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

Percentage Accurate: 88.9% → 97.7%

Time: 12.5s

Alternatives: 16

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.5× speedup

Math

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

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 0.0) (/ (/ x (- t z)) (- y z)) t_1)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= 0.0d0) then
        tmp = (x / (t - z)) / (y - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -0.0

   1. Initial program 83.1%

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

      1. *-un-lft-identity 83.1%

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

      2. times-frac 97.3%

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

   3. Applied egg-rr 97.3%

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

      1. associate-*l/ 97.4%

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

      2. *-un-lft-identity 97.4%

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

   5. Applied egg-rr 97.4%

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

   if -0.0 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 99.2%

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

4. Final simplification 98.0%

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

Alternative 2: 51.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ t_3 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+243}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) t)) (t_2 (/ (/ x t) y)) (t_3 (/ (- x) (* z t))))
   (if (<= t -5e-24)
     t_2
     (if (<= t 5e-121)
       (/ (/ (- x) z) y)
       (if (<= t 2.8e+88)
         t_1
         (if (<= t 1.5e+119)
           t_3
           (if (<= t 6.5e+149) t_1 (if (<= t 1.22e+243) t_3 t_2))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double t_2 = (x / t) / y;
	double t_3 = -x / (z * t);
	double tmp;
	if (t <= -5e-24) {
		tmp = t_2;
	} else if (t <= 5e-121) {
		tmp = (-x / z) / y;
	} else if (t <= 2.8e+88) {
		tmp = t_1;
	} else if (t <= 1.5e+119) {
		tmp = t_3;
	} else if (t <= 6.5e+149) {
		tmp = t_1;
	} else if (t <= 1.22e+243) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x / y) / t
    t_2 = (x / t) / y
    t_3 = -x / (z * t)
    if (t <= (-5d-24)) then
        tmp = t_2
    else if (t <= 5d-121) then
        tmp = (-x / z) / y
    else if (t <= 2.8d+88) then
        tmp = t_1
    else if (t <= 1.5d+119) then
        tmp = t_3
    else if (t <= 6.5d+149) then
        tmp = t_1
    else if (t <= 1.22d+243) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double t_2 = (x / t) / y;
	double t_3 = -x / (z * t);
	double tmp;
	if (t <= -5e-24) {
		tmp = t_2;
	} else if (t <= 5e-121) {
		tmp = (-x / z) / y;
	} else if (t <= 2.8e+88) {
		tmp = t_1;
	} else if (t <= 1.5e+119) {
		tmp = t_3;
	} else if (t <= 6.5e+149) {
		tmp = t_1;
	} else if (t <= 1.22e+243) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / y) / t
	t_2 = (x / t) / y
	t_3 = -x / (z * t)
	tmp = 0
	if t <= -5e-24:
		tmp = t_2
	elif t <= 5e-121:
		tmp = (-x / z) / y
	elif t <= 2.8e+88:
		tmp = t_1
	elif t <= 1.5e+119:
		tmp = t_3
	elif t <= 6.5e+149:
		tmp = t_1
	elif t <= 1.22e+243:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / t)
	t_2 = Float64(Float64(x / t) / y)
	t_3 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (t <= -5e-24)
		tmp = t_2;
	elseif (t <= 5e-121)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 2.8e+88)
		tmp = t_1;
	elseif (t <= 1.5e+119)
		tmp = t_3;
	elseif (t <= 6.5e+149)
		tmp = t_1;
	elseif (t <= 1.22e+243)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) / t;
	t_2 = (x / t) / y;
	t_3 = -x / (z * t);
	tmp = 0.0;
	if (t <= -5e-24)
		tmp = t_2;
	elseif (t <= 5e-121)
		tmp = (-x / z) / y;
	elseif (t <= 2.8e+88)
		tmp = t_1;
	elseif (t <= 1.5e+119)
		tmp = t_3;
	elseif (t <= 6.5e+149)
		tmp = t_1;
	elseif (t <= 1.22e+243)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-24], t$95$2, If[LessEqual[t, 5e-121], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.8e+88], t$95$1, If[LessEqual[t, 1.5e+119], t$95$3, If[LessEqual[t, 6.5e+149], t$95$1, If[LessEqual[t, 1.22e+243], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.9999999999999998e-24 or 1.21999999999999993e243 < t

