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

Percentage Accurate: 88.6% → 97.8%

Time: 8.9s

Alternatives: 15

Speedup: 0.5×

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: 88.6% 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

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{-283}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 5e-283) (/ (/ 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 <= 5e-283) {
		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 <= 5d-283) 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 <= 5e-283) {
		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 <= 5e-283:
		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 <= 5e-283)
		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 <= 5e-283)
		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, 5e-283], 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))) < 5.0000000000000001e-283

   1. Initial program 84.3%

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

      1. associate-/r* 96.9%

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

   3. Simplified 96.9%

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

   if 5.0000000000000001e-283 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 99.7%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 5 \cdot 10^{-283}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 2: 92.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{z}}{t - z}\\ \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- t z)) y)
     (if (<= t_1 5e+306) (/ x t_1) (- (/ (/ x z) (- t z)))))))

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 <= -((double) INFINITY)) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+306) {
		tmp = x / t_1;
	} else {
		tmp = -((x / z) / (t - z));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+306) {
		tmp = x / t_1;
	} else {
		tmp = -((x / z) / (t - z));
	}
	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 <= -math.inf:
		tmp = (x / (t - z)) / y
	elif t_1 <= 5e+306:
		tmp = x / t_1
	else:
		tmp = -((x / z) / (t - z))
	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 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t_1 <= 5e+306)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(-Float64(Float64(x / z) / Float64(t - z)));
	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 <= -Inf)
		tmp = (x / (t - z)) / y;
	elseif (t_1 <= 5e+306)
		tmp = x / t_1;
	else
		tmp = -((x / 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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], N[(x / t$95$1), $MachinePrecision], (-N[(N[(x / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision])]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 66.1%

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

   2. Taylor expanded in y around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-/r* 93.4%

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

   4. Simplified 93.4%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 4.99999999999999993e306

   1. Initial program 99.7%

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

   if 4.99999999999999993e306 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 73.5%

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

   2. Taylor expanded in y around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. distribute-frac-neg 67.9%

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

      3. associate-/r* 86.1%

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

   4. Simplified 86.1%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{z}}{t - z}\\ \end{array} \]

Alternative 3: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- t z)) y)
     (if (<= t_1 5e+306) (/ x t_1) (/ (/ -1.0 z) (/ (- t z) x))))))

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 <= -((double) INFINITY)) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+306) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+306) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x);
	}
	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 <= -math.inf:
		tmp = (x / (t - z)) / y
	elif t_1 <= 5e+306:
		tmp = x / t_1
	else:
		tmp = (-1.0 / z) / ((t - z) / x)
	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 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t_1 <= 5e+306)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(t - z) / x));
	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 <= -Inf)
		tmp = (x / (t - z)) / y;
	elseif (t_1 <= 5e+306)
		tmp = x / t_1;
	else
		tmp = (-1.0 / z) / ((t - 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[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], N[(x / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 66.1%

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

   2. Taylor expanded in y around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-/r* 93.4%

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

   4. Simplified 93.4%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 4.99999999999999993e306

   1. Initial program 99.7%

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

   if 4.99999999999999993e306 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 73.5%

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

      1. frac-2neg 73.5%

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

      2. div-inv 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

   3. Applied egg-rr 73.5%

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

      1. un-div-inv 73.5%

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

      2. *-un-lft-identity 73.5%

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

      3. times-frac 99.8%

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

      4. frac-2neg 99.8%

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

      5. clear-num 99.8%

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

      6. div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 86.2%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \]

Alternative 4: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -5e-272) t_1 (/ (/ x (- t z)) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -5e-272) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= (-5d-272)) then
        tmp = t_1
    else
        tmp = (x / (t - z)) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -5e-272) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -5e-272:
		tmp = t_1
	else:
		tmp = (x / (t - z)) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -5e-272)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -5e-272)
		tmp = t_1;
	else
		tmp = (x / (t - z)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-272], t$95$1, N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -4.99999999999999982e-272

   1. Initial program 99.5%

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

   if -4.99999999999999982e-272 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 84.3%

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

      1. associate-/l/ 96.5%

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

   3. Simplified 96.5%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq -5 \cdot 10^{-272}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \]

