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

Percentage Accurate: 89.0% → 97.6%

Time: 14.3s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.0% 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: 97.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (* (/ (pow (cbrt x) 2.0) (- y z)) (/ (cbrt x) (- t z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	return (pow(cbrt(x), 2.0) / (y - z)) * (cbrt(x) / (t - z));
}

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	return (Math.pow(Math.cbrt(x), 2.0) / (y - z)) * (Math.cbrt(x) / (t - z));
}

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(Float64((cbrt(x) ^ 2.0) / Float64(y - z)) * Float64(cbrt(x) / Float64(t - z)))
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(N[Power[N[Power[x, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(N[Power[x, 1/3], $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.7%

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

   1. add-cube-cbrt 89.1%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. times-frac 98.0%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   3. pow2 98.0%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

3. Applied egg-rr 98.0%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

4. Final simplification 98.0%

   \[\leadsto \frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

Alternative 2: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{y}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) y)))
   (if (<= z -4.8e+70)
     t_1
     (if (<= z -2.5e-15)
       (/ (- x) (* y z))
       (if (<= z -2.15e-44)
         (/ (- x) (* z t))
         (if (<= z 6e+84) (/ (/ x t) y) t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / y;
	double tmp;
	if (z <= -4.8e+70) {
		tmp = t_1;
	} else if (z <= -2.5e-15) {
		tmp = -x / (y * z);
	} else if (z <= -2.15e-44) {
		tmp = -x / (z * t);
	} else if (z <= 6e+84) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / y
    if (z <= (-4.8d+70)) then
        tmp = t_1
    else if (z <= (-2.5d-15)) then
        tmp = -x / (y * z)
    else if (z <= (-2.15d-44)) then
        tmp = -x / (z * t)
    else if (z <= 6d+84) then
        tmp = (x / t) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / y;
	double tmp;
	if (z <= -4.8e+70) {
		tmp = t_1;
	} else if (z <= -2.5e-15) {
		tmp = -x / (y * z);
	} else if (z <= -2.15e-44) {
		tmp = -x / (z * t);
	} else if (z <= 6e+84) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / y
	tmp = 0
	if z <= -4.8e+70:
		tmp = t_1
	elif z <= -2.5e-15:
		tmp = -x / (y * z)
	elif z <= -2.15e-44:
		tmp = -x / (z * t)
	elif z <= 6e+84:
		tmp = (x / t) / y
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / y)
	tmp = 0.0
	if (z <= -4.8e+70)
		tmp = t_1;
	elseif (z <= -2.5e-15)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (z <= -2.15e-44)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 6e+84)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / y;
	tmp = 0.0;
	if (z <= -4.8e+70)
		tmp = t_1;
	elseif (z <= -2.5e-15)
		tmp = -x / (y * z);
	elseif (z <= -2.15e-44)
		tmp = -x / (z * t);
	elseif (z <= 6e+84)
		tmp = (x / t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -4.8e+70], t$95$1, If[LessEqual[z, -2.5e-15], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-44], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+84], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.79999999999999974e70 or 5.99999999999999992e84 < z

   1. Initial program 82.7%

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

   2. Taylor expanded in y around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. associate-/r* 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   7. Simplified 57.9%

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

      1. expm1-log1p-u 57.7%

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

      2. expm1-udef 70.5%

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

      3. associate-/l/ 70.5%

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

      4. add-sqr-sqrt 36.0%

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

      5. sqrt-unprod 69.3%

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

      6. sqr-neg 69.3%

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

      7. sqrt-unprod 34.5%

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

      8. add-sqr-sqrt 70.5%

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

      9. *-commutative 70.5%

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

   9. Applied egg-rr 70.5%

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

       1. expm1-def 46.5%

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

       2. expm1-log1p 46.9%

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

       3. associate-/r* 57.2%

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

   11. Simplified 57.2%

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

   if -4.79999999999999974e70 < z < -2.5e-15

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-/r* 56.2%

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

   4. Simplified 56.2%

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

   5. Taylor expanded in t around 0 38.3%

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

      1. associate-*r/ 38.3%

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

      2. neg-mul-1 38.3%

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

      3. *-commutative 38.3%

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

   7. Simplified 38.3%

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

   if -2.5e-15 < z < -2.15000000000000007e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 19.2%

