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

Percentage Accurate: 89.7% → 98.0%

Time: 12.1s

Alternatives: 16

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: 89.7% 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: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-323}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y - z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (* (- y z) (- t z)))))
   (* x_s (if (<= t_1 -4e-323) t_1 (/ (/ x_m (- t z)) (- y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -4e-323) {
		tmp = t_1;
	} else {
		tmp = (x_m / (t - z)) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m / ((y - z) * (t - z))
    if (t_1 <= (-4d-323)) then
        tmp = t_1
    else
        tmp = (x_m / (t - z)) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -4e-323) {
		tmp = t_1;
	} else {
		tmp = (x_m / (t - z)) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = x_m / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -4e-323:
		tmp = t_1
	else:
		tmp = (x_m / (t - z)) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -4e-323)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m / Float64(t - z)) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -4e-323)
		tmp = t_1;
	else
		tmp = (x_m / (t - z)) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, -4e-323], t$95$1, N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -3.95253e-323

   1. Initial program 99.8%

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

   if -3.95253e-323 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 90.0%

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

Alternative 2: 64.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{y}}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+266}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{-y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-51}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m y) t)))
   (*
    x_s
    (if (<= y -1.12e+266)
      (/ (/ x_m z) (- y))
      (if (<= y -7.5e+172)
        t_1
        (if (<= y -1e+37)
          (/ x_m (* z (- y)))
          (if (<= y 7e-51) (/ x_m (* z (- z t))) t_1)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double tmp;
	if (y <= -1.12e+266) {
		tmp = (x_m / z) / -y;
	} else if (y <= -7.5e+172) {
		tmp = t_1;
	} else if (y <= -1e+37) {
		tmp = x_m / (z * -y);
	} else if (y <= 7e-51) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m / y) / t
    if (y <= (-1.12d+266)) then
        tmp = (x_m / z) / -y
    else if (y <= (-7.5d+172)) then
        tmp = t_1
    else if (y <= (-1d+37)) then
        tmp = x_m / (z * -y)
    else if (y <= 7d-51) then
        tmp = x_m / (z * (z - t))
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double tmp;
	if (y <= -1.12e+266) {
		tmp = (x_m / z) / -y;
	} else if (y <= -7.5e+172) {
		tmp = t_1;
	} else if (y <= -1e+37) {
		tmp = x_m / (z * -y);
	} else if (y <= 7e-51) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / y) / t
	tmp = 0
	if y <= -1.12e+266:
		tmp = (x_m / z) / -y
	elif y <= -7.5e+172:
		tmp = t_1
	elif y <= -1e+37:
		tmp = x_m / (z * -y)
	elif y <= 7e-51:
		tmp = x_m / (z * (z - t))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / y) / t)
	tmp = 0.0
	if (y <= -1.12e+266)
		tmp = Float64(Float64(x_m / z) / Float64(-y));
	elseif (y <= -7.5e+172)
		tmp = t_1;
	elseif (y <= -1e+37)
		tmp = Float64(x_m / Float64(z * Float64(-y)));
	elseif (y <= 7e-51)
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / y) / t;
	tmp = 0.0;
	if (y <= -1.12e+266)
		tmp = (x_m / z) / -y;
	elseif (y <= -7.5e+172)
		tmp = t_1;
	elseif (y <= -1e+37)
		tmp = x_m / (z * -y);
	elseif (y <= 7e-51)
		tmp = x_m / (z * (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -1.12e+266], N[(N[(x$95$m / z), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, -7.5e+172], t$95$1, If[LessEqual[y, -1e+37], N[(x$95$m / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-51], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -1.11999999999999996e266

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. associate-/r* 83.0%

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

      3. distribute-neg-frac2 83.0%

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

      4. neg-sub0 83.0%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{0 - \left(y - z\right)}} \]

      5. sub-neg 83.0%

         \[\leadsto \frac{\frac{x}{z}}{0 - \color{blue}{\left(y + \left(-z\right)\right)}} \]

      6. +-commutative 83.0%

         \[\leadsto \frac{\frac{x}{z}}{0 - \color{blue}{\left(\left(-z\right) + y\right)}} \]