Alternative 5: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -92000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-184}:\\ \;\;\;\;-\frac{\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -92000000.0)
   (/ (/ x y) (- t z))
   (if (<= y 1.4e-184) (- (/ (/ x z) (- t z))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -92000000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.4e-184) {
		tmp = -((x / z) / (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-92000000.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.4d-184) then
        tmp = -((x / z) / (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -92000000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.4e-184) {
		tmp = -((x / z) / (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -92000000.0:
		tmp = (x / y) / (t - z)
	elif y <= 1.4e-184:
		tmp = -((x / z) / (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -92000000.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.4e-184)
		tmp = Float64(-Float64(Float64(x / z) / Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -92000000.0)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.4e-184)
		tmp = -((x / z) / (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -92000000.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-184], (-N[(N[(x / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2e7

   1. Initial program 84.4%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 90.7%

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

   if -9.2e7 < y < 1.3999999999999999e-184

   1. Initial program 87.7%

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

   2. Taylor expanded in y around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. distribute-frac-neg 65.7%

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

      3. associate-/r* 75.7%

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

   4. Simplified 75.7%

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

   if 1.3999999999999999e-184 < y

   1. Initial program 90.2%

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

   2. Taylor expanded in t around inf 56.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -92000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-184}:\\ \;\;\;\;-\frac{\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 6: 82.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-167}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.1e-167)
   (/ (/ x (- t z)) y)
   (if (<= t 4.5e-10) (/ (/ (- x) z) (- y z)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-167) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 4.5e-10) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.1d-167)) then
        tmp = (x / (t - z)) / y
    else if (t <= 4.5d-10) then
        tmp = (-x / z) / (y - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-167) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 4.5e-10) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e-167:
		tmp = (x / (t - z)) / y
	elif t <= 4.5e-10:
		tmp = (-x / z) / (y - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.1e-167)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 4.5e-10)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.1e-167)
		tmp = (x / (t - z)) / y;
	elseif (t <= 4.5e-10)
		tmp = (-x / z) / (y - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.1e-167], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.5e-10], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.10000000000000017e-167

   1. Initial program 85.9%

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

   2. Taylor expanded in y around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. associate-/r* 66.6%

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

   4. Simplified 66.6%

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

   if -2.10000000000000017e-167 < t < 4.5e-10

   1. Initial program 90.8%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. associate-*r/ 79.9%

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

      2. neg-mul-1 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-/r* 87.2%

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

   4. Simplified 87.2%

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

   if 4.5e-10 < t

   1. Initial program 86.9%

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

      1. associate-/l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 84.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-167}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 7: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -140000 \lor \neg \left(z \leq 2.65 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

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 -140000.0) (not (<= z 2.65e+30)))
   (/ (/ x z) z)
   (* (/ x t) (/ 1.0 y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -140000.0) || !(z <= 2.65e+30)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) * (1.0 / 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 <= (-140000.0d0)) .or. (.not. (z <= 2.65d+30))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) * (1.0d0 / 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 <= -140000.0) || !(z <= 2.65e+30)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) * (1.0 / y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -140000.0) or not (z <= 2.65e+30):
		tmp = (x / z) / z
	else:
		tmp = (x / t) * (1.0 / y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -140000.0) || !(z <= 2.65e+30))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) * Float64(1.0 / 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 <= -140000.0) || ~((z <= 2.65e+30)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) * (1.0 / 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, -140000.0], N[Not[LessEqual[z, 2.65e+30]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e5 or 2.6500000000000002e30 < z

   1. Initial program 81.7%

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

   2. Taylor expanded in z around inf 68.2%

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

      1. unpow2 68.2%

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

      2. associate-/r* 78.0%

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

   4. Simplified 78.0%

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

   if -1.4e5 < z < 2.6500000000000002e30

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 58.8%

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

      1. *-un-lft-identity 58.8%

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

      2. times-frac 62.0%

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

   4. Applied egg-rr 62.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140000 \lor \neg \left(z \leq 2.65 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \end{array} \]

Alternative 8: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1020000 \lor \neg \left(z \leq 3 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1020000.0) (not (<= z 3e+82)))
   (/ (/ x z) z)
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1020000.0) || !(z <= 3e+82)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1020000.0d0)) .or. (.not. (z <= 3d+82))) then
        tmp = (x / z) / z
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1020000.0) || !(z <= 3e+82)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1020000.0) or not (z <= 3e+82):
		tmp = (x / z) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1020000.0) || !(z <= 3e+82))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1020000.0) || ~((z <= 3e+82)))
		tmp = (x / z) / z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1020000.0], N[Not[LessEqual[z, 3e+82]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e6 or 2.99999999999999989e82 < z