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

   3. Taylor expanded in y around 0 18.8%

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

      1. associate-*r/ 18.8%

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

      2. neg-mul-1 18.8%

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

   5. Simplified 18.8%

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

   if -2.15000000000000007e-44 < z < 5.99999999999999992e84

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 65.2%

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

      1. *-commutative 65.2%

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

      2. associate-/r* 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in t around inf 60.1%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 3: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e-228)
   (/ (/ x y) (- t z))
   (if (<= t 9.5e-134)
     (/ (/ (- x) z) y)
     (if (<= t 2.6e-47) (/ x (* y (- t z))) (/ x (* (- y z) t))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-228) {
		tmp = (x / y) / (t - z);
	} else if (t <= 9.5e-134) {
		tmp = (-x / z) / y;
	} else if (t <= 2.6e-47) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.8d-228)) then
        tmp = (x / y) / (t - z)
    else if (t <= 9.5d-134) then
        tmp = (-x / z) / y
    else if (t <= 2.6d-47) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-228) {
		tmp = (x / y) / (t - z);
	} else if (t <= 9.5e-134) {
		tmp = (-x / z) / y;
	} else if (t <= 2.6e-47) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e-228:
		tmp = (x / y) / (t - z)
	elif t <= 9.5e-134:
		tmp = (-x / z) / y
	elif t <= 2.6e-47:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e-228)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 9.5e-134)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 2.6e-47)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e-228)
		tmp = (x / y) / (t - z);
	elseif (t <= 9.5e-134)
		tmp = (-x / z) / y;
	elseif (t <= 2.6e-47)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e-228], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-134], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.6e-47], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.8000000000000001e-228

   1. Initial program 89.6%

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

      1. add-cube-cbrt 88.9%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 97.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 97.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   4. Taylor expanded in y around inf 60.1%

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

      1. associate-/r* 61.5%

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

   6. Simplified 61.5%

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

   if -1.8000000000000001e-228 < t < 9.5000000000000008e-134

   1. Initial program 95.1%

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

   2. Taylor expanded in y around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-/r* 62.4%

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

   4. Simplified 62.4%

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

   5. Taylor expanded in t around 0 59.4%

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

      1. associate-*r/ 59.4%

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

      2. neg-mul-1 59.4%

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

   7. Simplified 59.4%

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

   if 9.5000000000000008e-134 < t < 2.6e-47

   1. Initial program 86.1%

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

   2. Taylor expanded in y around inf 42.3%

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

      1. *-commutative 42.3%

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

   4. Simplified 42.3%

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

   if 2.6e-47 < t

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 81.2%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 4: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+114} \lor \neg \left(z \leq 2.4 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

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 -4.6e+114) (not (<= z 2.4e+76)))
   (/ (/ (- 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 <= -4.6e+114) || !(z <= 2.4e+76)) {
		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 <= (-4.6d+114)) .or. (.not. (z <= 2.4d+76))) 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 <= -4.6e+114) || !(z <= 2.4e+76)) {
		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 <= -4.6e+114) or not (z <= 2.4e+76):
		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 <= -4.6e+114) || !(z <= 2.4e+76))
		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 <= -4.6e+114) || ~((z <= 2.4e+76)))
		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, -4.6e+114], N[Not[LessEqual[z, 2.4e+76]], $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 < -4.6000000000000001e114 or 2.4e76 < z

   1. Initial program 81.7%

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

      1. add-cube-cbrt 81.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   4. Taylor expanded in t around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-/r* 92.9%