      7. associate--r+ 83.0%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{\left(0 - \left(-z\right)\right) - y}} \]

      8. neg-sub0 83.0%

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

      9. remove-double-neg 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in z around 0 83.0%

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

      1. neg-mul-1 83.0%

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

   8. Simplified 83.0%

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

   if -1.11999999999999996e266 < y < -7.4999999999999994e172 or 6.9999999999999995e-51 < y

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf 78.9%

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

      1. associate-/r* 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in t around inf 56.0%

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

   if -7.4999999999999994e172 < y < -9.99999999999999954e36

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf 83.9%

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

      1. *-commutative 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in t around 0 42.6%

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

      1. associate-*r/ 42.6%

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

      2. neg-mul-1 42.6%

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

      3. *-commutative 42.6%

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

   8. Simplified 42.6%

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

   if -9.99999999999999954e36 < y < 6.9999999999999995e-51

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. sub-neg 76.8%

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

      4. +-commutative 76.8%

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

      5. distribute-neg-in 76.8%

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

      6. remove-double-neg 76.8%

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

      7. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+266}:\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+172}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{y}}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+136}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{-z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m y) t)))
   (*
    x_s
    (if (<= t -1.18e+27)
      t_1
      (if (<= t 5.2e-27)
        (/ x_m (* z (- z y)))
        (if (<= t 6.6e+136)
          (/ x_m (* z (- z t)))
          (if (<= t 4.6e+154) t_1 (/ (/ x_m t) (- z)))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double tmp;
	if (t <= -1.18e+27) {
		tmp = t_1;
	} else if (t <= 5.2e-27) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 6.6e+136) {
		tmp = x_m / (z * (z - t));
	} else if (t <= 4.6e+154) {
		tmp = t_1;
	} else {
		tmp = (x_m / t) / -z;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m / y) / t
    if (t <= (-1.18d+27)) then
        tmp = t_1
    else if (t <= 5.2d-27) then
        tmp = x_m / (z * (z - y))
    else if (t <= 6.6d+136) then
        tmp = x_m / (z * (z - t))
    else if (t <= 4.6d+154) then
        tmp = t_1
    else
        tmp = (x_m / t) / -z
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double tmp;
	if (t <= -1.18e+27) {
		tmp = t_1;
	} else if (t <= 5.2e-27) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 6.6e+136) {
		tmp = x_m / (z * (z - t));
	} else if (t <= 4.6e+154) {
		tmp = t_1;
	} else {
		tmp = (x_m / t) / -z;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / y) / t
	tmp = 0
	if t <= -1.18e+27:
		tmp = t_1
	elif t <= 5.2e-27:
		tmp = x_m / (z * (z - y))
	elif t <= 6.6e+136:
		tmp = x_m / (z * (z - t))
	elif t <= 4.6e+154:
		tmp = t_1
	else:
		tmp = (x_m / t) / -z
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / y) / t)
	tmp = 0.0
	if (t <= -1.18e+27)
		tmp = t_1;
	elseif (t <= 5.2e-27)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (t <= 6.6e+136)
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	elseif (t <= 4.6e+154)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m / t) / Float64(-z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / y) / t;
	tmp = 0.0;
	if (t <= -1.18e+27)
		tmp = t_1;
	elseif (t <= 5.2e-27)
		tmp = x_m / (z * (z - y));
	elseif (t <= 6.6e+136)
		tmp = x_m / (z * (z - t));
	elseif (t <= 4.6e+154)
		tmp = t_1;
	else
		tmp = (x_m / t) / -z;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -1.18e+27], t$95$1, If[LessEqual[t, 5.2e-27], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+136], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+154], t$95$1, N[(N[(x$95$m / t), $MachinePrecision] / (-z)), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if t < -1.18000000000000006e27 or 6.59999999999999984e136 < t < 4.6e154

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 52.8%

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

      1. associate-/r* 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in t around inf 48.5%

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

   if -1.18000000000000006e27 < t < 5.20000000000000034e-27

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-rgt-neg-in 78.3%

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

      3. neg-sub0 78.3%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(y - z\right)\right)}} \]

