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

Percentage Accurate: 88.9% → 98.7%

Time: 12.6s

Alternatives: 15

Speedup: 0.8×

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: 98.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+295} \lor \neg \left(t_1 \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1}\\ \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (if (or (<= t_1 -2e+295) (not (<= t_1 2e+193)))
     (/ (/ x (- y z)) (- t z))
     (/ x t_1))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((t_1 <= -2e+295) || !(t_1 <= 2e+193)) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x / 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 = (y - z) * (t - z)
    if ((t_1 <= (-2d+295)) .or. (.not. (t_1 <= 2d+193))) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x / 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 = (y - z) * (t - z);
	double tmp;
	if ((t_1 <= -2e+295) || !(t_1 <= 2e+193)) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (t_1 <= -2e+295) or not (t_1 <= 2e+193):
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x / t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if ((t_1 <= -2e+295) || !(t_1 <= 2e+193))
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((t_1 <= -2e+295) || ~((t_1 <= 2e+193)))
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+295], N[Not[LessEqual[t$95$1, 2e+193]], $MachinePrecision]], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -2e295 or 2.00000000000000013e193 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 81.1%

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

      1. *-un-lft-identity 81.1%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in x around 0 81.1%

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

      1. associate-/l/ 99.9%

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

   6. Simplified 99.9%

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

   if -2e295 < (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000013e193

   1. Initial program 98.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -2 \cdot 10^{+295} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 2: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-16}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \end{array} \]

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 t) y)))
   (if (<= t -2.15e-47)
     t_1
     (if (<= t 1.55e-16)
       (/ (- x) (* y z))
       (if (<= t 3.2e+143)
         (/ (- x) (* z t))
         (if (<= t 2.5e+171) t_1 (/ (/ (- x) t) z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (t <= -2.15e-47) {
		tmp = t_1;
	} else if (t <= 1.55e-16) {
		tmp = -x / (y * z);
	} else if (t <= 3.2e+143) {
		tmp = -x / (z * t);
	} else if (t <= 2.5e+171) {
		tmp = t_1;
	} else {
		tmp = (-x / 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) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / y
    if (t <= (-2.15d-47)) then
        tmp = t_1
    else if (t <= 1.55d-16) then
        tmp = -x / (y * z)
    else if (t <= 3.2d+143) then
        tmp = -x / (z * t)
    else if (t <= 2.5d+171) then
        tmp = t_1
    else
        tmp = (-x / 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 t_1 = (x / t) / y;
	double tmp;
	if (t <= -2.15e-47) {
		tmp = t_1;
	} else if (t <= 1.55e-16) {
		tmp = -x / (y * z);
	} else if (t <= 3.2e+143) {
		tmp = -x / (z * t);
	} else if (t <= 2.5e+171) {
		tmp = t_1;
	} else {
		tmp = (-x / t) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	tmp = 0
	if t <= -2.15e-47:
		tmp = t_1
	elif t <= 1.55e-16:
		tmp = -x / (y * z)
	elif t <= 3.2e+143:
		tmp = -x / (z * t)
	elif t <= 2.5e+171:
		tmp = t_1
	else:
		tmp = (-x / t) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (t <= -2.15e-47)
		tmp = t_1;
	elseif (t <= 1.55e-16)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (t <= 3.2e+143)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (t <= 2.5e+171)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-x) / t) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	tmp = 0.0;
	if (t <= -2.15e-47)
		tmp = t_1;
	elseif (t <= 1.55e-16)
		tmp = -x / (y * z);
	elseif (t <= 3.2e+143)
		tmp = -x / (z * t);
	elseif (t <= 2.5e+171)
		tmp = t_1;
	else
		tmp = (-x / 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_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.15e-47], t$95$1, If[LessEqual[t, 1.55e-16], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+143], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+171], t$95$1, N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1499999999999999e-47 or 3.20000000000000016e143 < t < 2.5000000000000002e171

