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

Percentage Accurate: 88.9% → 97.8%

Time: 12.8s

Alternatives: 19

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: 97.8% accurate, 0.5× speedup

Math

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

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 (- y z)) (- t 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 / (y - z)) / (t - 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 / (y - z)) / (t - 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 / (y - z)) / (t - 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 / (y - z)) / (t - 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(y - z)) / Float64(t - 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 / (y - z)) / (t - 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[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - 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 85.4%

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

      1. associate-/r* 99.3%

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

   3. Simplified 99.3%

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

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

   1. Initial program 97.2%

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

4. Final simplification 98.7%

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

Alternative 2: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-20}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 0.21:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.5e-280)
   (/ (/ x y) (- t z))
   (if (<= t 4.3e-94)
     (/ (/ x z) z)
     (if (<= t 1.55e-20)
       (/ (/ x (- t z)) y)
       (if (<= t 0.21) (/ (- 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 (t <= -2.5e-280) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4.3e-94) {
		tmp = (x / z) / z;
	} else if (t <= 1.55e-20) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 0.21) {
		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 (t <= (-2.5d-280)) then
        tmp = (x / y) / (t - z)
    else if (t <= 4.3d-94) then
        tmp = (x / z) / z
    else if (t <= 1.55d-20) then
        tmp = (x / (t - z)) / y
    else if (t <= 0.21d0) 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 (t <= -2.5e-280) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4.3e-94) {
		tmp = (x / z) / z;
	} else if (t <= 1.55e-20) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 0.21) {
		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 t <= -2.5e-280:
		tmp = (x / y) / (t - z)
	elif t <= 4.3e-94:
		tmp = (x / z) / z
	elif t <= 1.55e-20:
		tmp = (x / (t - z)) / y
	elif t <= 0.21:
		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 (t <= -2.5e-280)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 4.3e-94)
		tmp = Float64(Float64(x / z) / z);
	elseif (t <= 1.55e-20)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 0.21)
		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 (t <= -2.5e-280)
		tmp = (x / y) / (t - z);
	elseif (t <= 4.3e-94)
		tmp = (x / z) / z;
	elseif (t <= 1.55e-20)
		tmp = (x / (t - z)) / y;
	elseif (t <= 0.21)
		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[t, -2.5e-280], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-94], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.55e-20], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 0.21], 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 5 regimes

2. if t < -2.50000000000000014e-280

   1. Initial program 90.6%

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

   2. Taylor expanded in y around inf 60.1%

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

      1. associate-/r* 60.5%

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

   4. Simplified 60.5%

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

   if -2.50000000000000014e-280 < t < 4.2999999999999998e-94

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf 56.1%

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

      1. unpow2 56.1%

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

   4. Simplified 56.1%

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

      1. associate-/r* 60.9%

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

      2. div-inv 60.9%

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

   6. Applied egg-rr 60.9%

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

      1. associate-*r/ 60.9%

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

      2. *-rgt-identity 60.9%

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

   8. Simplified 60.9%

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

   if 4.2999999999999998e-94 < t < 1.55e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 83.5%

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

      1. *-commutative 83.5%

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

   4. Simplified 83.5%

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

      1. *-un-lft-identity 83.5%

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

      2. *-commutative 83.5%

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

      3. times-frac 88.4%

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

   6. Applied egg-rr 88.4%

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

      1. associate-*l/ 88.3%

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

      2. *-lft-identity 88.3%

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

   8. Simplified 88.3%

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

   if 1.55e-20 < t < 0.209999999999999992

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   if 0.209999999999999992 < t