      4. sub-neg 78.3%

         \[\leadsto \frac{x}{z \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right)} \]

      5. +-commutative 78.3%

         \[\leadsto \frac{x}{z \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right)} \]

      6. associate--r+ 78.3%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)}} \]

      7. neg-sub0 78.3%

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

      8. remove-double-neg 78.3%

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

   5. Simplified 78.3%

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

   if 5.20000000000000034e-27 < t < 6.59999999999999984e136

   1. Initial program 92.0%

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

   3. Taylor expanded in y around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. distribute-rgt-neg-in 49.2%

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

      3. sub-neg 49.2%

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

      4. +-commutative 49.2%

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

      5. distribute-neg-in 49.2%

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

      6. remove-double-neg 49.2%

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

      7. unsub-neg 49.2%

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

   5. Simplified 49.2%

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

   if 4.6e154 < t

   1. Initial program 79.3%

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

   3. Taylor expanded in x around 0 79.3%

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

      1. associate-/l/ 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in t around inf 87.9%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-/r* 72.8%

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

      3. distribute-neg-frac2 72.8%

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

   9. Simplified 72.8%

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

Alternative 4: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{z} \cdot \frac{1}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (/ x_m z) (/ 1.0 z))))
   (*
    x_s
    (if (<= z -3e-50)
      t_1
      (if (<= z 1.95e-88)
        (/ (/ x_m y) t)
        (if (<= z 6.6e+36) (/ x_m (* z (- t))) t_1))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (1.0 / z);
	double tmp;
	if (z <= -3e-50) {
		tmp = t_1;
	} else if (z <= 1.95e-88) {
		tmp = (x_m / y) / t;
	} else if (z <= 6.6e+36) {
		tmp = x_m / (z * -t);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m / z) * (1.0d0 / z)
    if (z <= (-3d-50)) then
        tmp = t_1
    else if (z <= 1.95d-88) then
        tmp = (x_m / y) / t
    else if (z <= 6.6d+36) then
        tmp = x_m / (z * -t)
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (1.0 / z);
	double tmp;
	if (z <= -3e-50) {
		tmp = t_1;
	} else if (z <= 1.95e-88) {
		tmp = (x_m / y) / t;
	} else if (z <= 6.6e+36) {
		tmp = x_m / (z * -t);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / z) * (1.0 / z)
	tmp = 0
	if z <= -3e-50:
		tmp = t_1
	elif z <= 1.95e-88:
		tmp = (x_m / y) / t
	elif z <= 6.6e+36:
		tmp = x_m / (z * -t)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / z) * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -3e-50)
		tmp = t_1;
	elseif (z <= 1.95e-88)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (z <= 6.6e+36)
		tmp = Float64(x_m / Float64(z * Float64(-t)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / z) * (1.0 / z);
	tmp = 0.0;
	if (z <= -3e-50)
		tmp = t_1;
	elseif (z <= 1.95e-88)
		tmp = (x_m / y) / t;
	elseif (z <= 6.6e+36)
		tmp = x_m / (z * -t);
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -3e-50], t$95$1, If[LessEqual[z, 1.95e-88], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 6.6e+36], N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9999999999999999e-50 or 6.5999999999999997e36 < z

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. distribute-rgt-neg-in 77.2%

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

      3. sub-neg 77.2%

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

      4. +-commutative 77.2%

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

      5. distribute-neg-in 77.2%

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

      6. remove-double-neg 77.2%

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

      7. unsub-neg 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in z around inf 65.4%

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

      1. associate-/r* 72.1%

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

      2. div-inv 72.1%

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

   8. Applied egg-rr 72.1%

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

   if -2.9999999999999999e-50 < z < 1.94999999999999996e-88

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. associate-/r* 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in t around inf 62.6%

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

   if 1.94999999999999996e-88 < z < 6.5999999999999997e36

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 66.2%

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

      1. mul-1-neg 66.2%

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

      2. distribute-rgt-neg-in 66.2%

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

      3. sub-neg 66.2%

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

      4. +-commutative 66.2%

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

      5. distribute-neg-in 66.2%

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

      6. remove-double-neg 66.2%

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

      7. unsub-neg 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in z around 0 46.0%

