) {
		tmp = t_1;
	} else if (z <= 5.7e-95) {
		tmp = t_2;
	} else if (z <= 5.2e-22) {
		tmp = -x / (z * t);
	} else if (z <= 1.46e-10) {
		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 / t) / y
	tmp = 0
	if z <= -1.45e-73:
		tmp = t_1
	elif z <= 5.7e-95:
		tmp = t_2
	elif z <= 5.2e-22:
		tmp = -x / (z * t)
	elif z <= 1.46e-10:
		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(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -1.45e-73)
		tmp = t_1;
	elseif (z <= 5.7e-95)
		tmp = t_2;
	elseif (z <= 5.2e-22)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 1.46e-10)
		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 / t) / y;
	tmp = 0.0;
	if (z <= -1.45e-73)
		tmp = t_1;
	elseif (z <= 5.7e-95)
		tmp = t_2;
	elseif (z <= 5.2e-22)
		tmp = -x / (z * t);
	elseif (z <= 1.46e-10)
		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[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.45e-73], t$95$1, If[LessEqual[z, 5.7e-95], t$95$2, If[LessEqual[z, 5.2e-22], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.46e-10], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e-73 or 1.4600000000000001e-10 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. unpow2 65.4%

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

      2. associate-/r* 75.2%

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

   4. Simplified 75.2%

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

   if -1.45e-73 < z < 5.7e-95 or 5.2e-22 < z < 1.4600000000000001e-10

   1. Initial program 93.2%

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

      1. associate-/l/ 94.2%

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

      2. div-inv 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in t around inf 80.8%

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

   5. Taylor expanded in y around inf 69.5%

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

      1. un-div-inv 69.6%

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

   7. Applied egg-rr 69.6%

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

   if 5.7e-95 < z < 5.2e-22

   1. Initial program 99.8%

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

      1. associate-/l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in t around inf 62.7%

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

   5. Taylor expanded in y around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

   7. Simplified 54.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 10: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -1.05e+19)
     t_1
     (if (<= z 2.95e-93)
       (/ x (* y (- t z)))
       (if (<= z 1.5e+16) (/ x (* (- y z) t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.05e+19) {
		tmp = t_1;
	} else if (z <= 2.95e-93) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.5e+16) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-1.05d+19)) then
        tmp = t_1
    else if (z <= 2.95d-93) then
        tmp = x / (y * (t - z))
    else if (z <= 1.5d+16) then
        tmp = x / ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.05e+19) {
		tmp = t_1;
	} else if (z <= 2.95e-93) {
		tmp = x / (y * (t - z));
	} else if (z <= 1.5e+16) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -1.05e+19:
		tmp = t_1
	elif z <= 2.95e-93:
		tmp = x / (y * (t - z))
	elif z <= 1.5e+16:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.05e+19)
		tmp = t_1;
	elseif (z <= 2.95e-93)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 1.5e+16)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.05e+19)
		tmp = t_1;
	elseif (z <= 2.95e-93)
		tmp = x / (y * (t - z));
	elseif (z <= 1.5e+16)
		tmp = x / ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.05e+19], t$95$1, If[LessEqual[z, 2.95e-93], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+16], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e19 or 1.5e16 < z

   1. Initial program 80.6%

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

   2. Taylor expanded in z around inf 69.5%

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

      1. unpow2 69.5%

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

      2. associate-/r* 80.8%

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

   4. Simplified 80.8%

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

   if -1.05e19 < z < 2.95e-93

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 76.9%

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

      1. *-commutative 76.9%

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

   4. Simplified 76.9%

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

   if 2.95e-93 < z < 1.5e16

   1. Initial program 99.6%

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

   2. Taylor expanded in t around inf 66.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 11: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -6.6e+24)
     t_1
     (if (<= z 3.7e-93)
       (/ (/ x (- t z)) y)
       (if (<= z 1.46e+16) (/ x (* (- y z) t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -6.6e+24) {
		tmp = t_1;
	} else if (z <= 3.7e-93) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 1.46e+16) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-6.6d+24)) then
        tmp = t_1
    else if (z <= 3.7d-93) then
        tmp = (x / (t - z)) / y
    else if (z <= 1.46d+16) then
        tmp = x / ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -6.6e+24) {
		tmp = t_1;
	} else if (z <= 3.7e-93) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 1.46e+16) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -6.6e+24:
		tmp = t_1
	elif z <= 3.7e-93:
		tmp = (x / (t - z)) / y
	elif z <= 1.46e+16:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -6.6e+24)
		tmp = t_1;
	elseif (z <= 3.7e-93)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (z <= 1.46e+16)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -6.6e+24)
		tmp = t_1;
	elseif (z <= 3.7e-93)
		tmp = (x / (t - z)) / y;
	elseif (z <= 1.46e+16)
		tmp = x / ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -6.6e+24], t$95$1, If[LessEqual[z, 3.7e-93], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.46e+16], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999998e24 or 1.46e16 < z