   1. Initial program 82.0%

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

   2. Taylor expanded in t around inf 77.8%

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

      1. associate-/r* 87.0%

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

   4. Simplified 87.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-20}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 0.21:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-154}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 0.27:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.75e-154)
   (/ (/ x y) (- t z))
   (if (<= t 7.2e-63)
     (/ (/ (- x) z) (- y z))
     (if (<= t 1.22e-20)
       (/ x (* y (- t z)))
       (if (<= t 0.27) (/ (- 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 (t <= -2.75e-154) {
		tmp = (x / y) / (t - z);
	} else if (t <= 7.2e-63) {
		tmp = (-x / z) / (y - z);
	} else if (t <= 1.22e-20) {
		tmp = x / (y * (t - z));
	} else if (t <= 0.27) {
		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 (t <= (-2.75d-154)) then
        tmp = (x / y) / (t - z)
    else if (t <= 7.2d-63) then
        tmp = (-x / z) / (y - z)
    else if (t <= 1.22d-20) then
        tmp = x / (y * (t - z))
    else if (t <= 0.27d0) 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 (t <= -2.75e-154) {
		tmp = (x / y) / (t - z);
	} else if (t <= 7.2e-63) {
		tmp = (-x / z) / (y - z);
	} else if (t <= 1.22e-20) {
		tmp = x / (y * (t - z));
	} else if (t <= 0.27) {
		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 t <= -2.75e-154:
		tmp = (x / y) / (t - z)
	elif t <= 7.2e-63:
		tmp = (-x / z) / (y - z)
	elif t <= 1.22e-20:
		tmp = x / (y * (t - z))
	elif t <= 0.27:
		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 (t <= -2.75e-154)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 7.2e-63)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	elseif (t <= 1.22e-20)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 0.27)
		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 (t <= -2.75e-154)
		tmp = (x / y) / (t - z);
	elseif (t <= 7.2e-63)
		tmp = (-x / z) / (y - z);
	elseif (t <= 1.22e-20)
		tmp = x / (y * (t - z));
	elseif (t <= 0.27)
		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[t, -2.75e-154], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-63], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e-20], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.27], 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 5 regimes

2. if t < -2.75000000000000001e-154

   1. Initial program 91.5%

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

   2. Taylor expanded in y around inf 63.1%

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

      1. associate-/r* 65.0%

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

   4. Simplified 65.0%

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

   if -2.75000000000000001e-154 < t < 7.20000000000000016e-63

   1. Initial program 88.0%

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

   2. Taylor expanded in t around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. distribute-frac-neg 72.4%

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

      3. associate-/r* 81.7%

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

   4. Simplified 81.7%

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

   if 7.20000000000000016e-63 < t < 1.22000000000000003e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   4. Simplified 84.4%

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

   if 1.22000000000000003e-20 < t < 0.27000000000000002

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   if 0.27000000000000002 < t

   1. Initial program 82.0%

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

   2. Taylor expanded in t around inf 77.8%

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

      1. associate-/r* 87.0%

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

   4. Simplified 87.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-154}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 0.27:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 4: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;z \leq -5:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 0.092:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

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))))
   (if (<= z -5.0)
     (* (/ x z) (/ 1.0 z))
     (if (<= z 0.092)
       t_1
       (if (<= z 3.8e+28)
         (/ (/ x z) z)
         (if (<= z 1.55e+87) t_1 (/ 1.0 (* z (/ z x)))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -5.0) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 0.092) {
		tmp = t_1;
	} else if (z <= 3.8e+28) {
		tmp = (x / z) / z;
	} else if (z <= 1.55e+87) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	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)
    if (z <= (-5.0d0)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 0.092d0) then
        tmp = t_1
    else if (z <= 3.8d+28) then
        tmp = (x / z) / z
    else if (z <= 1.55d+87) then
        tmp = t_1
    else
        tmp = 1.0d0 / (z * (z / x))
    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);
	double tmp;
	if (z <= -5.0) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 0.092) {
		tmp = t_1;
	} else if (z <= 3.8e+28) {
		tmp = (x / z) / z;
	} else if (z <= 1.55e+87) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * t)
	tmp = 0
	if z <= -5.0:
		tmp = (x / z) * (1.0 / z)
	elif z <= 0.092:
		tmp = t_1
	elif z <= 3.8e+28:
		tmp = (x / z) / z
	elif z <= 1.55e+87:
		tmp = t_1
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -5.0)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 0.092)
		tmp = t_1;
	elseif (z <= 3.8e+28)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 1.55e+87)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	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);
	tmp = 0.0;
	if (z <= -5.0)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 0.092)
		tmp = t_1;
	elseif (z <= 3.8e+28)
		tmp = (x / z) / z;
	elseif (z <= 1.55e+87)
		tmp = t_1;
	else
		tmp = 1.0 / (z * (z / x));
	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] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.0], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.092], t$95$1, If[LessEqual[z, 3.8e+28], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.55e+87], t$95$1, N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5