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

      1. associate-*r/ 46.0%

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

      2. neg-mul-1 46.0%

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

      3. *-commutative 46.0%

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

   8. Simplified 46.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{z \cdot z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-88}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+37}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (* z z))))
   (*
    x_s
    (if (<= z -1.08e-47)
      t_1
      (if (<= z 1e-88)
        (/ (/ x_m y) t)
        (if (<= z 5e+37) (/ x_m (* z (- t))) t_1))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (z * z);
	double tmp;
	if (z <= -1.08e-47) {
		tmp = t_1;
	} else if (z <= 1e-88) {
		tmp = (x_m / y) / t;
	} else if (z <= 5e+37) {
		tmp = x_m / (z * -t);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m / (z * z)
    if (z <= (-1.08d-47)) then
        tmp = t_1
    else if (z <= 1d-88) then
        tmp = (x_m / y) / t
    else if (z <= 5d+37) then
        tmp = x_m / (z * -t)
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (z * z);
	double tmp;
	if (z <= -1.08e-47) {
		tmp = t_1;
	} else if (z <= 1e-88) {
		tmp = (x_m / y) / t;
	} else if (z <= 5e+37) {
		tmp = x_m / (z * -t);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = x_m / (z * z)
	tmp = 0
	if z <= -1.08e-47:
		tmp = t_1
	elif z <= 1e-88:
		tmp = (x_m / y) / t
	elif z <= 5e+37:
		tmp = x_m / (z * -t)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m / Float64(z * z))
	tmp = 0.0
	if (z <= -1.08e-47)
		tmp = t_1;
	elseif (z <= 1e-88)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (z <= 5e+37)
		tmp = Float64(x_m / Float64(z * Float64(-t)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m / (z * z);
	tmp = 0.0;
	if (z <= -1.08e-47)
		tmp = t_1;
	elseif (z <= 1e-88)
		tmp = (x_m / y) / t;
	elseif (z <= 5e+37)
		tmp = x_m / (z * -t);
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m / N[(z * z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.08e-47], t$95$1, If[LessEqual[z, 1e-88], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5e+37], N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08000000000000005e-47 or 4.99999999999999989e37 < z

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. distribute-rgt-neg-in 77.2%

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

      3. sub-neg 77.2%

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

      4. +-commutative 77.2%

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

      5. distribute-neg-in 77.2%

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

      6. remove-double-neg 77.2%

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

      7. unsub-neg 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in z around inf 65.4%

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

   if -1.08000000000000005e-47 < z < 9.99999999999999934e-89

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. associate-/r* 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in t around inf 62.6%

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

   if 9.99999999999999934e-89 < z < 4.99999999999999989e37

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 66.2%

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

      1. mul-1-neg 66.2%

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

      2. distribute-rgt-neg-in 66.2%

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

      3. sub-neg 66.2%

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

      4. +-commutative 66.2%

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

      5. distribute-neg-in 66.2%

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

      6. remove-double-neg 66.2%

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

      7. unsub-neg 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in z around 0 46.0%

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

      1. associate-*r/ 46.0%

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

      2. neg-mul-1 46.0%

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

      3. *-commutative 46.0%

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

   8. Simplified 46.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+86} \lor \neg \left(z \leq 2 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -6e+86) (not (<= z 2e+140)))
    (/ (/ x_m z) (- z t))
    (/ x_m (* (- y z) (- t z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+86) || !(z <= 2e+140)) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = x_m / ((y - z) * (t - z));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6d+86)) .or. (.not. (z <= 2d+140))) then
        tmp = (x_m / z) / (z - t)
    else
        tmp = x_m / ((y - z) * (t - z))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+86) || !(z <= 2e+140)) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = x_m / ((y - z) * (t - z));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -6e+86) or not (z <= 2e+140):
		tmp = (x_m / z) / (z - t)
	else:
		tmp = x_m / ((y - z) * (t - z))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -6e+86) || !(z <= 2e+140))
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -6e+86) || ~((z <= 2e+140)))
		tmp = (x_m / z) / (z - t);
	else
		tmp = x_m / ((y - z) * (t - z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -6e+86], N[Not[LessEqual[z, 2e+140]], $MachinePrecision]], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999954e86 or 2.00000000000000012e140 < z