   1. Initial program 83.7%

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

   2. Taylor expanded in y around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. associate-/r* 73.5%

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

   4. Simplified 73.5%

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

   5. Taylor expanded in t around inf 68.5%

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

   if -4.9999999999999998e-24 < t < 4.99999999999999989e-121

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/r* 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. neg-mul-1 50.3%

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

   7. Simplified 50.3%

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

   if 4.99999999999999989e-121 < t < 2.79999999999999989e88 or 1.50000000000000001e119 < t < 6.50000000000000015e149

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 50.5%

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

      1. *-un-lft-identity 50.5%

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

      2. times-frac 52.0%

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

   4. Applied egg-rr 52.0%

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

      1. associate-*l/ 52.2%

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

      2. *-un-lft-identity 52.2%

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

   6. Applied egg-rr 52.2%

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

   if 2.79999999999999989e88 < t < 1.50000000000000001e119 or 6.50000000000000015e149 < t < 1.21999999999999993e243

   1. Initial program 80.6%

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

   2. Taylor expanded in y around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. neg-mul-1 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in z around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. neg-mul-1 61.0%

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

   7. Simplified 61.0%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+119}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+243}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 3: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+243}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) t)) (t_2 (/ (- x) (* z t))))
   (if (<= t -2.1e-23)
     (/ 1.0 (* y (/ t x)))
     (if (<= t 5.3e-121)
       (/ (/ (- x) z) y)
       (if (<= t 1.5e+88)
         t_1
         (if (<= t 1.1e+112)
           t_2
           (if (<= t 7.2e+149)
             t_1
             (if (<= t 1.22e+243) t_2 (/ (/ x t) y)))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double t_2 = -x / (z * t);
	double tmp;
	if (t <= -2.1e-23) {
		tmp = 1.0 / (y * (t / x));
	} else if (t <= 5.3e-121) {
		tmp = (-x / z) / y;
	} else if (t <= 1.5e+88) {
		tmp = t_1;
	} else if (t <= 1.1e+112) {
		tmp = t_2;
	} else if (t <= 7.2e+149) {
		tmp = t_1;
	} else if (t <= 1.22e+243) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) / t
    t_2 = -x / (z * t)
    if (t <= (-2.1d-23)) then
        tmp = 1.0d0 / (y * (t / x))
    else if (t <= 5.3d-121) then
        tmp = (-x / z) / y
    else if (t <= 1.5d+88) then
        tmp = t_1
    else if (t <= 1.1d+112) then
        tmp = t_2
    else if (t <= 7.2d+149) then
        tmp = t_1
    else if (t <= 1.22d+243) then
        tmp = t_2
    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 t_1 = (x / y) / t;
	double t_2 = -x / (z * t);
	double tmp;
	if (t <= -2.1e-23) {
		tmp = 1.0 / (y * (t / x));
	} else if (t <= 5.3e-121) {
		tmp = (-x / z) / y;
	} else if (t <= 1.5e+88) {
		tmp = t_1;
	} else if (t <= 1.1e+112) {
		tmp = t_2;
	} else if (t <= 7.2e+149) {
		tmp = t_1;
	} else if (t <= 1.22e+243) {
		tmp = t_2;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / y) / t
	t_2 = -x / (z * t)
	tmp = 0
	if t <= -2.1e-23:
		tmp = 1.0 / (y * (t / x))
	elif t <= 5.3e-121:
		tmp = (-x / z) / y
	elif t <= 1.5e+88:
		tmp = t_1
	elif t <= 1.1e+112:
		tmp = t_2
	elif t <= 7.2e+149:
		tmp = t_1
	elif t <= 1.22e+243:
		tmp = t_2
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / t)
	t_2 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (t <= -2.1e-23)
		tmp = Float64(1.0 / Float64(y * Float64(t / x)));
	elseif (t <= 5.3e-121)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 1.5e+88)
		tmp = t_1;
	elseif (t <= 1.1e+112)
		tmp = t_2;
	elseif (t <= 7.2e+149)
		tmp = t_1;
	elseif (t <= 1.22e+243)
		tmp = t_2;
	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)
	t_1 = (x / y) / t;
	t_2 = -x / (z * t);
	tmp = 0.0;
	if (t <= -2.1e-23)
		tmp = 1.0 / (y * (t / x));
	elseif (t <= 5.3e-121)
		tmp = (-x / z) / y;
	elseif (t <= 1.5e+88)
		tmp = t_1;
	elseif (t <= 1.1e+112)
		tmp = t_2;
	elseif (t <= 7.2e+149)
		tmp = t_1;
	elseif (t <= 1.22e+243)
		tmp = t_2;
	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_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e-23], N[(1.0 / N[(y * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e-121], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.5e+88], t$95$1, If[LessEqual[t, 1.1e+112], t$95$2, If[LessEqual[t, 7.2e+149], t$95$1, If[LessEqual[t, 1.22e+243], t$95$2, N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.1000000000000001e-23