   1. Initial program 82.0%

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

   2. Taylor expanded in z around 0 51.0%

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

      1. div-inv 51.0%

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

      2. associate-/r* 50.9%

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

   4. Applied egg-rr 50.9%

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

      1. associate-*r/ 60.8%

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

      2. div-inv 60.8%

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

   6. Applied egg-rr 60.8%

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

   if -2.1499999999999999e-47 < t < 1.55e-16

   1. Initial program 92.5%

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

   2. Taylor expanded in z around 0 62.3%

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

      1. distribute-lft-out 62.3%

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

      2. mul-1-neg 62.3%

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

      3. distribute-rgt-neg-in 62.3%

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

      4. unsub-neg 62.3%

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

   4. Simplified 62.3%

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

   5. Taylor expanded in t around 0 44.4%

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

      1. associate-*r/ 44.4%

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

      2. neg-mul-1 44.4%

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

      3. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   if 1.55e-16 < t < 3.20000000000000016e143

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.6%

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

      1. associate-*r/ 63.6%

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

      2. neg-mul-1 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in z around 0 53.4%

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

      1. associate-*r/ 53.4%

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

      2. neg-mul-1 53.4%

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

      3. *-commutative 53.4%

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

   7. Simplified 53.4%

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

   if 2.5000000000000002e171 < t

   1. Initial program 83.1%

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

      1. *-un-lft-identity 83.1%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around inf 96.8%

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

   5. Taylor expanded in y around 0 80.0%

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

      1. associate-*l/ 80.1%

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

      2. neg-mul-1 80.1%

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

      3. distribute-neg-frac 80.1%

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

   7. Applied egg-rr 80.1%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-16}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+171}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \]

Alternative 3: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \end{array} \]

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 t) y)))
   (if (<= t -2.15e-44)
     t_1
     (if (<= t 8e-14)
       (/ (/ (- x) z) y)
       (if (<= t 8e+143)
         (/ (- x) (* z t))
         (if (<= t 1.8e+171) t_1 (/ (/ (- x) t) z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (t <= -2.15e-44) {
		tmp = t_1;
	} else if (t <= 8e-14) {
		tmp = (-x / z) / y;
	} else if (t <= 8e+143) {
		tmp = -x / (z * t);
	} else if (t <= 1.8e+171) {
		tmp = t_1;
	} else {
		tmp = (-x / 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) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / y
    if (t <= (-2.15d-44)) then
        tmp = t_1
    else if (t <= 8d-14) then
        tmp = (-x / z) / y
    else if (t <= 8d+143) then
        tmp = -x / (z * t)
    else if (t <= 1.8d+171) then
        tmp = t_1
    else
        tmp = (-x / 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 t_1 = (x / t) / y;
	double tmp;
	if (t <= -2.15e-44) {
		tmp = t_1;
	} else if (t <= 8e-14) {
		tmp = (-x / z) / y;
	} else if (t <= 8e+143) {
		tmp = -x / (z * t);
	} else if (t <= 1.8e+171) {
		tmp = t_1;
	} else {
		tmp = (-x / t) / z;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	tmp = 0
	if t <= -2.15e-44:
		tmp = t_1
	elif t <= 8e-14:
		tmp = (-x / z) / y
	elif t <= 8e+143:
		tmp = -x / (z * t)
	elif t <= 1.8e+171:
		tmp = t_1
	else:
		tmp = (-x / t) / z
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (t <= -2.15e-44)
		tmp = t_1;
	elseif (t <= 8e-14)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 8e+143)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (t <= 1.8e+171)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-x) / t) / z);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	tmp = 0.0;
	if (t <= -2.15e-44)
		tmp = t_1;
	elseif (t <= 8e-14)
		tmp = (-x / z) / y;
	elseif (t <= 8e+143)
		tmp = -x / (z * t);
	elseif (t <= 1.8e+171)
		tmp = t_1;
	else
		tmp = (-x / 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_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.15e-44], t$95$1, If[LessEqual[t, 8e-14], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 8e+143], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+171], t$95$1, N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.15000000000000007e-44 or 8.0000000000000002e143 < t < 1.80000000000000009e171

   1. Initial program 82.0%

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

   2. Taylor expanded in z around 0 51.0%

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

      1. div-inv 51.0%

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

      2. associate-/r* 50.9%

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

   4. Applied egg-rr 50.9%

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

      1. associate-*r/ 60.8%

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

      2. div-inv 60.8%

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

   6. Applied egg-rr 60.8%

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

   if -2.15000000000000007e-44 < t < 7.99999999999999999e-14

   1. Initial program 92.5%

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

   2. Taylor expanded in y around inf 60.2%

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

      1. *-commutative 60.2%

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

      2. associate-/r* 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in t around 0 50.8%