   1. Initial program 81.8%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. associate-/r* 96.5%

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

      3. distribute-neg-frac2 96.5%

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

      4. sub-neg 96.5%

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

      5. +-commutative 96.5%

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

      6. distribute-neg-in 96.5%

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

      7. remove-double-neg 96.5%

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

      8. unsub-neg 96.5%

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

   5. Simplified 96.5%

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

   if -5.99999999999999954e86 < z < 2.00000000000000012e140

   1. Initial program 97.6%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+86} \lor \neg \left(z \leq 2 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z - t}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -9.5e-78)
    (/ x_m (* y (- t z)))
    (if (<= y 4.5e-65) (/ 1.0 (* z (/ (- z t) x_m))) (/ (/ x_m (- y z)) t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-78) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 4.5e-65) {
		tmp = 1.0 / (z * ((z - t) / x_m));
	} else {
		tmp = (x_m / (y - z)) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.5d-78)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 4.5d-65) then
        tmp = 1.0d0 / (z * ((z - t) / x_m))
    else
        tmp = (x_m / (y - z)) / t
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-78) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 4.5e-65) {
		tmp = 1.0 / (z * ((z - t) / x_m));
	} else {
		tmp = (x_m / (y - z)) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -9.5e-78:
		tmp = x_m / (y * (t - z))
	elif y <= 4.5e-65:
		tmp = 1.0 / (z * ((z - t) / x_m))
	else:
		tmp = (x_m / (y - z)) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -9.5e-78)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 4.5e-65)
		tmp = Float64(1.0 / Float64(z * Float64(Float64(z - t) / x_m)));
	else
		tmp = Float64(Float64(x_m / Float64(y - z)) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -9.5e-78)
		tmp = x_m / (y * (t - z));
	elseif (y <= 4.5e-65)
		tmp = 1.0 / (z * ((z - t) / x_m));
	else
		tmp = (x_m / (y - z)) / t;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -9.5e-78], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-65], N[(1.0 / N[(z * N[(N[(z - t), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999997e-78

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -9.4999999999999997e-78 < y < 4.4999999999999998e-65

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. distribute-rgt-neg-in 81.2%

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

      3. sub-neg 81.2%

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

      4. +-commutative 81.2%

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

      5. distribute-neg-in 81.2%

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

      6. remove-double-neg 81.2%

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

      7. unsub-neg 81.2%

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

   5. Simplified 81.2%

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

      1. clear-num 80.2%

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

      2. inv-pow 80.2%

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

   7. Applied egg-rr 80.2%

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

      1. unpow-1 80.2%

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

      2. associate-/l* 84.1%

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

   9. Simplified 84.1%

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

   if 4.4999999999999998e-65 < y

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0 91.1%

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

      1. associate-/l/ 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in t around inf 62.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -9.5e-78)
    (/ x_m (* y (- t z)))
    (if (<= y 1.16e-92) (/ (/ x_m z) (- z t)) (/ (/ x_m (- y z)) t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-78) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 1.16e-92) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / (y - z)) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.5d-78)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 1.16d-92) then
        tmp = (x_m / z) / (z - t)
    else
        tmp = (x_m / (y - z)) / t
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-78) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 1.16e-92) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / (y - z)) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -9.5e-78:
		tmp = x_m / (y * (t - z))
	elif y <= 1.16e-92:
		tmp = (x_m / z) / (z - t)
	else:
		tmp = (x_m / (y - z)) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -9.5e-78)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 1.16e-92)
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x_m / Float64(y - z)) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -9.5e-78)
		tmp = x_m / (y * (t - z));
	elseif (y <= 1.16e-92)
		tmp = (x_m / z) / (z - t);
	else
		tmp = (x_m / (y - z)) / t;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -9.5e-78], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e-92], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999997e-78

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -9.4999999999999997e-78 < y < 1.1599999999999999e-92