   1. Initial program 80.6%

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

   2. Taylor expanded in z around inf 69.5%

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

      1. unpow2 69.5%

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

      2. associate-/r* 80.8%

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

   4. Simplified 80.8%

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

   if -6.5999999999999998e24 < z < 3.70000000000000002e-93

   1. Initial program 93.8%

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

      1. associate-/l/ 94.6%

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

      2. div-inv 94.5%

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

   3. Applied egg-rr 94.5%

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

      1. frac-times 93.8%

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

      2. clear-num 92.7%

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

      3. *-rgt-identity 92.7%

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

      4. associate-*r/ 92.0%

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

      5. associate-/r* 92.1%

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

   5. Applied egg-rr 92.1%

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

      1. *-un-lft-identity 92.1%

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

      2. div-inv 91.9%

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

      3. times-frac 94.4%

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

   7. Applied egg-rr 94.4%

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

   8. Taylor expanded in y around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/r* 78.4%

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

   10. Simplified 78.4%

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

   if 3.70000000000000002e-93 < z < 1.46e16

   1. Initial program 99.6%

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

   2. Taylor expanded in t around inf 66.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 12: 92.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+82} \lor \neg \left(z \leq 2.3 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3e+82) (not (<= z 2.3e+39)))
   (/ (/ (- x) z) (- y z))
   (/ x (* (- y z) (- t z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+82) || !(z <= 2.3e+39)) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3d+82)) .or. (.not. (z <= 2.3d+39))) then
        tmp = (-x / z) / (y - z)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+82) || !(z <= 2.3e+39)) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3e+82) or not (z <= 2.3e+39):
		tmp = (-x / z) / (y - z)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3e+82) || !(z <= 2.3e+39))
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3e+82) || ~((z <= 2.3e+39)))
		tmp = (-x / z) / (y - z);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3e+82], N[Not[LessEqual[z, 2.3e+39]], $MachinePrecision]], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999989e82 or 2.30000000000000012e39 < z

   1. Initial program 77.1%

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

   2. Taylor expanded in t around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. neg-mul-1 73.6%

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

      3. *-commutative 73.6%

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

      4. associate-/r* 94.1%

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

      5. distribute-frac-neg 94.1%

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

   4. Simplified 94.1%

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

   if -2.99999999999999989e82 < z < 2.30000000000000012e39

   1. Initial program 94.6%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+82} \lor \neg \left(z \leq 2.3 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 13: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e-67)
   (/ (/ x (- t z)) y)
   (if (<= y 2e-63) (/ (/ (- x) z) (- t z)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-67) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 2e-63) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.8d-67)) then
        tmp = (x / (t - z)) / y
    else if (y <= 2d-63) then
        tmp = (-x / z) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-67) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 2e-63) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-67:
		tmp = (x / (t - z)) / y
	elif y <= 2e-63:
		tmp = (-x / z) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-67)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 2e-63)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e-67)
		tmp = (x / (t - z)) / y;
	elseif (y <= 2e-63)
		tmp = (-x / z) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-67], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2e-63], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e-67

   1. Initial program 86.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. frac-times 86.7%

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

      2. clear-num 84.4%

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

      3. *-rgt-identity 84.4%

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

      4. associate-*r/ 93.5%

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

      5. associate-/r* 94.1%

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

   5. Applied egg-rr 94.1%

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

      1. *-un-lft-identity 94.1%

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

      2. div-inv 93.9%

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

      3. times-frac 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in y around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-/r* 86.7%

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

   10. Simplified 86.7%

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

   if -4.8e-67 < y < 2.00000000000000013e-63

   1. Initial program 92.4%

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

   2. Taylor expanded in y around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. associate-/r* 80.9%

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

      3. distribute-neg-frac 80.9%

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

   4. Simplified 80.9%

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

   if 2.00000000000000013e-63 < y

   1. Initial program 85.5%

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

      1. associate-/l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 62.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 14: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+22} \lor \neg \left(z \leq 1.46 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+22) (not (<= z 1.46e+16)))
   (/ (/ x z) z)
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+22) || !(z <= 1.46e+16)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.8d+22)) .or. (.not. (z <= 1.46d+16))) then
        tmp = (x / z) / z
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+22) || !(z <= 1.46e+16)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+22) or not (z <= 1.46e+16):
		tmp = (x / z) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e+22) || !(z <= 1.46e+16))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e+22) || ~((z <= 1.46e+16)))
		tmp = (x / z) / z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e+22], N[Not[LessEqual[z, 1.46e+16]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000004e22 or 1.46e16 < z