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

      1. associate-*r/ 50.8%

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

      2. neg-mul-1 50.8%

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

   7. Simplified 50.8%

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

   if 7.99999999999999999e-14 < t < 8.0000000000000002e143

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.6%

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

      1. associate-*r/ 63.6%

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

      2. neg-mul-1 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in z around 0 53.4%

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

      1. associate-*r/ 53.4%

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

      2. neg-mul-1 53.4%

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

      3. *-commutative 53.4%

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

   7. Simplified 53.4%

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

   if 1.80000000000000009e171 < t

   1. Initial program 83.1%

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

      1. *-un-lft-identity 83.1%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around inf 96.8%

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

   5. Taylor expanded in y around 0 80.0%

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

      1. associate-*l/ 80.1%

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

      2. neg-mul-1 80.1%

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

      3. distribute-neg-frac 80.1%

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

   7. Applied egg-rr 80.1%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+171}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \]

Alternative 4: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.2e-183)
   (/ (/ x (- t z)) y)
   (if (<= t 1.75e-6)
     (/ (/ (- x) z) (- y z))
     (if (<= t 4.5e+185) (/ x (* (- y z) t)) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-183) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.75e-6) {
		tmp = (-x / z) / (y - z);
	} else if (t <= 4.5e+185) {
		tmp = x / ((y - z) * t);
	} 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 <= (-1.2d-183)) then
        tmp = (x / (t - z)) / y
    else if (t <= 1.75d-6) then
        tmp = (-x / z) / (y - z)
    else if (t <= 4.5d+185) then
        tmp = x / ((y - z) * t)
    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 <= -1.2e-183) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.75e-6) {
		tmp = (-x / z) / (y - z);
	} else if (t <= 4.5e+185) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.2e-183:
		tmp = (x / (t - z)) / y
	elif t <= 1.75e-6:
		tmp = (-x / z) / (y - z)
	elif t <= 4.5e+185:
		tmp = x / ((y - z) * t)
	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 <= -1.2e-183)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 1.75e-6)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	elseif (t <= 4.5e+185)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	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 <= -1.2e-183)
		tmp = (x / (t - z)) / y;
	elseif (t <= 1.75e-6)
		tmp = (-x / z) / (y - z);
	elseif (t <= 4.5e+185)
		tmp = x / ((y - z) * t);
	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, -1.2e-183], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.75e-6], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+185], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.19999999999999996e-183

   1. Initial program 85.3%

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

   2. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/r* 68.3%

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

   4. Simplified 68.3%

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

   if -1.19999999999999996e-183 < t < 1.74999999999999997e-6

   1. Initial program 93.1%

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

      1. *-un-lft-identity 93.1%

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

      2. times-frac 97.4%

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

   3. Applied egg-rr 97.4%

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

   4. Taylor expanded in t around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. associate-/r* 85.0%

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

   6. Simplified 85.0%

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

   if 1.74999999999999997e-6 < t < 4.5000000000000002e185

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 91.2%

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

   if 4.5000000000000002e185 < t

   1. Initial program 81.8%

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

      1. *-un-lft-identity 81.8%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate-*l/ 99.9%

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

      2. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 5: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)))
   (if (<= t -6.2e-50)
     t_1
     (if (<= t 5.3e-14)
       (/ (- x) (* y z))
       (if (<= t 1.36e+143) (/ (- x) (* z t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (t <= -6.2e-50) {
		tmp = t_1;
	} else if (t <= 5.3e-14) {
		tmp = -x / (y * z);
	} else if (t <= 1.36e+143) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / y
    if (t <= (-6.2d-50)) then
        tmp = t_1
    else if (t <= 5.3d-14) then
        tmp = -x / (y * z)
    else if (t <= 1.36d+143) then
        tmp = -x / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (t <= -6.2e-50) {
		tmp = t_1;
	} else if (t <= 5.3e-14) {
		tmp = -x / (y * z);
	} else if (t <= 1.36e+143) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	tmp = 0
	if t <= -6.2e-50:
		tmp = t_1
	elif t <= 5.3e-14:
		tmp = -x / (y * z)
	elif t <= 1.36e+143:
		tmp = -x / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (t <= -6.2e-50)
		tmp = t_1;
	elseif (t <= 5.3e-14)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (t <= 1.36e+143)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	tmp = 0.0;
	if (t <= -6.2e-50)
		tmp = t_1;
	elseif (t <= 5.3e-14)
		tmp = -x / (y * z);
	elseif (t <= 1.36e+143)
		tmp = -x / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -6.2e-50], t$95$1, If[LessEqual[t, 5.3e-14], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e+143], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2000000000000004e-50 or 1.3599999999999999e143 < t