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. associate-/r* 86.0%

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

      3. distribute-neg-frac2 86.0%

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

      4. sub-neg 86.0%

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

      5. +-commutative 86.0%

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

      6. distribute-neg-in 86.0%

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

      7. remove-double-neg 86.0%

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

      8. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if 1.1599999999999999e-92 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0 90.7%

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

      1. associate-/l/ 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in t around inf 62.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -8.2e-78)
    (/ x_m (* y (- t z)))
    (if (<= y 2.05e-91) (/ (/ x_m z) (- z t)) (/ (/ x_m t) (- y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-78) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 2.05e-91) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.2d-78)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 2.05d-91) then
        tmp = (x_m / z) / (z - t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-78) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 2.05e-91) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -8.2e-78:
		tmp = x_m / (y * (t - z))
	elif y <= 2.05e-91:
		tmp = (x_m / z) / (z - t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -8.2e-78)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 2.05e-91)
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e-78)
		tmp = x_m / (y * (t - z));
	elseif (y <= 2.05e-91)
		tmp = (x_m / z) / (z - t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -8.2e-78], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-91], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999996e-78

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -8.1999999999999996e-78 < y < 2.05000000000000012e-91

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. associate-/r* 86.0%

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

      3. distribute-neg-frac2 86.0%

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

      4. sub-neg 86.0%

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

      5. +-commutative 86.0%

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

      6. distribute-neg-in 86.0%

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

      7. remove-double-neg 86.0%

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

      8. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if 2.05000000000000012e-91 < y

   1. Initial program 90.7%

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

      1. associate-/l/ 97.6%

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

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 60.7%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-104}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-22}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.35e-104)
    (/ x_m (* y (- t z)))
    (if (<= t 7e-22) (/ x_m (* z (- z y))) (/ (/ x_m t) (- y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-104) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 7e-22) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.35d-104)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 7d-22) then
        tmp = x_m / (z * (z - y))
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-104) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 7e-22) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.35e-104:
		tmp = x_m / (y * (t - z))
	elif t <= 7e-22:
		tmp = x_m / (z * (z - y))
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.35e-104)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 7e-22)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.35e-104)
		tmp = x_m / (y * (t - z));
	elseif (t <= 7e-22)
		tmp = x_m / (z * (z - y));
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.35e-104], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-22], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.3499999999999999e-104

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   if -1.3499999999999999e-104 < t < 7.00000000000000011e-22

   1. Initial program 94.4%

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

   3. Taylor expanded in t around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-in 82.5%

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

      3. neg-sub0 82.5%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(y - z\right)\right)}} \]

      4. sub-neg 82.5%

         \[\leadsto \frac{x}{z \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right)} \]

      5. +-commutative 82.5%

         \[\leadsto \frac{x}{z \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right)} \]

      6. associate--r+ 82.5%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)}} \]

      7. neg-sub0 82.5%

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

      8. remove-double-neg 82.5%

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

   5. Simplified 82.5%

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

   if 7.00000000000000011e-22 < 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/ 97.7%

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

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 84.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.1e-103)
    (/ x_m (* y (- t z)))
    (if (<= t 7.8e-22) (/ x_m (* z (- z y))) (/ x_m (* (- y z) t))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.1e-103) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 7.8e-22) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.1d-103)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 7.8d-22) then
        tmp = x_m / (z * (z - y))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.1e-103) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 7.8e-22) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.1e-103:
		tmp = x_m / (y * (t - z))
	elif t <= 7.8e-22:
		tmp = x_m / (z * (z - y))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.1e-103)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 7.8e-22)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.1e-103)
		tmp = x_m / (y * (t - z));
	elseif (t <= 7.8e-22)
		tmp = x_m / (z * (z - y));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.1e-103], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-22], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e-103

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   if -1.1e-103 < t < 7.79999999999999996e-22

   1. Initial program 94.4%

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

   3. Taylor expanded in t around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-in 82.5%

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

      3. neg-sub0 82.5%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(y - z\right)\right)}} \]

      4. sub-neg 82.5%

         \[\leadsto \frac{x}{z \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right)} \]

      5. +-commutative 82.5%

         \[\leadsto \frac{x}{z \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right)} \]

      6. associate--r+ 82.5%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)}} \]