   1. Initial program 80.6%

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

   2. Taylor expanded in z around inf 69.5%

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

      1. unpow2 69.5%

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

      2. associate-/r* 80.8%

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

   4. Simplified 80.8%

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

   if -3.8000000000000004e22 < z < 1.46e16

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 74.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+22} \lor \neg \left(z \leq 1.46 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 15: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -30000000000 \lor \neg \left(z \leq 1.42 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -30000000000.0) (not (<= z 1.42e+31)))
   (/ x (* y z))
   (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -30000000000.0) || !(z <= 1.42e+31)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-30000000000.0d0)) .or. (.not. (z <= 1.42d+31))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -30000000000.0) || !(z <= 1.42e+31)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -30000000000.0) or not (z <= 1.42e+31):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -30000000000.0) || !(z <= 1.42e+31))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -30000000000.0) || ~((z <= 1.42e+31)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -30000000000.0], N[Not[LessEqual[z, 1.42e+31]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e10 or 1.41999999999999997e31 < z

   1. Initial program 81.1%

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

   2. Taylor expanded in y around inf 40.0%

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

      1. *-commutative 40.0%

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

   4. Simplified 40.0%

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

   5. Taylor expanded in t around 0 38.0%

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

      1. associate-*r/ 38.0%

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

      2. neg-mul-1 38.0%

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

   7. Simplified 38.0%

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

      1. expm1-log1p-u 37.6%

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

      2. expm1-udef 50.8%

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

      3. add-sqr-sqrt 21.4%

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

      4. sqrt-unprod 49.4%

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

      5. sqr-neg 49.4%

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

      6. sqrt-unprod 29.6%

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

      7. add-sqr-sqrt 50.9%

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

      8. associate-/r* 50.8%

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

   9. Applied egg-rr 50.8%

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

       1. expm1-def 32.4%

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

       2. expm1-log1p 32.7%

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

       3. associate-/r* 36.3%

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

   11. Simplified 36.3%

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

   if -3e10 < z < 1.41999999999999997e31

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 58.8%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000000000 \lor \neg \left(z \leq 1.42 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 16: 60.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-73} \lor \neg \left(z \leq 1.3 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -3.8e-73) (not (<= z 1.3e-10))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-73) || !(z <= 1.3e-10)) {
		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 <= (-3.8d-73)) .or. (.not. (z <= 1.3d-10))) 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 <= -3.8e-73) || !(z <= 1.3e-10)) {
		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 <= -3.8e-73) or not (z <= 1.3e-10):
		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 <= -3.8e-73) || !(z <= 1.3e-10))
		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 <= -3.8e-73) || ~((z <= 1.3e-10)))
		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, -3.8e-73], N[Not[LessEqual[z, 1.3e-10]], $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 < -3.8000000000000003e-73 or 1.29999999999999991e-10 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. unpow2 65.4%

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

   4. Simplified 65.4%

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

   if -3.8000000000000003e-73 < z < 1.29999999999999991e-10

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 64.4%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-73} \lor \neg \left(z \leq 1.3 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 17: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-75} \lor \neg \left(z \leq 1.8 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e-75) (not (<= z 1.8e-10))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e-75) || !(z <= 1.8e-10)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.8d-75)) .or. (.not. (z <= 1.8d-10))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e-75) || !(z <= 1.8e-10)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e-75) or not (z <= 1.8e-10):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e-75) || !(z <= 1.8e-10))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e-75) || ~((z <= 1.8e-10)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e-75], N[Not[LessEqual[z, 1.8e-10]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000003e-75 or 1.8e-10 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. unpow2 65.4%

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

   4. Simplified 65.4%

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

   if -7.8000000000000003e-75 < z < 1.8e-10

   1. Initial program 93.9%

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

      1. associate-/l/ 93.2%

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

      2. div-inv 93.2%

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

   3. Applied egg-rr 93.2%

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

   4. Taylor expanded in t around inf 78.9%

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

   5. Taylor expanded in y around inf 65.8%

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

      1. un-div-inv 65.9%

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

   7. Applied egg-rr 65.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-75} \lor \neg \left(z \leq 1.8 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 18: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-73} \lor \neg \left(z \leq 1.75 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e-73) (not (<= z 1.75e-10))) (/ (/ x z) z) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-73) || !(z <= 1.75e-10)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.8d-73)) .or. (.not. (z <= 1.75d-10))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-73) || !(z <= 1.75e-10)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e-73) or not (z <= 1.75e-10):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e-73) || !(z <= 1.75e-10))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e-73) || ~((z <= 1.75e-10)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e-73], N[Not[LessEqual[z, 1.75e-10]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000003e-73 or 1.7499999999999999e-10 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. unpow2 65.4%