   1. Initial program 84.9%

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

   2. Taylor expanded in z around inf 67.6%

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

      1. unpow2 67.6%

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

   4. Simplified 67.6%

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

      1. associate-/r* 71.5%

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

      2. div-inv 71.5%

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

   6. Applied egg-rr 71.5%

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

   if -5 < z < 0.091999999999999998 or 3.7999999999999999e28 < z < 1.55e87

   1. Initial program 94.1%

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

   2. Taylor expanded in t around inf 74.5%

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

   if 0.091999999999999998 < z < 3.7999999999999999e28

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 78.3%

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

      1. unpow2 78.3%

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

   4. Simplified 78.3%

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

      1. associate-/r* 78.7%

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

      2. div-inv 78.3%

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

   6. Applied egg-rr 78.3%

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

      1. associate-*r/ 78.7%

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

      2. *-rgt-identity 78.7%

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

   8. Simplified 78.7%

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

   if 1.55e87 < z

   1. Initial program 77.3%

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

   2. Taylor expanded in z around inf 77.1%

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

      1. unpow2 77.1%

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

   4. Simplified 77.1%

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

      1. clear-num 77.1%

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

      2. inv-pow 77.1%

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

      3. associate-/l* 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

      2. associate-/r/ 92.9%

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

   8. Simplified 92.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 0.092:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 5: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.21:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y (- t z)))))
   (if (<= t -7.5e-277)
     t_1
     (if (<= t 2.8e-93)
       (/ (/ x z) z)
       (if (<= t 5.1e-20)
         t_1
         (if (<= t 0.21) (/ x (* z z)) (/ x (* (- y z) t))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double tmp;
	if (t <= -7.5e-277) {
		tmp = t_1;
	} else if (t <= 2.8e-93) {
		tmp = (x / z) / z;
	} else if (t <= 5.1e-20) {
		tmp = t_1;
	} else if (t <= 0.21) {
		tmp = x / (z * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * (t - z))
    if (t <= (-7.5d-277)) then
        tmp = t_1
    else if (t <= 2.8d-93) then
        tmp = (x / z) / z
    else if (t <= 5.1d-20) then
        tmp = t_1
    else if (t <= 0.21d0) then
        tmp = x / (z * z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double tmp;
	if (t <= -7.5e-277) {
		tmp = t_1;
	} else if (t <= 2.8e-93) {
		tmp = (x / z) / z;
	} else if (t <= 5.1e-20) {
		tmp = t_1;
	} else if (t <= 0.21) {
		tmp = x / (z * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (y * (t - z))
	tmp = 0
	if t <= -7.5e-277:
		tmp = t_1
	elif t <= 2.8e-93:
		tmp = (x / z) / z
	elif t <= 5.1e-20:
		tmp = t_1
	elif t <= 0.21:
		tmp = x / (z * z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (t <= -7.5e-277)
		tmp = t_1;
	elseif (t <= 2.8e-93)
		tmp = Float64(Float64(x / z) / z);
	elseif (t <= 5.1e-20)
		tmp = t_1;
	elseif (t <= 0.21)
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * (t - z));
	tmp = 0.0;
	if (t <= -7.5e-277)
		tmp = t_1;
	elseif (t <= 2.8e-93)
		tmp = (x / z) / z;
	elseif (t <= 5.1e-20)
		tmp = t_1;
	elseif (t <= 0.21)
		tmp = x / (z * z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e-277], t$95$1, If[LessEqual[t, 2.8e-93], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 5.1e-20], t$95$1, If[LessEqual[t, 0.21], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.49999999999999971e-277 or 2.79999999999999998e-93 < t < 5.10000000000000019e-20