   1. Initial program 85.9%

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

   2. Taylor expanded in z around 0 60.3%

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

      1. clear-num 60.2%

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

      2. inv-pow 60.2%

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

      3. associate-/l* 61.8%

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

   4. Applied egg-rr 61.8%

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

      1. unpow-1 61.8%

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

      2. associate-/r/ 68.2%

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

   6. Simplified 68.2%

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

   if -2.1000000000000001e-23 < t < 5.2999999999999996e-121

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/r* 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. neg-mul-1 50.3%

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

   7. Simplified 50.3%

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

   if 5.2999999999999996e-121 < t < 1.50000000000000003e88 or 1.1e112 < t < 7.1999999999999999e149

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 50.5%

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

      1. *-un-lft-identity 50.5%

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

      2. times-frac 52.0%

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

   4. Applied egg-rr 52.0%

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

      1. associate-*l/ 52.2%

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

      2. *-un-lft-identity 52.2%

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

   6. Applied egg-rr 52.2%

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

   if 1.50000000000000003e88 < t < 1.1e112 or 7.1999999999999999e149 < t < 1.21999999999999993e243

   1. Initial program 80.6%

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

   2. Taylor expanded in y around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. neg-mul-1 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in z around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. neg-mul-1 61.0%

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

   7. Simplified 61.0%

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

   if 1.21999999999999993e243 < t

   1. Initial program 75.1%

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

   2. Taylor expanded in y around inf 55.4%

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

      1. *-commutative 55.4%

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

      2. associate-/r* 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in t around inf 68.1%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+112}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+243}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 4: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{-x}{t - z}}{z}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.8e-87)
   (/ (/ x (- t z)) y)
   (if (<= t 5.5e-121)
     (/ (/ (- x) z) (- y z))
     (if (<= t 4e-35)
       (/ (/ (- x) (- t z)) z)
       (if (<= t 1.8e-21) (/ (- x) (* z (- y z))) (/ (/ x t) (- y z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e-87) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 5.5e-121) {
		tmp = (-x / z) / (y - z);
	} else if (t <= 4e-35) {
		tmp = (-x / (t - z)) / z;
	} else if (t <= 1.8e-21) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.8d-87)) then
        tmp = (x / (t - z)) / y
    else if (t <= 5.5d-121) then
        tmp = (-x / z) / (y - z)
    else if (t <= 4d-35) then
        tmp = (-x / (t - z)) / z
    else if (t <= 1.8d-21) then
        tmp = -x / (z * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e-87) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 5.5e-121) {
		tmp = (-x / z) / (y - z);
	} else if (t <= 4e-35) {
		tmp = (-x / (t - z)) / z;
	} else if (t <= 1.8e-21) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.8e-87:
		tmp = (x / (t - z)) / y
	elif t <= 5.5e-121:
		tmp = (-x / z) / (y - z)
	elif t <= 4e-35:
		tmp = (-x / (t - z)) / z
	elif t <= 1.8e-21:
		tmp = -x / (z * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.8e-87)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 5.5e-121)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	elseif (t <= 4e-35)
		tmp = Float64(Float64(Float64(-x) / Float64(t - z)) / z);
	elseif (t <= 1.8e-21)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.8e-87)
		tmp = (x / (t - z)) / y;
	elseif (t <= 5.5e-121)
		tmp = (-x / z) / (y - z);
	elseif (t <= 4e-35)
		tmp = (-x / (t - z)) / z;
	elseif (t <= 1.8e-21)
		tmp = -x / (z * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.8e-87], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 5.5e-121], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-35], N[(N[((-x) / N[(t - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.8e-21], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.7999999999999999e-87