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

      3. distribute-neg-frac 92.9%

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

      4. distribute-frac-neg 92.9%

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

   6. Simplified 92.9%

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

   if -4.6000000000000001e114 < z < 2.4e76

   1. Initial program 95.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+114} \lor \neg \left(z \leq 2.4 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 5: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-49}:\\ \;\;\;\;\frac{-x}{z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e-227)
   (/ (/ x y) (- t z))
   (if (<= t 5.4e-49) (* (/ (- x) z) (/ -1.0 z)) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-227) {
		tmp = (x / y) / (t - z);
	} else if (t <= 5.4e-49) {
		tmp = (-x / z) * (-1.0 / z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.8d-227)) then
        tmp = (x / y) / (t - z)
    else if (t <= 5.4d-49) then
        tmp = (-x / z) * ((-1.0d0) / z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-227) {
		tmp = (x / y) / (t - z);
	} else if (t <= 5.4e-49) {
		tmp = (-x / z) * (-1.0 / z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e-227:
		tmp = (x / y) / (t - z)
	elif t <= 5.4e-49:
		tmp = (-x / z) * (-1.0 / z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e-227)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 5.4e-49)
		tmp = Float64(Float64(Float64(-x) / z) * Float64(-1.0 / z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e-227)
		tmp = (x / y) / (t - z);
	elseif (t <= 5.4e-49)
		tmp = (-x / z) * (-1.0 / z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e-227], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-49], N[(N[((-x) / z), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8e-227

   1. Initial program 89.6%

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

      1. add-cube-cbrt 88.9%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 97.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 97.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   4. Taylor expanded in y around inf 60.1%

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

      1. associate-/r* 61.5%

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

   6. Simplified 61.5%

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

   if -1.8e-227 < t < 5.3999999999999999e-49

   1. Initial program 92.3%

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

      1. *-un-lft-identity 92.3%

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

      2. times-frac 97.6%

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

   3. Applied egg-rr 97.6%

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

   4. Taylor expanded in y around 0 72.6%

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

   5. Taylor expanded in t around 0 71.5%

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

      1. associate-*r/ 48.4%

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

      2. neg-mul-1 48.4%

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

   7. Simplified 71.5%

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

   if 5.3999999999999999e-49 < t

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 81.2%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-49}:\\ \;\;\;\;\frac{-x}{z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 6: 79.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-132}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e-33)
   (/ (/ x y) (- t z))
   (if (<= y 2.25e-132) (/ (- x) (* z (- t z))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-33) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.25e-132) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4d-33)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.25d-132) then
        tmp = -x / (z * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-33) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.25e-132) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4e-33:
		tmp = (x / y) / (t - z)
	elif y <= 2.25e-132:
		tmp = -x / (z * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e-33)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.25e-132)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e-33)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.25e-132)
		tmp = -x / (z * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4e-33], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e-132], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0000000000000002e-33

   1. Initial program 91.2%

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

      1. add-cube-cbrt 90.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.9%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.9%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   4. Taylor expanded in y around inf 82.7%

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

      1. associate-/r* 84.1%

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

   6. Simplified 84.1%

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

   if -4.0000000000000002e-33 < y < 2.25e-132

   1. Initial program 91.7%

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

   2. Taylor expanded in y around 0 79.2%

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

      1. associate-*r/ 79.2%

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

      2. neg-mul-1 79.2%

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

   4. Simplified 79.2%

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

   if 2.25e-132 < y

   1. Initial program 86.9%

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

   2. Taylor expanded in t around inf 54.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-132}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 7: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.9e-210)
   (/ (/ x (- t z)) y)
   (if (<= t 1.35e-45) (/ (- x) (* z (- y z))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.9e-210) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.35e-45) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.9d-210)) then
        tmp = (x / (t - z)) / y
    else if (t <= 1.35d-45) then
        tmp = -x / (z * (y - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.9e-210) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.35e-45) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.9e-210:
		tmp = (x / (t - z)) / y
	elif t <= 1.35e-45:
		tmp = -x / (z * (y - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.9e-210)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 1.35e-45)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.9e-210)
		tmp = (x / (t - z)) / y;
	elseif (t <= 1.35e-45)
		tmp = -x / (z * (y - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.9e-210], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.35e-45], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.90000000000000006e-210