   1. Initial program 82.5%

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

   2. Taylor expanded in z around 0 49.5%

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

      1. div-inv 49.5%

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

      2. associate-/r* 49.4%

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

   4. Applied egg-rr 49.4%

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

      1. associate-*r/ 63.8%

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

      2. div-inv 63.8%

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

   6. Applied egg-rr 63.8%

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

   if -6.2000000000000004e-50 < t < 5.3000000000000001e-14

   1. Initial program 92.5%

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

   2. Taylor expanded in z around 0 62.0%

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

      1. distribute-lft-out 62.0%

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

      2. mul-1-neg 62.0%

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

      3. distribute-rgt-neg-in 62.0%

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

      4. unsub-neg 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in t around 0 44.8%

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

      1. associate-*r/ 44.8%

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

      2. neg-mul-1 44.8%

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

      3. *-commutative 44.8%

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

   7. Simplified 44.8%

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

   if 5.3000000000000001e-14 < t < 1.3599999999999999e143

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.6%

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

      1. associate-*r/ 63.6%

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

      2. neg-mul-1 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in z around 0 53.4%

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

      1. associate-*r/ 53.4%

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

      2. neg-mul-1 53.4%

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

      3. *-commutative 53.4%

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

   7. Simplified 53.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 6: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{-52} \lor \neg \left(t \leq 9.8 \cdot 10^{-135}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.46e-52) (not (<= t 9.8e-135)))
   (/ x (* (- y z) t))
   (/ (/ (- x) z) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.46e-52) || !(t <= 9.8e-135)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (-x / z) / 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 ((t <= (-1.46d-52)) .or. (.not. (t <= 9.8d-135))) then
        tmp = x / ((y - z) * t)
    else
        tmp = (-x / z) / 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 ((t <= -1.46e-52) || !(t <= 9.8e-135)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (-x / z) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -1.46e-52) or not (t <= 9.8e-135):
		tmp = x / ((y - z) * t)
	else:
		tmp = (-x / z) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.46e-52) || !(t <= 9.8e-135))
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(Float64(-x) / z) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.46e-52) || ~((t <= 9.8e-135)))
		tmp = x / ((y - z) * t);
	else
		tmp = (-x / z) / 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[t, -1.46e-52], N[Not[LessEqual[t, 9.8e-135]], $MachinePrecision]], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.46000000000000003e-52 or 9.8000000000000005e-135 < t

   1. Initial program 87.8%

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

   2. Taylor expanded in t around inf 76.4%

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

   if -1.46000000000000003e-52 < t < 9.8000000000000005e-135

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. associate-/r* 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in t around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. neg-mul-1 53.3%

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

   7. Simplified 53.3%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{-52} \lor \neg \left(t \leq 9.8 \cdot 10^{-135}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \]

Alternative 7: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2.35 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.35e-78)
   (/ x (* y (- t z)))
   (if (<= t 2.1e+185) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.35e-78) {
		tmp = x / (y * (t - z));
	} else if (t <= 2.1e+185) {
		tmp = x / ((y - z) * t);
	} 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 <= 2.35d-78) then
        tmp = x / (y * (t - z))
    else if (t <= 2.1d+185) then
        tmp = x / ((y - z) * t)
    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 <= 2.35e-78) {
		tmp = x / (y * (t - z));
	} else if (t <= 2.1e+185) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 2.35e-78:
		tmp = x / (y * (t - z))
	elif t <= 2.1e+185:
		tmp = x / ((y - z) * t)
	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 <= 2.35e-78)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 2.1e+185)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	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 <= 2.35e-78)
		tmp = x / (y * (t - z));
	elseif (t <= 2.1e+185)
		tmp = x / ((y - z) * t);
	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, 2.35e-78], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+185], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.34999999999999985e-78