   1. Initial program 88.7%

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

   2. Taylor expanded in y around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-/r* 77.4%

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

   4. Simplified 77.4%

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

   if -4.7999999999999999e-87 < t < 5.50000000000000031e-121

   1. Initial program 89.4%

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

      1. *-un-lft-identity 89.4%

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

      2. times-frac 96.5%

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

   3. Applied egg-rr 96.5%

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

      1. associate-*l/ 96.6%

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

      2. *-un-lft-identity 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in t around 0 85.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{y - z} \]
   7. 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%

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

   8. Simplified 85.8%

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

   if 5.50000000000000031e-121 < t < 4.00000000000000003e-35

   1. Initial program 94.1%

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

      1. *-un-lft-identity 94.1%

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

      2. times-frac 94.1%

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

   3. Applied egg-rr 94.1%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.2%

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

   5. Applied egg-rr 94.2%

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

      1. clear-num 94.3%

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

      2. associate-/r/ 94.0%

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

   7. Applied egg-rr 94.0%

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

   8. Taylor expanded in y around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. associate-/l/ 71.7%

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

      3. distribute-neg-frac 71.7%

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

      4. distribute-neg-frac 71.7%

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

   10. Simplified 71.7%

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

   if 4.00000000000000003e-35 < t < 1.79999999999999995e-21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   if 1.79999999999999995e-21 < t

   1. Initial program 84.1%

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

      1. *-un-lft-identity 84.1%

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

      2. times-frac 98.4%

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

   3. Applied egg-rr 98.4%

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

      1. associate-*l/ 98.5%

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

      2. *-un-lft-identity 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in t around inf 85.1%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{-x}{t - z}}{z}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 5: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-103}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e+22)
   (/ (/ x y) t)
   (if (<= y -1.8e-22)
     (/ (- x) (* y z))
     (if (<= y -9e-201)
       (/ x (* y t))
       (if (<= y 6.8e-103) (/ (- x) (* z t)) (/ (/ x t) y))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+22) {
		tmp = (x / y) / t;
	} else if (y <= -1.8e-22) {
		tmp = -x / (y * z);
	} else if (y <= -9e-201) {
		tmp = x / (y * t);
	} else if (y <= 6.8e-103) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.2d+22)) then
        tmp = (x / y) / t
    else if (y <= (-1.8d-22)) then
        tmp = -x / (y * z)
    else if (y <= (-9d-201)) then
        tmp = x / (y * t)
    else if (y <= 6.8d-103) then
        tmp = -x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+22) {
		tmp = (x / y) / t;
	} else if (y <= -1.8e-22) {
		tmp = -x / (y * z);
	} else if (y <= -9e-201) {
		tmp = x / (y * t);
	} else if (y <= 6.8e-103) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e+22:
		tmp = (x / y) / t
	elif y <= -1.8e-22:
		tmp = -x / (y * z)
	elif y <= -9e-201:
		tmp = x / (y * t)
	elif y <= 6.8e-103:
		tmp = -x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e+22)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= -1.8e-22)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (y <= -9e-201)
		tmp = Float64(x / Float64(y * t));
	elseif (y <= 6.8e-103)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.2e+22)
		tmp = (x / y) / t;
	elseif (y <= -1.8e-22)
		tmp = -x / (y * z);
	elseif (y <= -9e-201)
		tmp = x / (y * t);
	elseif (y <= 6.8e-103)
		tmp = -x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e+22], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, -1.8e-22], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-201], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-103], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.1999999999999996e22