   1. Initial program 89.9%

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

   2. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/r* 65.6%

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

   4. Simplified 65.6%

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

   if -2.90000000000000006e-210 < t < 1.34999999999999992e-45

   1. Initial program 91.8%

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

   2. Taylor expanded in t around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. neg-mul-1 83.6%

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

   4. Simplified 83.6%

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

   if 1.34999999999999992e-45 < t

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 81.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 8: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3e-210)
   (/ (/ x (- t z)) y)
   (if (<= t 3.8e-44) (/ (/ (- x) z) (- y z)) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e-210) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 3.8e-44) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3d-210)) then
        tmp = (x / (t - z)) / y
    else if (t <= 3.8d-44) then
        tmp = (-x / z) / (y - z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e-210) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 3.8e-44) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -3e-210:
		tmp = (x / (t - z)) / y
	elif t <= 3.8e-44:
		tmp = (-x / z) / (y - z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3e-210)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 3.8e-44)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3e-210)
		tmp = (x / (t - z)) / y;
	elseif (t <= 3.8e-44)
		tmp = (-x / z) / (y - z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -3e-210], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 3.8e-44], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0000000000000001e-210

   1. Initial program 89.9%

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

   2. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/r* 65.6%

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

   4. Simplified 65.6%

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

   if -3.0000000000000001e-210 < t < 3.8000000000000001e-44

   1. Initial program 91.8%

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

      1. add-cube-cbrt 91.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 97.8%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 97.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   4. Taylor expanded in t around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. associate-/r* 89.8%

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

      3. distribute-neg-frac 89.8%

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

      4. distribute-frac-neg 89.8%

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

   6. Simplified 89.8%

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

   if 3.8000000000000001e-44 < t

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 81.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 9: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-165} \lor \neg \left(t \leq 1.75 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y} \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e-165) (not (<= t 1.75e-95)))
   (/ x (* (- y z) t))
   (* (/ -1.0 y) (/ x z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-165) || !(t <= 1.75e-95)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (-1.0 / y) * (x / z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.6d-165)) .or. (.not. (t <= 1.75d-95))) then
        tmp = x / ((y - z) * t)
    else
        tmp = ((-1.0d0) / y) * (x / z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-165) || !(t <= 1.75e-95)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (-1.0 / y) * (x / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -6.6e-165) or not (t <= 1.75e-95):
		tmp = x / ((y - z) * t)
	else:
		tmp = (-1.0 / y) * (x / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.6e-165) || !(t <= 1.75e-95))
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(-1.0 / y) * Float64(x / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.6e-165) || ~((t <= 1.75e-95)))
		tmp = x / ((y - z) * t);
	else
		tmp = (-1.0 / y) * (x / 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[t, -6.6e-165], N[Not[LessEqual[t, 1.75e-95]], $MachinePrecision]], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5999999999999996e-165 or 1.7499999999999999e-95 < t

   1. Initial program 87.9%

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

   2. Taylor expanded in t around inf 71.3%

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

   if -6.5999999999999996e-165 < t < 1.7499999999999999e-95

   1. Initial program 93.4%

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

   2. Taylor expanded in y around inf 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-/r* 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in t around 0 55.4%