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf 63.1%

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

      1. *-commutative 63.1%

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

   4. Simplified 63.1%

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

   if -7.49999999999999971e-277 < t < 2.79999999999999998e-93

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf 56.1%

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

      1. unpow2 56.1%

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

   4. Simplified 56.1%

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

      1. associate-/r* 60.9%

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

      2. div-inv 60.9%

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

   6. Applied egg-rr 60.9%

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

      1. associate-*r/ 60.9%

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

      2. *-rgt-identity 60.9%

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

   8. Simplified 60.9%

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

   if 5.10000000000000019e-20 < t < 0.209999999999999992

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. unpow2 100.0%

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

   4. Simplified 100.0%

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

   if 0.209999999999999992 < t

   1. Initial program 82.0%

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

   2. Taylor expanded in t around inf 77.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 0.21:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.21:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y (- t z)))))
   (if (<= t -2.15e-278)
     t_1
     (if (<= t 2e-94)
       (/ (/ x z) z)
       (if (<= t 6.2e-20)
         t_1
         (if (<= t 0.21) (/ x (* z z)) (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double tmp;
	if (t <= -2.15e-278) {
		tmp = t_1;
	} else if (t <= 2e-94) {
		tmp = (x / z) / z;
	} else if (t <= 6.2e-20) {
		tmp = t_1;
	} else if (t <= 0.21) {
		tmp = x / (z * 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) :: t_1
    real(8) :: tmp
    t_1 = x / (y * (t - z))
    if (t <= (-2.15d-278)) then
        tmp = t_1
    else if (t <= 2d-94) then
        tmp = (x / z) / z
    else if (t <= 6.2d-20) then
        tmp = t_1
    else if (t <= 0.21d0) then
        tmp = x / (z * 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 t_1 = x / (y * (t - z));
	double tmp;
	if (t <= -2.15e-278) {
		tmp = t_1;
	} else if (t <= 2e-94) {
		tmp = (x / z) / z;
	} else if (t <= 6.2e-20) {
		tmp = t_1;
	} else if (t <= 0.21) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (y * (t - z))
	tmp = 0
	if t <= -2.15e-278:
		tmp = t_1
	elif t <= 2e-94:
		tmp = (x / z) / z
	elif t <= 6.2e-20:
		tmp = t_1
	elif t <= 0.21:
		tmp = x / (z * z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (t <= -2.15e-278)
		tmp = t_1;
	elseif (t <= 2e-94)
		tmp = Float64(Float64(x / z) / z);
	elseif (t <= 6.2e-20)
		tmp = t_1;
	elseif (t <= 0.21)
		tmp = Float64(x / Float64(z * 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)
	t_1 = x / (y * (t - z));
	tmp = 0.0;
	if (t <= -2.15e-278)
		tmp = t_1;
	elseif (t <= 2e-94)
		tmp = (x / z) / z;
	elseif (t <= 6.2e-20)
		tmp = t_1;
	elseif (t <= 0.21)
		tmp = x / (z * 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_] := Block[{t$95$1 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e-278], t$95$1, If[LessEqual[t, 2e-94], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 6.2e-20], t$95$1, If[LessEqual[t, 0.21], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.15e-278 or 1.9999999999999999e-94 < t < 6.19999999999999999e-20

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf 63.1%

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

      1. *-commutative 63.1%

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

   4. Simplified 63.1%

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

   if -2.15e-278 < t < 1.9999999999999999e-94

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf 56.1%

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

      1. unpow2 56.1%

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

   4. Simplified 56.1%

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

      1. associate-/r* 60.9%

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

      2. div-inv 60.9%

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

   6. Applied egg-rr 60.9%

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

      1. associate-*r/ 60.9%

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

      2. *-rgt-identity 60.9%

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

   8. Simplified 60.9%

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

   if 6.19999999999999999e-20 < t < 0.209999999999999992

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. unpow2 100.0%

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

   4. Simplified 100.0%

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

   if 0.209999999999999992 < t

   1. Initial program 82.0%

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

   2. Taylor expanded in t around inf 77.8%

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

      1. associate-/r* 87.0%

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

   4. Simplified 87.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 0.21:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 7: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+116} \lor \neg \left(z \leq 1.5 \cdot 10^{+114}\right):\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.7e+116) (not (<= z 1.5e+114)))
   (* (/ -1.0 z) (/ x (- t z)))
   (/ x (* (- y z) (- t z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.7e+116) || !(z <= 1.5e+114)) {
		tmp = (-1.0 / z) * (x / (t - z));
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.7d+116)) .or. (.not. (z <= 1.5d+114))) then
        tmp = ((-1.0d0) / z) * (x / (t - z))
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.7e+116) || !(z <= 1.5e+114)) {
		tmp = (-1.0 / z) * (x / (t - z));
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -5.7e+116) or not (z <= 1.5e+114):
		tmp = (-1.0 / z) * (x / (t - z))
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.7e+116) || !(z <= 1.5e+114))
		tmp = Float64(Float64(-1.0 / z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.7e+116) || ~((z <= 1.5e+114)))
		tmp = (-1.0 / z) * (x / (t - z));
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.7e+116], N[Not[LessEqual[z, 1.5e+114]], $MachinePrecision]], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.69999999999999983e116 or 1.5e114 < z