   1. Initial program 88.2%

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

   2. Taylor expanded in z around 0 54.2%

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

      1. *-un-lft-identity 54.2%

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

      2. times-frac 63.8%

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

   4. Applied egg-rr 63.8%

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

      1. associate-*l/ 63.8%

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

      2. *-un-lft-identity 63.8%

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

   6. Applied egg-rr 63.8%

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

   if -4.1999999999999996e22 < y < -1.7999999999999999e-22

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. associate-/r* 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in t around 0 40.1%

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

      1. associate-*r/ 40.1%

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

      2. neg-mul-1 40.1%

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

      3. *-commutative 40.1%

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

   7. Simplified 40.1%

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

   if -1.7999999999999999e-22 < y < -9.0000000000000004e-201

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 35.9%

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

   if -9.0000000000000004e-201 < y < 6.80000000000000006e-103

   1. Initial program 90.4%

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

   2. Taylor expanded in y around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. neg-mul-1 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in z around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. neg-mul-1 46.6%

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

   7. Simplified 46.6%

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

   if 6.80000000000000006e-103 < y

   1. Initial program 85.8%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-/r* 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in t around inf 56.1%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-103}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 6: 92.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t - z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+131)
   (/ (/ (- x) z) (- y z))
   (if (<= z 1.3e+32) (/ x (* (- y z) (- t z))) (/ (/ (- x) (- t z)) z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+131) {
		tmp = (-x / z) / (y - z);
	} else if (z <= 1.3e+32) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (-x / (t - z)) / z;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.8d+131)) then
        tmp = (-x / z) / (y - z)
    else if (z <= 1.3d+32) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (-x / (t - z)) / z
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+131) {
		tmp = (-x / z) / (y - z);
	} else if (z <= 1.3e+32) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (-x / (t - z)) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+131:
		tmp = (-x / z) / (y - z)
	elif z <= 1.3e+32:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (-x / (t - z)) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+131)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	elseif (z <= 1.3e+32)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(Float64(-x) / Float64(t - z)) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+131)
		tmp = (-x / z) / (y - z);
	elseif (z <= 1.3e+32)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (-x / (t - z)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+131], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+32], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / N[(t - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000004e131

   1. Initial program 70.1%

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

      1. *-un-lft-identity 70.1%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.8%

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

      2. *-un-lft-identity 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 89.9%

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

      1. associate-*r/ 62.5%

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

      2. neg-mul-1 62.5%

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

   8. Simplified 89.9%

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

   if -3.8000000000000004e131 < z < 1.3000000000000001e32

   1. Initial program 95.4%

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

   if 1.3000000000000001e32 < z

   1. Initial program 74.1%

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

      1. *-un-lft-identity 74.1%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. associate-/l/ 90.9%

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

      3. distribute-neg-frac 90.9%

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

      4. distribute-neg-frac 90.9%

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

   10. Simplified 90.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t - z}}{z}\\ \end{array} \]

Alternative 7: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-105}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e-73)
   (/ (/ x (- t z)) y)
   (if (<= y 7.2e-105) (/ (- x) (* z (- t z))) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-73) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 7.2e-105) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2d-73)) then
        tmp = (x / (t - z)) / y
    else if (y <= 7.2d-105) then
        tmp = -x / (z * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-73) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 7.2e-105) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2e-73:
		tmp = (x / (t - z)) / y
	elif y <= 7.2e-105:
		tmp = -x / (z * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e-73)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 7.2e-105)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2e-73)
		tmp = (x / (t - z)) / y;
	elseif (y <= 7.2e-105)
		tmp = -x / (z * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2e-73], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7.2e-105], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999999e-73