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

      2. associate-/r* 75.2%

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

   4. Simplified 75.2%

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

   if -3.8000000000000003e-73 < z < 1.7499999999999999e-10

   1. Initial program 93.9%

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

      1. associate-/l/ 93.2%

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

      2. div-inv 93.2%

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

   3. Applied egg-rr 93.2%

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

   4. Taylor expanded in t around inf 78.9%

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

   5. Taylor expanded in y around inf 65.8%

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

      1. un-div-inv 65.9%

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

   7. Applied egg-rr 65.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-73} \lor \neg \left(z \leq 1.75 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 19: 46.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7000000000000:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -7000000000000.0)
   (/ x (* y z))
   (if (<= z 2.8e+101) (/ x (* y t)) (/ x (* z t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7000000000000.0) {
		tmp = x / (y * z);
	} else if (z <= 2.8e+101) {
		tmp = x / (y * t);
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7000000000000.0d0)) then
        tmp = x / (y * z)
    else if (z <= 2.8d+101) then
        tmp = x / (y * t)
    else
        tmp = x / (z * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7000000000000.0) {
		tmp = x / (y * z);
	} else if (z <= 2.8e+101) {
		tmp = x / (y * t);
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -7000000000000.0:
		tmp = x / (y * z)
	elif z <= 2.8e+101:
		tmp = x / (y * t)
	else:
		tmp = x / (z * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7000000000000.0)
		tmp = Float64(x / Float64(y * z));
	elseif (z <= 2.8e+101)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(x / Float64(z * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7000000000000.0)
		tmp = x / (y * z);
	elseif (z <= 2.8e+101)
		tmp = x / (y * t);
	else
		tmp = x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -7000000000000.0], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+101], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7e12

   1. Initial program 81.8%

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

   2. Taylor expanded in y around inf 35.0%

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

      1. *-commutative 35.0%

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

   4. Simplified 35.0%

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

   5. Taylor expanded in t around 0 35.1%

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

      1. associate-*r/ 35.1%

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

      2. neg-mul-1 35.1%

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

   7. Simplified 35.1%

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

      1. expm1-log1p-u 34.7%

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

      2. expm1-udef 46.4%

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

      3. add-sqr-sqrt 17.1%

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

      4. sqrt-unprod 44.3%

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

      5. sqr-neg 44.3%

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

      6. sqrt-unprod 29.5%

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

      7. add-sqr-sqrt 46.3%

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

      8. associate-/r* 46.3%

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

   9. Applied egg-rr 46.3%

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

       1. expm1-def 29.9%

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

       2. expm1-log1p 30.3%

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

       3. associate-/r* 33.5%

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

   11. Simplified 33.5%

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

   if -7e12 < z < 2.79999999999999981e101

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 57.9%

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

   if 2.79999999999999981e101 < z

   1. Initial program 76.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 46.8%

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

   5. Taylor expanded in y around 0 44.9%

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

      1. associate-*r/ 44.9%

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

      2. associate-/r* 43.7%

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

      3. neg-mul-1 43.7%

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

   7. Simplified 43.7%

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

      1. expm1-log1p-u 43.4%

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

      2. expm1-udef 59.5%

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

      3. div-inv 59.5%

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

      4. frac-times 59.5%

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

      5. add-sqr-sqrt 23.9%

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

      6. sqrt-unprod 59.1%

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

      7. sqr-neg 59.1%

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

      8. sqrt-unprod 35.8%

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

      9. add-sqr-sqrt 59.7%

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

      10. metadata-eval 59.7%

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

      11. div-inv 59.7%

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

      12. clear-num 59.7%

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

      13. inv-pow 59.7%

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

      14. pow-flip 59.7%

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

      15. metadata-eval 59.7%

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

      16. pow1 59.7%

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

   9. Applied egg-rr 59.7%

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

       1. expm1-def 43.0%

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

       2. expm1-log1p 43.3%

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

       3. *-commutative 43.3%

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

   11. Simplified 43.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7000000000000:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]

Alternative 20: 39.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

2. Taylor expanded in z around 0 44.4%

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

3. Final simplification 44.4%

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

Developer target: 87.2% 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 2023240 
(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))))