   1. Initial program 77.5%

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

   2. Taylor expanded in y around 0 77.4%

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

      1. associate-*r/ 77.4%

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

      2. neg-mul-1 77.4%

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

   4. Simplified 77.4%

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

      1. neg-mul-1 77.4%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

   if -5.69999999999999983e116 < z < 1.5e114

   1. Initial program 94.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+116} \lor \neg \left(z \leq 1.5 \cdot 10^{+114}\right):\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 8: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-74}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-27)
   (/ (/ x y) (- t z))
   (if (<= y 2.15e-74) (* (/ -1.0 z) (/ x (- t z))) (/ (/ x (- y z)) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-27) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.15e-74) {
		tmp = (-1.0 / z) * (x / (t - z));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d-27)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.15d-74) then
        tmp = ((-1.0d0) / z) * (x / (t - z))
    else
        tmp = (x / (y - z)) / t
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-27) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.15e-74) {
		tmp = (-1.0 / z) * (x / (t - z));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-27:
		tmp = (x / y) / (t - z)
	elif y <= 2.15e-74:
		tmp = (-1.0 / z) * (x / (t - z))
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-27)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.15e-74)
		tmp = Float64(Float64(-1.0 / z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e-27)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.15e-74)
		tmp = (-1.0 / z) * (x / (t - z));
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-27], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-74], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5000000000000001e-27

   1. Initial program 85.7%

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

   2. Taylor expanded in y around inf 76.0%

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

      1. associate-/r* 80.1%

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

   4. Simplified 80.1%

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

   if -2.5000000000000001e-27 < y < 2.14999999999999986e-74

   1. Initial program 88.6%

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

   2. Taylor expanded in y around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. neg-mul-1 75.1%

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

   4. Simplified 75.1%

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

      1. neg-mul-1 75.1%

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

      2. times-frac 83.1%

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

   6. Applied egg-rr 83.1%

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

   if 2.14999999999999986e-74 < y

   1. Initial program 91.7%

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

   2. Taylor expanded in t around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-/r* 79.4%

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

   4. Simplified 79.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-74}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]

Alternative 9: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-26} \lor \neg \left(z \leq 0.000225\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \end{array} \end{array} \]

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-26) (not (<= z 0.000225)))
   (/ (/ x z) z)
   (* (/ x y) (/ 1.0 t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.5e-26) || !(z <= 0.000225)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / y) * (1.0 / 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-26)) .or. (.not. (z <= 0.000225d0))) then
        tmp = (x / z) / z
    else
        tmp = (x / y) * (1.0d0 / 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-26) || !(z <= 0.000225)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / y) * (1.0 / t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4.5e-26) or not (z <= 0.000225):
		tmp = (x / z) / z
	else:
		tmp = (x / y) * (1.0 / t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.5e-26) || !(z <= 0.000225))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / 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-26) || ~((z <= 0.000225)))
		tmp = (x / z) / z;
	else
		tmp = (x / y) * (1.0 / 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-26], N[Not[LessEqual[z, 0.000225]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999999e-26 or 2.2499999999999999e-4 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 65.6%

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

      1. unpow2 65.6%

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

   4. Simplified 65.6%

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

      1. associate-/r* 71.7%

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

      2. div-inv 71.7%

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

   6. Applied egg-rr 71.7%

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

      1. associate-*r/ 71.7%

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

      2. *-rgt-identity 71.7%

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

   8. Simplified 71.7%

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

   if -4.4999999999999999e-26 < z < 2.2499999999999999e-4

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 66.1%

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

      1. *-un-lft-identity 66.1%

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

      2. times-frac 68.0%

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

   4. Applied egg-rr 68.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-26} \lor \neg \left(z \leq 0.000225\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \end{array} \]