      7. neg-sub0 82.5%

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

      8. remove-double-neg 82.5%

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

   5. Simplified 82.5%

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

   if 7.79999999999999996e-22 < t

   1. Initial program 86.9%

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

   3. Taylor expanded in t around inf 84.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -3.5e-80)
    (/ x_m (* y (- t z)))
    (if (<= y 9.2e-51) (/ x_m (* z (- z t))) (/ (/ x_m y) t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-80) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 9.2e-51) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.5d-80)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 9.2d-51) then
        tmp = x_m / (z * (z - t))
    else
        tmp = (x_m / y) / t
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-80) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 9.2e-51) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -3.5e-80:
		tmp = x_m / (y * (t - z))
	elif y <= 9.2e-51:
		tmp = x_m / (z * (z - t))
	else:
		tmp = (x_m / y) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -3.5e-80)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 9.2e-51)
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x_m / y) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -3.5e-80)
		tmp = x_m / (y * (t - z));
	elseif (y <= 9.2e-51)
		tmp = x_m / (z * (z - t));
	else
		tmp = (x_m / y) / t;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -3.5e-80], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-51], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000015e-80

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -3.50000000000000015e-80 < y < 9.20000000000000007e-51

   1. Initial program 93.4%

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

   3. Taylor expanded in y around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. distribute-rgt-neg-in 81.6%

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

      3. sub-neg 81.6%

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

      4. +-commutative 81.6%

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

      5. distribute-neg-in 81.6%

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

      6. remove-double-neg 81.6%

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

      7. unsub-neg 81.6%

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

   5. Simplified 81.6%

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

   if 9.20000000000000007e-51 < y

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 77.7%

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

      1. associate-/r* 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in t around inf 54.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-48} \lor \neg \left(z \leq 1.3 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -7.8e-48) (not (<= z 1.3e+79)))
    (/ x_m (* z z))
    (/ (/ x_m y) t))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e-48) || !(z <= 1.3e+79)) {
		tmp = x_m / (z * z);
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.8d-48)) .or. (.not. (z <= 1.3d+79))) then
        tmp = x_m / (z * z)
    else
        tmp = (x_m / y) / t
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e-48) || !(z <= 1.3e+79)) {
		tmp = x_m / (z * z);
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -7.8e-48) or not (z <= 1.3e+79):
		tmp = x_m / (z * z)
	else:
		tmp = (x_m / y) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e-48) || !(z <= 1.3e+79))
		tmp = Float64(x_m / Float64(z * z));
	else
		tmp = Float64(Float64(x_m / y) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e-48) || ~((z <= 1.3e+79)))
		tmp = x_m / (z * z);
	else
		tmp = (x_m / y) / t;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -7.8e-48], N[Not[LessEqual[z, 1.3e+79]], $MachinePrecision]], N[(x$95$m / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -7.800000000000001e-48 or 1.30000000000000007e79 < z

   1. Initial program 87.5%

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

   3. Taylor expanded in y around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. distribute-rgt-neg-in 79.5%

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

      3. sub-neg 79.5%

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

      4. +-commutative 79.5%

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

      5. distribute-neg-in 79.5%

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

      6. remove-double-neg 79.5%

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

      7. unsub-neg 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in z around inf 67.6%

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

   if -7.800000000000001e-48 < z < 1.30000000000000007e79

   1. Initial program 97.6%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. associate-/r* 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in t around inf 52.8%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-48} \lor \neg \left(z \leq 1.3 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-47} \lor \neg \left(z \leq 2.4 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.05e-47) (not (<= z 2.4e-72)))
    (/ x_m (* z z))
    (/ x_m (* y t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-47) || !(z <= 2.4e-72)) {
		tmp = x_m / (z * z);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.05d-47)) .or. (.not. (z <= 2.4d-72))) then
        tmp = x_m / (z * z)
    else
        tmp = x_m / (y * t)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-47) || !(z <= 2.4e-72)) {
		tmp = x_m / (z * z);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -1.05e-47) or not (z <= 2.4e-72):
		tmp = x_m / (z * z)
	else:
		tmp = x_m / (y * t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e-47) || !(z <= 2.4e-72))
		tmp = Float64(x_m / Float64(z * z));
	else
		tmp = Float64(x_m / Float64(y * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e-47) || ~((z <= 2.4e-72)))
		tmp = x_m / (z * z);
	else
		tmp = x_m / (y * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -1.05e-47], N[Not[LessEqual[z, 2.4e-72]], $MachinePrecision]], N[(x$95$m / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-47 or 2.4e-72 < z