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

      1. associate-*r/ 55.4%

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

      2. neg-mul-1 55.4%

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

   7. Simplified 55.4%

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

      1. associate-/l/ 49.8%

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

      2. neg-mul-1 49.8%

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

      3. times-frac 55.4%

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

   9. Applied egg-rr 55.4%

      \[\leadsto \color{blue}{\frac{-1}{y} \cdot \frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-165} \lor \neg \left(t \leq 1.75 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+144} \lor \neg \left(z \leq 1.1 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.6e+144) (not (<= z 1.1e+57)))
   (/ x (* z (- y z)))
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e+144) || !(z <= 1.1e+57)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.6d+144)) .or. (.not. (z <= 1.1d+57))) then
        tmp = x / (z * (y - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e+144) || !(z <= 1.1e+57)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -7.6e+144) or not (z <= 1.1e+57):
		tmp = x / (z * (y - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.6e+144) || !(z <= 1.1e+57))
		tmp = Float64(x / Float64(z * Float64(y - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.6e+144) || ~((z <= 1.1e+57)))
		tmp = x / (z * (y - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.6e+144], N[Not[LessEqual[z, 1.1e+57]], $MachinePrecision]], N[(x / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.60000000000000053e144 or 1.1e57 < z

   1. Initial program 83.4%

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

      1. add-cube-cbrt 83.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.5%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.5%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   4. Taylor expanded in t around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. associate-/r* 93.9%

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

      3. distribute-neg-frac 93.9%

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

      4. distribute-frac-neg 93.9%

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

   6. Simplified 93.9%

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

      1. expm1-log1p-u 92.8%

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

      2. expm1-udef 81.6%

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

      3. associate-/l/ 81.6%

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

      4. add-sqr-sqrt 39.0%

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

      5. sqrt-unprod 77.6%

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

      6. sqr-neg 77.6%

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

      7. sqrt-unprod 41.7%

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

      8. add-sqr-sqrt 80.3%

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

   8. Applied egg-rr 80.3%

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

      1. expm1-def 80.3%

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

      2. expm1-log1p 80.3%

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

      3. *-commutative 80.3%

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

   10. Simplified 80.3%

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

   if -7.60000000000000053e144 < z < 1.1e57

   1. Initial program 94.0%

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

   2. Taylor expanded in t around inf 61.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+144} \lor \neg \left(z \leq 1.1 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 11: 52.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-68}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y} \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.4e-68)
   (/ (/ (- x) z) y)
   (if (<= z 6.4e+81) (/ (/ x t) y) (* (/ -1.0 y) (/ x z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e-68) {
		tmp = (-x / z) / y;
	} else if (z <= 6.4e+81) {
		tmp = (x / t) / y;
	} else {
		tmp = (-1.0 / y) * (x / z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.4d-68)) then
        tmp = (-x / z) / y
    else if (z <= 6.4d+81) then
        tmp = (x / t) / y
    else
        tmp = ((-1.0d0) / y) * (x / z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e-68) {
		tmp = (-x / z) / y;
	} else if (z <= 6.4e+81) {
		tmp = (x / t) / y;
	} else {
		tmp = (-1.0 / y) * (x / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.4e-68:
		tmp = (-x / z) / y
	elif z <= 6.4e+81:
		tmp = (x / t) / y
	else:
		tmp = (-1.0 / y) * (x / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.4e-68)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (z <= 6.4e+81)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(-1.0 / y) * Float64(x / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.4e-68)
		tmp = (-x / z) / y;
	elseif (z <= 6.4e+81)
		tmp = (x / t) / y;
	else
		tmp = (-1.0 / y) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.4e-68], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 6.4e+81], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(-1.0 / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e-68

   1. Initial program 87.1%

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

   2. Taylor expanded in y around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. associate-/r* 56.1%

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

   4. Simplified 56.1%

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

   5. Taylor expanded in t around 0 50.4%

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

      1. associate-*r/ 50.4%

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

      2. neg-mul-1 50.4%

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

   7. Simplified 50.4%

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

   if -1.4000000000000001e-68 < z < 6.4e81

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-/r* 70.2%

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

   4. Simplified 70.2%

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

   5. Taylor expanded in t around inf 61.2%

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

   if 6.4e81 < z

   1. Initial program 82.8%

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

   2. Taylor expanded in y around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-/r* 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in t around 0 61.7%