Alternative 10: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.4e-25)
   (* (/ x z) (/ 1.0 z))
   (if (<= z 5.4e-12) (* (/ x y) (/ 1.0 t)) (/ (/ x z) z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e-25) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 5.4e-12) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = (x / 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 <= (-2.4d-25)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 5.4d-12) then
        tmp = (x / y) * (1.0d0 / t)
    else
        tmp = (x / 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 <= -2.4e-25) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 5.4e-12) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.4e-25:
		tmp = (x / z) * (1.0 / z)
	elif z <= 5.4e-12:
		tmp = (x / y) * (1.0 / t)
	else:
		tmp = (x / z) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.4e-25)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 5.4e-12)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	else
		tmp = Float64(Float64(x / 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 <= -2.4e-25)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 5.4e-12)
		tmp = (x / y) * (1.0 / t);
	else
		tmp = (x / 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, -2.4e-25], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-12], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000009e-25

   1. Initial program 86.5%

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

   2. Taylor expanded in z around inf 63.1%

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

      1. unpow2 63.1%

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

   4. Simplified 63.1%

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

      1. associate-/r* 66.5%

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

      2. div-inv 66.6%

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

   6. Applied egg-rr 66.6%

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

   if -2.40000000000000009e-25 < z < 5.39999999999999961e-12

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 66.1%

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

      1. *-un-lft-identity 66.1%

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

      2. times-frac 68.0%

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

   4. Applied egg-rr 68.0%

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

   if 5.39999999999999961e-12 < z

   1. Initial program 84.7%

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

   2. Taylor expanded in z around inf 68.8%

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

      1. unpow2 68.8%

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

   4. Simplified 68.8%

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

      1. associate-/r* 78.6%

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

      2. div-inv 78.5%

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

   6. Applied egg-rr 78.5%

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

      1. associate-*r/ 78.6%

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

      2. *-rgt-identity 78.6%

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

   8. Simplified 78.6%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 11: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-25)
   (* (/ x z) (/ 1.0 z))
   (if (<= z 6e-8) (* (/ x y) (/ 1.0 t)) (/ 1.0 (* z (/ z x))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-25) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 6e-8) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.1d-25)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 6d-8) then
        tmp = (x / y) * (1.0d0 / t)
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-25) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 6e-8) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e-25:
		tmp = (x / z) * (1.0 / z)
	elif z <= 6e-8:
		tmp = (x / y) * (1.0 / t)
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e-25)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 6e-8)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e-25)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 6e-8)
		tmp = (x / y) * (1.0 / t);
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e-25], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-8], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.10000000000000002e-25

   1. Initial program 86.5%

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

   2. Taylor expanded in z around inf 63.1%

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

      1. unpow2 63.1%

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

   4. Simplified 63.1%

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

      1. associate-/r* 66.5%

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

      2. div-inv 66.6%

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

   6. Applied egg-rr 66.6%

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

   if -2.10000000000000002e-25 < z < 5.99999999999999946e-8

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 66.1%

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

      1. *-un-lft-identity 66.1%

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

      2. times-frac 68.0%

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

   4. Applied egg-rr 68.0%

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

   if 5.99999999999999946e-8 < z

   1. Initial program 84.7%

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

   2. Taylor expanded in z around inf 68.8%

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

      1. unpow2 68.8%

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

   4. Simplified 68.8%

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

      1. clear-num 68.8%

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

      2. inv-pow 68.8%

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

      3. associate-/l* 79.5%

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

   6. Applied egg-rr 79.5%

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

      1. unpow-1 79.5%

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

      2. associate-/r/ 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 12: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-281)
   (/ (/ x y) (- t z))
   (if (<= t 1.35e-61) (/ (/ x z) z) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-281) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.35e-61) {
		tmp = (x / z) / 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 <= (-4.2d-281)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.35d-61) then
        tmp = (x / z) / 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 <= -4.2e-281) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.35e-61) {
		tmp = (x / z) / 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 <= -4.2e-281:
		tmp = (x / y) / (t - z)
	elif t <= 1.35e-61:
		tmp = (x / z) / 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 <= -4.2e-281)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.35e-61)
		tmp = Float64(Float64(x / z) / 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 <= -4.2e-281)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.35e-61)
		tmp = (x / z) / 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, -4.2e-281], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-61], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999998e-281