   1. Initial program 90.0%

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

   3. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. distribute-rgt-neg-in 75.9%

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

      3. sub-neg 75.9%

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

      4. +-commutative 75.9%

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

      5. distribute-neg-in 75.9%

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

      6. remove-double-neg 75.9%

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

      7. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in z around inf 59.1%

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

   if -1.05e-47 < z < 2.4e-72

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 61.4%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-47} \lor \neg \left(z \leq 2.4 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-44} \lor \neg \left(z \leq 1.25 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x\_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -6.8e-44) (not (<= z 1.25e+68)))
    (/ x_m (* y z))
    (/ x_m (* y t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e-44) || !(z <= 1.25e+68)) {
		tmp = x_m / (y * z);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.8d-44)) .or. (.not. (z <= 1.25d+68))) then
        tmp = x_m / (y * z)
    else
        tmp = x_m / (y * t)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e-44) || !(z <= 1.25e+68)) {
		tmp = x_m / (y * z);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -6.8e-44) or not (z <= 1.25e+68):
		tmp = x_m / (y * z)
	else:
		tmp = x_m / (y * t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -6.8e-44) || !(z <= 1.25e+68))
		tmp = Float64(x_m / Float64(y * z));
	else
		tmp = Float64(x_m / Float64(y * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -6.8e-44) || ~((z <= 1.25e+68)))
		tmp = x_m / (y * z);
	else
		tmp = x_m / (y * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -6.8e-44], N[Not[LessEqual[z, 1.25e+68]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000033e-44 or 1.2500000000000001e68 < z

   1. Initial program 87.7%

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

   3. Taylor expanded in t around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. associate-/r* 84.1%

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

      3. distribute-neg-frac2 84.1%

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

      4. neg-sub0 84.1%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{0 - \left(y - z\right)}} \]

      5. sub-neg 84.1%

         \[\leadsto \frac{\frac{x}{z}}{0 - \color{blue}{\left(y + \left(-z\right)\right)}} \]

      6. +-commutative 84.1%

         \[\leadsto \frac{\frac{x}{z}}{0 - \color{blue}{\left(\left(-z\right) + y\right)}} \]

      7. associate--r+ 84.1%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{\left(0 - \left(-z\right)\right) - y}} \]

      8. neg-sub0 84.1%

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

      9. remove-double-neg 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in z around 0 38.8%

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

      1. neg-mul-1 38.8%

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

   8. Simplified 38.8%

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

      1. add-sqr-sqrt 19.2%

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

      2. sqrt-unprod 30.5%

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

      3. sqr-neg 30.5%

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

      4. sqrt-unprod 16.8%

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

      5. div-inv 16.8%

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

      6. add-sqr-sqrt 34.8%

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

      7. associate-/l* 30.0%

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

   10. Applied egg-rr 30.0%

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

       1. associate-/l/ 30.0%

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

       2. associate-*r/ 30.0%

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

       3. *-rgt-identity 30.0%

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

   12. Simplified 30.0%

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

   if -6.80000000000000033e-44 < z < 1.2500000000000001e68

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 51.5%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-44} \lor \neg \left(z \leq 1.25 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \frac{x\_m}{y \cdot t} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t) :precision binary64 (* x_s (/ x_m (* y t))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (x_m / (y * t));
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * (x_m / (y * t))
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (x_m / (y * t));
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	return x_s * (x_m / (y * t))

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(x_m / Float64(y * t)))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (x_m / (y * t));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.7%

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

3. Taylor expanded in z around 0 34.4%

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

4. Final simplification 34.4%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer Target 1: 88.4% 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 2024144 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ x (* (- y z) (- t z))) 0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z))))))

  (/ x (* (- y z) (- t z))))