   1. Initial program 81.4%

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

   2. Taylor expanded in z around inf 69.6%

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

      1. unpow2 69.6%

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

      2. associate-/r* 79.9%

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

   4. Simplified 79.9%

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

   if -1.02e6 < z < 2.99999999999999989e82

   1. Initial program 93.6%

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

   2. Taylor expanded in t around inf 69.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1020000 \lor \neg \left(z \leq 3 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 9: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e-108)
   (/ x (* y (- t z)))
   (if (<= y -1.15e-293) (/ 1.0 (/ z (/ x z))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-108) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.15e-293) {
		tmp = 1.0 / (z / (x / 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 <= (-4.4d-108)) then
        tmp = x / (y * (t - z))
    else if (y <= (-1.15d-293)) then
        tmp = 1.0d0 / (z / (x / 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 <= -4.4e-108) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.15e-293) {
		tmp = 1.0 / (z / (x / 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 <= -4.4e-108:
		tmp = x / (y * (t - z))
	elif y <= -1.15e-293:
		tmp = 1.0 / (z / (x / 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 <= -4.4e-108)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -1.15e-293)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e-108)
		tmp = x / (y * (t - z));
	elseif (y <= -1.15e-293)
		tmp = 1.0 / (z / (x / 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, -4.4e-108], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-293], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4000000000000002e-108

   1. Initial program 82.9%

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

   2. Taylor expanded in y around inf 73.6%

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

      1. *-commutative 73.6%

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

   4. Simplified 73.6%

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

   if -4.4000000000000002e-108 < y < -1.14999999999999998e-293

   1. Initial program 81.8%

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

   2. Taylor expanded in z around inf 52.3%

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

      1. unpow2 52.3%

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

   4. Simplified 52.3%

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

      1. clear-num 52.3%

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

      2. inv-pow 52.3%

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

   6. Applied egg-rr 52.3%

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

      1. unpow-1 52.3%

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

      2. associate-/l* 67.6%

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

   8. Simplified 67.6%

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

   if -1.14999999999999998e-293 < y

   1. Initial program 92.6%

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

   2. Taylor expanded in t around inf 59.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 10: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-184}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e-106)
   (/ x (* y (- t z)))
   (if (<= y 1.4e-184) (/ x (* z (- z t))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e-106) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.4e-184) {
		tmp = x / (z * (z - t));
	} 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 <= (-5.6d-106)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.4d-184) then
        tmp = x / (z * (z - t))
    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 <= -5.6e-106) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.4e-184) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e-106:
		tmp = x / (y * (t - z))
	elif y <= 1.4e-184:
		tmp = x / (z * (z - t))
	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 <= -5.6e-106)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.4e-184)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.6e-106)
		tmp = x / (y * (t - z));
	elseif (y <= 1.4e-184)
		tmp = x / (z * (z - t));
	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, -5.6e-106], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-184], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.59999999999999977e-106

   1. Initial program 82.7%

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

   2. Taylor expanded in y around inf 73.2%

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

      1. *-commutative 73.2%

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

   4. Simplified 73.2%

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

   if -5.59999999999999977e-106 < y < 1.3999999999999999e-184

   1. Initial program 90.5%

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

      1. frac-2neg 90.5%

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

      2. div-inv 90.5%

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

      3. distribute-rgt-neg-in 90.5%

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

   3. Applied egg-rr 90.5%

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

   4. Taylor expanded in y around 0 74.2%

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

   if 1.3999999999999999e-184 < y

   1. Initial program 90.2%

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

   2. Taylor expanded in t around inf 56.8%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-184}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 11: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-184}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-106)
   (/ (/ x y) (- t z))
   (if (<= y 1.12e-184) (/ x (* z (- z t))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-106) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.12e-184) {
		tmp = x / (z * (z - t));
	} 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 <= (-9d-106)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.12d-184) then
        tmp = x / (z * (z - t))
    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 <= -9e-106) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.12e-184) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -9e-106:
		tmp = (x / y) / (t - z)
	elif y <= 1.12e-184:
		tmp = x / (z * (z - t))
	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 <= -9e-106)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.12e-184)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e-106)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.12e-184)
		tmp = x / (z * (z - t));
	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, -9e-106], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e-184], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999911e-106