   1. Initial program 90.6%

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

   2. Taylor expanded in y around inf 60.1%

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

      1. associate-/r* 60.5%

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

   4. Simplified 60.5%

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

   if -4.1999999999999998e-281 < t < 1.34999999999999997e-61

   1. Initial program 88.9%

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

   2. Taylor expanded in z around inf 53.0%

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

      1. unpow2 53.0%

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

   4. Simplified 53.0%

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

      1. associate-/r* 57.3%

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

      2. div-inv 57.3%

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

   6. Applied egg-rr 57.3%

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

      1. associate-*r/ 57.3%

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

      2. *-rgt-identity 57.3%

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

   8. Simplified 57.3%

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

   if 1.34999999999999997e-61 < t

   1. Initial program 86.1%

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

   2. Taylor expanded in t around inf 75.9%

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

      1. associate-/r* 82.9%

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

   4. Simplified 82.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 13: 46.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -380000 \lor \neg \left(z \leq 3.5 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -380000.0) (not (<= z 3.5e+56))) (/ x (* z t)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -380000.0) || !(z <= 3.5e+56)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-380000.0d0)) .or. (.not. (z <= 3.5d+56))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -380000.0) || !(z <= 3.5e+56)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -380000.0) or not (z <= 3.5e+56):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -380000.0) || !(z <= 3.5e+56))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -380000.0) || ~((z <= 3.5e+56)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -380000.0], N[Not[LessEqual[z, 3.5e+56]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e5 or 3.49999999999999999e56 < z

   1. Initial program 81.8%

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

   2. Taylor expanded in y around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in z around 0 42.4%

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

      1. associate-*r/ 42.4%

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

      2. neg-mul-1 42.4%

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

      3. *-commutative 42.4%

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

   7. Simplified 42.4%

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

      1. expm1-log1p-u 42.1%

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

      2. expm1-udef 56.0%

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

      3. add-sqr-sqrt 31.5%

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

      4. sqrt-unprod 53.7%

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

      5. sqr-neg 53.7%

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

      6. sqrt-unprod 24.4%

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

      7. add-sqr-sqrt 55.3%

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

   9. Applied egg-rr 55.3%

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

       1. expm1-def 38.9%

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

       2. expm1-log1p 39.2%

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

   11. Simplified 39.2%

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

   if -3.8e5 < z < 3.49999999999999999e56

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 56.2%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -380000 \lor \neg \left(z \leq 3.5 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 46.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+118} \lor \neg \left(z \leq 1.3 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -4.1e+118) (not (<= z 1.3e+89))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+118) || !(z <= 1.3e+89)) {
		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 <= (-4.1d+118)) .or. (.not. (z <= 1.3d+89))) 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 <= -4.1e+118) || !(z <= 1.3e+89)) {
		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 <= -4.1e+118) or not (z <= 1.3e+89):
		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 <= -4.1e+118) || !(z <= 1.3e+89))
		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 <= -4.1e+118) || ~((z <= 1.3e+89)))
		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, -4.1e+118], N[Not[LessEqual[z, 1.3e+89]], $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 < -4.0999999999999997e118 or 1.3e89 < z

   1. Initial program 78.7%

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

   2. Taylor expanded in y around inf 42.5%

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

      1. *-commutative 42.5%

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

   4. Simplified 42.5%

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

   5. Taylor expanded in t around 0 42.4%

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

      1. associate-*r/ 42.4%

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

      2. neg-mul-1 42.4%

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

      3. *-commutative 42.4%

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

   7. Simplified 42.4%

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

      1. expm1-log1p-u 42.2%

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

      2. expm1-udef 63.8%

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

      3. add-sqr-sqrt 30.7%

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

      4. sqrt-unprod 62.1%

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

      5. sqr-neg 62.1%

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

      6. sqrt-unprod 33.0%

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

      7. add-sqr-sqrt 63.7%

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

      8. *-commutative 63.7%

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

      9. associate-/r* 63.7%

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

   9. Applied egg-rr 63.7%

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

       1. expm1-def 39.8%

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

       2. expm1-log1p 40.0%

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

       3. associate-/l/ 42.4%

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

   11. Simplified 42.4%

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

   if -4.0999999999999997e118 < z < 1.3e89

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 50.9%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+118} \lor \neg \left(z \leq 1.3 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-26} \lor \neg \left(z \leq 1.75 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e-26) (not (<= z 1.75e-9))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-26) || !(z <= 1.75e-9)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4d-26)) .or. (.not. (z <= 1.75d-9))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-26) || !(z <= 1.75e-9)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4e-26) or not (z <= 1.75e-9):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e-26) || !(z <= 1.75e-9))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e-26) || ~((z <= 1.75e-9)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e-26], N[Not[LessEqual[z, 1.75e-9]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0000000000000002e-26 or 1.75e-9 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 65.6%