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

      1. associate-*r/ 61.7%

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

      2. neg-mul-1 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/l/ 48.1%

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

      2. neg-mul-1 48.1%

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

      3. times-frac 61.7%

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

   9. Applied egg-rr 61.7%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-68}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 12: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-72} \lor \neg \left(z \leq 3.05 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e-72) (not (<= z 3.05e+82)))
   (/ (/ (- x) z) y)
   (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e-72) || !(z <= 3.05e+82)) {
		tmp = (-x / z) / y;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.1d-72)) .or. (.not. (z <= 3.05d+82))) then
        tmp = (-x / z) / y
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e-72) || !(z <= 3.05e+82)) {
		tmp = (-x / z) / y;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e-72) or not (z <= 3.05e+82):
		tmp = (-x / z) / y
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.1e-72) || !(z <= 3.05e+82))
		tmp = Float64(Float64(Float64(-x) / z) / y);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.1e-72) || ~((z <= 3.05e+82)))
		tmp = (-x / z) / y;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.1e-72], N[Not[LessEqual[z, 3.05e+82]], $MachinePrecision]], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000003e-72 or 3.0499999999999999e82 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in y around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/r* 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in t around 0 55.0%

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

      1. associate-*r/ 55.0%

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

      2. neg-mul-1 55.0%

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

   7. Simplified 55.0%

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

   if -4.10000000000000003e-72 < z < 3.0499999999999999e82

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-/r* 70.2%

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

   4. Simplified 70.2%

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

   5. Taylor expanded in t around inf 61.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-72} \lor \neg \left(z \leq 3.05 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 13: 46.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+120} \lor \neg \left(z \leq 48000000000000\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.06e+120) (not (<= z 48000000000000.0)))
   (/ x (* z t))
   (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.06e+120) || !(z <= 48000000000000.0)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.06d+120)) .or. (.not. (z <= 48000000000000.0d0))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.06e+120) || !(z <= 48000000000000.0)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.06e+120) or not (z <= 48000000000000.0):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.06e+120) || !(z <= 48000000000000.0))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.06e+120) || ~((z <= 48000000000000.0)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.06e+120], N[Not[LessEqual[z, 48000000000000.0]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05999999999999994e120 or 4.8e13 < z

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 42.4%

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

   3. Taylor expanded in y around 0 39.1%

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

      1. associate-*r/ 39.1%

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

      2. neg-mul-1 39.1%

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

   5. Simplified 39.1%

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

      1. expm1-log1p-u 38.9%

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

      2. expm1-udef 72.6%

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

      3. add-sqr-sqrt 35.7%

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

      4. sqrt-unprod 70.2%

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

      5. sqr-neg 70.2%

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

      6. sqrt-unprod 36.6%

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

      7. add-sqr-sqrt 72.3%

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

      8. *-commutative 72.3%

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

      9. associate-/r* 72.3%

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

   7. Applied egg-rr 72.3%

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

      1. expm1-def 46.1%

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

      2. expm1-log1p 46.4%

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

      3. associate-/l/ 37.5%

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

      4. *-commutative 37.5%

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

   9. Simplified 37.5%

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

   if -1.05999999999999994e120 < z < 4.8e13

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 51.5%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+120} \lor \neg \left(z \leq 48000000000000\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+64} \lor \neg \left(z \leq 7.2 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+64) (not (<= z 7.2e+48))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+64) || !(z <= 7.2e+48)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.1d+64)) .or. (.not. (z <= 7.2d+48))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+64) || !(z <= 7.2e+48)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+64) or not (z <= 7.2e+48):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+64) || !(z <= 7.2e+48))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e+64) || ~((z <= 7.2e+48)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+64], N[Not[LessEqual[z, 7.2e+48]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0999999999999999e64 or 7.19999999999999967e48 < z

   1. Initial program 83.7%

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

   2. Taylor expanded in y around inf 49.8%

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

      1. *-commutative 49.8%

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

      2. associate-/r* 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in t around 0 56.4%