   1. Initial program 88.3%

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

   2. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

   4. Simplified 59.1%

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

   if 2.34999999999999985e-78 < t < 2.1e185

   1. Initial program 96.9%

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

   2. Taylor expanded in t around inf 77.6%

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

   if 2.1e185 < t

   1. Initial program 81.8%

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

      1. *-un-lft-identity 81.8%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate-*l/ 99.9%

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

      2. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.35 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 8: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.1e-14)
   (/ (/ x (- t z)) y)
   (if (<= t 2.25e+185) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.1e-14) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.25e+185) {
		tmp = x / ((y - z) * t);
	} 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 <= 1.1d-14) then
        tmp = (x / (t - z)) / y
    else if (t <= 2.25d+185) then
        tmp = x / ((y - z) * t)
    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 <= 1.1e-14) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.25e+185) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.1e-14:
		tmp = (x / (t - z)) / y
	elif t <= 2.25e+185:
		tmp = x / ((y - z) * t)
	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 <= 1.1e-14)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 2.25e+185)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	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 <= 1.1e-14)
		tmp = (x / (t - z)) / y;
	elseif (t <= 2.25e+185)
		tmp = x / ((y - z) * t);
	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, 1.1e-14], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.25e+185], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.1e-14

   1. Initial program 88.3%

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

   2. Taylor expanded in y around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-/r* 66.9%

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

   4. Simplified 66.9%

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

   if 1.1e-14 < t < 2.2500000000000001e185

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 86.6%

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

   if 2.2500000000000001e185 < t

   1. Initial program 81.8%

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

      1. *-un-lft-identity 81.8%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate-*l/ 99.9%

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

      2. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2.35 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.35e+185) (/ x (* (- y 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 <= 2.35e+185) {
		tmp = x / ((y - 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 <= 2.35d+185) then
        tmp = x / ((y - 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 <= 2.35e+185) {
		tmp = x / ((y - 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 <= 2.35e+185:
		tmp = x / ((y - 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 <= 2.35e+185)
		tmp = Float64(x / Float64(Float64(y - 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 <= 2.35e+185)
		tmp = x / ((y - 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, 2.35e+185], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.34999999999999986e185

   1. Initial program 90.6%

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

   if 2.34999999999999986e185 < t

   1. Initial program 81.8%

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

      1. *-un-lft-identity 81.8%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate-*l/ 99.9%

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

      2. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.35 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 10: 96.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (1.0d0 / (y - z)) * (x / (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.7%

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

   1. *-un-lft-identity 89.7%

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

   2. times-frac 96.0%

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

3. Applied egg-rr 96.0%

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

4. Final simplification 96.0%

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

Alternative 11: 50.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-12} \lor \neg \left(z \leq 2.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

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 -2e-12) (not (<= z 2.5e-45))) (/ (- x) (* z t)) (/ (/ x y) t)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-12) || !(z <= 2.5e-45)) {
		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 <= (-2d-12)) .or. (.not. (z <= 2.5d-45))) 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 <= -2e-12) || !(z <= 2.5e-45)) {
		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 <= -2e-12) or not (z <= 2.5e-45):
		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 <= -2e-12) || !(z <= 2.5e-45))
		tmp = Float64(Float64(-x) / Float64(z * t));
	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 <= -2e-12) || ~((z <= 2.5e-45)))
		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, -2e-12], N[Not[LessEqual[z, 2.5e-45]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999996e-12 or 2.49999999999999988e-45 < z