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

      1. unpow2 65.6%

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

   4. Simplified 65.6%

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

   if -4.0000000000000002e-26 < z < 1.75e-9

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 66.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-26} \lor \neg \left(z \leq 1.75 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 16: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-25} \lor \neg \left(z \leq 3.9 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e-25) (not (<= z 3.9e-8))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e-25) || !(z <= 3.9e-8)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.6d-25)) .or. (.not. (z <= 3.9d-8))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e-25) || !(z <= 3.9e-8)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e-25) or not (z <= 3.9e-8):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.6e-25) || !(z <= 3.9e-8))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.6e-25) || ~((z <= 3.9e-8)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.6e-25], N[Not[LessEqual[z, 3.9e-8]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e-25 or 3.89999999999999985e-8 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 65.6%

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

      1. unpow2 65.6%

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

   4. Simplified 65.6%

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

   if -2.6e-25 < z < 3.89999999999999985e-8

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 66.1%

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

      1. associate-/r* 68.7%

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

   4. Simplified 68.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-25} \lor \neg \left(z \leq 3.9 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 17: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-25} \lor \neg \left(z \leq 1.85 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e-25) (not (<= z 1.85e-6))) (/ x (* z z)) (/ (/ x y) t)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-25) || !(z <= 1.85e-6)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.95d-25)) .or. (.not. (z <= 1.85d-6))) then
        tmp = x / (z * z)
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-25) || !(z <= 1.85e-6)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e-25) or not (z <= 1.85e-6):
		tmp = x / (z * z)
	else:
		tmp = (x / y) / t
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e-25) || !(z <= 1.85e-6))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e-25) || ~((z <= 1.85e-6)))
		tmp = x / (z * z);
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e-25], N[Not[LessEqual[z, 1.85e-6]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e-25 or 1.8500000000000001e-6 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 65.6%

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

      1. unpow2 65.6%

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

   4. Simplified 65.6%

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

   if -1.95e-25 < z < 1.8500000000000001e-6

   1. Initial program 93.1%

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

      1. associate-/r* 93.0%

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

   3. Simplified 93.0%

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

      1. add-cube-cbrt 91.8%

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

      2. pow3 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in z around 0 66.1%

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

      1. associate-/l/ 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-25} \lor \neg \left(z \leq 1.85 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 18: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-26} \lor \neg \left(z \leq 0.0064\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4e-26) (not (<= z 0.0064))) (/ (/ x z) z) (/ (/ x y) t)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e-26) || !(z <= 0.0064)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.4d-26)) .or. (.not. (z <= 0.0064d0))) then
        tmp = (x / z) / z
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e-26) || !(z <= 0.0064)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e-26) or not (z <= 0.0064):
		tmp = (x / z) / z
	else:
		tmp = (x / y) / t
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e-26) || !(z <= 0.0064))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.4e-26) || ~((z <= 0.0064)))
		tmp = (x / z) / z;
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e-26], N[Not[LessEqual[z, 0.0064]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000013e-26 or 0.00640000000000000031 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 65.6%

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

      1. unpow2 65.6%

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

   4. Simplified 65.6%

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

      1. associate-/r* 71.7%

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

      2. div-inv 71.7%

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

   6. Applied egg-rr 71.7%

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

      1. associate-*r/ 71.7%

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

      2. *-rgt-identity 71.7%

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

   8. Simplified 71.7%

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

   if -3.40000000000000013e-26 < z < 0.00640000000000000031

   1. Initial program 93.1%

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

      1. associate-/r* 93.0%

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

   3. Simplified 93.0%

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

      1. add-cube-cbrt 91.8%

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

      2. pow3 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in z around 0 66.1%

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

      1. associate-/l/ 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-26} \lor \neg \left(z \leq 0.0064\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 19: 39.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

2. Taylor expanded in z around 0 41.9%

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

3. Final simplification 41.9%

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

Developer target: 87.8% 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 2023290 
(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))))