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

      1. associate-*r/ 56.4%

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

      2. neg-mul-1 56.4%

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

   7. Simplified 56.4%

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

      1. expm1-log1p-u 56.2%

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

      2. expm1-udef 70.5%

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

      3. associate-/l/ 70.5%

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

      4. add-sqr-sqrt 34.7%

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

      5. sqrt-unprod 70.2%

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

      6. sqr-neg 70.2%

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

      7. sqrt-unprod 35.8%

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

      8. add-sqr-sqrt 70.5%

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

      9. *-commutative 70.5%

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

   9. Applied egg-rr 70.5%

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

       1. expm1-def 45.6%

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

       2. expm1-log1p 46.0%

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

   11. Simplified 46.0%

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

   if -3.0999999999999999e64 < z < 7.19999999999999967e48

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 52.2%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+64} \lor \neg \left(z \leq 7.2 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 48.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+69} \lor \neg \left(z \leq 1.75 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.15e+69) (not (<= z 1.75e+86))) (/ x (* y z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.15e+69) || !(z <= 1.75e+86)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.15d+69)) .or. (.not. (z <= 1.75d+86))) then
        tmp = x / (y * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.15e+69) || !(z <= 1.75e+86)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.15e+69) or not (z <= 1.75e+86):
		tmp = x / (y * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.15e+69) || !(z <= 1.75e+86))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.15e+69) || ~((z <= 1.75e+86)))
		tmp = x / (y * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.15e+69], N[Not[LessEqual[z, 1.75e+86]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.15000000000000004e69 or 1.75000000000000009e86 < z

   1. Initial program 82.7%

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

   2. Taylor expanded in y around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. associate-/r* 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   7. Simplified 57.9%

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

      1. expm1-log1p-u 57.7%

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

      2. expm1-udef 70.5%

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

      3. associate-/l/ 70.5%

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

      4. add-sqr-sqrt 36.0%

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

      5. sqrt-unprod 69.3%

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

      6. sqr-neg 69.3%

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

      7. sqrt-unprod 34.5%

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

      8. add-sqr-sqrt 70.5%

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

      9. *-commutative 70.5%

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

   9. Applied egg-rr 70.5%

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

       1. expm1-def 46.5%

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

       2. expm1-log1p 46.9%

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

   11. Simplified 46.9%

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

   if -3.15000000000000004e69 < z < 1.75000000000000009e86

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-/r* 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in t around inf 54.6%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+69} \lor \neg \left(z \leq 1.75 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 16: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+118} \lor \neg \left(z \leq 3.3 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.45e+118) (not (<= z 3.3e+47))) (/ (/ x z) t) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.45e+118) || !(z <= 3.3e+47)) {
		tmp = (x / z) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.45d+118)) .or. (.not. (z <= 3.3d+47))) then
        tmp = (x / z) / t
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.45e+118) || !(z <= 3.3e+47)) {
		tmp = (x / z) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.45e+118) or not (z <= 3.3e+47):
		tmp = (x / z) / t
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.45e+118) || !(z <= 3.3e+47))
		tmp = Float64(Float64(x / z) / t);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.45e+118) || ~((z <= 3.3e+47)))
		tmp = (x / z) / t;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.45e+118], N[Not[LessEqual[z, 3.3e+47]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4500000000000002e118 or 3.2999999999999999e47 < z