   1. Initial program 87.7%

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

   2. Taylor expanded in y around 0 77.2%

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

      1. associate-*r/ 77.2%

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

      2. neg-mul-1 77.2%

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

   4. Simplified 77.2%

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

   5. Taylor expanded in z around 0 46.2%

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

      1. associate-*r/ 46.2%

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

      2. neg-mul-1 46.2%

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

      3. *-commutative 46.2%

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

   7. Simplified 46.2%

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

   if -1.99999999999999996e-12 < z < 2.49999999999999988e-45

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 56.7%

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

      1. *-un-lft-identity 56.7%

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

      2. times-frac 64.7%

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

   4. Applied egg-rr 64.7%

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

      1. associate-*l/ 64.7%

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

      2. *-lft-identity 64.7%

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

   6. Simplified 64.7%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-12} \lor \neg \left(z \leq 2.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 12: 46.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+57} \lor \neg \left(z \leq 8.2 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.32e+57) (not (<= z 8.2e+32))) (/ x (* z t)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.32e+57) || !(z <= 8.2e+32)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.32d+57)) .or. (.not. (z <= 8.2d+32))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.32e+57) || !(z <= 8.2e+32)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.32e+57) or not (z <= 8.2e+32):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.32e+57) || !(z <= 8.2e+32))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.32e+57) || ~((z <= 8.2e+32)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.32e+57], N[Not[LessEqual[z, 8.2e+32]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32000000000000001e57 or 8.19999999999999961e32 < z

   1. Initial program 84.7%

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

   2. Taylor expanded in y around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   4. Simplified 81.3%

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

      1. expm1-log1p-u 80.9%

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

      2. expm1-udef 72.3%

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

      3. add-sqr-sqrt 33.8%

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

      4. sqrt-unprod 64.1%

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

      5. sqr-neg 64.1%

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

      6. sqrt-unprod 36.6%

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

      7. add-sqr-sqrt 69.7%

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

   6. Applied egg-rr 69.7%

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

      1. expm1-def 68.4%

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

      2. expm1-log1p 68.4%

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

      3. associate-/r* 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in z around 0 43.5%

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

       1. *-commutative 43.5%

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

   11. Simplified 43.5%

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

   if -1.32000000000000001e57 < z < 8.19999999999999961e32

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 52.3%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+57} \lor \neg \left(z \leq 8.2 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 13: 48.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+57} \lor \neg \left(z \leq 2.2 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.9e+57) (not (<= z 2.2e+32))) (/ x (* z t)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e+57) || !(z <= 2.2e+32)) {
		tmp = x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.9d+57)) .or. (.not. (z <= 2.2d+32))) then
        tmp = x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e+57) || !(z <= 2.2e+32)) {
		tmp = x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.9e+57) or not (z <= 2.2e+32):
		tmp = x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.9e+57) || !(z <= 2.2e+32))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.9e+57) || ~((z <= 2.2e+32)))
		tmp = x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.9e+57], N[Not[LessEqual[z, 2.2e+32]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e57 or 2.20000000000000001e32 < z

   1. Initial program 84.7%

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

   2. Taylor expanded in y around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   4. Simplified 81.3%

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

      1. expm1-log1p-u 80.9%

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

      2. expm1-udef 72.3%

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

      3. add-sqr-sqrt 33.8%

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

      4. sqrt-unprod 64.1%

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

      5. sqr-neg 64.1%

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

      6. sqrt-unprod 36.6%

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

      7. add-sqr-sqrt 69.7%

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

   6. Applied egg-rr 69.7%

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

      1. expm1-def 68.4%

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

      2. expm1-log1p 68.4%

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

      3. associate-/r* 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in z around 0 43.5%

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

       1. *-commutative 43.5%

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

   11. Simplified 43.5%

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

   if -1.8999999999999999e57 < z < 2.20000000000000001e32

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 52.3%

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

      1. div-inv 52.3%

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

      2. associate-/r* 52.2%

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

   4. Applied egg-rr 52.2%

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

      1. associate-*r/ 56.7%

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

      2. div-inv 56.7%

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

   6. Applied egg-rr 56.7%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+57} \lor \neg \left(z \leq 2.2 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 14: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 7.5e-78) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.5e-78) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 7.5d-78) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.5e-78) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 7.5e-78:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 7.5e-78)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 7.5e-78)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 7.5e-78], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.50000000000000041e-78

   1. Initial program 88.3%

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

   2. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

   4. Simplified 59.1%

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

   if 7.50000000000000041e-78 < t

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 78.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 15: 39.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.7%

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

2. Taylor expanded in z around 0 36.3%

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

3. Final simplification 36.3%

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

Developer target: 87.9% 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 2023314 
(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))))