   1. Initial program 88.7%

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

   2. Taylor expanded in y around inf 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-/r* 82.3%

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

   4. Simplified 82.3%

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

   if -1.99999999999999999e-73 < y < 7.19999999999999929e-105

   1. Initial program 89.3%

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

   2. Taylor expanded in y around 0 77.3%

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

      1. associate-*r/ 77.3%

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

      2. neg-mul-1 77.3%

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

   4. Simplified 77.3%

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

   if 7.19999999999999929e-105 < y

   1. Initial program 85.8%

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

      1. *-un-lft-identity 85.8%

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

      2. times-frac 95.2%

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

   3. Applied egg-rr 95.2%

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

      1. associate-*l/ 95.4%

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

      2. *-un-lft-identity 95.4%

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

   5. Applied egg-rr 95.4%

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

   6. Taylor expanded in t around inf 58.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-105}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 8: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.05e-86)
   (/ (/ x (- t z)) y)
   (if (<= t 9.6e-22) (/ (/ (- x) z) (- y z)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.05e-86) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 9.6e-22) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.05d-86)) then
        tmp = (x / (t - z)) / y
    else if (t <= 9.6d-22) then
        tmp = (-x / z) / (y - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.05e-86) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 9.6e-22) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.05e-86:
		tmp = (x / (t - z)) / y
	elif t <= 9.6e-22:
		tmp = (-x / z) / (y - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.05e-86)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 9.6e-22)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.05e-86)
		tmp = (x / (t - z)) / y;
	elseif (t <= 9.6e-22)
		tmp = (-x / z) / (y - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.05e-86], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 9.6e-22], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0499999999999999e-86

   1. Initial program 88.7%

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

   2. Taylor expanded in y around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-/r* 77.4%

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

   4. Simplified 77.4%

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

   if -2.0499999999999999e-86 < t < 9.60000000000000009e-22

   1. Initial program 90.4%

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

      1. *-un-lft-identity 90.4%

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

      2. times-frac 96.2%

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

   3. Applied egg-rr 96.2%

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

      1. associate-*l/ 96.3%

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

      2. *-un-lft-identity 96.3%

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

   5. Applied egg-rr 96.3%

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

   6. Taylor expanded in t around 0 82.6%

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

      1. associate-*r/ 45.9%

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

      2. neg-mul-1 45.9%

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

   8. Simplified 82.6%

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

   if 9.60000000000000009e-22 < t

   1. Initial program 84.1%

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

      1. *-un-lft-identity 84.1%

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

      2. times-frac 98.4%

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

   3. Applied egg-rr 98.4%

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

      1. associate-*l/ 98.5%

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

      2. *-un-lft-identity 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in t around inf 85.1%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.8e-22)
   (/ 1.0 (* y (/ t x)))
   (if (<= t 5.5e-121) (/ (/ (- x) z) y) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e-22) {
		tmp = 1.0 / (y * (t / x));
	} else if (t <= 5.5e-121) {
		tmp = (-x / 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 <= (-4.8d-22)) then
        tmp = 1.0d0 / (y * (t / x))
    else if (t <= 5.5d-121) then
        tmp = (-x / 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 <= -4.8e-22) {
		tmp = 1.0 / (y * (t / x));
	} else if (t <= 5.5e-121) {
		tmp = (-x / 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 <= -4.8e-22:
		tmp = 1.0 / (y * (t / x))
	elif t <= 5.5e-121:
		tmp = (-x / 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 <= -4.8e-22)
		tmp = Float64(1.0 / Float64(y * Float64(t / x)));
	elseif (t <= 5.5e-121)
		tmp = Float64(Float64(Float64(-x) / 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 <= -4.8e-22)
		tmp = 1.0 / (y * (t / x));
	elseif (t <= 5.5e-121)
		tmp = (-x / 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, -4.8e-22], N[(1.0 / N[(y * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-121], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.80000000000000005e-22