   1. Initial program 83.1%

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

   2. Taylor expanded in t around inf 39.7%

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

   3. Taylor expanded in y around 0 39.6%

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

      1. associate-*r/ 39.6%

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

      2. neg-mul-1 39.6%

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

   5. Simplified 39.6%

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

      1. expm1-log1p-u 39.4%

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

      2. expm1-udef 74.2%

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

      3. add-sqr-sqrt 36.1%

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

      4. sqrt-unprod 71.9%

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

      5. sqr-neg 71.9%

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

      6. sqrt-unprod 38.1%

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

      7. add-sqr-sqrt 74.2%

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

      8. *-commutative 74.2%

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

      9. associate-/r* 74.2%

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

   7. Applied egg-rr 74.2%

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

      1. expm1-def 49.1%

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

      2. expm1-log1p 49.4%

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

   9. Simplified 49.4%

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

   if -2.4500000000000002e118 < z < 3.2999999999999999e47

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-/r* 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in t around inf 53.6%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+118} \lor \neg \left(z \leq 3.3 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 17: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+69} \lor \neg \left(z \leq 4.6 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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+69) (not (<= z 4.6e+86))) (/ (/ x z) y) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+69) || !(z <= 4.6e+86)) {
		tmp = (x / z) / y;
	} 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+69)) .or. (.not. (z <= 4.6d+86))) then
        tmp = (x / z) / y
    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+69) || !(z <= 4.6e+86)) {
		tmp = (x / z) / y;
	} 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+69) or not (z <= 4.6e+86):
		tmp = (x / z) / y
	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+69) || !(z <= 4.6e+86))
		tmp = Float64(Float64(x / z) / y);
	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+69) || ~((z <= 4.6e+86)))
		tmp = (x / z) / y;
	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+69], N[Not[LessEqual[z, 4.6e+86]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000028e69 or 4.59999999999999979e86 < z

   1. Initial program 82.7%

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

   2. Taylor expanded in y around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. associate-/r* 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   7. Simplified 57.9%

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

      1. expm1-log1p-u 57.7%

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

      2. expm1-udef 70.5%

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

      3. associate-/l/ 70.5%

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

      4. add-sqr-sqrt 36.0%

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

      5. sqrt-unprod 69.3%

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

      6. sqr-neg 69.3%

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

      7. sqrt-unprod 34.5%

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

      8. add-sqr-sqrt 70.5%

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

      9. *-commutative 70.5%

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

   9. Applied egg-rr 70.5%

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

       1. expm1-def 46.5%

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

       2. expm1-log1p 46.9%

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

       3. associate-/r* 57.2%

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

   11. Simplified 57.2%

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

   if -3.80000000000000028e69 < z < 4.59999999999999979e86

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-/r* 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in t around inf 54.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+69} \lor \neg \left(z \leq 4.6 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 18: 70.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.7e-44) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.7e-44) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.7d-44) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.7e-44) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.7e-44:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.7e-44)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.7e-44)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.7e-44], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.70000000000000008e-44

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 56.5%

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

      1. *-commutative 56.5%

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

   4. Simplified 56.5%

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

   if 1.70000000000000008e-44 < t

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 81.2%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 19: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.75 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.75e-46) (/ (/ x (- t z)) y) (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.75e-46) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.75d-46) then
        tmp = (x / (t - z)) / y
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.75e-46) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.75e-46:
		tmp = (x / (t - z)) / y
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.75e-46)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.75e-46)
		tmp = (x / (t - z)) / y;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.75e-46], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.7500000000000001e-46

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 56.5%

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

      1. *-commutative 56.5%

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

      2. associate-/r* 61.0%

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

   4. Simplified 61.0%

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

   if 1.7500000000000001e-46 < t

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 81.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.75 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 20: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.7%

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

   1. add-cube-cbrt 89.1%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. times-frac 98.0%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   3. pow2 98.0%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

3. Applied egg-rr 98.0%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
4. Step-by-step derivation

   1. associate-*r/ 95.7%

      \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

   2. associate-*l/ 95.7%

      \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

   3. unpow2 95.7%

      \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

   4. add-cube-cbrt 96.5%

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

5. Applied egg-rr 96.5%

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

6. Final simplification 96.5%

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

Alternative 21: 39.9% 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 89.7%

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

2. Taylor expanded in z around 0 41.0%

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

3. Final simplification 41.0%

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

Developer target: 88.0% 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 2023308 
(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))))