   1. Initial program 82.7%

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

      1. associate-/r* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 78.0%

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

   if -8.99999999999999911e-106 < y < 1.11999999999999997e-184

   1. Initial program 90.5%

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

      1. frac-2neg 90.5%

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

      2. div-inv 90.5%

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

      3. distribute-rgt-neg-in 90.5%

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

   3. Applied egg-rr 90.5%

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

   4. Taylor expanded in y around 0 74.2%

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

   if 1.11999999999999997e-184 < y

   1. Initial program 90.2%

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

   2. Taylor expanded in t around inf 56.8%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-184}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 12: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+52} \lor \neg \left(z \leq 9.8 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -1.82e+52) (not (<= z 9.8e+86))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.82e+52) || !(z <= 9.8e+86)) {
		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 <= (-1.82d+52)) .or. (.not. (z <= 9.8d+86))) 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 <= -1.82e+52) || !(z <= 9.8e+86)) {
		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 <= -1.82e+52) or not (z <= 9.8e+86):
		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 <= -1.82e+52) || !(z <= 9.8e+86))
		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 <= -1.82e+52) || ~((z <= 9.8e+86)))
		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, -1.82e+52], N[Not[LessEqual[z, 9.8e+86]], $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 < -1.8199999999999999e52 or 9.7999999999999999e86 < z

   1. Initial program 78.0%

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

   2. Taylor expanded in y around inf 48.2%

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

      1. *-commutative 48.2%

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

   4. Simplified 48.2%

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

   5. Taylor expanded in t around 0 48.1%

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

      1. associate-*r/ 48.1%

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

      2. neg-mul-1 48.1%

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

      3. *-commutative 48.1%

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

   7. Simplified 48.1%

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

      1. expm1-log1p-u 47.7%

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

      2. expm1-udef 60.7%

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

      3. add-sqr-sqrt 28.3%

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

      4. sqrt-unprod 58.3%

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

      5. sqr-neg 58.3%

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

      6. sqrt-unprod 32.6%

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

      7. add-sqr-sqrt 60.9%

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

      8. *-commutative 60.9%

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

   9. Applied egg-rr 60.9%

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

       1. expm1-def 46.7%

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

       2. expm1-log1p 47.0%

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

       3. *-commutative 47.0%

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

   11. Simplified 47.0%

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

   if -1.8199999999999999e52 < z < 9.7999999999999999e86

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 51.6%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+52} \lor \neg \left(z \leq 9.8 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 13: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-55} \lor \neg \left(z \leq 850000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -1.05e-55) (not (<= z 850000.0))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-55) || !(z <= 850000.0)) {
		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 <= (-1.05d-55)) .or. (.not. (z <= 850000.0d0))) 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 <= -1.05e-55) || !(z <= 850000.0)) {
		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 <= -1.05e-55) or not (z <= 850000.0):
		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 <= -1.05e-55) || !(z <= 850000.0))
		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 <= -1.05e-55) || ~((z <= 850000.0)))
		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, -1.05e-55], N[Not[LessEqual[z, 850000.0]], $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 < -1.0500000000000001e-55 or 8.5e5 < z

   1. Initial program 82.5%

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

   2. Taylor expanded in z around inf 62.6%

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

      1. unpow2 62.6%

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

   4. Simplified 62.6%

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

   if -1.0500000000000001e-55 < z < 8.5e5

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0 65.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-55} \lor \neg \left(z \leq 850000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-57} \lor \neg \left(z \leq 500000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -1e-57) (not (<= z 500000.0))) (/ (/ x z) z) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-57) || !(z <= 500000.0)) {
		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 <= (-1d-57)) .or. (.not. (z <= 500000.0d0))) 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 <= -1e-57) || !(z <= 500000.0)) {
		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 <= -1e-57) or not (z <= 500000.0):
		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 <= -1e-57) || !(z <= 500000.0))
		tmp = Float64(Float64(x / 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 <= -1e-57) || ~((z <= 500000.0)))
		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, -1e-57], N[Not[LessEqual[z, 500000.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999955e-58 or 5e5 < z

   1. Initial program 82.5%

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

   2. Taylor expanded in z around inf 62.6%

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

      1. unpow2 62.6%

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

      2. associate-/r* 70.9%

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

   4. Simplified 70.9%

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

   if -9.99999999999999955e-58 < z < 5e5

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0 65.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-57} \lor \neg \left(z \leq 500000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 40.0% 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 87.9%

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

2. Taylor expanded in z around 0 39.7%

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

3. Final simplification 39.7%

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

Developer target: 87.6% 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 2023192 
(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))))