   1. Initial program 85.9%

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

   2. Taylor expanded in z around 0 60.3%

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

      1. clear-num 60.2%

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

      2. inv-pow 60.2%

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

      3. associate-/l* 61.8%

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

   4. Applied egg-rr 61.8%

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

      1. unpow-1 61.8%

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

      2. associate-/r/ 68.2%

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

   6. Simplified 68.2%

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

   if -4.80000000000000005e-22 < t < 5.50000000000000031e-121

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/r* 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. neg-mul-1 50.3%

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

   7. Simplified 50.3%

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

   if 5.50000000000000031e-121 < t

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 69.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 10: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e-200)
   (/ (/ x y) t)
   (if (<= y 2.1e-104) (/ (- x) (* z t)) (/ (/ x t) y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-200) {
		tmp = (x / y) / t;
	} else if (y <= 2.1e-104) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.8d-200)) then
        tmp = (x / y) / t
    else if (y <= 2.1d-104) then
        tmp = -x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-200) {
		tmp = (x / y) / t;
	} else if (y <= 2.1e-104) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e-200:
		tmp = (x / y) / t
	elif y <= 2.1e-104:
		tmp = -x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e-200)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 2.1e-104)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e-200)
		tmp = (x / y) / t;
	elseif (y <= 2.1e-104)
		tmp = -x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e-200], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 2.1e-104], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.80000000000000007e-200

   1. Initial program 88.3%

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

   2. Taylor expanded in z around 0 45.5%

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

      1. *-un-lft-identity 45.5%

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

      2. times-frac 48.9%

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

   4. Applied egg-rr 48.9%

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

      1. associate-*l/ 48.9%

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

      2. *-un-lft-identity 48.9%

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

   6. Applied egg-rr 48.9%

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

   if -2.80000000000000007e-200 < y < 2.09999999999999999e-104

   1. Initial program 90.4%

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

   2. Taylor expanded in y around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. neg-mul-1 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in z around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. neg-mul-1 46.6%

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

   7. Simplified 46.6%

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

   if 2.09999999999999999e-104 < y

   1. Initial program 85.8%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-/r* 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in t around inf 56.1%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 11: 46.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+53} \lor \neg \left(z \leq 9.5 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -4.5e+53) (not (<= z 9.5e+73))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.5e+53) || !(z <= 9.5e+73)) {
		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 <= (-4.5d+53)) .or. (.not. (z <= 9.5d+73))) 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 <= -4.5e+53) || !(z <= 9.5e+73)) {
		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 <= -4.5e+53) or not (z <= 9.5e+73):
		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 <= -4.5e+53) || !(z <= 9.5e+73))
		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 <= -4.5e+53) || ~((z <= 9.5e+73)))
		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, -4.5e+53], N[Not[LessEqual[z, 9.5e+73]], $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 < -4.5000000000000002e53 or 9.4999999999999996e73 < z

   1. Initial program 77.4%

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

   2. Taylor expanded in y around inf 40.5%

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

      1. *-commutative 40.5%

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

      2. associate-/r* 56.7%

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

   4. Simplified 56.7%

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

   5. Taylor expanded in t around 0 51.2%

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

      1. associate-*r/ 51.2%

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

      2. neg-mul-1 51.2%

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

   7. Simplified 51.2%

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

      1. expm1-log1p-u 50.8%

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

      2. expm1-udef 58.5%

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

      3. associate-/l/ 58.5%

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

      4. add-sqr-sqrt 24.5%

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

      5. sqrt-unprod 56.1%

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

      6. sqr-neg 56.1%

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

      7. sqrt-unprod 34.2%

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

      8. add-sqr-sqrt 58.7%

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

   9. Applied egg-rr 58.7%

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

       1. expm1-def 36.5%

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

       2. expm1-log1p 36.9%

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

       3. *-commutative 36.9%

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

   11. Simplified 36.9%

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

   if -4.5000000000000002e53 < z < 9.4999999999999996e73

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 52.5%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+53} \lor \neg \left(z \leq 9.5 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 12: 48.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+53} \lor \neg \left(z \leq 9.5 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -5.8e+53) (not (<= z 9.5e+88))) (/ x (* y z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+53) || !(z <= 9.5e+88)) {
		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 <= (-5.8d+53)) .or. (.not. (z <= 9.5d+88))) 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 <= -5.8e+53) || !(z <= 9.5e+88)) {
		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 <= -5.8e+53) or not (z <= 9.5e+88):
		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 <= -5.8e+53) || !(z <= 9.5e+88))
		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 <= -5.8e+53) || ~((z <= 9.5e+88)))
		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, -5.8e+53], N[Not[LessEqual[z, 9.5e+88]], $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 < -5.8000000000000004e53 or 9.50000000000000059e88 < z

   1. Initial program 78.8%

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

   2. Taylor expanded in y around inf 41.7%

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

      1. *-commutative 41.7%

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

      2. associate-/r* 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in t around 0 52.8%

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

      1. associate-*r/ 52.8%

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

      2. neg-mul-1 52.8%

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

   7. Simplified 52.8%

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

      1. expm1-log1p-u 52.4%

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

      2. expm1-udef 60.4%

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

      3. associate-/l/ 60.4%

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

      4. add-sqr-sqrt 25.3%

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

      5. sqrt-unprod 57.8%

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

      6. sqr-neg 57.8%

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

      7. sqrt-unprod 35.2%

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

      8. add-sqr-sqrt 60.5%

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

   9. Applied egg-rr 60.5%

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

       1. expm1-def 37.6%

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

       2. expm1-log1p 37.9%

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

       3. *-commutative 37.9%

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

   11. Simplified 37.9%

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

   if -5.8000000000000004e53 < z < 9.50000000000000059e88

   1. Initial program 93.0%

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

   2. Taylor expanded in y around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-/r* 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in t around inf 54.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+53} \lor \neg \left(z \leq 9.5 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 13: 70.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.7e-94) (/ 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 <= 3.7e-94) {
		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 <= 3.7d-94) 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 <= 3.7e-94) {
		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 <= 3.7e-94:
		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 <= 3.7e-94)
		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 <= 3.7e-94)
		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, 3.7e-94], 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 < 3.6999999999999998e-94

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 61.4%

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

      1. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   if 3.6999999999999998e-94 < t

   1. Initial program 86.3%

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

   2. Taylor expanded in t around inf 71.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 14: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 4.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 4.8e-94) (/ x (* y (- t z))) (/ (/ x t) (- y z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.8e-94) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 4.8d-94) then
        tmp = x / (y * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.8e-94) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 4.8e-94:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4.8e-94)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 4.8e-94)
		tmp = x / (y * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 4.8e-94], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.8e-94

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 61.4%

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

      1. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   if 4.8e-94 < t

   1. Initial program 86.3%

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

      1. *-un-lft-identity 86.3%

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

      2. times-frac 97.5%

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

   3. Applied egg-rr 97.5%

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

      1. associate-*l/ 97.6%

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

      2. *-un-lft-identity 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in t around inf 77.1%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 15: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 5.5e-94) (/ (/ x (- t z)) y) (/ (/ x t) (- y z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.5e-94) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 5.5d-94) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.5e-94) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 5.5e-94:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 5.5e-94)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 5.5e-94)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 5.5e-94], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.49999999999999989e-94

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/r* 67.9%

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

   4. Simplified 67.9%

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

   if 5.49999999999999989e-94 < t

   1. Initial program 86.3%

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

      1. *-un-lft-identity 86.3%

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

      2. times-frac 97.5%

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

   3. Applied egg-rr 97.5%

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

      1. associate-*l/ 97.6%

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

      2. *-un-lft-identity 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in t around inf 77.1%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 16: 39.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.0%

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

2. Taylor expanded in z around 0 40.3%

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

3. Final simplification 40.3%

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

Developer target: 87.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023298 
(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))))